Convective Heat Transfer in Cross-Flow Tube Arrangement

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THE UNIVERSITY OF GLASGOW

CONVECTIVE HEAT TRANSFER IN CROSS-FLOW TUBE ARRANGEMENT

A THESIS SUBMITTED FOR THE DEGREE OF Ph.D. BY H. STUART HOLDEN. B.Sc.. A.R.T.C.

JANUARY 1950

ProQuest Number: 13870204

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CONTENTS LIST

PP Synopsis .

1

Introduction

3

Part I

- Review

6

A - Single Tube Experiments

6

1 - Mean Convective HeatTransfer Coefficients 2 - Temperature Variation aroundTube 3 - Variation in Convection Heat Transfer Coefficients around tube

8 11 11

(a) Early Experiments

12

(b) Indirect Methods

12

(c) Heated Cylinders

13

(d) Collected Curves.

14

B - Tube Bank Experiments 1 - Mean Convective Heat Transfer Coefficients

15 15

2 - Variation of Heat Transfer Coefficients around tube 17 I C — Summary of Review.

18

Part II A

-

Experimental Investigation .

pp

Apparatus

20

1 - Aim and Scope of Investigation

'

20

2 - Wind Tunnel

21

3 - Tubes

22

A - Test Tube

22

B - Experimental Tehhniques 1 - Calibrations

’

2I 4.

21+

(a) Air Plow

2I 4.

(b) Temperatures

26

2 - Preliminary Tests

28

3 - Experimental Procedure

30

(a) Single Tube Tests

30

(b) Tube Bank Tests

51

Part III - Experimental Results and Discussion WP 33

A - Single Tube Results 1 - Mean Convective Heat Transfer Coefficients "between air and external tube surface

33

2 - Tube Wall Temperature Variation around tube

36

(a) Effect of Reynolds Number at Constant Air Temperature

36

(1=) Effect of Air temperature at Constant Reynolds Number

37

3 - Variation in Convective Heat Transfer Coefficient around tube.

37

(a) Analysis of Circumferential heat flow in tube Wall

39

lb) Relationship between heat transfer rates at inner and outer surfaces

^-1

(c) ”Apparent” and Real NusseltNumbers

kk

(d) Effect of Reynolds Number on Heat Transfer at front and rear of tube

k5

(e) Effect of Tube Thickness B - Tube Bank Results .

hd

1 - Mean Heat Transfer Coefficient between air and external tubesurface. (a) Average Nusselt Number for Bank of Tubes (b) Row to row variation in mean Nusselt Number in Bankof Tubes

30 50

-

2 - Tube Wall Temperature Variation around Tube

51 53

pp3 - Variation in Heat Transfer Coefficient around tubes

55

(a) Single Row of Tubes

55

(b) Two and Three Rows of Tubes

55

(c) Six Rows of Tubes

55

C - Conclusions

58

Part IV - Appendix 1. Bibliography

62

2.

Rotation

6k

3*

Tables of Results

66 et seq.

SYNOPSIS An. experimental study is presented of point to-point variation in heat transfer around a tube placed across a hot air stream and water cooled internally.

A

single tube is first examined and then individual tubes in tube banks. In the first part, methods and results of previous workers are reviewed;

attention had been

confined to variation at outer surface of single tube. The form of such variations are established.

No comparable

work has been carried out on the variation of heat transfer at inner surface, nor has there been any extension to individual tubes in banks. The second part describes apparatus designed specifically for investigation.

The outstanding feature

is a fluted core which, placed in tube, allows measurement of actual heat transfer at inner surface for each 20° angular interval round tube.

Calibrations and preliminary

tests are detailed. In the third part experimental results are given and discussed.

For single tube mean heat transfer

coefficients are given, and also the variation in wall surface temperature around tube.

The variations in heat

transfer round inner surface are given and shown to diverge

markedly from established variation for outer surface. Analysis, which allows for circumferential heat flow induced by wall temperature variation, gives correlation between inner and outer surface variations.

The effects

of varying conditions on relationship between inner and ouiirvariations in heat transfer coefficients are examined. Individual tubes in banks are similarly treated.

Mean

heat transfer coefficients for banks and for different rows in bank are derived. Temperature and heat transfer variations explain increasing effectiveness of rear portion of tube from first to third row and emphasise exceptional conditions around second row tube. given.

Results are summarised and conclusions

INTRODUCTION The work described in this thesis forms the first part of a major investigation on natural circulation in boiler tube banks.

