Thermal Characteristics and Convection in Nanofluids 9789813342477, 9789813342484

Table of contents :
Preface
Contents
About the Authors
1 Introduction
1.1 Heat Transfer
1.2 Fundamentals of Thermal Convection
1.2.1 Newton’s Law of Cooling
1.2.2 Nusselt Number
1.3 Thermophysical Properties
1.3.1 Thermal Conductivity
1.3.2 Viscosity
1.3.3 Density and Specific Heat Capacity
1.4 Application Area of Convection Heat Transfer
1.4.1 Applications in Automotive
1.4.2 Applications in Air Conditioners and Domestic Refrigerator
1.4.3 Industrial Cooling Applications
1.4.4 Solar Devices
1.4.5 Electronic Applications
1.4.6 Geology and Metrology
1.5 Methods to Enhance Heat Transfer
1.5.1 Active Methods
1.5.2 Passive Methods
References
2 Nanofluids: Definition & Classification
2.1 Addition of Solid Particles
2.2 Nanofluids
2.2.1 Beginning of Nanofluids
2.2.2 Advantages of Nanofluids
2.3 Types of Nanofluids
2.3.1 On the Basis of Base Fluids
2.3.2 On the Basis of Nanoparticle’s Material
2.3.3 Special Category
References
3 Synthesis of Nanofluids
3.1 Nanoparticles
3.1.1 Different Types of Nanoparticles
3.1.2 Nanoparticle Synthesis
3.1.3 Nanoparticle Characterization Techniques
3.2 Synthesis of Nanofluids
3.2.1 Two-Step Method
3.2.2 One-Step Method
3.2.3 Case Studies on Synthesis of Different Nanofluids
References
4 Characterization of Nanofluids
4.1 Thermal Conductivity
4.1.1 Theoretical Models
4.1.2 Experimental Studies
4.2 Viscosity
4.2.1 Theoretical Studies
4.2.2 Experimental Work
4.2.3 Case Study: Investigation of Thermal Conductivity and Viscosity of Nanofluids Using Design of Experiment Approach
4.3 Density
4.4 Specific Heat Capacity
References
5 Stability of Nanofluids
5.1 Stability Evaluation Methods
5.1.1 Sedimentation Method
5.1.2 Zeta Potential
5.1.3 Ultraviolet–Visible (UV–Vis) Spectrophotometry
5.1.4 Dynamic Light Scattering (DLS)
5.2 Case Study: Stability Exploration of Alumina/Water Nanofluid
5.2.1 Zeta Potential Variation
5.3 Factors Affecting the Stability of Nanofluids
5.3.1 Effect of PH
5.3.2 Effect of Sonication Time
5.3.3 Effect of Surfactant
5.3.4 Effect of Nanoparticles Shape, Size and Concentration
References
6 Forced Convection in Nanofluids
6.1 Laminar Regime of Forced Convection
6.2 Turbulent Regime of Forced Convection
6.2.1 Methods Used to Enhance the Turbulence in the Pipe Flow
6.2.2 Case Study: Turbulent Forced Convection in the Pipe Flow
6.2.3 Summary of Other Important Studies
References
7 Natural Convection in Nanofluids
7.1 Natural Convection in Water
7.2 Natural Convection in Nanofluids
7.2.1 Case Study: Natural Convection in Al2O3/Water Nanofluid
7.2.2 Natural Convection in Magnetic Nanofluids Inside an Open Cavity
7.2.3 Case Study: Numerical Study on the Natural Convection in Magnetite Nanofluid
7.3 Results and Discussions
References
8 Applications of Nanofluids
8.1 Application in Automobile
8.2 Application in Solar Collectors
8.3 Application in Computer Cooling Systems
8.4 Application in Porous Medium
8.5 Other Applications
References

Citation preview

Lecture Notes in Mechanical Engineering

Aditya Kumar Sudhakar Subudhi

Thermal Characteristics and Convection in Nanofluids

Lecture Notes in Mechanical Engineering Series Editors Francisco Cavas-Martínez, Departamento de Estructuras, Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesco Gherardini, Dipartimento di Ingegneria, Università di Modena e Reggio Emilia, Modena, Italy Mohamed Haddar, National School of Engineers of Sfax (ENIS), Sfax, Tunisia Vitalii Ivanov, Department of Manufacturing Engineering Machine and Tools, Sumy State University, Sumy, Ukraine Young W. Kwon, Department of Manufacturing Engineering and Aerospace Engineering, Graduate School of Engineering and Applied Science, Monterey CA, USA Justyna Trojanowska, Poznan University of Technology, Poznan, Poland

Lecture Notes in Mechanical Engineering (LNME) publishes the latest developments in Mechanical Engineering—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNME. Volumes published in LNME embrace all aspects, subfields and new challenges of mechanical engineering. Topics in the series include: • • • • • • • • • • • • • • • • •

Engineering Design Machinery and Machine Elements Mechanical Structures and Stress Analysis Automotive Engineering Engine Technology Aerospace Technology and Astronautics Nanotechnology and Microengineering Control, Robotics, Mechatronics MEMS Theoretical and Applied Mechanics Dynamical Systems, Control Fluid Mechanics Engineering Thermodynamics, Heat and Mass Transfer Manufacturing Precision Engineering, Instrumentation, Measurement Materials Engineering Tribology and Surface Technology

To submit a proposal or request further information, please contact the Springer Editor of your location: China: Dr. Mengchu Huang at [email protected] India: Priya Vyas at [email protected] Rest of Asia, Australia, New Zealand: Swati Meherishi at [email protected] All other countries: Dr. Leontina Di Cecco at [email protected] To submit a proposal for a monograph, please check our Springer Tracts in Mechanical Engineering at http://www.springer.com/series/11693 or contact [email protected] Indexed by SCOPUS. All books published in the series are submitted for consideration in Web of Science.

More information about this series at http://www.springer.com/series/11236

Aditya Kumar · Sudhakar Subudhi

Thermal Characteristics and Convection in Nanofluids

Aditya Kumar Department of Mechanical and Industrial Engineering Indian Institute of Technology Roorkee Roorkee, India

Sudhakar Subudhi Department of Mechanical and Industrial Engineering Indian Institute of Technology Roorkee Roorkee, India

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-981-33-4247-7 ISBN 978-981-33-4248-4 (eBook) https://doi.org/10.1007/978-981-33-4248-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Nanofluids, the colloidal suspension of nanoparticles into conventional base fluids, have massive potential in the area of heat transfer. The book covers the synthesis, characterization, stability, heat transfer and application of nanofluids. The authors cover the different types of nanofluids, their preparation methods as well as its effects on the stability and thermophysical properties of nanofluids. It provides a discussion on the mechanism behind the change in the thermal properties of nanofluids and heat transfer behavior. The following are the features of the book: • Latest information and discussion on the preparation and advanced characterization of nanofluids. • Stability analysis of nanofluids and discussion on why it is essential for the industrial application. • Discussion on the parameters and mechanism affecting thermophysical properties. • Free and forced convection heat transfer by nanofluids both numerically and experimentally. • Discussion on thermal boundary layer properties in convection. • Future directions for heat transfer application to make the production and application of nanofluids industrial level. The book contains the basics of thermal properties and heat transfer for the readers who may be from an adequate background of heat transfer. It also provides a discussion on nanofluids at the nanoscale level, which helps to understand the basics of nanofluids. The book is focused on the novel attributes, utilization strategies and applications of the nanofluids in the heat transfer research area. Nanofluids, the colloidal suspension of nanoparticles into the conventional basefluids, are developing rapidly as a smart fluid in the nanoscience and nanotechnology. In the last few years, different kinds of nanofluids have gained the significant attention not only in heat transfer industry but also in the medical and biological sciences. The main objective of the book is to provide a critical and comprehensive review of the recent advances in the synthesis, characterization, mechanism in convection heat transfer

v

vi

Preface

and application of the nanofluids. This book is a valuable resource for researchers, scientists and engineers alike. Roorkee, India

Aditya Kumar Sudhakar Subudhi

Acknowledgements The authors extremely acknowledge the work of Dr. Rajesh Choudhary and Dr. Deepak Khurana on the natural and forced convection in nanofluids. We would like to thank the Indian Institute of Technology Roorkee for providing the essential support and funding for the research in the field of nanofluids. We would like to thank our research group without whom this book could not have been written. We would like to thank the staff at Springer for their help and support.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Fundamentals of Thermal Convection . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Newton’s Law of Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Nusselt Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Thermophysical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Density and Specific Heat Capacity . . . . . . . . . . . . . . . . . . . . . 1.4 Application Area of Convection Heat Transfer . . . . . . . . . . . . . . . . . . 1.4.1 Applications in Automotive . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Applications in Air Conditioners and Domestic Refrigerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Industrial Cooling Applications . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4 Solar Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.5 Electronic Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.6 Geology and Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Methods to Enhance Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 Active Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Passive Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 1 2 2 3 3 4 5 5 5

2 Nanofluids: Definition & Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Addition of Solid Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Beginning of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Advantages of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Types of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 On the Basis of Base Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 On the Basis of Nanoparticle’s Material . . . . . . . . . . . . . . . . . 2.3.3 Special Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 11 12 13 15 16 16 17 17 20

6 7 7 7 7 8 8 8 9

vii

viii

Contents

3 Synthesis of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Different Types of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Nanoparticle Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Nanoparticle Characterization Techniques . . . . . . . . . . . . . . . 3.2 Synthesis of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Two-Step Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 One-Step Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Case Studies on Synthesis of Different Nanofluids . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 25 28 30 31 31 35 35 39

4 Characterization of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Theoretical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Experimental Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Case Study: Investigation of Thermal Conductivity and Viscosity of Nanofluids Using Design of Experiment Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Specific Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 45 57 60 60 65

69 82 83 84

5 Stability of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Stability Evaluation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Sedimentation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Zeta Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Ultraviolet–Visible (UV–Vis) Spectrophotometry . . . . . . . . . 5.1.4 Dynamic Light Scattering (DLS) . . . . . . . . . . . . . . . . . . . . . . . 5.2 Case Study: Stability Exploration of Alumina/Water Nanofluid . . . . 5.2.1 Zeta Potential Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Factors Affecting the Stability of Nanofluids . . . . . . . . . . . . . . . . . . . 5.3.1 Effect of PH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Effect of Sonication Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Effect of Surfactant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Effect of Nanoparticles Shape, Size and Concentration . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91 91 91 93 93 95 96 96 99 99 100 102 105 107

6 Forced Convection in Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Laminar Regime of Forced Convection . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Turbulent Regime of Forced Convection . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Methods Used to Enhance the Turbulence in the Pipe Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109 109 117 123

Contents

ix

6.2.2 Case Study: Turbulent Forced Convection in the Pipe Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.2.3 Summary of Other Important Studies . . . . . . . . . . . . . . . . . . . 135 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7 Natural Convection in Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Natural Convection in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Natural Convection in Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Case Study: Natural Convection in Al2 O3 /Water Nanofluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Natural Convection in Magnetic Nanofluids Inside an Open Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Case Study: Numerical Study on the Natural Convection in Magnetite Nanofluid . . . . . . . . . . . . . . . . . . . . . 7.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151 151 155

8 Applications of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Application in Automobile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Application in Solar Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Application in Computer Cooling Systems . . . . . . . . . . . . . . . . . . . . . 8.4 Application in Porous Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

207 207 212 214 214 219 220

163 180 186 195 200

About the Authors

Aditya Kumar is a Research Professional did his Doctor of Philosophy (Ph.D.) focused on the characteristics of convection heat transfer in nanofluids at sustainable power and energy system lab, Department of Mechanical & Industrial Engineering, Indian Institute of Technology Roorkee. He received his Master’s degree in Thermal Engineering from Indian Institute of Technology Roorkee in 2015. He is Experienced Researcher with a demonstrated history of working in the area related to heat transfer application of nanofluids from the last 5+ years. He published and contributed in the several leading international peer-reviewed journals. He attended and presented papers in the several national and international conferences on the various topic related to nanofluids. Currently, he is working on the natural convection heat transfer by the magnetic nanofluids. He is also involved in designing and performing several experiments on the force as well as on natural convection small-scale experiments. Sudhakar Subudhi is Associate Professor at the Department of Mechanical & Industrial Engineering, Indian Institute of Technology Roorkee. He received his Master’s and Doctor of Philosophy (Ph.D.) degree from the Department of Mechanical Engineering, Indian Institute of Science, Bangalore, on the field of turbulent free convection in 2004 and 2009, respectively. He worked as Scientist-SC and installed a “Temperature sensors calibration lab” at Indian Space Research Organization Satellite Center, Bangalore. He has worked as Assistant Professor and developed new course, titled “Experimental methods in fluid flow and heat transfer” in the year 2011 at NIT Calicut. Currently, he is working in various research areas in thermal engineering, e.g. solar-assisted cooling, thermal comfort, heat transfer by nanofluids, etc. He has authored a number of research articles published in the peer-reviewed international journals. He is Reviewer of numerous reputed journals such as Physics of Fluids (AIP), Renewable and Sustainable Energy (Elsevier), Applied Thermal Engineering (Elsevier), Experimental Heat Transfer (Taylor and Francis) and Heat and Mass Transfer (Springer). He delivered talks on the nanofluids applications at the several national and international conferences. He is working in the area related to thermal convection & nanofluids from the last 15+ years.

xi

Chapter 1

Introduction

1.1 Heat Transfer Heat transfer is the rate of energy interaction between two systems having a temperature difference. Fundamentally, the three modes of heat transfer are: (a) conduction (b) convection and (c) radiation. Conduction represents energy transport by means of molecular motion within the materials. Conduction heat transfer prevailed in solids where molecules are held closed by the intermolecular forces and heat is easily transferred by lattice vibration of molecules compared to fluids, as shown in Fig. 1.1. Convection is the mode of heat transfer by means of the bulk motion of fluids, as shown in Fig. 1.2. Convection dominants in the fluids only because of the significant bulk movement of materials are not possible in the solids. Radiation is the only mode of heat transfer where no medium is required to flow heat across the temperature difference. Radiation heat transfer represents the motion of electromagnetic waves emitted from a body having a temperature higher than the absolute zero.

1.2 Fundamentals of Thermal Convection Thermal convection is ubiquitous in nature and technical applications and provides important and wide purpose, for example, boiling of coffee, atmosphere warming, solar heaters, mixing of oceans and electronics assemblies. The convection can be categorized into forced convection and natural convection. Forced convection involved the motion of fluids molecules by means of external sources (pumps, blower AND fans). While when the fluid motions arise from the natural forces like gravity and buoyancy, the convection of this type is known as natural convection or free convection.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Kumar and S. Subudhi, Thermal Characteristics and Convection in Nanofluids, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4248-4_1

1

2

1 Introduction

Fig. 1.1 Heat flows (conduction heat transfer) by the temperature difference inside a solid body

Th Tc Solid

Heat flows

Fig. 1.2 Heat transfer by the convection mode of heat transfer into the fluid

1.2.1 Newton’s Law of Cooling The rate of heat transfer by convection is governed by Newton’s law of cooling which represents that heat transfer is proportional to the temperature difference. Mathematically, q = h T

(1.1)

where q is the heat flux, T is the temperature difference between heated surface and the bulk fluid temperature and h is the heat transfer coefficient. Table 1.1 reports the heat transfer coefficient values.

1.2.2 Nusselt Number It is the non-dimensional number representing the global heat transfer in the convection heat transfer studies. Nusselt number is the ratio of convective and conductive heat transfer through the boundary inside a fluid.

1.2 Fundamentals of Thermal Convection Table 1.1 Convection heat transfer coefficient, h (W/m2 K)

Types of fluids and flow

3 h

Free convection Air

6–30

Water

20–100

Oils

50–250

Forced convection

Nu =

Air

10–350

Water

300–1200

Oils

300–1700

Boiling

2500–100,000

Condensation

4000–25,000

h hL Convective heat transfer = = conductive heat transfer k/L k

where h is the convective heat transfer coefficient of the fluid, k is the thermal conductivity of fluid and L is the characteristic length.

1.3 Thermophysical Properties The thermophysical properties of any fluid play a very critical role in heat transport phenomena. Some of the essential thermophysical properties are thermal conductivity, density, viscosity and specific heat. The basic definitions of the abovementioned properties are given below, and we will discuss these essential properties in the next chapters.

1.3.1 Thermal Conductivity Among the thermophysical properties, thermal conductivity is the most important and interesting property. Thermal conductivity of any material is the measurement of the potential to conduct heat. Thermal conductivity is generally denoted by the k and the SI unit is W/mK. The high thermal conductivity of the material means the heat flow inside the material is very high. Metals have higher thermal conductivity. Low thermal conductivity of a material means that the material’s ability to transfer heat is low. Wood is an example of material which has low thermal conductivity. Thermal conductivity is defined by the following equation. q = −k∇T

(1.2)

4 Table 1.2 Thermal conductivity of some common materials [1]

1 Introduction Material

Thermal conductivity (W/mK)

Gold

314

Silver

406

Copper

388

Aluminum

205

Iron

79.5

Water at 20 °C

0.6

Wood

0.12–0.04

Air at 0 °C

0.024

where q is the heat flux, k is the thermal conductivity and ∇T is the temperature gradient. Thermal conductivity of some common materials is given in Table 1.2.

1.3.2 Viscosity Viscosity is the resistance among the layers of fluid when subjected to shear, and the resistance is due to the intermolecular forces of cohesion and molecular momentum exchanges. The ideal fluid has zero viscosity or has no resistance, and it can be observed at very low temperature in superfluid. The dynamic viscosity is either by μ or η, and the SI unit is Pascal-second (Pa-s). The dynamic viscosity is given by the following equation. τ =μ where τ is the shear stress and fluids is given in Table 1.3. Table 1.3 Viscosity of the common liquids and gases [2]

∂u ∂y

∂u ∂y

(1.3)

is the velocity gradient. The viscosity of common

Fluids

Viscosity (Pa-s)

Water

0.001

Mercury

0.0016

Oil

0.66

Glycerine

1.49

Acetone

0.00032

Alcohol

0.0012

Blood

0.004

1.3 Thermophysical Properties Table 1.4 Density of common materials

5 Material

Density (kg/m3 )

Water at 20 °C

998

Mercury

13,600

Milk

1030

Gold

19,300

Copper

8500

Iron

7800

Air

1.2

1.3.3 Density and Specific Heat Capacity Density of any material is the mass per unit volume, or more precisely, it is called as specific weight. The specific heat capacity is the amount of heat required to raise the temperature of 1-gram mass by 1 °C. Mathematically, the density is given as ρ=

m V

(1.4)

where ρ is the density, m is mass and V is the volume. The SI unit of the density is kg/m3 . The density of the common material is given in Table 1.4.

1.4 Application Area of Convection Heat Transfer Convection heat transfer is ubiquitous in nature; it is essential not only in technology but also in the household or daily life. The heat is transferred by the convection only in many real-life applications such as solar collectors and car radiators. Few broadly categorized fields for the applications of the convective heat transfer are given below.

1.4.1 Applications in Automotive The heat transfer in the automobile parts takes place by this mode of heat transfer. Car radiator is using forced convection to transfer heat from the engine. The conventional heat transfer fluids are used in the car radiator to transfer the heat. The coolant is taking heat from the engine block and heads, and then, this heated fluid is cooled in the radiator by the air stream. Figure 1.3 shows the schematic of the experimental arrangement for the study of the performance of the car radiator with various kinds of fluids.

6

1 Introduction

Fig. 1.3 Schematic diagram of the experimental arrangement to study the car radiator performance [3]

1.4.2 Applications in Air Conditioners and Domestic Refrigerator The heat is removed from the room or refrigerator by the convection methods only, and the cold air from the air conditioner and freezing unit sinks, and the warm air rises and recirculated. This circulation process of air sets the convection heat transfers to cool the system. The coolant takes the heat from the room or the space to the outside environment. Figure 1.4 shows the arrangement used by the Rahman et al. [4], to

Fig. 1.4 Arrangement to study the air conditioning with solar power a photograph b schematic experimental setup [4]

1.4 Application Area of Convection Heat Transfer

7

study the solar-powered air conditioning system, basically used the convective heat transfer.

1.4.3 Industrial Cooling Applications Heat exchangers at different industries are working on the forced convection which is efficiently taking the heat from one place to another. Industries have used various types of heat exchangers to transfer heat from one point to other. Most of the heat exchangers have used various fluids to exchange the heat.

1.4.4 Solar Devices Solar devices like solar heater are taking heat from the solar radiation, and that heat is carried from one place to another by the motion of the fluids. In solar collector, fluids are used to take heat from the collector to the desired output.

1.4.5 Electronic Applications In electronic devices like computers, the heat is removed by fan or water, which is an example of forced convection. Many electronic equipments have used the water or air for cooling purpose by convective heat transfer. Both natural and forced convections are used to cool the electronics instruments.

1.4.6 Geology and Metrology The heat is transported from the mantle of the earth to the surface by convection currents. The oceanic water around the equator circulates toward the poles by convection currents. These are the few examples of the convections showing its diverse presence in nature, and it is also present in our daily life like cooking of food, boiling of water, hot coffee.

8

1 Introduction

1.5 Methods to Enhance Heat Transfer To make the heat transfer system efficient and effective, there is a need to enhance the heat transfer. There are a number of techniques available to enhance the heat transfer which is broadly categorized into two.

1.5.1 Active Methods In these methods, external power is required to enhance heat transfer. Mechanical stirring using rotating mechanisms, surface vibrations, fluid vibration at a frequency and jet impingement are some examples of active methods to enhance the heat transfer. The method involves the external power, which is the extra cost that has to be considered while designing the heat transfer instrument.

1.5.2 Passive Methods In these methods, the special measures are taken place to the heat transfer area in order to enhance the heat transfer. Surface roughness, extended surfaces, inserts in the tube and helical tube are some examples of the passive methods of heat transfer. Nanofluids are the new advanced branch of the passive methods, in which the improved thermophysical properties of the convectional fluids by adding nanoparticles help to augment heat transfer. Summary The chapter briefly discussed the fundamentals of heat transfer and different modes of the heat transfer. The thermal convection in the fluids and different thermophysical properties associated with the thermal convection are discussed. The important applications of the convective heat transfer are listed and deliberated. Various methods to enhance the heat transfer are finally deliberated.

References

9

References 1. Young, H. D. & Sears, F. W. (1992). University physics. Addison-Wesley Pub. Co. 2. Gustafson, D. R. (1980). Physics: Health and the human body. 3. Tijani, A. S. & Sudirman, A. S. bin. (2018). Thermos-physical properties and heat transfer characteristics of water/anti-freezing and Al2 O3 /CuO based nanofluid as a coolant for car radiator. International Journal of Heat and Mass Transfer, 118, 48–57. 4. Rahman, S., et al. (2019). Performance enhancement of a solar powered air conditioning system using passive techniques and SWCNT/R-407c nano refrigerant. Case Studies in Thermal Engineering, 16, 100565.

Chapter 2

Nanofluids: Definition & Classification

2.1 Addition of Solid Particles In the nineteenth century, Maxwell [1] proposed the idea of thermal conductivity enhancement by adding the solid particles of higher thermal conductivity into conventional base fluids. As mentioned earlier in Chap. 1, the thermal conductivity is the measure of the ability to transfer heat, which means that higher thermal conductivity means high heat transfer and lower means less. Later in the twentieth century, scientist and researchers have used a number of efforts to enhance heat transfer by dispersing solid particles of millimeter to micrometer sized into the conventional base fluids. Metals like copper and silver have the thermal conductivity much higher (around 400–500 times) than the base fluid. Vand [2] and Robinson [3] have used such types of metals and metallic oxide particles to suspend in base fluids like ethylene glycol, propylene glycol and urine. Several mathematical and experimental studies have been reported by the researchers like Leal [4] Chung et al. [5], Kianjah et al. [6], Ozbelge et al. [7] and Murray [8] on the heat transfer characteristics of fluids which contains the solid particles of micrometer sized. Researchers have reported significant enhancement in the heat transfer coefficients by using such fluids. However, rapid settling and aggregations of these large particles caused the major problems for the scientist during the use of such fluids. The problem of sedimentation and aggregation of micron-sized solid particles resulted in the corrosion and blockage in the application field. Booth [9], Frankel et al. [10], Nir et al. [11] and Kao et al. [12] have reported another major problem associated with such kinds of fluids which increased viscosity because of large particles. High viscosity is required higher pumping power and affected the heat transport by slowing down the fluid stream.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Kumar and S. Subudhi, Thermal Characteristics and Convection in Nanofluids, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4248-4_2

11

12

2 Nanofluids: Definition & Classification

2.2 Nanofluids Nanofluid is the colloidal suspension of solid nanoparticles of higher thermal conductivity material into the conventional basic fluids. Perhaps, active methods like providing vibrations or rotations may enhance the heat transfer, but these techniques have certain disadvantages. On the other hand, nanofluids as one of the passive methods increase the thermal properties of conventional base fluids. Enhanced thermal conductivity is the sole reason to make nanofluids. S.U.S. Choi, a scientist from Argonne National Laboratory, USA, in 1995 suspended the nano-sized solid particles into the base fluids to enhance the thermal conductivity of the conventional fluids and suggested the term nanofluids [13]. Later on, a number of studies reported the enhancement in the thermal conductivity which enhances the heat transfer due to nanoparticle addition in the conventional fluids in various applications. A plethora of literature on nanofluids is reported in various fields of science and nature since 1995, and the interest in the domain of nanofluids is increasing exponentially as shown in Fig. 2.1. The thermal conductivity of the heat transfer fluids plays an important role for the continuous efficient heat transfer. Overwhelming demand for high heat flow processes at the industrial level has embodied the new sophisticated technologies like nanofluids, for the new and efficient option in a sustainable manner. Generally, metals have much higher thermal conductivity compared to conventional fluids. Table 2.1 shows the thermal conductivities of the materials used to prepared nanofluids.

Fig. 2.1 Articles published on the nanofluids. Source https://www.sciencedirect.com/, https://www. tandfonline.com/, https://journals.sagepub.com/, https://asmedigitalcollection.asme.org/

2.2 Nanofluids

13

Table 2.1 Thermal conductivities of common materials (nanoparticles and base fluids) used for nanofluids at room temperature, 300 K Materials Metals

Metal oxide

Base fluids (conventional fluids)

Thermal conductivity (W/mK) Silver

406

Copper

385

Gold

314

Aluminum

205

Iron

79.5

Aluminum oxide

40

Copper oxide

32.9

Iron oxide

10

Titanium dioxide

8.3

Silicon dioxide

1.5

Water

0.615

Ethylene glycol

0.252

Engine oil

0.145

Transformer oil

0.126

2.2.1 Beginning of Nanofluids This era of modern technology has used the nanofluids as a new field related to nanotechnology. After S U S Choi, the researchers start experiments on nanoparticles rather than microsized particles. Nanofluids pose less difficulties compared to micrometer-sized particles. Thermal performance enhancement using nanofluid is an effective growing area of research which is still in its infant stage. The main reason for enhancement in heat transfer of nanofluids is their increased thermal conductivity compared to base fluid. But many researchers in their studies showed that the increase in heat transfer of nanofluids is much higher compared to the increase in thermal conductivity, and the relation between the two is not linear. It means that there is some other mechanism involved in high heat transfer characteristics of nanofluids [14]. The thermal conductivity is experimentally investigated by one of the following methods: transient hot-wire method, transient plane source method (these two methods are extensively used), steady-state parallel plate method (thermal conductivity measurement using parallel plates), temperature oscillation technique, 3 technique and thermal comparator technique [15]. Out of these, transient hot-wire method is mostly employed method. In transient hot-wire method, a metallic wire (sometimes made of alloy) is used as a temperature sensor as well as heating element. The wire is enveloped by the fluid (liquid) whose thermal conductivity is to be experimentally measured. The metallic wire/alloy is heated by circuiting current through it. The experiment is very fast, and due to quick response, natural convection is avoided. Thermal conductivity is the most important property of the nanofluids. Based on the literature, the parameters which influence the thermal conductivity of nanofluids are

14

2 Nanofluids: Definition & Classification

shape and size of nanoparticles, temperature, concentration, particle motion and so on. Cylindrical shapes provide better heat transfer compared to spherical because of systematic aggregation of cylindrical particles. This is the reason for high thermal conductivity of carbon nanotube (CNT) nanoparticles. Smaller size particles show larger enhancement in thermal conductivity compared to larger size particles due to increased surface area to volume ratio. He et al. [16] investigated experimentally the effect of size of nanoparticles on the thermal conductivity of TiO2 dispersed in distilled water. The experiments were performed on particle sizes of 95, 145 and 210 nm, dispersed in a volume fraction of 0.6%. Nanofluids with small size particles were reported to have higher thermal conductivity compared to larger particles. The increment in effective thermal conductivity was observed to be 3.36, 2.24 and 1.13% at particle size of 95, 145 and 210 nm, respectively. Chon et al. [17] investigated experimentally the thermal conductivity of Al2 O3 nanoparticles dispersed in distilled water. The heat transfer was found to be increasing with decreasing particle size. Particle concentration of nanoparticles in the base fluid is one of the important variables which affects thermal conductivity of nanofluids. Many studies showed that thermal conductivity of nanofluids increases nonlinearly with increase in particle concentration. Choi et al. [18] showed that suspension of a fraction of nanotubes can create sufficient rise in thermal conductivity of the nanofluids. The maximum increase in thermal conductivity was 160% compared to base fluid. Eastman et al. [19] also performed research on CNT and showed nonlinear relationship between nanofluid concentration and thermal conductivity. Vakili et al. [20] investigated experimentally the thermal conductivity of TiO2 dispersed in ethylene glycol and water (60:40) mixture. A nonlinear rise in thermal conductivity of TiO2 nanofluids was observed with increase in particle concentration. Hwang et al. [21] experimentally investigated the thermal conductivity of Al2 O3 nanoparticles dispersed in distilled water, at particle volume percentage of 0.01–0.3%. The thermal conductivity increase of 1.44% was observed for 0.3 vol% at 21 °C of nanofluid compared to base fluid. Li and Peterson [22] experimentally investigated the thermal conductivity of water-based CuO and Al2 O3 nanofluids at volume fractions of 2, 4, 6 and 10%. A high thermal conductivity was observed for both nanofluids. At 10 vol%, thermal conductivity increase of 30% was observed for water-based Al2 O3 nanofluid. Brownian motion is an important phenomenon which affects the effective thermal conductivity of nanofluids. Researchers working on this area investigated that the Brownian motion of nanoparticles causes the thermal conductivity to increase. The nanoparticles provide an increased surface area for the collisions to take place. The momentum of nanoparticles increases due to collision, so they can transport thermal energy more efficiently. The Brownian motion is closely related to temperature. Various literatures on the effect of temperature on nanofluid’s thermal conductivity show that there is an increase in thermal conductivity of nanofluids with rise in temperature. Das et al. [23] experimentally investigated the thermal conductivity of

2.2 Nanofluids

15

Al2 O3 /water and CuO/water nanofluids with the variation in temperature. Considerable rise in thermal conductivity was observed with the rise in the temperature. At 1 vol% and 21 °C, the enhancement in thermal conductivity was about 2%, which increases to 10.8% at 51 °C, for Al2 O3 /water nanofluids. CuO/water was observed to have better heat transfer characteristics than Al2 O3 /water. The increase in Brownian motion of nanoparticles at higher temperature increases the thermal conductivity of the nanofluids. Gupta et al. [24] investigated the effect of temperature on the thermal conductivity of graphene nanofluids. It was reported by the authors that the thermal conductivity increases with rise in temperature. Clustering is another parameter which affects the thermal conductivity. Keblinksi et al. [25] proposed nanoparticle clustering as one of the four effective parameters on thermal conductivity of nanofluids. Zhu et al. [26] also observed that clustering in the form of alignment of nanoparticle was responsible for the thermal conductivity rise while working with Fe3 O4 /water nanofluid. Another factor which is responsible for variation in thermal conductivity of nanofluids is the variation of pH of the fluid. Xie et al. [27] were the first who investigated the effect of pH of the nanofluid on its thermal conductivity. They observed that increasing pH value results in decreasing thermal conductivity of Al2 O3 /water nanofluid. Lee et al. [28] also stated pH dependency of nanofluid thermal conductivity. They showed that the thermal conductivity of distilled water-based CuO nanofluid increases 3 times as pH decreases from pH = 8 to pH = 3. To prevent the nanoparticles from agglomeration, the additives are generally employed, especially surfactants. Eastman et al. [19] have investigated the effect of thioglycolic acid as an additive on Cu/ethylene glycol nanofluid. They presented that additive can strongly affect the effective thermal conductivity of nanofluid.

2.2.2 Advantages of Nanofluids The nanofluid, a colloidal suspension, shows promising results for heat transfer in a number of applications. The following are the advantages of suspending nanoparticles into the conventional base fluids: • The effective thermal conductivity of the fluid is significantly improved. • Stability of the fluid is enhanced. • More surface to volume ratio of nano-sized particles helps in enhancing the heat transfer. • The aggregation of particles and clogging of flow loop by nanoparticles is reduced. • Enhancement in the nanoparticles movements leads to high heat transfer. • Highly applicable to the existing system without any huge modifications. • The thermophysical properties can be adjusted according to the need of the applications.

16

2 Nanofluids: Definition & Classification

2.3 Types of Nanofluids There are number of ways in which the nanofluids can be categorized; broadly, they can be classified as shown in Fig. 2.2. The classification is explained as.

2.3.1 On the Basis of Base Fluids The nanoparticles are dispersed into the base fluids for the improvement of the thermophysical properties. There are different base fluids available for the dispersion of such particles. Water has been used extensively by the researcher to study different effects of various types of nanoparticles [21, 29–35]. Recently, Rashidi et al. [36] have studied the performance of water-based calcium carbonate nanofluids and reported various results showing the huge potential of nanofluids. A number of other studies are still going on the water-based nanofluids [37–54]. Researchers have studied the ethylene glycol, transformer oil and engine oil-based nanofluids for various effects and applications [34, 35, 55]. Based on the applications, different types of base fluids are used for the nanofluids; for example, to study the effect on engine cooling, the engine oil would be used as a base fluid of the nanofluids [55].

On the basis of base fluids

Nanofluids

On the basis of material of nanoparticles

Special Cateogry

Fig. 2.2 Classification of the nanofluids

Water Ethylene Glycol Engine Oil Transformer Oil

Metals (Ag, Cu, Ni, Au) Ceramics (Oxides, Sulfides, Carbides) Alloys (Fe-Ni, Cu-Zn) Carbon-based (Carbon nanotubes, Graphene, graphite)

Hybrid Nanofluids Magnetic Nanofluids

2.3 Types of Nanofluids

17

2.3.2 On the Basis of Nanoparticle’s Material Several studies have reported the effect on the performance and thermophysical properties of the convectional base fluids by adding a very small amount of nanoparticles. The materials of the nanoparticles include metals (gold, silver, copper, aluminum etc.) [30, 56–58], metal oxides (Al2 O3 , Fe2 O3 , CuO, TiO2 , ZnO, etc.) [33, 59–63] and carbon-based (carbon nanotubes, graphite, diamond, etc.) [64–67]. The gold and silver nanoparticles have the higher thermal conductivity, but only few studies have been reported so far because of their cost. However, these nanoparticles show a great potential in solar collector [68]. Recently, Sundar et al. [68] have studied on the copper nanofluid and reported the efficiency and energy analysis, which shows the enhancement in the efficiency. The cost associated with the pure metal nanofluids is high, and it is one of the reasons researcher used alternative materials for nanofluids. Metal oxides are extensively used to study the effects on the thermophysical properties of the fluids. Some of the study on metal oxide nanofluids is shown in Table 2.2. The carbon is one of the mostly available elements on the earth. The typical carbon allotropes like diamond, graphite and carbon nanotubes (as shown in Fig. 2.3) are of particular interest, due to their higher thermal conductivity. Researchers have focused on the carbon material-based nanofluids because of their high thermal conductivity. Several studies have been reported on the potential of such nanofluids [33, 69, 70].

2.3.3 Special Category This is the category of nanofluids, which include the type of nanofluids that exhibit special characteristics, e.g., magnetic nanofluids, hybrid nanofluids. A. Magnetic nanofluids Magnetic nanofluids (MNFs), the colloidal suspension of ferromagnetic nanomaterial, have been taken into research fascinatingly. After contemplating its distinctive interesting properties and unique eximious features, it offers numerous applications, not only in heat transfer field but also immensely prevalent in medical, biological, aerospace, electronics and solar sciences. MNFs constitute a special class of nanofluids that exhibit both magnetic and fluid properties. MNFs are the suspension of ferromagnetic nanoparticles (maghemite, magnetite, cobalt, nickel, etc.) into the non-magnetic base fluids. Other than the enhancement in thermal conductivity, MNFs have one more exceptional feature that it has the magnetic properties as well, i.e., a fluid with magnetic properties. It enables that MNFs can be controlled by applying the magnetic field. Such features of this kind of smart nanofluids make it eligible for the numerous plethora of field. Magnetic nanofluids or ferrofluid are the special class of the nanofluids having distinct unique features. These are the suspension of ferromagnetic nanoparticles such as maghemite, magnetite, cobalt and nickel

18

2 Nanofluids: Definition & Classification

Table 2.2 Reported studies on the metal oxides nanofluids References

Nanoparticles

Base fluid

Particle conc.

Temp. range

Thermal conductivity enhancement

Das et al. [23]

Al2 O3 CuO

Water

1 and 4 vol%

21–51 °C

9.4–24.3%

Chon et al. [17]

Al2 O3

Water

1 and 4 vol%

21–71 °C

30%

Li and Peterson [22]

Al2 O3

De-ionized water

0.5–6 vol%

28–36 °C

0.5–26%

Timofeeva et al. [80]

Al2 O3

Water and EG

2.5–10 vol%

23 °C

10% for water and 13% for EG-based nanofluids

Yoo et al. [81]

TiO2 Al2 O3 Fe WO3

Water

0.3–1 vol%

25 °C

4%

Lee et al. [82]

Al2 O3

Water

0.01–0.3 vol%

21 °C

1.44% at 0.3 vol%

Murshed et al. [83]

Al2 O3

Water and EG

0.5–1 vol%

21–60 °C

Around 12%

Vakili et al. [20]

TiO2

Water and EG

0.5–1.5 vol%

–

6.67%

Oh et al. [84]

Al2 O3

Water and EG

1–4 vol%

25 °C

13.3% for water and 9.7% for EG-based nanofluids

Chandrasekar et al. [85]

Al2 O3

Water

0.32–3 vol%

25 °C

9.7% at 3 vol%

Gowda et al. [86]

Al2 O3 CuO

Water and EG

0.5–5 vol%

25 °C

12% for water and 14% for EG-based nanofluids

Ali and Yunus [86]

Al2 O3

Water and EG

0.2–1.4 vol%

25 °C

9% for water and 12% for EG-based nanofluids

into the non-magnetic base fluids. In particular, the magnetic nanofluid is a smart fluid magnetically controllable (Engler et al. [71]; Odenbach [72, 73]; Rosensweig [74]; Shliomis [75, 76]; Zablotsky et al. [77]) and has the potential for a variety of applications.

2.3 Types of Nanofluids

19

Fig. 2.3 Carbon allotropes extensively examined and used for the preparation of nanofluids [79]

B. Hybrid nanofluids These are the advanced nanofluids, which are prepared by the combination of two or more than two material’s nanoparticles dispersion into the base fluids. Jana et al. [78] have studied the hybrid nanofluids and compared them with the single material nanofluid and reported that the hybrid nanofluids are not showing as much improvement in the thermal conductivity as found in single or monotype nanofluids. They have also reported that the stability of hybrid nanofluid is more than that of the single material nanofluids, which can lead to preserve the thermal conductivity of nanofluids much longer time before settling of nanoparticles. Summary In this chapter, the definition and the brief history of the nanofluids have been comprehensively discussed. Different classifications of the nanofluids are explained in a systematic manner. All the categories of the classification have been properly deliberated.