To enable an assessment to be made

of the variation in heat reception and therefore of natural circulation from row to row, detailed knowledge is required of the variation in heat transfer rate from row to row and also round any individual tube in a bank.

A study of

available data revealed that there were many gaps which could only be bridged by an experimental investigation using new techniques, in particular the measurement of local tube temperatures and heat reception rates. In addition, attention had been drawn to the persistency of failures in the second row tubes of a water, tube boiler, and it was decided to examine carefully the local variation in convective heating which must have given rise to these failures. A hydrodynamic approach to the second row tube problem has already been made and, as a result,there is experimental evidence that the pressure gradients have their maximum values on the surface of the second row tubes.

The absence of the knowledge necessary to translate

this evidence into terms of heat transfer and temperature gradients have rendered it inconclusive.

The present work represents an approach to the problem from the heat transfer angle.

It has been preceded

by a survey of the published information relating to variations in temperature and in heat transfer coefficients round a tube in cross flow.

It was found that the case of

heat transfer from a gas stream to a cylinder in crossflow had been examined by several investigators.

They had found

that the heat transfer coefficient between the gas and the external surface varied locally round the cylinder and had established the form of that variation.

Various experimental

methods had been used but in no case were they carried far enough to allow of correlation between the variations in heat transfer rates at the inner and outer surfaces of a tube and the tube wall temperatures, nor of assessing the circumferential heat flow in the tube metal.

The variations

around a tube placed in a tube bank had received little attention. It appeared necessary that further work should be undertaken with a view to filling gaps in existing information,to explaining certain anomalies, and to extending the fundamental knowledge to the detailed actions around the tubes in a tube bank. The need for such knowledge is made more urgent by the ever increasing demands in heat transfer rates in

5

■boiler practice.

.

A few years ago a heat intake of 120,000

B.ThU. per hour per square foot of tube surface was considered high for a fire-row tube in boiler practice, now 200,000 is accepted, and if modern advances in combustion technique are to be fully utilised much higher rates still must be faced.

When it is remembered that

these figures are mean rates for the tube then a detailed knowledge of the point-to-point variations around the tube assumes a new importance.

Undoubtedly greater attention

to temperature stresses will be demanded and these cannot be satisfactorily assessed without precise information on the temperature gradients in the tube wall. Thus any work which will advance existing knowledge on % these important aspects is fully justified.

i

PART I

-

REVIEW

-PRESENTATION AMD CORRELATION OF HEAT TRANSFER RESULTS The rate of heat transfer between two fluids separated by a solid wall is dependent upon the resistance to heat flow offered by the fluid on either side of the wall and the conductivity of the wall.

For the case of a

gas flowing past a bank of metal tubes through which a vapour or liquid is passing, the overall heat transfer coefficient is largely controlled by the resistance of the gas film.

As this case is commonly met with in practice,

many experiments have been carried out to obtain values of the heat transfer coefficient between gas and tube wall for various gas flow conditions. The results of such tests are presented in many forms, and in the past empirical equations were often used; such equations had a very limited application* The large number of independent variables affecting the convective heat transfer in any experiment have made the use of dimensionless groups universal in reporting results.

In the case of forced convection, where

natural convection effects are small, it can be shown by dimensional analysis that /

*>cd = C f ^ v , £ t £ ) ~ T J\ A k J

or Nu where

=

£

(He, Pr)

- convective heat transfer coefficient gas to metal cf

as Diameter of tube

M

= Conductivity coefficient of the gas - density

V1 JU

=

velocity

=

viscosity

Cfr = Specific Heat Nu ke.

= Nusselt Number = =

k

Reynolds’* = yU

fir = Prandtl

"

=

/c That is, the Nusselt Number is a function of the Reynolds Number and the Prandtl Number, the two latter numbers "being dependent respectively on the velocity distribution and the temperature distribution in the gas stream. As Pr varies but slightly over a wide range of temperature for gases of the same atomic number, this equation may be reduced to Nu

= j' (Re)

which, when expressed as a power function, gives Nu

=

a(Re)n

Thus the results of experiments using air or any other

diatomic gas may be presented and correlated in this form. The selection of a temperature at which to evaluate the physical properties of the gas in this equation has led to some difficulty in correlation. workers "base their values of k,^#t and jP