20

2 Nanofluids: Definition & Classification

References 1. Maxwell, J. C. (1873). A treatise on electricity and magnetism (vol. 1). Clarendon press. 2. Vand, V. (1948). Viscosity of solutions and suspensions. II. Experimental determination of the viscosity–concentration function of spherical suspensions. Journal of Physical Chemistry, 52, 300–314. 3. Robinson, J. V. (1949). The Viscosity of Suspensions of Spheres. Journal of Physical Colloid Chemistry, 53, 1042–1056. 4. Leal, L. G. (1973). On the effective conductivity of a dilute suspension of spherical drops in the limit of low particle Peclet number. Chemical Engineering Communications, 1, 21–31. 5. Chung, Y. C., & Leal, L. G. (1982). An experimental study of the effective thermal conductivity of a sheared suspension of rigid spheres. International Journal of Multiphase Flow, 8, 605–625. 6. Kianjah, H., & Dhir, V. K. (1989). Experimental and analytical investigation of dispersed flow heat transfer. Experimental Thermal and Fluid Science, 2, 410–424. 7. Özbelge, T. A., & Somer, T. G. (1988). Hydrodynamic and heat transfer characteristics of liquid—solid suspensions in horizontal turbulent pipe flow. Chemical Engineering Journal, 38, 111–122. 8. Murray, D. B. (1994). Local enhancement of heat transfer in a particulate cross flow—II experimental data and predicted trends. International Journal of Multiphase Flow, 20, 505–513. 9. Booth, F. (1950). The electroviscous effect for suspensions of solid spherical particles. Proceedings of the Royal Society London A Mathematical and Physical Sciences, 203, 533–551. 10. Frankel, N. A., & Acrivos, A. (1967). On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 22, 847–853. 11. Nir, A., & Acrivos, A. (1974). Experiments on the effective viscosity of concentrated suspensions of solid spheres. International Journal of Multiphase Flow, 1, 373–381. 12. Van Kao, S., Nielsen, L. E. & Hill, C. T. (1975). Rheology of concentrated suspensions of spheres. I. Effect of the liquid—solid interface. Journal of Colloid and Interface Science, 53, 358–366. 13. Choi, S. U. S. & Eastman, J. A. (1995). Enhancing thermal conductivity of fluids with nanoparticles. 14. Chopkar, M., Das, P. K., & Manna, I. (2006). Synthesis and characterization of nanofluid for advanced heat transfer applications. Scripta Materialia, 55, 549–552. 15. Paul, G., Chopkar, M., Manna, I., & Das, P. K. (2010). Techniques for measuring the thermal conductivity of nanofluids: A review. Renewable and Sustainable Energy Reviews, 14, 1913– 1924. 16. He, Y., et al. (2007). Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe. International Journal of Heat and Mass Transfer, 50, 2272–2281. 17. Chon, C. H., Kihm, K. D., Lee, S. P., & Choi, S. U. S. (2005). Empirical correlation finding the role of temperature and particle size for nanofluid (Al2 O3 ) thermal conductivity enhancement. Applied Physics Letters, 87, 153107. 18. Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E., & Grulke, E. A. (2001). Anomalous thermal conductivity enhancement in nanotube suspensions. Applied Physics Letters, 79, 2252– 2254. 19. Eastman, J. A., Choi, S. U. S., Li, S., Yu, W., & Thompson, L. J. (2001). Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters, 78, 718–720. 20. Vakili, M., Mohebbi, A., & Hashemipour, H. (2013). Experimental study on convective heat transfer of TiO2 nanofluids. Heat and Mass Transfer, 49, 1159–1165. 21. Hwang, K. S., Jang, S. P., & Choi, S. U. S. (2009). Flow and convective heat transfer characteristics of water-based Al2 O3 nanofluids in fully developed laminar flow regime. International Journal of Heat and Mass Transfer, 52, 193–199.

References

21

22. Li, C. H., & Peterson, G. P. (2006). Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids). Journal of Applied Physics, 99, 84314. 23. Das, S. K., Putra, N., Thiesen, P., & Roetzel, W. (2003). Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer, 125, 567–574. 24. Sen Gupta, S., et al. (2011). Thermal conductivity enhancement of nanofluids containing graphene nanosheets. Journal of Applied Physics, 110, 84302. 25. Keblinski, P., Phillpot, S. R., Choi, S. U. S., & Eastman, J. A. (2002). Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). International Journal of Heat and Mass Transfer, 45, 855–863. 26. Zhu, H., Zhang, C., Liu, S., Tang, Y. & Yin, Y. (2006). Effects of nanoparticle clustering and alignment on thermal conductivities of Fe3 O4 aqueous nanofluids Effects of nanoparticle clustering and alignment on thermal conductivities of Fe3 O4 aqueous nanofluids. 023123, 4–7. 27. Xie, H., et al. (2002). Thermal conductivity enhancement of suspensions containing nanosized alumina particles. Journal of Applied Physics, 91, 4568–4572. 28. Lee, D., Kim, J.-W., & Kim, B. G. (2006). A new parameter to control heat transport in nanofluids: Surface Charge state of the particle in suspension. Journal of Physical Chemistry B, 110, 4323–4328. 29. Nguyen, C. T., et al. (2008). Viscosity data for Al2 O3 -water nanofluid-hysteresis: is heat transfer enhancement using nanofluids reliable? International Journal of Thermal Sciences, 47, 103– 111. 30. Hammami, Y. El, Hattab, M. El, Mir, R. & Mediouni, T. (2015). Numerical study of natural convection of nanofluid in a square enclosure in the presence of the magnetic field. 230–239. 31. Nabati Shoghl, S., Jamali, J. & Keshavarz Moraveji, M. (2016). Electrical conductivity, viscosity, and density of different nanofluids: An experimental study. Experimental Thermal and Fluid Science, 74, 339–346. 32. Byrne, M. D., Hart, R. A., & Da Silva, A. K. (2012). Experimental thermal-hydraulic evaluation of CuO nanofluids in microchannels at various concentrations with and without suspension enhancers. International Journal of Heat and Mass Transfer, 55, 2684–2691. 33. Meibodi, M. E., et al. (2010). An estimation for velocity and temperature profiles of nanofluids in fully developed turbulent flow conditions. International Communications in Heat and Mass Transfer, 37, 895–900. 34. Kumar, A. & Subudhi, S. (2018). Preparation, characteristics, convection and applications of magnetic nanofluids: A review. Heat and Mass Transfer und Stoffuebertragung, 54. 35. Raj, P., & Subudhi, S. (2018). A review of studies using nanofluids in flat-plate and direct absorption solar collectors. Renewable and Sustainable Energy Reviews, 84, 54–74. 36. Rashidi, M., Kalantariasl, A., Saboori, R., Haghani, A., & Keshavarz, A. (2021). Performance of environmental friendly water-based calcium carbonate nanofluid as enhanced recovery agent for sandstone oil reservoirs. Journal of Petroleum Science and Engineering, 196, 107644. 37. Mukherjee, S., Jana, S., Chandra Mishra, P., Chaudhuri, P., & Chakrabarty, S. (2021). Experimental investigation on thermo-physical properties and subcooled flow boiling performance of Al2 O3 /water nanofluids in a horizontal tube. International Journal of Thermal Sciences, 159, 106581. 38. Mahmoudpour, M., & Pourafshary, P. (2021). Investigation of the effect of engineered water/nanofluid hybrid injection on enhanced oil recovery mechanisms in carbonate reservoirs. Journal of Petroleum Science and Engineering, 196, 107662. 39. Naghdbishi, A., Yazdi, M. E., & Akbari, G. (2020). Experimental investigation of the effect of multi-wall carbon nanotube—Water/glycol based nanofluids on a PVT system integrated with PCM-covered collector. Applied Thermal Engineering, 178, 115556. 40. Ahmed, W., et al. (2020). Effect of ZnO-water based nanofluids from sonochemical synthesis method on heat transfer in a circular flow passage. International Communications in Heat and Mass Transfer, 114, 104591. 41. Naveenkumar, R., Ramesh Kumar, S., Giridharan, R. & Senthil Kumaran, S. (2020). Thermal Performance Enhancement in a Plain Tube fitted with perforated twisted tape insert using water based Al2 O3 Nanofluid. Materials Today: Proceedings, 22, 2274–2282.

22

2 Nanofluids: Definition & Classification

42. Aleem, M., Asjad, M. I., Shaheen, A., & Khan, I. (2020). MHD Influence on different water based nanofluids (TiO2 , Al2 O3 , CuO) in porous medium with chemical reaction and newtonian heating. Chaos, Solitons & Fractals, 130, 109437. 43. Azimikivi, H., Purmahmud, N. & Mirzaee, I. (2020). Rib shape and nanoparticle diameter effects on natural convection heat transfer at low turbulence two-phase flow of Al2 O3 -Water nanofluid inside a square cavity: Based on Buongiorno’s two-phase model. Thermal Science and Engineering Progress, 100587. https://doi.org/10.1016/j.tsep.2020.100587. 44. Alshayji, A., Asadi, A., & Alarifi, I. M. (2020). On the heat transfer effectiveness and pumping power assessment of a diamond-water nanofluid based on thermophysical properties: An experimental study. Powder Technology, 373, 397–410. 45. Das, R. K., Sokhal, G. S., & Sehgal, S. S. (2020). A numerical study on the performance of water based copper oxide nanofluids in compact channel. Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2020.02.956. 46. Sharma, P., Kumar, V., Singh Sokhal, G., Dasaroju, G. & Kumar Bulasara, V. (2020). Numerical study on performance of flat tube with water based copper oxide nanofluids. Materials Today: Proceedings, 21, 1800–1808. 47. Hu, Y.-P., Li, Y.-R., Lu, L., Mao, Y.-J., & Li, M.-H. (2020). Natural convection of water-based nanofluids near the density maximum in an annulus. International Journal of Thermal Sciences, 152, 106309. 48. Maaref, S., Kantzas, A., & Bryant, S. L. (2020). The effect of water alternating solvent based nanofluid flooding on heavy oil recovery in oil-wet porous media. Fuel, 282, 118808. 49. Arora, S., et al. (2020). Performance and cost analysis of photovoltaic thermal (PVT)-compound parabolic concentrator (CPC) collector integrated solar still using CNT-water based nanofluids. Desalination, 495, 114595. 50. Sahota, L., Arora, S., Singh, H. P., & Sahoo, G. (2020). Thermo-physical characteristics of passive double slope solar still loaded with MWCNTs and Al2 O3 -water based nanofluid. Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2020.01.600. 51. Ansarpour, M., Danesh, E., & Mofarahi, M. (2020). Investigation the effect of various factors in a convective heat transfer performance by ionic liquid, ethylene glycol, and water as the base fluids for Al2 O3 nanofluid in a horizontal tube: A numerical study. International Communications in Heat and Mass Transfer, 113, 104556. 52. Gallego, A., Herrera, B., Buitrago-Sierra, R., Zapata, C., & Cacua, K. (2020). Influence of filling ratio on the thermal performance and efficiency of a thermosyphon operating with Al2 O3 -water based nanofluids. Nano-Structures & Nano-Objects, 22, 100448. 53. Abdelrazik, A. S., et al. (2020). Optical, stability and energy performance of water-based MXene nanofluids in hybrid PV/thermal solar systems. Solar Energy, 204, 32–47. 54. Gallego, A., et al. (2020). Experimental evaluation of the effect in the stability and thermophysical properties of water-Al2 O3 based nanofluids using SDBS as dispersant agent. Advanced Powder Technology, 31, 560–570. 55. Kumar, A. & Subudhi, S. (2019). Preparation, characterization and heat transfer analysis of nanofluids used for engine cooling. Applied Thermal Engineering, 160. 56. Paul, G., Pal, T., & Manna, I. (2010). Thermo-physical property measurement of nano-gold dispersed water based nanofluids prepared by chemical precipitation technique. Journal of Colloid and Interface Science, 349, 434–437. 57. Phuoc, T. X., Soong, Y., & Chyu, M. K. (2007). Synthesis of Ag-deionized water nanofluids using multi-beam laser ablation in liquids. Optics and Lasers in Engineering, 45, 1099–1106. 58. Margeat, O., Respaud, M., Amiens, C., Lecante, P., & Chaudret, B. (2010). Ultrafine metallic Fe nanoparticles: Synthesis, structure and magnetism. Beilstein Journal of Nanotechnology, 1, 108–118. 59. Katiyar, A., Dhar, P., Nandi, T., & Das, S. K. (2016). Magnetic field induced augmented thermal conduction phenomenon in magneto-nanocolloids. Journal of Magnetism and Magnetic Materials, 419, 588–599. 60. Karimi, A. S. Afghahi, S. S., Shariatmadar, H. & Ashjaee, M. (2014). Experimental investigation on thermal conductivity of MFe2 O4 (M = Fe and Co) magnetic nanofluids under influence of magnetic field. Thermochimica Acta, 598, 59–67.

References

23

61. Lee, S., Choi, S. U.-S., Li, S., & Eastman, J. A. (1999). Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer, 121, 280–289. 62. Liu, M., Zhou, M., Yang, H., Ren, G., & Zhao, Y. (2016). Titanium dioxide nanoparticles modified three dimensional ordered macroporous carbon for improved energy output in microbial fuel cells. Electrochimica Acta, 190, 463–470. 63. Shen, L. P., Wang, H., Dong, M., Ma, Z. C. & Wang, H. B. (2012). Solvothermal synthesis and electrical conductivity model for the zinc oxide-insulated oil nanofluid. Physics Letters, Section A: General, Atomic and Solid State, 376, 1053–1057. 64. Su, F., Ma, X., & Lan, Z. (2011). The effect of carbon nanotubes on the physical properties of a binary nanofluid. Journal of the Taiwan Institute of Chemical Engineers, 42, 252–257. 65. Yang, L., Xu, J., Du, K., & Zhang, X. (2017). Recent developments on viscosity and thermal conductivity of nanofluids. Powder Technology, 317, 348–369. 66. Sharma, T., Mohana Reddy, A. L., Chandra, T. S. & Ramaprabhu, S. (2008). Development of carbon nanotubes and nanofluids based microbial fuel cell. International Journal of Hydrogen Energy, 33, 6749–6754. ˙ 67. Zyła, G., Vallejo, J. P., Fal, J., & Lugo, L. (2018). Nanodiamonds—Ethylene Glycol nanofluids: Experimental investigation of fundamental physical properties. International Journal of Heat and Mass Transfer, 121, 1201–1213. 68. Bandarra Filho, E. P., Mendoza, O. S. H., Beicker, C. L. L., Menezes, A. & Wen, D. (2014). Experimental investigation of a silver nanoparticle-based direct absorption solar thermal system. Energy Conversion and Management, 84, 261–267. 69. Lamas, B., Abreu, B., Fonseca, A., Martins, N., & Oliveira, M. (2012). Assessing colloidal stability of long term MWCNT based nanofluids. Journal of Colloid and Interface Science, 381, 17–23. 70. Yang, J., et al. (2011). Measurement of the intrinsic thermal conductivity of a multiwalled carbon nanotube and its contact thermal resistance with the substrate. Small (Weinheim an der Bergstrasse, Germany), 7, 2334–2340. 71. Engler, H., Borin, D., & Odenbach, S. (2009). Thermomagnetic convection influenced by the magnetoviscous effect Thermomagnetic convection influenced by the magnetoviscous effect.. https://doi.org/10.1088/1742-6596/149/1/012105. 72. Odenbach, S., & Störk, H. (1998). Shear dependence of field-induced contributions to the viscosity of magnetic fluids at low shear rates. Journal of Magnetism and Magnetic Materials, 183, 188–194. 73. Odenbach, S. (2003). Magnetic fluids—Suspensions of magnetic dipoles and their magnetic control. Journal of Physics: Condensed Matter, 15. 74. Rosensweig, R. E. (1969). Viscosity of magnetic fluid in a magnetic field. Journal of Colloid and Interface Science, 20, 680–687. 75. Shliomis, M. (1972). Effective viscosity of magnetic suspensions. Soviet Physics, JETP, 34, 1291–1294. 76. Shliomis, M. I., & Morozov, K. I. (1994). Negative viscosity of ferrofluid under alternating magnetic field. Physics of Fluids, 6, 2855–2861. 77. Zablotsky, D., Mezulis, A., & Blums, E. (2009). Surface cooling based on the thermomagnetic convection: Numerical simulation and experiment. International Journal of Heat and Mass Transfer, 52, 5302–5308. 78. Jana, S., Salehi-Khojin, A., & Zhong, W.-H. (2007). Enhancement of fluid thermal conductivity by the addition of single and hybrid nano-additives. Thermochimica Acta, 462, 45–55. 79. Chamsa-Ard, W., Brundavanam, S., Fung, C. C., Fawcett, D. & Poinern, G. (2017). Nanofluid types, their synthesis, properties and incorporation in direct solar thermal collectors: A Review. Nanomater. (Basel, Switzerland), 7, 131. 80. Timofeeva, E. V., et al. (2007). Thermal conductivity and particle agglomeration in alumina nanofluids: Experiment and theory. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 76, 28–39. 81. Yoo, D.-H., Hong, K. S., & Yang, H.-S. (2007). Study of thermal conductivity of nanofluids for the application of heat transfer fluids. Thermochimica Acta, 455, 66–69.

24

2 Nanofluids: Definition & Classification

82. Lee, J.-H. H., et al. (2008). Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3nanoparticles. International Journal of Heat and Mass Transfer, 51, 2651–2656. 83. Murshed, S. M. S., Leong, K. C., & Yang, C. (2008). Investigations of thermal conductivity and viscosity of nanofluids. International Journal of Thermal Sciences, 47, 560–568. 84. Oh, D.-W., Jain, A., Eaton, J. K., Goodson, K. E., & Lee, J. S. (2008). Thermal conductivity measurement and sedimentation detection of aluminum oxide nanofluids by using the 3ω method. International Journal of Heat and Fluid Flow, 29, 1456–1461. 85. Chandrasekar, M., Suresh, S. & Chandra Bose, A. (2010). xperimental investigations and theoretical determination of thermal conductivity and viscosity of Al2 O3 /water nanofluid. Experimental Thermal and Fluid Science, 34, 210–216. 86. Ali, F. M., Yunus, W. M. M., & Talib, Z. A. (2013). Study of the effect of particles size and volume fraction concentration on the thermal conductivity and thermal diffusivity of Al2O3 nanofluids. International Journal of Physical Sciences, 8, 1442–1457.

Chapter 3

Synthesis of Nanofluids

3.1 Nanoparticles Nanoparticles are the sub-microscopic size (1–100 nm) particles with the dimensions measured in manometers (nm). Nanoparticles can be of any materials, and they can exist in environment and nature. They are applicable to various areas like engineering, medical, etc., due to their unique features [1]. Nanoparticles can be of any shape such as spheres, cubes, cylinders and tubes, but mostly, they are designed to meet the needs of the applications they are going to use. Figure 3.1 shows scanning electron microscope photographs of the Al2 O3 nanoparticles. There are a number of proofs that indicate that nanoparticles existed in nature a long time ago from ancient times.

3.1.1 Different Types of Nanoparticles There are a number of classification for the nanoparticles based on surface morphologies, types of materials, etc. A. On the basis of surface morphologies In this classification, nanoparticles can be divided into different types on the basis of shapes, size and structure. Their shape can be spherical, tube tetragonal, cube, chisel, etc., and the size of the nanoparticles can be varied which is related to the properties associated with them. There are several techniques to measure the shape and size of the nanoparticles like scanning electron microscopy (SEM), transmission electron microscopy (TEM), dynamic light scattering (DLS), X-ray diffraction, zeta potential, etc. Figure 3.1 shows the images of Al2 O3 nanoparticles obtained from the SEM. The SEM is used to collect the information about surface morphology, chemical composition, size and structure of the materials. In SEM, the images are © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Kumar and S. Subudhi, Thermal Characteristics and Convection in Nanofluids, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4248-4_3

25

26

3 Synthesis of Nanofluids

Fig. 3.1 Scanning electron microscope photographs of Al2 O3 nanoparticles at different magnification

produced by the scanning the surface by a focused beam of high-energy electron, which produce signals of different types that contain the information about materials. Figure 3.2 shows the TEM images of the cubic iron oxide nanoparticles of various sizes (9–20 nm) [1]. TEM is used to study the information about particle size distribution, shape and crystallinity of a sample. In the TEM, the beam of electrons is transmitted through specimen, and the electron’s interaction with material’s atom formed an image. It is a powerful tool to analyze the quality, shape and size of the materials. Figure 3.3 shows different shapes and sizes of the nanoparticles reported by the researchers. Link et al. [2] have prepared the gold nanoparticles and studied on size dependence of plasma absorption, and Fig. 3.3a and b shows the gold nanoparticle TEM image for shape and size distribution. Pyatenko et al. [3] have reported the new method to prepare silver nanoparticles. Figure 3.3c and d shows TEM images of the spherical silver nanoparticles along with some nanorod-type nanoparticle shapes with the size range from 10 to 80 nm. Tahara et al. [4] have prepared the rod-type titanium dioxide nanoparticles by bead milling process and studied their optical properties, shown shapes and size in Fig. 3.3e and f.

3.1 Nanoparticles

27

Fig. 3.2 TEM images of the cubic iron oxide nanoparticles(9–20 nm); scale bar: 50 nm [1]

B. On the basis of type of materials The nanoparticles can be divided into different categories by the type of materials, and these categories are: metals, metal oxides, ceramics, carbon materials, etc. Metaltype nanoparticles include gold, silver, copper; metal oxides include aluminum oxide, titanium oxide, iron oxide, silicon oxide, zinc oxide, etc.; carbon-based materials include diamond, carbon nanotube, graphite, etc. Metallic nanoparticles have some advantages like enhance Rayleigh scattering, strong plasma absorption; however, there are some disadvantages associated with them. They are thermodynamically unstable and can undergo transformation. They are difficult to prepare, and while preparing, oxide or nitride formation is aggravated [5]. Metal oxide nanoparticles are applicable to many areas and have unique properties and stability. Their high density and limited size of corners and edges on surface lead to many unique features and application. Al2 O3 , ZnO, CuO, Fe2 O3 , Fe3 O4 , TiO2 MgO, AgO CeO2 ZrO2 and SiO2 are some examples of metal oxide nanoparticles [6]. Fe3 O4 is a special kind of metal oxide nanoparticle which exhibits the magnetic properties. This type of nanoparticles changes their behavior in the presence of magnetic field and can be applicable to the variety of fields not only in engineering but also in medical or biology field [7]. Carbon-based nanoparticles are being studied by the number of researchers because of their extraordinary properties. Some of the structure of carbon-based material is shown in Fig. 3.4. Carbon nanotubes have been used for both in biomedical [8] and engineering field [9]. High thermal conductivity of such nanoparticles enables them to be applicable in energy transfer fields.

28

3 Synthesis of Nanofluids

Fig. 3.3 TEM images of various nanoparticles a gold nanoparticle shapes [2] b histograms of size distribution of gold nanoparticles [2] c spherical silver nanoparticles [3] (inset: size distribution) d spherical- and rod-type silver nanoparticles [3] (inset: size distribution) e and f rod-type titanium dioxide nanoparticles by bead milling process [4]

3.1.2 Nanoparticle Synthesis There are a number of methods available to synthesized nanoparticles, and they can be classified into two categories: One is top to bottom approach and the other one is bottom to top approach, as shown in the Fig. 3.5. Top to bottom approaches are the ones in which the materials are converted into nano-sized objects from the large materials, as shown in Fig. 3.6. On the other hand,

3.1 Nanoparticles

29

Fig. 3.4 Various types structure of carbon-based nanomaterials [34]

Fig. 3.5 Broadly classified methods to prepare to nanoparticles

Nanoparticles Synthesis

Top to Bottom Approach

Bottom to top Approach

bottom to top approaches are involved in building the nano-sized particles from the arrangement of atom level elements, as shown in the Fig. 3.7. In mechanical milling method, mostly, the metallic and ceramics nanoparticles are produced. Traditional high-energy ball mills which equipped with the grinding objects are used to pulverized the materials. Other top to bottom approach methods are electro-explosion, sputtering mechanochemical processing and laser ablation. Bottom to top approach includes the methods like chemical vapor deposition, chemical vapor condensation, precipitation, sol–gel, etc.

30

3 Synthesis of Nanofluids

Fig. 3.6 Flow diagram and the methods of the preparation of nanoparticles from physical methods

Fig. 3.7 Flow diagram and the methods of the preparation of nanoparticles from chemical methods

3.1.3 Nanoparticle Characterization Techniques The nanoparticles are characterized by various modern techniques by different researchers. Figure 3.8 shows the techniques associated with the measuring properties. The X-ray diffraction (XRD) is used for the identification of crystallinity by analyzing the x-ray pattern of the samples. SEM and TEM are already discussed in the Sect. 3.1.1 and used to determine the shape and size of the nanoparticles. Atomic force microscopy (AFM) is used for the imaging of any type of surface and used for shape and size of the nanoparticles. UV–visible absorption spectroscopy (UV–VS)

3.1 Nanoparticles

31

Fig. 3.8 Common characterization techniques for the nanoparticles

is used to determine the shape and size of the nanoparticles. Zeta sizer is used to measure the size and electrophoretic mobility of the nanoparticles. Fourier transform infrared spectroscopy (FTIR) is used for the identification of organic, polymeric and inorganic materials.

3.2 Synthesis of Nanofluids A uniformly dispersed and stable nanofluid is highly applicable to various categories of applications, so the key step to achieve the highly stable nanofluids is the synthesis of nanofluid. Various types of nanofluids are synthesized by different physical and chemical processes. Agglomeration of particles and various other properties depend on the preparation of nanofluids. Preparation of the nanofluids is one of the first key steps toward effective applications or studies of nanofluids. As mentioned earlier, nanofluids are produced by the uniform dispersion of solid nanoparticles into the conventional base fluids. There are number of methods present to prepare stable uniform nanofluids. Broadly, they can be categorized into two methods to synthesize nanofluids, viz. one-step and two-step method.

3.2.1 Two-Step Method In most of the experimental studies, two-step methods have been used to prepare nanofluids, as concluded from Table 3.1. In this method, first, the solid particles in the range of 1–100 nm are manufactured by using various techniques as discussed previously followed by the dispersion of nanoparticles in base fluids using processes such as ultrasonication, magnetic agitation and shear mixing. The two-step method involves two steps to prepare nanofluids. The first step includes the preparation or

DW

DI

DW

DW

Xuan et al. [35]

Asirvatham et al. [36]

Zhu et al. [37]

Oh et al. [38]

DW

DI

EG

DW

DW

DW

DW

Kerosene

DW

Das et al. [13]

Murshed et al. [40]

Hong and Yanga [41]

Duangthongsuk et al. [42]

Chandrasekar et al. [22]

Li et al. [43]

Patel et al. [44]

Yu et al. [45]

Vakili et al. [46]

EG + DW

DW

Wang et al. [39]

EG

Base fluid

Author

TiO2

Fe3 O4

Al2 O3

CuO

Al2 O3

TiO2

Fe

25

15

11

25

43

21

–

15

28.6

CuO TiO2

38.4

25

45

106

10

100

Particle diameter (nm)

Al2 O3

Al2 O3

Al2 O3

Graphite

CuO

Cu

Nano-particles

Table 3.1 Reported experimental studies on the preparation of nanofluids

0.5–1 vol%

0–1.2 vol%

0.8 vol%

0.1 wt%

0.33–5 vol%

0–1.2 vol%

0–0.55 vol%

0–5 vol%

1–4 vol%

0–0.08 wt%

1–8 vol%

1–5.5 vol%

0.5 wt%

0.003 vol%

0–5 vol%

Concentra-tion

4h

80 min

6h

1h

6h

2h

70 min

8–10 h

11 h

15 min

15 h

30 min

2–7 h

–

Ultrasoni-cation

pH control

Oleic acid

X

SDBS and pH control

X

X

SDS

Oleic acid and CTAB

X

SDBS and pH control

X

PVP and pH control

X

Laurate salt

Dispersant/Additive

32 3 Synthesis of Nanofluids

3.2 Synthesis of Nanofluids

33

Fig. 3.9 Preparation of the nanofluids (Fe3 O4 -Water) by the two-step methods

purchasing of nanoparticles, and the second step is comprising the dispersion of nanoparticles into base fluid by ultrasonication, as shown in Fig. 3.9. As mentioned above, the nanoparticle can be synthesized by two approaches, bottom-top and top-down. Top-down approach consists of lithography (used to produce arrays of nanoparticles), attrition/ball milling, etching of structure, etc. The attrition or milling process is used to grind/crush the base material having the size of the order of cm to nanoparticles. The major difficulty with this approach is the inadequate shape and range of size of nanoparticles along with the surface and interface contamination by the milling tools and atmosphere. To produce nanoparticles in a bulk quantity, a large system is mandatory which makes this approach expensive. On the other hand, high production rate of nanoparticles is principal advantage of top-down approach, whereas bottom-up approach consists of different chemical processes to produce the nanoparticles of desired shape and size. Sol–gel, precipitation, hydrothermal, electrodeposition, inert gas condensation and pyrolysis processes such as spray or flame pyrolysis are well-known processes of this approach. This process starts from atomic structure and accumulates in the nanoparticles. For example, in the sol–gel process, solid particles of larger size dissolve into the liquid (sol) through hydrolysis followed by condensation of the sol into gel form. The gel is dried to remove liquid phases and is heated up at the higher temperature for dehydration. Through densification and the decomposition of the gel at higher temperature, nanoparticles of desired shape and size occur. Mirjalili et al. [10] synthesize the α-Al2 O3 powder of nanosize by using sol–gel method. Bottom-up approach is less expensive than the top-down approach but with a slow rate of production.

34

3 Synthesis of Nanofluids

The synthesized nanoparticles using both approaches are stored in the dry state, resulted in the agglomeration of nanoparticles before the dispersion in the base fluid, and those agglomerates settle down due to their heavy mass. Further, the higher surface energy of nanoparticles and attractive Van der Waals forces also enhance the nanoparticle agglomeration in dispersed state and cause to poor dispersion and sedimentation. Due to these effective factors, Das et al. [11] found that a higher particle concentration of nanoparticles, 10 times more than the single-step method, is required to increase the heat transfer. For this reason, it is essential to breakdown such agglomerates to prevent the settling of nanoparticles. Several mechanical devices, like ultrasonicator (bath or probe type), magnetic stirrer, etc., are used for a time period, known as sonication time, to breakdown the agglomerates. The mass production of nanoparticles in industries is encouraging factor for the two-step method to prepare the nanofluids. The two-step method is effective for the oxide nanofluids than the preparation of metallic nanoparticles of higher thermal conductivity, experienced by Das et al. [11]. Lee et al. [12] prepared the oxide nanofluids (Al2 O3 and CuO) using the two-step method. The Al2 O3 and CuO nanoparticles of area-weighted particle diameter of 38.4 and 23.6 nm were synthesized by the gas condensation process (bottom-up approach) and dispersed uniformly in the base fluid such as distilled water and ethylene glycol. Das et al. [13] also used the similar nanoparticles, Al2 O3 and CuO of volume-weighted particle diameter of 38.4 and 28.6 nm. The two-step process was followed to prepare the nanofluids; first, the nanoparticles were manufactured by the physical vapor synthesis method, mixed with the distilled water, and then ultrasonicated for the uniform dispersion of nanoparticles. To find the effect of nanoparticles size on the thermal conductivity of nanofluids, Chon et al. [14] prepared the Al2 O3 -water nanofluids for different particles having nominal diameter of 11, 47 and 150 nm, using the two-step process and sonicated for the better suspension. Similarly, Li and Peterson [15] also reported the effect of particle size on the thermal conductivity by dispersing the spherical gamma Al2 O3 nanoparticles of particle diameter of 38.4 nm in deionized water by two-step process. Timofeeva et al. [16] characterized the water and ethylene glycol-based Al2 O3 nanofluids of particle diameter of 11, 20 and 40 nm, prepared by the two-step process and investigated the effect of agglomeration on the physical properties of nanofluids. Yoo et al. [17] used various nanoparticles (TiO2 , Al2 O3 , Fe and WO3 ) synthesized by the chemical vapor deposition process to prepare the nanofluids and dispersed the nanoparticles in the deionized water by the ultrasonic cell disrupter to break down the clusters of nanoparticles. Brolossy et al. [18] first synthesized the alumina nanoparticle by the sol–gel method by reaction of the aqueous ammonium bicarbonate and aqueous aluminum precursor in the presence of cetyl trimethyl ammonium bromide surfactant (CTAB) followed by the stirring and drying and uniform dispersion in the deionized water using the ultrasonication. The other ways of dispersion of nanoparticles in the base fluid were used by Wang et al. [19] and used mechanical blending, coating particles with polymers and filtration to prepare the water, vacuum pump oil and engine oil-based γ-Al2 O3 nanofluids along with the ultrasonication.

3.2 Synthesis of Nanofluids

35

3.2.2 One-Step Method One-step method principally used to disperse metallic nanoparticles directly in the base fluid to minimize the possibilities of agglomeration of particles. By using physical vapor deposition (PVD) or liquid-chemical method to prepare the nanofluids, Li et al. [20] found that the stability of dispersed medium can be increased by avoiding various processes like drying, storage, transportation and dispersion of particles in a base fluid by using mechanical blending or ultrasonic vibration. The one-step method is sub-divided further in the physical and chemical one-step method. The physical one-step method involves the vaporization of bulk metal piece and condensation of the vapor into the base fluid directly, while in the chemical one-step method, the chemical compound of desired metallic nanoparticles reacts with various surfactants or other chemicals, and nanofluid is obtained as the product of chemical reactions. The laser ablation technique was used to prepare the Al2 O3 -water nanofluids by Piriyawong et al. [21]. An aluminum pallet was used as the target material and a laser light at a wavelength of 1064 nm was focused to the target material at a different laser energy with a repetition rate of 2 Hz for the total time of 40 min and confirmed the oxidation of Al nanoparticles through the optical absorption spectra. The particle concentration in Al2 O3 /DIW nanofluids was increased with the laser energy. Due to the more collision between the vapor/atoms at higher laser energy, the particles of large diameter were formed. Chandrasekar et al. [22] used one-step method to prepare the Al2 O3 /water nanofluid by microwave-assisted chemical precipitation of aqueous solution of aluminum chloride. Zhu et al. [23] reported that the particle size in one-step method can be controlled by adjusting the synthesis parameters such as reaction temperature, injection rate and concentration of reducing agent. High production cost and low production capability are the main drawbacks to this method. The production rate of nanofluid by one-step method is very low, which makes this method operational only for the laboratory research. Another disadvantage is the dispersion of nanoparticles is compitable with the low vapor pressure base fluids, such as ethylene glycol.

3.2.3 Case Studies on Synthesis of Different Nanofluids A. Alumina Nanofluids The alumina nanofluids can be prepared by both methods, but most of the researchers are preferred two-step method, as shown in the Table 3.2. Alumina nanofluids are the widely studied nanofluids because it is cost effective and easily available material. In Sects. 3.2.1 and 3.2.2, it has already been discussed about the research associated with the preparation of alumina nanofluids.

36

3 Synthesis of Nanofluids

Table 3.2 Synthesis process used for the Al2 O3 nanofluids Authors

Particle size (nm)

Base fluid

Concentration

Synthesis process

Lee et al. [12]

38.4

Water and EG

1–5 vol%

Two-step

Das et al. [13]

38.4

Water

1 and 4 vol%

Two-step

Chon et al. [14]

11, 47 and 150

Water

1 and 4 vol%

Two-step

Li and Peterson [15]

36 and 47

DI Water

0.5–6 vol%

Two-step

Timofeeva et al. [16]

11, 20 and 40

Water and EG

2.5–10 vol%

Two-step

Yoo et al. [17]

48

DI Water

0.3–1 vol%

Two-step

Lee et al. [47]

30

DI Water

0.01–0.3 vol%

Two-step

Murshed et al. [48] 80 and 150

DI Water and EG

0.5–1 vol%

Two-step

Oh et al. [38]

45

Water and EG

1–4 vol%

Two-step

Gowda et al. [49]

10

DI Water and EG

0.5–5 vol%

Two-step

Pastoriza-Gallego et al. [50]

43

EG

1.5–8.6 vol%

Two-step

Longo and Zilio [51]

165 and 285

Water

1–4 vol%

Two-Step

Azizian et al. [52]

70

Water

1.6–13.1 vol%

Two-step

Murshed [53]

80

EG

1–5 vol%

Two-step

Barbes et al. [54]

45

DI Water and EG

3.7–9.3 vol%

Two-step

Brolossy et al. [18] 5

Water

0.1–1 vol%

Two-step

Sundar et al. [55]

36.5

EG/W (50:50)

0.2–0.8 vol%

Two-step

Darzi et al. [56]

20

Water

0.25–1 vol%

Two-step

Elias et al. [57]

13

EG/W (50:50)

0.2–1 vol%

Two-step

Esfe et al. [58]

5

DI Water

0.25–5 vol%

Two-step

Lee et al. [59]

71.6, 114.5 and 136.8

Water

0.51 vol%

Two-step

Piriyawong et al. [21]

26, 38 and 53

DI Water

–

One-step

Chandrasekar et al. [22]

43

Water

0.32–3 vol%

One-step

EG

0.2–1.4 vol%

One-step

Ali and Yunus [60] 11

B. Magnetic Nanofluids The preparation of magnetic nanofluids has been done by the researchers by both the methods. Table 3.3 summarizes different studies associated by the preparation of magnetic nanofluids. It is evident from this table that most of the studies are used the two-step method. The magnetic nanoparticles are first prepared by a standard coprecipitation method, as shown in Fig. 3.10. This method is the simplest and efficient to obtain the magnetic nanoparticles. Laurent et al. [24], Peternele et al. [25] and Saien

3.2 Synthesis of Nanofluids

37

Table 3.3 The reported literature on the preparation of magnetic nanofluids Authors

Material of nanoparticles

Base fluid

Concentration

Particle size (nm)

Process

Aksenov et al. [61]

Fe3 O4 and CoFe2 O4

Water

6.5 and 2 vol%

–

Two-step

Li et al. [62] Fe3 O4 and Fe

Water

1–5 vol%

20 and 26

One-step and two-step

Bica et al. [63]

Fe

Water

0.15 vol%

Less than 10

One-step

Hong et al. [64]

Fe2 O3

DI water

0.02 wt%

5–25

Two-step

Singh et al. [65]

Cr2 O3

Distilled water

0.1 wt%

30–80

Two-step

Li and Xuan Fe3 O4 [66]

Water

1.0 vol%

10

One-step

Abareshi et al. [67]

Water

0–3 vol%

10

Two-step

Yu et al. [45] Fe3 O4

Kerosene

1.0 vol%

15

Two-step

Kudelcik et al. [68]

Fe3 O4

Transformer oil ITO 100

0.2, 1 and 2 vol%

10.6

Two-step

Lajvardi et al. [69]

Fe3 O4

Water

5 vol%

10 ± 5

Two-step

Abareshi et al. [70]

α-Fe2 O3

Glycerol

0.125–0.75 vol%

5

Two-step

Nabeel Rashin and Hemalatha [71]

Fe3 O4

Water

0.2, 0.4, 0.6, 0.8 and 1 vol%

11

One-step

Sundar et al. Fe3 O4 [72]

EG-water

0–1 vol%

11.42

Two-step

Sundar et al. Fe3 O4 [73]

Distilled water

0.02–0.6 vol%

36

Two-step

Gavili et al. [74]

Fe3 O4

DI water

5 vol%

10 ± 3

Two-step

Gu et al. [75] Fe3 O4

DI water

0.5–2.5 vol%

8–12

Two-step

Nabeel Rashin and Hemalatha [76]

Water

0.2–1 vol%

14

Two-step

Karimi et al. Fe3 O4 and [77] CoFe2 O4

DI water

0–4.8 vol%

10 and 15

Two-step

Goharkhah et al. [78]

Fe3 O4

Water

1–2 vol%

30

Two-step

Bagheli et al. [79]

Fe3 O4

DI water

0.1–0.5 vol%

14.2

Two-step

Fe3 O4

CoFe2 O4

(continued)

38

3 Synthesis of Nanofluids

Table 3.3 (continued) Authors

Material of nanoparticles

Base fluid

Concentration

Particle size (nm)

Process

Wang et al. [80]

Fe3 O4

Water

0.5–5 vol%

7.5

Two-step

Fig. 3.10 Flow diagram of the co-precipitation method to prepare Fe3 O4 magnetic nanoparticles. The inset shows the two-step method to prepare magnetic nanofluid

et al. [26] have used the co-precipitation method to prepare to magnetic nanoparticles. An aqueous mixture of ferrous and ferric in the form of hydrated chloride salts in the alkaline medium in the ratio of Fe3+ /Fe2+ :: 2/1 is used for the preparation of magnetic nanoparticles. The flow diagram of the procedure of the co-precipitation method is shown 3.10. After obtaining the nanoparticles, the magnetic nanofluids are obtained by the uniform dispersion by the ultrasonication process. The process is shown in the inset of Fig. 3.10. Oleic acid is the general surfactant used for the stability of magnetic nanofluids. C. Hybrid Nanofluids There are several methods and techniques used by the researchers to prepare hybrid nanofluids. Suresh et al. [27] synthesized the Al2 O3 -Cu/water hybrid nanofluids

3.2 Synthesis of Nanofluids

39

by two-step method and studied its thermophysical properties. Thermochemical synthesis method is used to prepare Al2 O3 -Cu nanopowder, and it consists of stages: spray-drying, oxidation of precursor powder, reduction by hydrogen and homogenization. The water solution of nitrates of copper and aluminum is prepared in the relative proportion of 90:10; then, the solution is spray dried at 180 °C to obtain the precursor powder. The powder is heated first in air environment and then in hydrogen environment. Then, the powder is ball milled at certain rpm for a period of time. Sundar et al. [28] prepared the MWCNT-Fe3 O4 /water hybrid nanofluid by the two-step methods. Madhest et al. [29] have studied the Cu-TiO2 hybrid nanofluid by preparing the nanofluid by stirring and dispersion methods. Similar kinds of methods are used by the researchers to prepare the hybrid nanofluids. D. Carbon-based nanofluids The multi-walled carbon nanotube (MWCNT) is one of the kinds of carbon-based nanomaterial of cylindrical shape which is dispersed into the liquid media by the mechanical and chemical methods [30]. Wen et al. [31] prepared the MWCNT/water nanofluids by the two-step method, and the MWCNT nanoparticles are purchased and uniformly dispersed by the sonication. Su et al. [32] prepared the carbon nanotube (CNT)-ammonia binary fluid by uniform suspension and modified the surface of CNTs by the nitric acid. Meibodi et al. [33] prepared the carbon nanotube/water nanofluid by the two-step method, and carbon nanotubes are separately prepared by the catalytic decomposition and dispersed in water by sonication. Summary The chapter deals with the nanofluids synthesis. The first section of the chapter summarizes the nanoparticles, preparation of nanoparticle, type of nanoparticles and characterization techniques of the nanoparticles. Nanoparticles are categorized into different categories, and their preparation techniques are properly discussed. Different characterization techniques of the nanoparticles are briefly discussed. Synthesis of nanofluids and the type of methods to prepare nanofluids are discussed in the next section. There are two methods to prepare nanofluids; the first one is one-step and the other one is two-step. These two techniques have been thoroughly deliberated with the summarization of various investigations performed by the researchers on these techniques.