Some

on the hulk

temperature of the gas and others on the mean tube temperature. k

In this thesis, as in most recent works,

andyU. are evaluated at a gas film temperature tf ,

defined as

that is, the mean temperature between the gas stream and the tube;

and p

and V are combined in G-, the mass flow

of air per unit area based on the minimum flow area past the tube. A further problem in correlation is the difference between the curves of different authorities for the physical properties used in evaluating results. Graphs of the variation of k andp by more than 5%.

with temperature may differ

Throughout this paper, the values of the ,

physical properties of air as given by Keenan and Kaye

a

are used. SECTION A - SINGLE TUBE EXPERIMENTS (1) Mean Convective Heat Transfer Coefficient

The majority of experimenters have used a single heated cylinder mounted across a duct through which a stream of air was passed.

The heat transfer

coefficient for any air flow condition was obtained by measuring the rate of heat loss from the tube surface, the mean temperature difference between the surface and the air, and the external surface area of the cylinder. Various methods have been adopted to obtain the heat loss from the cylinder.

Hughes

2

and others have

taken the weight of steam condensed in the cylinder; ^ U *5 Hilpert , Small and Griffith and Awbery-^ have measured the electrical input to heaters mounted in -the cylinder; while King

6

3 and Hilpert , for low values of Reynolds

Number, have used an electrically heated wire as the ’cylinder/.

Reiher^, however, directly measured the heat

received by water passing through a tube placed across a stream of hot air.

The convective heat transfer

coefficient was obtained after correcting for radiant heat transfer. The results of many experiments have been 8 9 correlated by Fishenden and Saunders , Schack and more 10 recently McAdams . The recommended curve of McAdams is shown in Pig. 1 as a plot of Nu to a base of Re, the various experimental values agreeing within 20%.

The results of

n a. i

N u s s e lt

Sin c l e

Num ber

to

T u b e , /ls

R e y m q i-q s

C31v£ m

by

N u m b er

A\c A

NUMBER

SO

NUSSELT

ioo 90

50

A

5

T

W AT

:t e a .p, :

plo t:

»>y : r ^ o j i u i m .$ SCHWAB; PDR

HEATED

c y l :iw: dbh

(a) Early Experiments:

By measuring the heat loss

from an electrically heated metal strip set into the wall of an ebonite cylinder, when the cylinder was placed in a cold air stream, Page and Falkener Kirpitchev

1 *5

1 *5 1it , Small and.

have shown that the rate of cooling of the

strip varied as the cylinder was rotated through small angular displacements.

These experiments all show a

maximum value of heat transfer at about I4.O0 from the upstream point and a minimum at the front and sides of. the tube.

The results of these tests cannot be applied

generally to heated tubes, as the temperature conditions in the air stream around a locally heated cylinder will differ from those around a completely heated surface. (b)

Indirect Experiments:

Circumferential variations iG in heat transfer have been deduced by Lohrisch , who related measurements of the rate of diffusion of a gas from the surface of a tube to values of heat transfer. Winding and Cheney

17

measured the change in dimensions

of a cylinder of naphthalene placed in a wind tunnel, and by an analogy between mass transfer and heat transfer, converted their results to values of heat transfer. Heat transfer values have also been presented by Klein1®,

who used cylinders of ice placed in a hot

air stream.

The local variations in the rate of melting

of the ice were used to calculate the variations in heat

transfer coefficient for the surface of the cylinder. The results of these three experimenters must be applied with caution, as the air flow pattern around the various cylinders used would be different from that around a heated or cooled tube, and thus it is to be expected that the heat transfer would also differ. (c)

Using Heated Cylinders:

Small^

carried out

experiments using a heated metal cylinder in which an insulated thermopile was inserted in an axial slot. The tube was placed in an air stream and by rotating the f tube, readings from the thermopile at different angular positions were obtained.

By relating the mean value of

these readings to the mean heat transfer to the cylinder, the variations in heat transfer around the cylinder v/ere obtained. Tests made by Paltz and Starr, reported by Drew and Ryan

19

give values of the heat transfer for

axial strips around the inside of a 3.2 ins. outside diameter and J in. thick brass tube for one value of Reynolds number. The results were obtained by measuring the condensation of steam in slots on the inside of the tube when cold air was blown past the outer surface of the tube.

The

assumption is made that the tube wall is at a uniform temperature corresponding to the saturation temperature of the steam, ana one resuios are px'eHen'ooo, as heat____

transfer rates from the outer surface.