References 1. Helen, J. & Dobson, P. (2019). Nanoparticle. Encyclopædia Britannica. 2. Link, S., & El-Sayed, M. A. (1999). Size and temperature dependence of the plasmon absorption of colloidal gold nanoparticles. The Journal of Physical Chemistry B, 103, 4212–4217. 3. Pyatenko, A., Yamaguchi, M., & Suzuki, M. (2007). Synthesis of spherical silver nanoparticles with controllable sizes in aqueous solutions. Journal of Physical Chemistry C, 111, 7910–7917. 4. Tahara, T., et al. (2014). Low-energy bead-milling dispersions of rod-type titania nanoparticles and their optical properties. Advanced Powder Technology, 25, 1492–1499.

40

3 Synthesis of Nanofluids

5. Venkatesh, N. (2018). Metallic nanoparticle: A review. Biomedical Journal of Scientific & Technical Research, 4, 3765–3775. 6. Chavali, M. S., & Nikolova, M. P. (2019). Metal oxide nanoparticles and their applications in nanotechnology. SN Applied Sciences, 1, 607. 7. Kumar, A. & Subudhi, S. (2018). Preparation, characteristics, convection and applications of magnetic nanofluids: A review. Heat and Mass Transfer und Stoffuebertragung, 54. 8. Maiti, D., Tong, X., Mou, X., & Yang, K. (2019). Carbon-based nanomaterials for biomedical applications: A recent study. Frontiers in Pharmacology, 9, 1401. 9. Subash, S. & Chowdhury, M. H. (2009). High efficiency carbon nanotube based solar cells for electronics devices. In Proceedings of the 2009 12th International symposium on integrated circuits (pp. 240–243). 10. Murjalili, F., Mohamad, H., & Chuah, L. (2011). Preparation of nano-scale α-Al2 O3 powder by the sol-gel method. Ceramics-Silikáty, 55, 378–383. 11. Das, S. K., Choi, S. U., Yu, W. & Pradeep, T. (2007). Nanofluids: Science and technology. Wiley Online Library. 12. Lee, S., Choi, S. U.-S., Li, S., & Eastman, J. A. (1999). Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer, 121, 280–289. 13. Das, S. K., Putra, N., Thiesen, P., & Roetzel, W. (2003). Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer, 125, 567–574. 14. Chon, C. H., Kihm, K. D., Lee, S. P., & Choi, S. U. S. (2005). Empirical correlation finding the role of temperature and particle size for nanofluid (Al2 O3 ) thermal conductivity enhancement. Applied Physics Letters, 87, 153107. 15. Li, C. H., & Peterson, G. P. (2006). Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids). Journal of Applied Physics, 99, 84314. 16. Timofeeva, E. V. et al. (2007) Thermal conductivity and particle agglomeration in alumina nanofluids: Experiment and theory. Physical Review E—Statistical Nonlinear, Soft Matter Physics, 76, 28–39 (2007). 17. Yoo, D.-H., Hong, K. S., & Yang, H.-S. (2007). Study of thermal conductivity of nanofluids for the application of heat transfer fluids. Thermochimica Acta, 455, 66–69. 18. El-Brolossy, T. A., & Saber, O. (2013). Non-intrusive method for thermal properties measurement of nanofluids. Experimental Thermal and Fluid Science, 44, 498–503. 19. Wang, X., Xu, X., & Choi, S. U. S. (1999). Thermal conductivity of nanoparticle—Fluid mixture. Journal of Thermophysics and Heat Transfer, 13, 474–480. 20. Li, Y., Zhou, J., Tung, S., Schneider, E., & Xi, S. (2009). A review on development of nanofluid preparation and characterization. Powder Technology, 196, 89–101. 21. Piriyawong, V., Thongpool, V., Asanithi, P., & Limsuwan, P. (2012). Preparation and characterization of alumina nanoparticles in deionized water using laser ablation technique. Journal of Nanomaterials, 2012, 819403. 22. Chandrasekar, M., Suresh, S. & Chandra Bose, A. (2010). Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2 O3 /water nanofluid. Experimental Thermal and Fluid Science, 34, 210–216. 23. Zhu, H., Han, D., Meng, Z., Wu, D., & Zhang, C. (2011). Preparation and thermal conductivity of CuO nanofluid via a wet chemical method. Nanoscale Research Letters, 6, 181. 24. Laurent, S., et al. (2008). Magnetic iron oxide nanoparticles: synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications. Chemical Reviews, 108, 2064–2110. 25. Peternele, W. S., et al. (2014). Experimental investigation of the coprecipitation method: An approach to obtain magnetite and maghemite nanoparticles with improved properties. Journal of Nanomaterials, 2014, 682985. 26. Saien, J., Bamdadi, H., & Daliri, S. (2015). Liquid–liquid extraction intensification with magnetite nanofluid single drops under oscillating magnetic field. Journal of Industrial and Engineering Chemistry, 21, 1152–1159.

References

41

27. Suresh, S., Venkitaraj, K. P., Selvakumar, P., & Chandrasekar, M. (2011). Synthesis of Al2O3– Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids and Surfaces A: Physicochemical and Engineering, 388, 41–48. 28. Sundar, L. S., Singh, M. K., & Sousa, A. C. M. (2014). Enhanced heat transfer and friction factor of MWCNT–Fe3 O4 /water hybrid nanofluids. International Communications in Heat and Mass Transfer, 52, 73–83. 29. Madhesh, D., Parameshwaran, R., & Kalaiselvam, S. (2014). Experimental investigation on convective heat transfer and rheological characteristics of Cu–TiO2 hybrid nanofluids. Experimental Thermal and Fluid Science, 52, 104–115. 30. Hilding, J., Grulke, E. A., George Zhang, Z. & Lockwood, F. (2003). Dispersion of carbon nanotubes in liquids. Journal of Dispersion Science and Technology, 24, 1–41. 31. Wen, D., & Ding, Y. (2004). Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids). Journal of Thermophysics and Heat Transfer, 18, 481–485. 32. Su, F., Ma, X., & Lan, Z. (2011). The effect of carbon nanotubes on the physical properties of a binary nanofluid. Journal of the Taiwan Institute of Chemical Engineers, 42, 252–257. 33. Meibodi, M. E., et al. (2010). An estimation for velocity and temperature profiles of nanofluids in fully developed turbulent flow conditions. International Communications in Heat and Mass Transfer, 37, 895–900. 34. Cha, C., Shin, S. R., Annabi, N., Dokmeci, M. R., & Khademhosseini, A. (2013). Carbon-based nanomaterials: Multifunctional materials for biomedical engineering. ACS Nano, 7, 2891– 2897. 35. Xuan, Y., & Li, Q. (2000). Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid Flow, 21, 58–64. 36. Asirvatham, L. G., Vishal, N., Gangatharan, S. K., & Lal, D. M. (2009). Experimental study on forced convective heat transfer with low volume fraction of CuO/Water nanofluid. Energies, 2, 97–119. 37. Zhu, H., et al. (2007). Preparation and thermal conductivity of suspensions of graphite nanoparticles. Carbon NY, 45, 226–228. 38. Oh, D.-W., Jain, A., Eaton, J. K., Goodson, K. E., & Lee, J. S. (2008). Thermal conductivity measurement and sedimentation detection of aluminum oxide nanofluids by using the 3ω method. International Journal of Heat and Fluid Flow, 29, 1456–1461. 39. Wang, X., Zhu, D. & Yang, S. (2009). Investigation of pH and SDBS on enhancement of thermal conductivity in nanofluids. Chemical Physics Letter, 470, 107–111. 40. Murshed, S. M. S., Leong, K. C., & Yang, C. (2005). Enhanced thermal conductivity of TiO2 — Water based nanofluids. International Journal of Thermal Sciences, 44, 367–373. 41. Hong, T. K., Yang, H. S., & Choi, C. J. (2005). Study of the enhanced thermal conductivity of Fe nanofluids. Journal of Applied Physics, 97, 64311. 42. Duangthongsuk, W., & Wongwises, S. (2010). Comparison of the effects of measured and computed thermophysical properties of nanofluids on heat transfer performance. Experimental Thermal and Fluid Science, 34, 616–624. 43. Li, X. F., et al. (2008). Thermal conductivity enhancement dependent pH and chemical surfactant for Cu-H2 O nanofluids. Thermochimica Acta, 469, 98–103. 44. Patel, H. E., Anoop, K. B., Sundararajan, T. & Das, S. K. A. (2006). Micro-convection model for thermal conductivity of nanofluids. In Nanoscale (p. 8.240). Begell House Inc.. https://doi. org/10.1615/ihtc13. 45. Yu, W., Xie, H., Chen, L., & Li, Y. (2010). Enhancement of thermal conductivity of kerosenebased Fe3 O4 nanofluids prepared via phase-transfer method. Colloids Surfaces A Physicochem. Engineering Aspects, 355, 109–113. 46. Vakili, M., Mohebbi, A., & Hashemipour, H. (2013). Experimental study on convective heat transfer of TiO2 nanofluids. Heat and Mass Transfer, 49, 1159–1165. 47. Lee, J.-H. H., et al. (2008). Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2 O3 nanoparticles. International Journal of Heat and Mass Transfer, 51, 2651–2656.

42

3 Synthesis of Nanofluids

48. Murshed, S. M. S., Leong, K. C., & Yang, C. (2008). Investigations of thermal conductivity and viscosity of nanofluids. International Journal of Thermal Sciences, 47, 560–568. 49. Gowda, R., et al. (2010). Effects of particle surface charge, species, concentration, and dispersion method on the thermal conductivity of nanofluids. Advances in Mechanical Engineering, 2, 807610. 50. Pastoriza-Gallego, M. J., Lugo, L., Legido, J. L., & Piñeiro, M. M. (2011). Thermal conductivity and viscosity measurements of ethylene glycol-based Al2 O3 nanofluids. Nanoscale Research Letters, 6, 221. 51. Longo, G. A., & Zilio, C. (2011). Experimental measurement of thermophysical properties of oxide-water nano-fluids down to ice-point. Experimental Thermal and Fluid Science, 35, 1313–1324. 52. Azizian, R., et al. (2014). Effect of magnetic field on laminar convective heat transfer of magnetite nanofluids. International Journal of Heat and Mass Transfer, 68, 94–109. 53. Murshed, S. M. S. (2012). Simultaneous Measurement of Thermal Conductivity, Thermal Diffusivity, and Specific Heat of Nanofluids. Heat Transfer Engineering, 33, 722–731. 54. Barbés, B., et al. (2013). Thermal conductivity and specific heat capacity measurements of Al2 O3 nanofluids. Journal of Thermal Analysis and Calorimetry, 111, 1615–1625. 55. Syam Sundar, L., Venkata Ramana, E., Singh, M. K. & Sousa, A. C. M. (2014). Thermal conductivity and viscosity of stabilized ethylene glycol and water mixture Al2 O3 nanofluids for heat transfer applications: An experimental study. International Communications in Heat and Mass Transfer 56, 86–95. 56. Rabienataj Darzi, A. A., Farhadi, M. & Sedighi, K. (2014). Experimental investigation of convective heat transfer and friction factor of Al2 O3 /water nanofluid in helically corrugated tube. Experimental Thermal and Fluid Science, 57, 188–199. 57. Elias, M. M., et al. (2014). Experimental investigation on the thermo-physical properties of Al2 O3 nanoparticles suspended in car radiator coolant. International Communications in Heat and Mass Transfer, 54, 48–53. 58. Hemmat Esfe, M. et al. (2015). Experimental study on thermal conductivity of ethylene glycol based nanofluids containing Al2 O3 nanoparticles. International Journal of Heat and Mass Transfer, 88, 728–734. 59. Lee, J., Han, K., & Koo, J. (2014). A novel method to evaluate dispersion stability of nanofluids. International Journal of Heat and Mass Transfer, 70, 421–429. 60. Ali, F. M., Yunus, W. M. M., & Talib, Z. A. (2013). Study of the effect of particles size and volume fraction concentration on the thermal conductivity and thermal diffusivity of Al2 O3 nanofluids. International Journal of Physical Sciences, 8, 1442–1457. 61. Aksenov, V. L., et al. (2003). Aggregation in non-ionic water-based ferrofluids by small-angle neutron scattering. Journal of Magnetism and Magnetic Materials, 258, 452–455. 62. Li, Q., Xuan, Y., & Wang, J. (2005). Experimental investigations on transport properties of magnetic fluids. Experimental Thermal and Fluid Science, 30, 109–116. 63. Bica, D., et al. (2007). Sterically stabilized water based magnetic fluids: synthesis, structure and properties. Journal of Magnetism and Magnetic Materials, 311, 17–21. 64. Hong, H., et al. (2007). Enhanced thermal conductivity by the magnetic field in heat transfer nanofluids containing carbon nanotube. Synthetic Metals, 157, 437–440. 65. Singh, D. K., Pandey, D. K., & Yadav, R. R. (2009). An ultrasonic characterization of ferrofluid. Ultrasonics, 49, 634–637. 66. Lian, W., Xuan, Y., & Li, Q. (2009). Characterization of miniature automatic energy transport devices based on the thermomagnetic effect. Energy Conversion and Management, 50, 35–42. 67. Abareshi, M., Goharshadi, E. K., Mojtaba Zebarjad, S., Khandan Fadafan, H. & Youssefi, A. (2010). Fabrication, characterization and measurement of thermal conductivity of Fe3 O4 nanofluids. The Journal of Magnetism and Magnetic Materials, 322, 3895–3901. 68. Kudelcik, J., Bury, P., Kopcansky, P., & Timko, M. (2010). Dielectric breakdown in mineral oil ITO 100 based magnetic fluid. Physics Procedia, 9, 78–81. 69. Lajvardi, M., et al. (2010). Experimental investigation for enhanced ferrofluid heat transfer under magnetic field effect. Journal of Magnetism and Magnetic Materials, 322, 3508–3513.

References

43

70. Abareshi, M., Sajjadi, S. H., Zebarjad, S. M., & Goharshadi, E. K. (2011). Fabrication, characterization, and measurement of viscosity of α-Fe2 O3 -glycerol nanofluids. Journal of Molecular Liquids, 163, 27–32. 71. Nabeel Rashin, M. & Hemalatha, J. (2012). Magnetic and ultrasonic investigations on magnetite nanofluids. Ultrasonics, 52, 1024–1029. 72. Syam Sundar, L., Venkata Ramana, E., Singh, M. K. & De Sousa, A. C. M. (2012). Viscosity of low volume concentrations of magnetic Fe3 O4 nanoparticles dispersed in ethylene glycol and water mixture. Chemical Physics Letters, 554, 236–242. 73. Sundar, L. S., Singh, M. K., & Sousa, A. C. M. (2013). Thermal conductivity of ethylene glycol and water mixture based Fe3 O4 nanofluid. International Communications in Heat and Mass Transfer. https://doi.org/10.1016/j.icheatmasstransfer.2013.08.026. 74. Gavili, A., Zabihi, F., Isfahani, T. D., & Sabbaghzadeh, J. (2012). The thermal conductivity of water base ferrofluids under magnetic field. Experimental Thermal and Fluid Science, 41, 94–98. 75. Gu, H., et al. (2013). Ubbelohde viscometer measurement of water-based Fe3 O4 magnetic fluid prepared by coprecipitation. Journal of Magnetism and Magnetic Materials, 348, 88–92. 76. Nabeel Rashin, M. & Hemalatha, J. (2014). Magnetic and ultrasonic studies on stable cobalt ferrite magnetic nanofluid. Ultrasonics, 54, 834–840. 77. Karimi, A. S. Afghahi, S. S., Shariatmadar, H. & Ashjaee, M. (2014). Experimental investigation on thermal conductivity of MFe2 O4 (M = Fe and Co) magnetic nanofluids under influence of magnetic field. Thermochimica Acta, 598, 59–67. 78. Goharkhah, M., Salarian, A., Ashjaee, M., & Shahabadi, M. (2015). Convective heat transfer characteristics of magnetite nanofluid under the influence of constant and alternating magnetic field. Powder Technology, 274, 258–267. 79. Bagheli, S., Fadafan, H. K., Orimi, R. L., & Ghaemi, M. (2015). Synthesis and experimental investigation of the electrical conductivity of water based magnetite nanofluids. Powder Technology, 274, 426–430. 80. Wang, L., Wang, Y., Yan, X., Wang, X., & Feng, B. (2016). Investigation on viscosity of Fe3 O4 nanofluid under magnetic field. International Communications in Heat and Mass Transfer, 72, 23–28.

Chapter 4

Characterization of Nanofluids

4.1 Thermal Conductivity As mentioned in the first chapter, in 1995, S U S Choi comes up with the term nanofluid after mixing the nano-sized particles into the convectional base fluids to enhance the thermal conductivity of the fluid Choi et al. [1]. Later, many studies investigated and reported similar trends about the thermal conductivity of nanofluids. The thermal conductivity of nanofluid depends on various factors such as shape, size, concentration, temperature, dispersion of nanoparticles in base fluid, the stability of a suspension, nanoparticle clustering, pH variation, chemical additives and surfactant Khurana et al. [2] and Puliti et al. [3]. The thermal conductivity of nanofluid is composed of two components, viz. static thermal conductivity and dynamic thermal conductivity. In static thermal conductivity, the effect of nanolayer surrounding the nanoparticle is investigated, whereas the effect of randomly oriented Brownian motion, on the thermal conductivity, comes under the dynamic part of thermal conductivity. The scientists have studied the thermal conductivity of nanofluid by changing these abovementioned pertinent parameters, and they have found impressive and exciting results. The correct measurement and prediction of the thermal conductivity of nanofluids is always a challenging task for the researchers due to the involvement of numerous different parameters.

4.1.1 Theoretical Models Many researchers have developed theoretical models and correlations by considering various factors to find thermal conductivity. Maxwell [4] has reported the first theoretical correlation for the thermal conductivity of solid–liquid mixture considering the concentration of solids. Table 4.1 reports these significant theoretical correla-

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Kumar and S. Subudhi, Thermal Characteristics and Convection in Nanofluids, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4248-4_4

45

Gharagozloo et al. [27]

Koo et al. [19]

Jang et al. [15]

Xue et al. [11]

Leong et al. [10]

Yu et al. [9]

Bruggeman [88]

Jefferey [6]

Hamilton and Crosser [5]

Maxwell [4]

Authors

 1+ hr

3

knf = kbf

Include effect of nanolayer, the solid-like layer of base fluid molecules around the suspended solid particle into the Maxwell equation

     = [(3φ − 1)2 (kp /kb )2 + 2 − 3φ)2 + 2 2 + 9φ − 9φ 2 kp /kb

Extension of Maxwell model

n represents the shape

It did not consider the shape of suspended solid particles

Remarks

kagg +(n−1)kbf −(n−1)φagg (kbf −kagg ) kagg +(n−1)kbf +φagg (kbf −kagg )

Influence of aggregates has been taken into consideration

Effect of thermophoresis on the thermal conductivity of nanofluids with the Brownian motion and osmophoresis

Role of Brownian motion taken into consideration



  3  3   3   3  3 h h φ 1+ hr −1 1+ hr (knl −kf )+kf −1 knl 2 1+ 2r − 1+ hr +1 +(kp +2knl ) 1+ 2r   3 3  3  3  h 1+ 2r (kp +2knl )−(kp −knl )φ 1+ hr −1 1+ 2rh + 1+ hr −1

knf = kbf (1 − φ) + kp φ + 3C1 ddbfp kbf Red2p Pr φ  1 φkb 3kbf 5 k T P = 6π μbf kp +2kbf 1 × 10 ρbf c pbf T

knf =

(kp −knl )φ

Mathematical expression   k p +2kbf +2(kp −kbf )φ knf = kbf k p +2kbf −(kp −kbf )φ   k +(n−1)kbf −(n−1)φ (kbf −kp ) knf = kbf p k +(n−1)k +φ k −k ( bf p ) p bf   3β 3 9β 3 α+2 3β 4 knf 2 2 = 1 + 3β + φ + + + 3β 6 kbf 4 16 2α+3 2   kb √ 1 keff = 4 (3φ − 1) kp + (2 − 3φ)kb + 4 

  3 kp +2kbf +2(kp −kbf ) 1+ hr φ knf =  3 kbf kp +2kbf −(kp −kbf ) 1+ hr φ

Table 4.1 Mathematical models to predict the thermal conductivity of nanofluids

46 4 Characterization of Nanofluids

4.1 Thermal Conductivity

47

tions developed by the researchers. The Maxwell model is representative of all the theoretical models for thermal conductivity. The classical models by Maxwell model, Hamilton–Crosser model [5], Jeffery model [6], etc., investigated the thermal conductivity of solid suspension in liquid by considering only the particle concentration and thermal conductivity of base fluid and solid particles. The first reported investigation of thermal conductivity of solid suspension in a base fluid is conducted by Maxwell [4] by considering the thermal conductivity of suspended solid particles and base fluid, and particle concentration, as shown in Eq. (4.1). knf = kbf



  kp + 2kbf + 2 kp − kbf φ  kp + 2kbf − kp − kbf φ

(4.1)

Here, k nf , k bf , k p denote the thermal conductivity of suspension, base fluid, suspended solid particles, respectively, and φ is particle concentration of suspended solid particles. The Maxwell model is a representative of all classical models to estimate the thermal conductivity of suspension. The Maxwell model did not consider the shape of suspended solid particles, which is later considered by Hamilton and Crosser [5] for estimating the thermal conductivity, theoretically, as shown in Eq. (4.2) and also conducted the experiments using the micron-sized solid particles, aluminum and balsa wood, dispersed in the rubber.

knf = kbf

  kp + (n − 1)kbf − (n − 1)φ kbf − kp  kp + (n − 1)kbf + φ kbf − kp

(4.2)

Here, n is a function of sphericity (), which is a measure of shape with respect to the sphere. The sphericity is defined, by Hakon [7], as the ratio of the surface area of a sphere, having the equal volume as the particle, to the surface area of the particle and given as:  2/3 π 1/3 6Vp = As

(4.3)

Here, the V p and As are volume and surface area of the solid particle. The maximum value of sphericity is equal to 1, for the sphere. Hamilton and Crosser [5] upgraded the Maxwell model (Eq. 4.2) by adopting the effect of particle shape on the thermal conductivity in the form of n, equal to 3/. By substituting the n = 3 for sphere, Eq. (4.2) is reduced to the Maxwell model (Eq. 4.1), which is only applicable to the spherical particles. The effect of shape on solid suspended particle is not important in Hamilton and Crosser model (Eq. 4.3), when the ratio of the thermal conductivities of the particle and base fluid is below about 100, while the thermal conductivity of

48

4 Characterization of Nanofluids

suspension increased with the particle concentration. Another model is proposed by the Jeffrey [6], as given in Eq. (4.4);

3β 3 knf 9β 3 α + 2 3β 4 2 2 = 1 + 3βφ + φ 3β + + . + 6 kbf 4 16 2α + 3 2

(4.4)

where α and β are constants and defined as: α=

kp ;β = kbf





kp kp −1 / +2 kbf kbf

(4.5)

Jeffrey [6] extended the Maxwell model to estimate the thermal conductivity of suspension, with the consideration of interaction between the pairs of suspended spheres. Effect of Nanolayer In the suspension of solid particles in the base fluid, an ordered layer of base fluid molecule covers the particle, as depicted in Fig. 4.1. The ordered layer is a solid-like structure and has different thermal properties than the particle and base fluid. This ordered layer is known as nanolayer, in case of nanofluids, or interface layer. When heat from the suspended solid particle is conducted to the base fluid, a discontinuous temperature distribution is occurred at the nanolayer and causes a temperature gradient. The generated temperature gradient is proportional to the heat flow, and the ratio of temperature gradient to the heat flow is known as thermal resistance at the nanolayer and inversely proportional to the nanolayer area. The thermal resistance at nanolayer, which is occurred when the heat flow from particle to base fluid, is known a Kapitza resistance. The presence of nanolayer around the solid particle is experimentally confirmed by Yu et al. [8] using the X-ray reflectivity study. The density oscillation near the solid– liquid interface is observed in three layers with the spacing of molecular size. As mentioned, the thermal properties of nanolayer are different from the particle and base Fig. 4.1 Schematic of nanolayer around the nanoparticle in base fluid

4.1 Thermal Conductivity

49

fluid and can lead to the enhancement in thermal conductivity of nanofluid. Yu et al. [9] involved the effect of nanolayer, the solid-like layer of base fluid molecules around the suspended solid particle, into Maxwell’s model to estimate the thermal conductivity of suspension. It is assumed that the base fluid molecules in this nanolayer had the intermediate physical properties than the solid particle and base fluid and expected to contribute into increased thermal conductivity of suspension. Yu et al. [9] have assumed an equivalent particle, which is formed by combining the effect of nanolayer with the suspended particle, and used very low particle concentration to prevent the overlapping of the equivalent particles. The assumption is resulting in an increased particle concentration (φ e ), as:

h 3 φe = φ 1 + r

(4.6)

where h is nanolayer thickness and r is radius of suspended particle. The model is proposed to estimate the thermal conductivity of suspension as:

knf =

  3  kp + 2kbf + 2 kp − kbf 1 + hr φ  3 kbf  kp + 2kbf − kp − kbf 1 + hr φ

(4.7)

The effect of nanolayer on the thermal conductivity of suspension is found significant only for the particle of small size (r ~ h) and observed a three- to eightfold enhancement in thermal conductivity of suspension for the suspended solid particles of radius smaller than 5 nm. But Eq. (4.7) is reduced to Maxwell’s model for larger solid particles (r  h). Leong et al. [10] have proposed a model to predict the thermal conductivity of nanofluid by taking the thermal conductivity and thickness of the nanolayer at nanoparticles. In the proposed model, nanolayer is taken as a separate component along with the nanoparticle and base fluid and model is formulated in two steps: (1) modeling of temperature field and gradient, and (2) formulation of the effective thermal conductivity model, as given in Eq. (4.8).

   3     h 3 − 1+ h 3 +1 kp − knl φ 1 + hr − 1 knl 2 1 + 2r r knf =   h 3k + 2k − k − k φ 1 + 2r p p nl nl 

 3 3 3     h h knl − kf + kf φ 1+ r − 1 1 + hr + kp + 2knl 1 + 2r 

  3    h 3 + 1+ h 3 −1 1 + hr −1 1 + 2r r 

(4.8)

where k p , k nl , k f are thermal conductivity of solid particle, nanolayer and base fluid, and φ is particle concentration. In the absence of nanolayer, Eq. (4.8) is reduced to Maxwell’s model. The presented model is found in agreement with the thermal conductivity of water-based Al2 O3 nanofluid measured by the transient.hot wire method.

50

4 Characterization of Nanofluids

In another study, Xue et al. [11] have investigated the effect of complex nanoparticle, composed of interfacial shell and nanoparticle, on the thermal conductivity of nanofluid along with the particle size, and proposed a model based on Fourier’s law of heat conduction, as given in Eq. (4.9). 

 knf − kbf φ 1−  kp kbf 2knf + kbf   k   knf − kp 2kp + knl − kbfp knl − kp 2kp + knf φ +      =0 kp kbf kp + 2knf 2kp + knl + 2 kp knl − kp kp − knf kbf

(4.9)

The results of theoretical model, Eq. (4.9), are in agreement with the experimental results of thermal conductivity of CuO/water and CuO/EG nanofluids. The former studies involved the effect of nanolayer in determining the thermal conductivity, but are incapable to provide the method or procedure to measure the thickness of nanolayer. Tso et al. [12] have predicated the thermal conductivity of nanofluid after accounting the nanolayer effect by formulating a semi-analytical model, an improved model presented by Leong et al. [10], and also determined the thickness of nanolayer. A linear variation in thermal conductivity in the nanolayer, decreasing from nanoparticle to the base fluid, is assumed.     3φv23 knl 3r 3 kp + v1 kp + 2knl + r 3 1 − v23 φ knf     = kbf 3φv23 knl 3r 3 kf + v1 kp + 2knl + r 3 1 − v23 φ   3   v2 (2kbf + knl ) kp + 2knl + 2(kbf − knl ) knl − kp  3    v2 (2kbf + knl ) kp + 2knl + 2(kbf − knl ) knl − kp

(4.10)

where v1 = 3r 2 h + 3rh2 + h3 and v2 = 1 + h/r. The nanolayer thickness (h/r) is also determined based on the semi-analytical value based on proposed model, Eq. (4.11) with the linear variation in thermal conductivity of nanolayer, and given as: h = D1 a −D2 r

(4.11)

where the values of D1 and D2 for the water-based Al2 O3 nanofluid are 3.042 and 1.059, and for EG-based Al2 O3 nanofluid are 1.8082 and 0.912, respectively. It is also observed from Eq. (4.11) that the thickness of nanolayer depends on the base fluid. For the same nanoparticle material, the increased nanoparticle size caused to decrease in the nanolayer thickness for the water-based nanofluid, while opposite is found for the ethylene glycol-based nanofluid, the larger nanoparticle radius resulted in the thicker nanolayer. The direct effect of nanolayer on the thermal conductivity of nanofluid is investigated by Alipour et al. [13] and proposed a model to estimate the thermal conductivity of nanofluid, as given in Eq. (4.12).

4.1 Thermal Conductivity

51

      kp + 2knl β13 φβ 3 (knl − kf ) + kbf + knl φ kp − knl 2β13 − β 3 + 1     knf = β13 kp + 2knl − kp − knl β13 + β 3 − 1 ⎡ ⎤  1 ⎢ +⎣

 dp

6φ π

αnf μnf kb kp T

+

3

h 4πr (r +h)knl

⎥ ⎦

(4.12)

where β=1 + h/r; β 1 = 1 + h/ 2r; α nf and μnf are thermal diffusivity and dynamic viscosity of nanofluid, k b is Boltzmann’s constant and d p is diameter of nanoparticle. The first term in right side of Eq. (4.12) denotes the static thermal conductivity, while second term represents the dynamic thermal conductivity due to Brownian motion. The effect of nanolayer on the thermal conductivity of nanofluid is significant only when the ratio of particle radius to the nanolayer thickness (r/h) is almost small. In the opposite case, the nanolayer did not affect the heat conduction in the nanofluid, as a part of dynamic thermal conductivity. The proposed model is found in agreement with the experimental values of thermal conductivity of water-based Al2 O3 and CuO nanofluids. Another important model to estimate the thermal conductivity of nanofluid, as a function of size and concentration of nanoparticles, thermal conductivity of nanoparticles and base fluid and thickness of nanolayer, is proposed by the Feng et al. (2007) based on the 2D lattice model which is used due to the random distribution of nanoparticles in nanofluid. The term ‘equivalent nanoparticle’ is used for the combination of nanoparticle and nanolayer. The presented model is formulated in two distinct portions: for non-aggregated nanoparticles and for clusters (aggregated nanoparticles), the first and second terms in right side of Eq. (4.13), respectively.

  3  kp + 2kbf + 2 kp − kbf 1 + hr φ knf = (1 − α)  3 kbf  kp + 2kbf − kp − kbf 1 + hr φ

  3

   3 1 + hr φkbf 1 h 3 r +h 3 1+ ln −1 +α 1− φ kbf 2 r β β (r + h)(1 − β) (4.13) where β = 1 − (k bf /k pe ) and k pe is thermal conductivity of equivalent nanoparticle and given as:

kpe

     3  2 1 − kknlp + 1 + hr 1 + 2kkpnl kknlp   kp   = 3  knl 1 + 2kkpnl − 1 + 1 + hr kp

(4.14)

When the thermal conductivity of nanolayer is twice the thermal conductivity of base fluid, the thermal conductivity of nanofluid is decreased with the increased particle size, and when the thermal conductivity of both nanolayer and base fluid is

52

4 Characterization of Nanofluids

equal, no effect of nanolayer is observed on the thermal conductivity of nanofluid. Feng et al. [14] also have concluded for the constant particle concentration that the probability of aggregation of nanoparticles is increased when the size of nanoparticle is decreased. It is caused due to strong van der Waals forces for small inter-particle distance. By using the molecular dynamics modeling of inter- and intramolecular interactions of the components including the nanoparticle, base fluid and nanolayer, Puliti et al. [3] reported a highly ordered layer of base fluid molecules around the nanoparticles and higher heat flux at the nanolayer, which resulted in the increased thermal conductivity of nanofluids. Based on the above-presented models, the effect of nanolayer on the thermal conductivity of nanofluid can be summarized as: • The nanolayer affects the thermal conductivity of nanofluid only for the nanoparticles of small size and for the thickness of nanolayer almost equal to the radius of nanoparticle, (r ~ h). • An enhancement in thermal conductivity of nanofluid having the nanoparticle of radius smaller than 5 nm is occurred. • For the same nanoparticle material, the thickness of nanolayer is a function of base fluid, water or ethylene glycol. • With increasing the nanoparticle size, thickness of nanolayer is decreased for the water-based nanofluid, while it is increased for the ethylene glycol-based nanofluid. • When the thermal conductivity of nanolayer is twice the thermal conductivity of base fluid, the thermal conductivity of nanofluid is decreased with the increased particle size. Effect of Brownian Motion In 1827, Robert Brown, a Scottish biologist, notified the zigzag motion of pollen grains in water but did not recognize the reason behind the motion. In 1906, Einstein predicted a relation between the Brownian motion and size of suspended spherical solid particle based on the kinetic theory and calculated the diffusion coefficient for the spherical particle. The Brownian motion can be defined as a stochastic movement of small solid particles suspended in the base fluid where the solid particles collide with each other and transfer the momentum, and resulted in the chaotic and nondirected movements. Jang et al. [15] have investigated the role of Brownian motion on the thermal conductivity of nanofluids by considering the four modes of energy transport in nanofluids, collision between the base fluid molecules, thermal diffusion in nanoparticles in base fluid, collision between nanoparticles due to Brownian motion and thermal interaction between the nanoparticles and base fluid molecules. The effect of collision between the nanoparticles due to Brownian motion on the thermal conductivity of nanofluids is very small than the other modes; hence, it is neglected, and a model is proposed based on the remaining three modes to estimate the thermal conductivity of nanofluids, as given in Eq. (4.15).

4.1 Thermal Conductivity

53

knf = kbf (1 − φ) + kp φ + 3C1

dbf kbf Red2p Pr φ dp

(4.15)

where C 1 is proportional constant, Re is Reynolds number and Pr is Prandtl number. The Reynolds number can be defined as Redp =

V dp ρkB T = ν 3π μ2 dplbf

(4.16)

where lbf is the mean free path for the water molecule. The thermal conductivity of suspension is found to be increased with the particle concentration and particle’s thermal conductivity, while increment is higher for the base fluids of lower thermal conductivity. Xiao et al. [16] have proposed an analytical model to predict the thermal conductivity of nanofluids by considering the fractal distribution of nanoparticles in base fluid, as given by Eq. (4.17).    kbf kp − 2φ kbf − kp + 2kbf  knf = kp + φ kbf − kp + 2kbf

  1  1/8  1/2 2 −df −1 d K 1−df −1)(4−df )1/8 dnp,av f ( 2kB T K 3 + Cdbf kbf ∝ πρp 2df −1 df −1 +

 −1/4 3/2 Pr 1 − K 2−df (4 − df )3/8 (2 − df )−1 df dnp,av

(4.17)

where C is a constant relevant to the thermal boundary layer and equal to 236, K is a constant, equal to 10−3 , d f is fractal dimension of nanoparticles, d np,av is average diameter of nanoparticles, α is thermal diffusion coefficient, ρ p is density of nanoparticle and d bf is equivalent diameter of base fluid molecule. The first and second terms of the right side in Eq. (4.15) are the thermal conductivity due to stationary nanoparticles dispersed in base fluid and by heat convection due to the Brownian motion of nanoparticles, respectively. Based on Eq. 4.17, Xiao et al. [16] have observed that the increased size of nanoparticles resulted in the reduction of thermal conductivity, because the Brownian motion is decreased with the particle size and less convection due to nanoparticles occurred. The significance of Brownian motion of nanoparticles on the increment in the thermal conductivity of nanofluids is only found when the average diameter of nanoparticles is smaller than the 16 nm. Another observation is found that the thermal conductivity of nanofluids is increased with the temperature due to decrease in the viscosity of nanofluid and resulted in the enhanced Brownian motion of nanoparticles, and consequently, the convection due to nanoparticles is increased. The results observed by Xiao et al. [16] are similar to the Jang et al. [15], like the thermal conductivity of nanofluid is increased with the temperature and the increment is higher for the smaller particles than the larger. Prasher et al. [17] have proposed a convective-conduction model, called multisphere Brownian model (MSBM), based on the Brownian motion to predict the thermal conductivity of nanofluids using the order-of-magnitude analysis. The

54

4 Characterization of Nanofluids

effect of conduction of nanoparticles, thermal boundary resistance (Rb ) between the nanoparticle and base fluid, and convection contribution of nanoparticles on the thermal conductivity of nanofluid is included in the proposed model, given in Eq. (4.18),      kp (1 + 2α) + 2km + 2φ kp (1 − α) − km knf m 0.333     = 1 + A Re Pr φ kbf kp (1 + 2α) + 2km − φ kp (1 − α) − km (4.18) where A and m are constants, A is independent of the fluid type, whereas m is a function of fluid type, and for water-based nanofluids, equal to 4 × 104 and 2.5% ± 15%, respectively. The thermal conductivity of matrix is denoted by k m , and nanoparticle Biot number is denoted by α, which is given as α=

2Rb km dnp

(4.19)

The primary reason of enhanced thermal conductivity of nanofluid is found as the Brownian motion of nanoparticle-induced convection. The increase in temperature and particle concentration enhanced the thermal conductivity of nanofluids. Gupta et al. [18] have conducted a study using Brownian dynamics simulation to determine the inter-particle potential based on the Debye length and surface interaction of the nanoparticle and base fluid. About 6% enhancement in the thermal conductivity of nanofluid is reported only due to Brownian motion of nanoparticles without taking the thermal diffusion into account. This effect of Brownian motion is limited by the volume concentration for the particular particle diameter and becomes constant beyond the particle size (≥10 nm). The impact of Brownian motion on the thermal conductivity is also investigated by the Kooet al. [19] and found that the effect of Brownian motion on the thermal conductivity decreases with the particle size and particle concentration. At low particle concentration (φ < 0.5 vol%), the enhancement in thermal conductivity is observed independent of the particle interactions, while contradictory behavior is reported at higher particle concentration (φ > 1.0 vol%). Murshed et al. [20] have formulated the contribution of Brownian motion in thermal conductivity of nanofluid by considering the static and dynamic mechanisms and proposed a model as given in Eq. (4.20). ⎧  ⎪ ⎪ ⎨ kp − knl φ 1 + knf =  ⎪ ⎪ ⎩ 1+

       h 3 −1 k 2 1+ h 3 − 1+ h 3 +1 nl r r 2r  h 3k + 2k − k − k φ p p nl nl 2r

 ⎫        h 3 φ 1 + h 3 − 1 1 + h 3k − k + k ⎪ + kp + 2knl 1 + 2r ⎬ nl f f ⎪ r r

   3    ⎪ ⎪ h 3 + 1+ h 3 −1 ⎭ −1 1 + 2r 1 + hr r

⎫ ! " 3 ⎪  ⎪ " ⎪ " 3kB T 1 − 1.5 1 + hr φ ⎪ ⎬ " " + 0.4465ρn C pn r φ #   3 ⎪ ⎪ h ⎪ ⎪ 3 ⎪ ⎪ 2πρn 1 + r r ⎪ ⎪ ⎭ ⎩ ⎧ ⎪ ⎪ ⎪ ⎪ ⎨

(4.20)

4.1 Thermal Conductivity

55

The first term in Eq. (4.20) is contribution of static mechanisms including the nanolayer, particle concentration and thermal conductivity of nanoparticle, nanolayer and base fluid, similarly given by Leong et al. [10], and second term shows the influence of dynamic mechanisms such as Brownian motion. It is observed that the static mechanisms caused the enhancement of the thermal conductivity primarily while the contribution of Brownian motion is effective only for smaller particle size and low particle concentration. Mehta et al. [21] have modified the Maxwell model by assuming that the thermal conductivity of nanofluids depends on the microconvection heat transfer due to the Brownian motion and thermal conductivity of nanoparticles and observed an enhancement in the thermal conductivity of nanofluid by increasing the nanoparticle size and concentration. Paul et al. [22] also reported the role of Brownian motion in the enhancement of thermal conductivity of nanofluids. As an enhancement of 100% in thermal conductivity is observed at high temperature of 70 °C, but reduction is found by increasing the size of nanoparticles. Based on the above-presented models, the effect of Brownian motion on the thermal conductivity of nanofluid can be summarized as: • The Brownian motion is a function of particle size and temperature of nanofluid. It is slow for the large size of nanoparticles and higher for small size. With the temperature, the Brownian motion of nanoparticles is increased. • The increased size of nanoparticles resulted in the decrease of thermal conductivity due to decreased Brownian motion which caused less convection due to nanoparticles. • Thermal conductivity is increased with the temperature due to decrease in the viscosity of nanofluid and enhanced Brownian motion of nanoparticles. • The significance of Brownian motion on the thermal conductivity of nanofluids is reported when the average diameter of nanoparticles is smaller than the 16 nm and for the low particle concentration. Effect of Thermophoresis The nanoparticles, dispersed in the base fluid, tend to move from hot region to cold region, and the velocity of movement depends on the temperature gradient. This behavior of nanoparticles is known as thermophoresis, and it occurs due to striking of base fluid molecules on the nanoparticles in the hot region with very high velocity than that of cold temperature region. The molecules of base fluid from both the regions, hot and cold, strike the nanoparticles, but due to higher force applied by the hot region molecules, excited by the higher temperature, the nanoparticle is forced to move toward the cold region and heat convection from hot to cold region takes place. Thermophoresis is a non-equilibrium transport mechanism due to temperature gradient which is driving force of thermophoresis. Koo et al. [19] have compared the effect of thermophoresis on the thermal conductivity of nanofluids with the Brownian motion and osmophoresis and formulated the contribution of thermophoresis effect in the thermal conductivity of nanofluids, as given by Eq. (4.21).