This assumption

can hardly he accepted in the light of the temperature distribution as given in Pigs, 2 and 3. Krujilin and Schwab

12

and Krujilin

20

deduce

the heat transfer at the outer surface of an internally heated tube by calculating the conduction through the tube wall from' experimentally obtained values of the surface temperature and an assumed constant internal surface temperature.

The justification for taking the internal

surface temperature as constant in this case is in doubt, as Hilpert^

has measured small variations of internal

surface temperature on a similarly heated tube. A very complete set of results have been published by Schmidt and Wenner

21

who used a steam

heated cylinder, in the side of which, in a small insulated slot, an electric element was inserted.

The heat transfer

at any point was obtained by measuring the electrical input to maintain the element at a constant temperature.

A small

error is to be expected in these results as they are based on readings of a tube at constant external temperature (d) General: A selection of the results of these experimenters, covering the range of Reynolds Humber being considered, are shown in Pig,A.

In each case the variation

in Nusselt Number round the half circumference of the tube

2;ipo< V A g ito o iA ;w ; v i u s s i i x ; : : : T~ AC:C>UKip ;TU& L

N*h«rje h 3 cqetff of heat tfansfe LmhU/br.fll%bni

j_______

....

sw .v A ^ tQ u s

.fcxpjsw * \ s,:n

t :c r s

d*tube dmmeter (f O L ; . 4.. . Icf gae cpi^ucfiAlS' 21,000.

R.

6000 © MUOIWB. «'Q4EUUE.Y.

SMALL. ■ p « T i W C W R 7 400p.

© K R lHIUWl

tiSlSiC.1

is shown to a "base of angle measured from the front of the tube. The general shape of these curves has been confirmed using optical methods "by Joukovsky, Kirejew 22 and Schamschew and it can also he related to the characteristics of the gas flow pattern round the tube. The rate of heat transfer is dependent upon the air film thickness and the degree of turbulence at the tube surface and varies from a maximum at the front to a minimum where the flow lines break away from the surface. Thereafter there is an increase due to the vortices formed towards the rear of the tube. It should be noted that the various results in Fig .4 show that the value of Nu at the rear of the tube, 180°, increases much more rapidly with increasing Re, than does the value at the front of the tube, 0°.

B - TUBE BANK EXPERIMENTS 4l.

Mean Heat Transfer coefficient:

The results of experimental investigations of the heat transfer between air and banks of tubes are, as in the case of single tubes, generally presented as a plot of Mean Nusselt Number to Reynolds Number.

A comparison

of the various results shows that the rate of heat transfer

varies greatly with the tube arrangement and the number of rows of tubes present. Extensive tests using hanks of tubes ten rows O ~Z Oil deep have been carried out by Huge J and Pierson to investigate the effect of tube arrangement on heat transfer. Their results have been correlated by G-rimison

and fair

agreement is found with the results of other experimenters. Kuznetzoff and Lokshin^

have also carried out tests with

varying tube spacing, their results are found to be somewhat lower than those given by Grimison, but show the same general trend. The results of the many tube bank tests have 07 pQ been correlated by Lander and Fishenden and Saunders To permit of easy application to design problem, factors that are dependent on the tube configuration and Re are given, to be applied in an equation of the form. / \& Nu = a(Re) x factor. In general it is found that the rate of heat transfer with “in-line” tube banks is lower than with staggered arrangements.

In the case of the "in-line" tubes hm is

increased by placing the tubes closer together across the flow path, but only slight alteration in the value of % is noted when the spacing in the direction of flow is altered.

For staggered banks, however, the heat transfer

may be considerably increased by reducing the row to row distance, and only slightly varied by altering the distance between the tubes in the rows. To assess the effect of the number of rows of 7 tubes present in a tube bank, Reiher carried out tests using banks containing different numbers of rows.

Prom

these tests a mean value of hm for each bank was calculated and the value was found to increase with the number of 2*5 rows. Similar effects are shown by Grimison . o 29 Griffith and Awbery-' and Winding ^ have shown that the mean heat transfer rate in a row increases from the first to the third row and then remains nearly constant for further rows.

These experiments were made

using a heated test tube placed in a bank of unheated tubes, the heat transfer coefficient being based on the approach air temperature. x As in the case of a single tube, it has been shown 30, 31> that the angle between the tube axis in a bank and the direction of air flow.-has little effect on heat transfer values. 2. Variation of Heat Transfer Coefficient around Tube. Only one series of curves is available in the literature showing how the variation in heat transfer

around a tube is affected "by the position of the tube in a tube hank.