56

4 Characterization of Nanofluids

kTP =

1 φkb 3kbf  1 × 105 ρbf c pbf T 6π μbf kp + 2kbf

(4.21)

Here, ΔT denotes the temperature gradient in the base fluid. The enhancement in the thermal conductivity of nanofluids due to thermophoresis is independent of the size of nanoparticles, and impact of thermophoresis on thermal conductivity is less than the Brownian motion, but more than the osmophoresis. Aminfar et al. [23] also confirmed that the effect of thermophoresis on the thermal conductivity is less than the Brownian motion of nanoparticles. A Lagrangian–Eulerian approach is applied to investigate the effect of Brownian motion and thermophoresis on the thermal conductivity of nanofluids and concluded that the velocity of nanoparticles is observed more at the wall region than that of center due to thermophoresis and the velocity is decreased with the particle size. Further, the effect of thermophoresis on the microconvection is observed very low than the Brownian motion. The effect of Brownian motion and thermophoresis is reported negligible on the thermal conductivity. Effect of Particle Size and Aggregation Elimelech et al. [24] have reported that the aggregation of nanoparticles, dispersed in the base fluid, is an outcome of two processes, transport and attachment. Due to Brownian motion, base fluid motion or sedimentation, the nanoparticles move in the base fluid and collide with each other under the transport process. An attractive (van der Waals or hydrodynamic) interaction of colliding nanoparticles transformed in the attachment of particles and formation of aggregation in the attachment process, while repulsive (electric or steric) interaction resulted in the stable suspension of nanoparticles in the base fluid. The effect of aggregation on the thermal conductivity of nanofluids is investigated in numerous studies. Evans et al. [25] have investigated the influence of aggregation and nanolayer on the thermal conductivity of nanofluids using the homogenization and Monte Carlo simulation of heat conduction on aggregates. A fractal cluster having a radius of gyration is assumed which is composed of backbone, a linear chain-like structure of nanoparticles, which cover the full extent of the cluster and dead ends, the remaining nanoparticles in the cluster other than the backbone. A rapid enhancement in the thermal conductivity is observed with the increase in the size of aggregate, and it is caused due to rapid heat conduction in the backbone of cluster, whose size also increased. The enhancement due to aggregation is dependent strongly on the chemical dimension and radius of gyration of aggregates. Gao et al. [26] also found that the aggregation of nanoparticles contributes primarily in the enhancement of thermal conductivity of Al2 O3 nanofluids compared to the effect of the Brownian motion. Gharagozloo et al. [27] have conducted the experimental investigation and proposed a model based on the Monte Carlo simulation to inspect the influence of aggregates on the thermal conductivity of nanofluids, as given in Eq. 4.22.  kagg + (n − 1)kbf − (n − 1)φagg kbf − kagg  knf = kbf kagg + (n − 1)kbf + φagg kbf − kagg

(4.22)

4.1 Thermal Conductivity

57

where k agg and φ agg are the thermal conductivity and particle concentration of aggregates and n = 3 for the spherical nanoparticles. Initially, the impact of aggregates on the thermal conductivity of nanofluids is found higher than the viscosity and opposite is observed when the size of aggregates becomes large. Wensel et al. [28] have measured an enhancement of 10% in the thermal conductivity of Al2 O3 nanofluids and based on the visual inspection concluded that the enhancement is occurred due to the aggregation of nanoparticles and type of nanoparticle material. Chopkar et al. [29] have measured the thermal conductivity of water and EGbased Al2 Cu and Ag2 Al nanofluids to investigate the effect of particle size on the thermal conductivity of nanofluids. Up to 100% enhancement is reported in the thermal conductivity of nanofluids only for 1.5 vol% particle concentration and with the decreasing of particle size. Similar decrement in the thermal conductivity of silver nanofluids is reported by Paul et al. [30] with increasing the particle size.

4.1.2 Experimental Studies Number of techniques have been applied to measure the thermal conductivity of nanofluids, such as short hot wire (SHW) method, temperature oscillation technique, 3-omega method, microliter hot strip device, steady-state measurement using cutbar apparatus, transient hot wire (THW) method and transient plate source (TPS) method. To explore the effect of nanoparticles on the thermal conductivity of base fluids, numerous experimental investigations had been organized, as given in Table 4.2. These experimental investigations examined the influence of various parameters such as particle concentration, thermal conductivity of base fluid and nanoparticles, particle size and shape, pH value and zeta potential on the thermal conductivity of nanofluids. In general, the thermal conductivity of nanofluids is enhanced linearly or in a parabolic fashion with the volume concentration of nanoparticles. The enhancement in thermal conductivity is increased with the temperature. But it is not enlightened that the increment in the thermal conductivity of nanofluids with the temperature is due to rise in the thermal conductivity of base fluid or nanoparticle, or it is due to augmented Brownian motion. No alteration or decrement in the thermal conductivity of nanofluids at lower temperature (≤10 °C) is reported by the Longo et al. [31], while enhancement in the thermal conductivity of nanofluids is reported with the higher temperature and particle concentration at more than 1 vol%. With the decreasing diameter of nanoparticles, the specific surface area of particles is increased and resulted in the enhanced interfacial area which caused the higher heat transfer at particle surface and improved thermal conductivity. Also, a reduction in thermal conductivity is found when the particle size becomes smaller than the phonon mean free path by Brolossy et al. [32]. Chon et al. [33] have reported that by increasing the particle size, the thermal conductivity of nanofluids is decreased due to lower Brownian motion which is increased at higher temperature and enhances the thermal conductivity of nanofluids.

1 and 4 vol%

Water

Deionized water

Water and EG

Chon et al. [33]

Li et al. [89]

Timofeeva et al. [35]

2.5–10 vol%

0.5–6 vol%

1 and 4 vol%

Das et al. [78] Water

Particle concentration

1–5 vol%

Base fluid

Lee et al. [37] Water and EG

References

23 °C

28–36 °C

21–71 °C

21–51 °C

25 °C

Temperature range

KD2 Pro

Steady-state cut-bar method

Miniaturized conductivity measurement based on THW

Temperature oscillation technique

THW

Thermal conductivity instrument

10% for water and 13% for EG-based nanofluids

0.5–26%

30%

9.4–24.3%

14% for water and 10% for EG-based nanofluids

Thermal conductivity enhancement

Table 4.2 Experimental investigations focused on the thermal conductivity of nanofluids

=1+



d0 dp

kp k0

0.369  0.7476

Pr 0.9955 Re1.2321

(continued)

The enhancement in thermal conductivity is higher for particle size of 40 nm, followed by 11 nm and 20 nm in the water-based nanofluids, while for the EG-based nanofluids, enhancement is higher for the particle size of 20 nm, followed by 11 nm and 40 nm. The enhancement is increased with the elapsed time due to agglomeration

Observed that the Brownian motion is only responsible for the mixing of nanoparticles, not for the heat convection phenomena

64.7φ 0.746

k k0

Thermal conductivity of nanofluid decreased with the particle size due to decreased Brownian motion. To estimate the thermal conductivity of nanofluids, an empirical correlation is proposed as

The thermal conductivity of nanofluids increased with the particle concentration and temperature

With the increased particle concentration, an increment in the thermal conductivity of nanofluids is found and enhancement is higher for the EG-based nanofluids

Others

58 4 Characterization of Nanofluids

Water

EG

EG/W (50:50)

Water

EG/W (50:50)

Water

Jin-ze et al. [34]

Longo et al. [90]

Sundar et al. [91]

Darzi et al. [68]

Elias et al. [92]

Esfe et al. [93]

Lee et al. [94] Water

Base fluid

References

Table 4.2 (continued)

0.51%

0.2–1%

0.25–1%

0.2–0.8%

1–4%

1–5%

Particle concentration

10–80 °C

10–50 °C

29–58 °C

15–50 °C

10–50 °C

25 °C

Temperature range

Thermal conductivity enhancement

THW

KD2 Pro

KD2 Pro

KD2 Pro

Apparatus from P.A. Hilton

4.6% and 5.7% for water and EG-based nanofluids

32.5% at 5 vol% and at 55 °C

8.3% at 1 vol%

8% at 1 vol%

From 9.8 to 17.89%

Thermal constant 9–29% analyzer, hot disk

Thermal constant 40% for 500 nm analyzer, hot disk at 5 vol%

Thermal conductivity instrument

The enhancement in the thermal conductivity is higher for lower size of nanoparticles and increased with the temperature

To estimate the thermal conductivity of nanofluids, an empirical correlation is proposed as

At constant particle concentration, thermal conductivity is increased by increasing the temperature from 10 to 50 °C

To estimate the thermal conductivity of nanofluids, an empirical correlation is proposed as   Tmax −0.09214 0.07379 k φ k0 = 1.262 T min An increment in the thermal conductivity is observed with the particle concentration and temperature

Aggregation of nanoparticles enhanced the thermal conductivity

By increasing the particle diameter, the thermal conductivity of nanofluids also increased

Others

4.1 Thermal Conductivity 59

60

4 Characterization of Nanofluids

But contrary results reported the increased thermal conductivity with the particle diameter by Jin-ze et al. [34] and Timofeeva et al. [35] The thermal conductivity of nanofluids is improved with the surface charge on the particle surface which is increased with the decreasing pH value by Gowda et al. [36] The thermal conductivity enhancement is higher for the base fluids of lower thermal conductivity and the nanoparticles of higher thermal conductivity by Lee et al. [37]. Corcione [38] also proposed an empirical correlation to predict the thermal conductivity of Al2 O3 , TiO2 , SiO2 and CuO nanofluids based on the experimental findings reported in the literature. The proposed correlation, as given in Eq. (4.23), is valid for the particle concentration up to 9 vol%, particle diameter from 10 to 150 nm and temperature from 21 to 51 °C.

10 0.03 kp T knf 0.4 0.66 = 1 + 4.4Re Pr φ 0.66 kbf Tbf, f r kbf

(4.23)

The correlation is proved in good agreement with the experimental results, while the theoretical models such as presented by Maxwell [4] underestimated the thermal conductivity of nanofluids and depicted a linear increment with the particle concentration.

4.2 Viscosity An increment in the viscosity of mixture due to suspended nanoparticles is comparatively less than the micron-sized particles and affects less to fluid flow processes (e.g., forced convection) due to very smaller particle size, less than 100 nm. But some processes, those not involving the fluid flow, like natural convection, are affected by the little increment in the viscosity due to dispersion of nanoparticles. Therefore, it is mandatory to consider the viscosity as a key parameter to investigate the heat transfer in nanofluids. Abundant studies, theoretical and experimental, have been directed on the prediction or measurement of viscosity variation due to nanoparticle dispersion and are summarized herein.

4.2.1 Theoretical Studies In the early age of investigations on the viscosity of the suspension, large number of mathematical models were presented to correlate that the different parameters affected the viscosity of suspension and also have genuine significance in present consequence. The presented mathematical models are based on the Brownian motion, hydrodynamic interaction, electroviscous effect and so on, as given in Table 4.3.

4.2 Viscosity

61

Table 4.3 Reported theoretical models for calculating the viscosity of suspension References

Correlations

Einstein [39]

μ μ0

= (1 + 2.5φ)

Kuntiz [40]

μ μ0

=

Robinson [41]

μ μ0

=1+

Hinch et al. [42]

Batchelor [43]

Vand [44]



1+0.5φ (1−φ)4

Graham [48]

Based on the Brownian motion and valid for low particle concentration



Valid for high particle concentration (up to 50%)

2.5φ (1−S  φ)

Extension of Einstein’s equation; for higher concentration

μ = μ0 $   78 1 + φ 25 +  2 441 + 35

(6D/γ )2 1+(6D/γ )2

 + ...

  = 1 + 2.5φ + 6.2φ 2 μμ0 = 1 + 2.5φ + 7.349φ 2 + .. loge

μ μ0

Consider slip mechanism at walls for higher concentrations and included the average fraction of time spent in collisions

2.5φ (1−Qφ)

= (interaction b/w particles) μ 2 μ0 = 1 + 2.5φ + 7.349φ + . . (collision b/w particles)   μ 125 2 = 1 + 2.5φ + μ0 64φmax φ + . . . μ μ0

=

9 4

1+





h 2a

−1

Based on cage model; more adequate at higher concentrations



 1 h a

−

 1  1+ ah

Brinkman [49]

μ μ0

=

Cohen et al. [50]

μ μ0

 = 1 + 2.5φ + 4.59φ 2

Avsec et al. [58]

μ μ0

=

μ μ0

=1+

Consider Brownian motion and valid for low volume concentration Brownian motion and valid for homogenous solution

= 2.5φ (no interaction b/w particles)

(1 + 2.5φ)

Masoumi et al. [59]

%

μ μ0

loge μμ0

Simha [46]

Remarks

−

 1+

1  2 h a

Based on Einstein work and used cell + theory to calculate the viscosity, valid for entire range of concentration Assumed the mixture as continuum

1 (1−φ)2.5

Viscoelastic behavior of particles is calculated

Based on statistical approach at molecular 1+(2.5φe )+(2.5φe ) +(2.5φe ) +(2.5φe ) +· · · level and assume a liquid layer on nanoparticles 2

1 μ0

×

ρp VB dp2   C 3 π dp 6φ

72C

3

4

=

   μ−1 0.09d p − 0.393 − 1.133d p + 2.771 φ 0

Based on Brownian motion and function of particle diameter and concentration

62

4 Characterization of Nanofluids

Brownian Motion In 1827, Robert Brown, a Scottish biologist, notified the zigzag motion of pollen grains in water but did not recognize the reason behind the motion. In 1906, Einstein formulated a relation between the Brownian motion and size of suspended spherical solid particle based on the kinetic theory and calculated the diffusion coefficient for the spherical particle. Einstein [39] is the first to investigate the influence of the motion of the spherical particles on the viscosity of base liquid by using hydrodynamic equations. Einstein’s correlation is based on the Brownian motion of solid spherical particles in the base fluid and is valid for only dilute solutions. Einstein also introduced a shape factor, which depended on the shape, rigidity and Brownian motion of particles, in his expression, and resulted that the coefficient of internal friction for a low particle concentration of suspended spherical particles is increased by a fraction which is equal to 2.5 times the total volume of the suspended spherical particles in a unit volume. But, Kuntiz [40] has not agreed with Einstein’s equation and set a new expression to compute the viscosity of solution of suspended particles having a higher concentration as 50% of solutions of substances such as sugars, glycogen, casein and rubber. To prove the accuracy of his expression, he computed the specific volume of solute and found that specific volume remains approximately constant for various concentrations of solute. Both Einstein and Kuntiz did not consider the interaction between the particles while estimating the viscosity of suspended particles. Robinson [41] has extended Einstein’s equation to determine the viscosity of higher concentration of suspended spheres and experimentally investigated the viscosity of suspended glass spheres having a diameter of 10–20 microns and different types of base fluids such as motor oil, castor oil, polyethylene glycol, corn syrup and sucrose solution. Through experiments, Robinson [41] has observed the similar viscosity of solution to the base fluid at low concentrations of glass spheres similar to Einstein’s equation. Hinch et al. [42] have investigated the rheology of a mixture of suspended spherical solid particles of low volume concentration into the base fluid and considered the effect of rotary Brownian motion in shear flow for different cases of aspect ratio and dimensionless shear rate λ/D. For the nearly spherical particles, a shear thinning behavior of suspension is found with constant limiting values of effective viscosity for very large or very small values of the ratio of diffusion coefficient to the shear rate. For the transition region between the high and low shear, the effective viscosity is decreased with increasing the shear strength (D/γ ). Batchelor [43] investigated the effect of Brownian motion on the bulk stress in a suspension of interacting rigid spherical particles and derived an explicit expression to evaluate the contribution of Brownian motion to the bulk stress for statistically homogeneous suspension. Hydrodynamic Interaction Two types of interactions occurred in the colloidal dispersion; one is Brownian motion between the particle–particle, and other is hydrodynamic interaction between the dispersed and dispersion medium. The effect of hydrodynamic interaction on the viscosity of the colloidal dispersion is investigated by many researchers. Vand [44]

4.2 Viscosity

63

derived the mathematical expression to determine the viscosity of suspended spheres with and without considering the interaction between the suspended spheres. Derivation to calculate the viscosity of suspended particles without considering the interaction between the particles is similar to the Arrhenius formula. Vand [44] also derived an expression to estimate the viscosity by considering the collisions between the suspended spheres caused by shearing motion of liquid with unequal velocity of different lamina, which primarily depended upon the concentration of spheres. The effect of the average fraction of time, particles spent in collision, on the shear rate is also considered. The expressions were valid for a wide range of concentrations of solid particles. Frankel et al. [45] have reported through their asymptotic analysis an expression to calculate the maximum attainable concentration of the suspended particles in the solution and expressed the high influence of the hydrodynamic interaction between the suspended particles on the viscosity rise in comparison with collisions, aggregations and inertial effects occurred. Simha [46] investigated the effect of the spherical shape arrangement of solid particles around the central particle, called cells, to the hydrodynamic interaction between the suspended solid spherical particles. The viscosity of suspension is increased proportionally with the radius of the cell which is a function of particle concentration. Krieger et al. [47] investigated the non-Newtonian behavior of the suspended rigid spherical particles. A flow equation is formulated based on the mechanism of interactions between the suspended neighboring spherical particles by applying shear rate, and a relation is found between the viscosity and shear rate. On the basis of work of Einstein [39] and Frankel et al. [45], Graham [48] neglected the effect of inertia, Brownian, London– van der Waals and electroviscous effect on the viscosity and used a cell theory to drive an expression to estimate the viscosity of suspension for the entire range of particle concentration of solid suspended particles. For the very dilute and concentrated suspension, the formulated expression is reduced to Einstein’s equation and Frankel and Acrivos’s equation, respectively. Brinkman [49] formulated the expression to evaluate the viscosity of spherical solid particles suspended in the fluid by assuming the mixture as a continuum and found increase in viscosity with particle concentration. Cohen et al. [50] investigated the Newtonian viscosity and viscoelastic behavior of concentrated neutral hard-sphere colloidal suspension. An increased effective viscosity is estimated at very high frequencies above that of the pure solvent by the fraction of colloidal particle pairs at contact when particles collide, exchange momentum and therefore contribute to the dissipation. Cheng et al. [51] have proposed two expressions to evaluate the effective viscosity of suspended particles in fluid: first, without considering the dynamic effects between the particles and fluid, and then extended former to exponent formula to evaluate the effective viscosity for high particle concentration up to 35% after considering the inter-particle collisions and random motion of particles, i.e., Brownian motion. Barthelmes et al. [52] theoretically examined the effect of concentrated suspension (up to 20%) of non-spherical solid particles and shear rate on the transient behavior of particle size distribution and suspension viscosity. The population balance model is considered for the coagulation and fragmentation of suspended particles.

64

4 Characterization of Nanofluids

Electroviscous Effect When a solid particle is brought in the contact with liquid, particle’s surface acquired a charge due to ionization, ion adsorption or ion dissolution. Due to charged particles, counterions (ions of opposite charges) are attracted toward the surface of the particle and co-ions (ions of like charge) are repelled away from the surface. The occurred charge difference at the surface of the particle and the surrounded liquid leads to the formation of double layers of ions, known as electric double layer (EDL). The EDL consists of two layers of ions, an inner layer of counterions, known as compact layer or stern layer, and outer layer of co-ion. The ions are distributed due to the influence of electrical forces and random thermal motion in outer layer, known as diffuse layer. Due to the charge difference at the boundary of compact layer and diffuse layer, an electrical potential, called zeta potential, is occurred. Debye length, thickness of the EDL, depends on the inverse of the square root of the ion concentration in the liquid and surface potential of the flow boundary. Booth [53] considered the effect of surface charge and electrical double layer on the effective viscosity of solid suspension and modified Einstein’s equation for very dilute suspension and thickness of double layer. The effective viscosity of solid suspension increased with the thickness of electrical double layer, and the same effect vanished when the radius of the solid particle is large as compared to the thickness of electrical double layer. Russel [54] neglected the effect of hydrodynamic interactions and double-layer distortion and considered the viscous force on individual particles and Brownian motion of individual suspended particles. He estimated the viscosity of suspension by using the secondary electroviscous effect. Natraj et al. [55] have found numerically that viscosity is decreased as the double-layer distortion is enhanced due to the additional stresses produced by the electrical interaction between the distorted ions and charge on the particle, and modification in fluid flow due to electrical body forces associated with charged spheres. Ruiz-Reina et al. [56] developed a theoretical model to investigate the electroviscous effect including hydrodynamic interactions between the suspended particles and overlapping of the electric double layers. For doing so, the cell model theory is used by considering the thickness of electric double layer comparable with the inter-particle distance. Due to higher number of ions in the electric double layer for low zeta potential, more distortion of the flow around the particle is occurred and resulted in the increased dissipation energy as well as viscosity of suspension and opposite occurred for the high value of zeta potential and distortion of the flow reduced. Ohshima [57] derived an expression for the effective viscosity of the dilute suspension of charged mercury drops. The effective viscosity of suspension is estimated to equal to that of uncharged rigid spheres at very high zeta potential, and the phenomenon is called as solidification effect. Particularly for the nanofluids, the classical and statistical approaches were used to evaluate the physical properties of nanofluids in the literature. Whereas classical mechanics is not proved a better option for the insight into the microstructure, on the foundation of better insight in the intermolecular and intramolecular interaction between the particles, statistical mechanics calculated the physical and thermal properties of nanofluids with a good agreement compared to experimental data.

4.2 Viscosity

65

Avsec et al. [58] formulated an expression to calculate the effective viscosity of nanofluids based on the statistical approach by considering molecular level layering of the liquid on the particle interface and clustering in nanoparticles. An effective volume concentration is used based on the thickness liquid layers on the particle interface to calculate the viscosity, and it is found very good agreement with the experimental results for nanofluids of TiO2 and Al2 O3 nanoparticles having 27-nm and 13-nm mean diameter, respectively. Masoumi et al. [59] formulated an equation to evaluate the viscosity of suspended particles as a function of temperature, particle diameter, Brownian motion and relative distance between the particles in suspension. The effective viscosity of suspension is decreased with temperature for constant particle concentration.

4.2.2 Experimental Work Most of the theoretical models to calculate the viscosity of nanofluids are suitable only for very low volume concentration. These models were derived as a function of base fluid viscosity and volume concentration. In actual practice, viscosity of base fluid is also a function of the operating temperature. The theoretical models did not consider the influence of temperature on the viscosity of suspension. For fully understanding the viscosity of nanofluids with the influence of volume concentration, temperature, particle size and base fluid, a precise review of experimental investigations is summarized herein. Initially, micron-sized particles such as solid spherical glass beads were used as suspended material to enhance the thermal performance of the base fluids by Robinson [41], Lewis et al. [60] and Hinchet al [42]. The suspended particles having the diameter in the order of 10–130 microns were dispersed in various types of base fluids such as water, glycerol, motor oil, castor oil and polyethylene glycol. The effect of size distribution of suspended particles on the viscosity is investigated by Robinson [41], Nir et al. [61] and Kao et al. [62], and resulted that the viscosity of suspension decreased as the size distribution increased. Other phenomena were investigated experimentally such as electroviscous effect on the solid particles suspended in the base fluid by Harmsen et al. [63] and Hiemenz et al. [64]. Harmsen et al. [63] measured the electroviscous effect on different concentrations of AgI sol and observed three causes for viscosity decrement such as change in the form of the particles, change in shape of the particles and liberation of electrolyte and concluded that later one affected viscosity more than others due to aging, e.g., increase in conductivity and activity of negative iodide ions. Al 2 O3 Nanofluids Water is the common fluid used in most of the heat transfer process as a heat carrier. In the literature, large numbers of the investigations were done to explore the viscosity characteristics of Al2 O3 nanofluids, shown in Table 4.4., and experimentally exhibited the viscosity of γ-alumina (Al2 O3 ) by using Brookfield rotating viscometer

66

4 Characterization of Nanofluids

Table 4.4 Experimental studies conducted on the viscosity of Al2 O3 nanofluids References

Size (nm)

Base fluid

Particle concentration Temperature range range (%) (°C)

Pak et al. [67]

13

Water

1.34 and 2.78

Wang et al. [66]

20

Water

1–6

25 °C

Darzi et al. [68]

20

Water

0.25, 0.5 and 1

26–55

Mosavian et al. [69]

20

Water

0.2–3

25

20–70

Duan [70]

25

Water

1–3

15–55

Tavman et al.

30

Water

0.5 and 1.5

20–50

Hwang et al. [95]

30 ± 5

Water

0.01–0.5

21

Nguyen et al. [71]

36

Water

1 and 4

20–70

Heyhat et al. [96] 40

Water

0.1–2

20–60

Chandrasekara et al. [97]

43

Water

1–5

25

Sekhar et al. [98] 47

Water

0.01–1

22–45

Murshed et al. [99]

Water

1–5

25

Anoop et al. [72] 95–100

Water

0.5–6

25

Lee et al. [100]

Water

1–3

25

EG/W (20:80, 40:60, 60:40)

0.3–1.5

10–60

80

155

Sundar et al. [73] 36 Yu et al. [101]

30

EG/W (45:55)

1 and 2

10–60

Mojarrad et al. [74]

20–30

EG/W (50:50)

0.25, 0.5 and 0.7

20–50

Said et al. [76]

13

Water, EG/W (60:40)

0.05 and 0.1

25–70

Kulkarni et al. [102]

45

EG/W (60:40)

6

10–40

Sahoo et al. [75] 53

EG/W (60:40)

1–10

0–90

for the range of volume concentration of suspended particles varied from 1 to 10%. Through experiments, an increment in viscosity is observed with the particle concentration of suspended particles but unaffected due to pH variation of the suspension. The shear thinning behavior of γ -Al2 O3 at 3 vol% is also observed, as viscosity of nanofluids decreased with the shear rate. The relative viscosity of γ-Al2 O3 is maximized around 200 at 10 vol% due to high surface area. Putra et al. [65] also reported the Newtonian behavior of the Al2 O3 /water nanofluids for constant particle concentration. Wang et al. [66] have dispersed the Al2 O3 nanoparticle in water by three different methods, mechanical blending using a blending machine and ultrasonic bath, polymer

4.2 Viscosity

67

coatings of styrene maleic anhydride to the nanoparticle during the blending process and filtration to remove agglomerated particles of larger size. A low relative viscosity is found for polymer coating method due to better separation of particles. The obtained results were not in agreement with the Pak et al. [67] results as they applied electrostatic repulsion between particles to prevent the settling of solid particles and got maximum relative viscosity of 1.8 for 5 vol%. For the similar particle size, particle concentration and operating temperature conditions, Darzi et al. [68] have found an enhancement of 41% in the viscosity of Al2 O3 nanofluids which is only 8% for Wang et al. (1999). The nanoparticles were dispersed using the magnetic stir followed by ultrasonic vibration. Mosavian et al. [69] have found an enhancement of 15% in the viscosity of Al2 O3 nanofluids for similar conditions. The Newtonian behavior of the Al2 O3 nanofluids is observed as the viscosity is almost constant over the range of shear rate. Duan [70] dispersed the nanoparticles having particle size of 25 nm in the water by using magnetic stir followed by ultrasonication process and reported an increment of 52% in the viscosity of Al2 O3 nanofluid for 3 vol% at the temperature of 15 °C and 55 °C, and Newtonian behavior of nanofluids. Nguyen et al. [71] have observed higher enhancement in relative viscosity for Al2 O3 /water nanofluid for 36-nm particle diameters for the temperature range from 20 °C to 75 °C. The correlations to calculate the relative viscosities were proposed for the particle concentration of 1 and 4 vol%, as shown in Eqs. (4.24) and (4.25), respectively. μ = μ0 (1.1250 − 0.0007T )

(4.24)

 μ = μ0 2.1275 − 0.0215T + 0.0002T 2

(4.25)

Due to difference in method of preparation, particle size and different operating conditions, different enhancement in the viscosity with the particle concentration and reduction with temperature is found. Reduction in the viscosity is due to increment in the Brownian motion due to temperature increase. The higher rate of reduction in viscosity is occurred for higher particle concentration of nanoparticles at constant temperature. Anoop et al. [72] have investigated that the presence of EDL caused the electroviscous effect on the viscosity of electrostatically stabilized Al2 O3 /water nanofluids. A cone and plate rheometer is used to measure the viscosity as a function of volume concentration of suspended particles and particle size. The reduction in primary electroviscous coefficient is measured with the particle size of nanoparticles, and it observed the Newtonian behavior of nanofluids. The effect of pH value of the suspension on the viscosity is also measured and found no influence due to formation of EDL of negligible thickness. The nanoparticles were also mixed into the ethylene glycol and water (EG/W) solution to enhance the heat transfer rate in the cold regions. Three different blend concentrations of EG into the water, 20:80, 40:60 and 60:40, are used by Sundar et al. [73] to examine the viscous behavior of Al2 O3 nanofluids.

68

4 Characterization of Nanofluids

Almost three times increment in viscosity is found for the 60:40 concentration of EG/W at 35 °C for 1.5 vol%; beyond this temperature, a decrement in relative viscosity is found. Mojarrad et al. [74] also found around 50% increment in the viscosity of EG/W (50:50)-based nanofluid at 50 °C. Sahoo et al. [75] also depicted the same behavior of viscosity as increment and reduction in the relative viscosity with the particle concentration and temperature. A 3.5 times increment in the viscosity of nanofluids occurred for 10 vol% concentration than the 1% at −35 °C, but the increment in the viscosity exponentially diminished with temperatures. Non-Newtonian behavior of nanofluids is observed at lower temperature, from −35 °C to 0 °C, and above this range, nanofluids behaved as Newtonian fluids. The correlation is formulated, as given in Eq. (4.26), based on the experimental results to predict the viscosity. μ = Ae( T +Cφ ) B

(4.26)

where A, B and C are constants, and their values for cold regime (−35 °C to 0 °C) are 1.22 × 10−6 , 4285 and 0.1448, respectively. For hot regime (0 °C to 90 °C), A, B and C are 2.392 × 10−4 , 2903 and 0.1265, respectively. Said et al. [76] have shown a different side of the viscosity performance of EG/W (60:40)-based nanofluids, as low viscosity of nanofluid is observed than that of the base fluid for 0.05 vol%. A decrement of 13% in the viscosity is measured at 65 °C than the base fluid EG/W (60:40), and it found the Newtonian behavior of nanofluids, but the unusual behavior of decreased viscosity is not explained. Corcione [38] proposed an empirical correlation to predict the dynamic viscosity of Al2 O3 , TiO2 , SiO2 and CuO nanofluids based on the experimental findings reported in the literature. The proposed correlation, as given in Eq. (4.27), is valid for the ranges of particle concentration from 0.01 to 7.1 vol%, particle diameter from 25 to 200 nm and temperature from 20 to 60 °C. μnf 1 = −0.3  μbf 1 − 34.87 dp /df φ 1.03

(4.27)

where d f denotes the equivalent diameter of a base fluid molecule and is expressed as

6M 1/3 df = 0.1 N πρbf

(4.28)

The correlation is proved in good agreement with the experimental results, while the theoretical models such as presented by Brinkman [49] underestimated the viscosity of nanofluids. The effect of various parameters on the viscosity of nanofluids, from theoretical or experimental studies, is summarized in the following.

4.2 Viscosity

69

• An increment in the viscosity of nanofluid is reported with the concentration of nanoparticles. • The effective viscosity of solid suspension is increased with the thickness of electrical double layer, and the same effect is vanished when the radius of the solid particle is large as compared to the thickness of electrical double layer. • The viscosity of nanofluids is decreased as the size distribution of dispersed solid particles is increased. • The decrement in the viscosity of nanofluids is observed with the temperature due to increment in the Brownian motion, for constant particle concentration. • The viscosity of nanofluids is decreased with increasing the shear strength. • The viscosity of nanofluids is decreased as the double-layer distortion is enhanced because the additional stresses are produced by the electrical interaction between the distorted ions and charge on the particle.

4.2.3 Case Study: Investigation of Thermal Conductivity and Viscosity of Nanofluids Using Design of Experiment Approach The properties behave differently when the particle concentration, particle diameter and temperature of nanofluids change. So, it is important to investigate the combined effect of particle size, particle concentration and temperature on the thermal conductivity and viscosity of nanofluids. Literature shows that both thermal conductivity and viscosity for nanofluids are high compared to base fluid. While thermal conductivity rise is beneficial, the viscosity rise increases pressure drop. So, both the properties should be optimized so that maximum thermal conductivity can be obtained at minimum viscosity rise. In this case study, the design of experiments (DOE) approach and utility concept are used to analyze and optimize the thermal conductivity and viscosity of nanofluids, with the following objectives. 1. To investigate the individual effect and interaction effect of three important independent variables (particle concentration, particle diameter and temperature) on the thermal conductivity and viscosity of Al2 O3 /water nanofluids. 2. To optimize the properties for maximum thermal conductivity and minimum viscosity. 3. To collectively optimize the thermal conductivity (higher the better) and viscosity (lower the better), using utility concept. The variables were selected at two levels each: particle concentration (0.1–1%), particle diameter (20–40 nm) and temperature (10–40 °C). The factors (variables) and their levels were selected based on brainstorming sessions and based on literature review.

70

4 Characterization of Nanofluids

Methodology The step-by-step procedure for investigating the thermal conductivity and viscosity of Al2 O3 /water nanofluids is as follows: 1. 2. 3. 4.

Deciding the variables (factors) and their levels. Planning the experiments using DOE. Performing experiments to get the responses. Analyzing the variables and testing significance of model using analysis of variance (ANOVA). 5. Finding the optimal condition for the maximum thermal conductivity and minimum viscosity of the nanofluids. 6. Comparing predicted value with experimental value and confirmation of optimality. Size of the Al2 O3 nanoparticles employed for thermal conductivity and viscosity is 20 and 40 nm. A two-step procedure is followed for nanofluid preparation. The ultrasonication is done for one hour which is an accepted method for dispersing the nanoparticles in the base fluid. No sedimentation is observed for Al2 O3 nanoparticles after 24 h of preparation of nanofluids. Thermal conductivity of the nanofluids is measured using KD2 Pro Thermal Properties Analyzer. The viscosity of the nanofluids is measured using Modular Compact Rheometer at a constant shear rate of 100 s−1 . Nanofluids showed Newtonian behavior in the low particle concentration range of 0.l to 1 vol%. Based on experimental design, four samples were prepared for experimental investigation. The particle concentration and particle diameter of the prepared Al2 O3 /water nanofluid samples were as follows: 0.1 vol% and 20 nm; 1 vol% and 20 nm; 0.1 vol% and 40 nm; and 1 vol% and 40 nm, as shown in Fig. 4.2. The thermal conductivity and viscosity of all four samples are measured at 10 °C and 40 °C. For validation, experiments were done for water at four different temperatures ranging from 10 to 40 °C. The experimental results were compared with theoretical

Fig. 4.2 Photographs of Al2 O3 /water nanofluid samples after 24 h of preparation of nanofluids

4.2 Viscosity

71

results of water (Eqs. 4.29 and 4.30), given by Popiel et al. [77]. The formulae are valid in the temperature range of 0 to 150 °C with an uncertainty of ± 2% for thermal conductivity and ± 1% for viscosity measurement. k = a + bT + cT 1.5 + dT 2 + eT 0.5

(4.29)

where a = 0.5650285, b = 0.0026363895, c = −0.00012516934, d = −1.5154918 × 10−6 , e = −0.0009412945. μ=

1 a + bT + cT 2 + dT 3

(4.30)

where a = 557.82468, b = 19.408782, c = 0.1360459, d = – 3.1160832 × 10−4 . The comparison of experimental results with that of theoretical is plotted in Figs. 4.3 and 4.4. It can be seen that there is a good agreement between experimental data and theoretical predictions for both thermal conductivity and viscosity of water. The average deviation between experimental and theoretical results is observed to be 0.42 and 2.07% for thermal conductivity and viscosity, respectively. Each of the experiments is conducted two times. So, in total 16 experiments were conducted for each response. The lower level is coded as ‘L1’ or simply ‘1’, and the higher level is coded as ‘L2’ or simply ‘2’. The factors and levels are given in Table 4.5. A full factorial design is developed for investigation of thermal conductivity and viscosity. The plan of experiment designed for analysis is given in Table 4.6.

Fig. 4.3 Comparison of experimental data of water with that of theoretical predictions for thermal conductivity

72

4 Characterization of Nanofluids

Fig. 4.4 Comparison of experimental data of water with that of theoretical predictions for viscosity Table 4.5 Factors and their levels for thermal conductivity and viscosity measurement Label

Factors

Unit

A

Particle conc. (φ)

vol%

Levels L1

L2

0.1

1

B

Particle diameter (d p )

nm

20

40

C

Temperature (T)

°C

10

40

Table 4.6 Plan of experiments for thermal conductivity and viscosity in actual and coded units Exp. No.

Actual units

Coded

 (vol%)

d p (nm)

T (°C)

A

B

C

1

0.1

20

10

1

1

1

2

1

20

10

2

1

1

3

0.1

40

10

1

2

1

4

1

40

10

2

2

1

5

0.1

20

40

1

1

2

6

1

20

40

2

1

2

7

0.1

40

40

1

2

2

8

1

40

40

2

2

2

4.2 Viscosity

73

Table 4.7 Response (thermal conductivity and viscosity ratio) obtained based on the experimental plan Exp. No.

Coded

Response (R) Thermal conductivity ratio (k r = k nf /k bf )

Viscosity ratio (μr = μnf /μbf )

A

B

C

R1

R2

Avg.

R1

R2

Avg.

1

1

1

1

1.0207

1.0172

1.0189

1.0079

1.0071

1.0075

2

2

1

1

1.0430

1.0413

1.0422

1.0716

1.0803

1.0759

3

1

2

1

1.0052

1.0138

1.0095

1.0448

1.0527

1.0488

4

2

2

1

1.0293

1.0310

1.0301

1.0983

1.0913

1.0948

5

1

1

2

1.0460

1.0429

1.0444

1.0031

1.0016

1.0024

6

2

1

2

1.1159

1.1143

1.1151

1.0676

1.0597

1.0637

7

1

2

2

1.0190

1.0238

1.0214

1.0519

1.0582

1.0550

8

2

2

2

1.1048

1.0984

1.1016

1.1116

1.1226

1.1171

Table 4.7 shows the response obtained for thermal conductivity ratio (k r ) and viscosity ratio (μr ). The thermal conductivity ratio defined the ratio of thermal conductivity of nanofluid (k nf ) to the thermal conductivity of base fluid (k bf ). Similarly, the viscosity ratio (μnf ) is defined as viscosity of nanofluid to the viscosity of base fluid (μbf ). Here, response or output is designated as ‘R’. Figure 4.5 shows the main effect and interaction effect of the considered factors on the thermal conductivity ratio of Al2 O3 /water nanofluids. From the figures, it is clear that the thermal conductivity of the nanofluids increases with increasing particle concentration and temperature while by increasing particle diameter the thermal conductivity decreases. A similar variation in thermal conductivity of nanofluids is reported by Das et al. [78]. Small-size nanoparticles have high Brownian motion and chaotic movement. The increased Brownian motion results in enhanced thermal conductivity of nanofluids due to the dominant microconvection at the nanoscale. From the interaction effect plots (Fig. 4.5d–f), it can be concluded that interaction of φ and T (A × C) significantly affects the thermal conductivity of nanofluids. Interaction effect is important when the lines are not parallel and tend to meet at some place. Parallel lines are an indicative of almost no interaction. Figure 4.6 shows the main and interaction effect of the factors on the viscosity ratio of nanofluids. From the main effect plots (Fig. 4.6a–c), it can be seen that particle concentration highly affects the nanofluid viscosity followed by particle diameter. The viscosity of nanofluids is observed to be increasing with increasing particle concentration (Fig. 4.6a). The viscosity of the nanofluids is also observed to be increasing with increasing particle diameter (Fig. 4.6b). The particles of larger size offer higher resistance to flow, and hence the effective viscosity of the nanofluids increases. A similar trend of increasing viscosity with increasing particle size is reported by He et al. [79] and Nguyen et al. [80].

74

4 Characterization of Nanofluids

(a) Main effect of particle concentration

(b) Main effect of particle diameter

(c) Main effect of temperature

(d) Interaction effect of particle diameter and particle concenteration

(e) Interaction effect of particle diameter and temperature

(f) Interaction effect of temperature and particle concenteration

Fig. 4.5 Main effect and interaction effect of thermal conductivity ratio (k r )

4.2 Viscosity

75

(a) Main effect of particle concentration

(b) Main effect of particle diameter

(c) Main effect of temperature

(d) Interaction effect of particle diameter and particle concenteration

(e) Interaction effect of particle diameter and temperature

(f) Interaction effect of temperature and particle concenteration

Fig. 4.6 Main effect and interaction effect of viscosity ratio (μr)

Figure 4.6e shows the interaction effect of temperature and particle diameter. With the increase in particle size, the resistance offered by the cohesive forces increases which in turn increases viscosity. If the temperature is also varied simultaneously with the variation in particle diameter, the Brownian motion effect comes into the play.

76

4 Characterization of Nanofluids

Table 4.8 Analysis of variance for thermal conductivity ratio (kr) Source

Sum of squares (SS)

Mean of squares (MS)

F-value

p-value

Model

0.021510

DOF 6

0.003585

268.10