These curves refer to a tube in the 5th row

of a staggered tube hank and were obtained hy Winding and Cheney

17

using their technique of measuring the

change in dimensions of a naphthalene cylinder.

Their

curves are given in Pig.5 and show a very high rate of heat transfer at a point some 120° from the upstream point of the tube •

It should he noted that a maximum value at

this point has been shown to he present in single tube 20

experiments when the value of Re is above, 150*000 (

' \

•

21

C - REVIEW SUMMARISED The review may be briefly summarised as

follows: (1)

Experimental work on mean heat transfer rates to'

single tubes and also to tube banks has been fairly comprehensive and the results of the various workers properly correlated, (2 )

The work on variation of heat transfer round the

single tube has been very limited and has produced certain anomalies which cannot be satisfactorily explained in the light of existing knowledge.

Attention, with one exception

has been confined to the outside surface of the tube, where it has been shown there is a marked variation in heat transfer rates.

Where these experiments were carried out

rtANK.

■40

C £. a u. o

?0 3 £ i 'X

is

OlRtCTVOVJ

OP Alt? PUO>*J o

5 0

Cu^vE. Mg

so II ,II cxl — DECREES gEVaOLOS Wjg S7.000

I ?

41,0°°

3

^S^OO

A

10 500

iso

with tubes, it was generally assumed that the temperature round the inside of the tube was constant, thus implying a uniform rate of heat transfer at the inner wall surface; yet, in the one exception where heat transfer rates for the inside surface were measured, the results indicated a variation similar to that given by other workers for the outside, (3)

The variation of temperature around the tube wall

has received very little attention although it has been clearly shown that a variation does occur.

Such variation

must induce circumferential heat flow and this, in turn, will affect the relationship between the variations in heat transfer coefficients at the outer tube surface and those at the inner surface.

No consideration has so far been

given to these aspects. (i4)

Only one very limited and indirect attempt has been

made to investigate variations round a tube placed in a bank ,

A

-

APPARATUS

1 . AIM

AND SCOPE OP PRESENT INVESTIGATION

In the

light of the Review, it was decided that

the first step should he further experimental work on a single tube

placed across a hot

direct readings of

air stream to provide

tube temperature variations,, and direct

measurement of the variations in heat transfer rates round the inside surface of the tube.

This information when

correlated to existing knowledge of the variations in heat transfer rates at the outer tube surface, would give a much clearer picture of the local conditions around the v/all of a tube and would probably give some knowledge of the radial and circumferential components of heat flow at any point.

Such knowledge would represent a decided

advance towards precise assessment of temperature stresses in the metal. Having established the necessary technique, for the case of the single tube the work would then be extended to tube banks.

In this way the influence of

the tubes upon the gas flow pattern already seen in hydrodynamic tests could be examined in the light of the heat transfer results.

The apparatus used was designed specifically for this investigation.

It comprised a recirculating

wind tunnel with air heater and facilities for placing a single water-cooled tube or bank of tubes in the hot air stream.

The measurement of tube v/all temperatures

and heat transfer rates round the tube was made possible by the design of a special test tube.

This tube was used

alone in the single tube tests, but during tests on tube banks it could be substituted for any one of the ordinary tubes forming the bank.

The necessary

instrumentation was provided. 2.

Wind Tunnel:

.To provide the hot air stream a totally enclosed recirculating wind tunnel was designed and constructed as in Figs. 6 to 8 .

Air passes from the

variable speed fan along the lower.duct, through a bank of controlled electric heating coils and into a large plenum chamber.

Flow variations are damped out

in this chamber, as the air flows at low speed up through a screen of expanded metal sheets.

The air leaves at a

uniform temperature and flows through a convergent passage to the test section, then returns to the fan inlet by way of the upper ducting.

The design permits

of air speeds up to 50 ft./sec. in the unrestricted test section and air temperatures from 200°p to 600 °?

t e *»t

secTtow

10 * i • ■

; 4

Musselt j M u k b e , ! ' '

'

j '

i > • | ;; •j

'

7 !T 7' 1 T ' t t T :T ' di • 7 I

*T“ T •

w it h A n ^ u.e ;.raiR .H- ir s b . i ■ i ; i| ‘ . L . J? " V, \ f ' i f { V |S^jrt1 '."4 j I jj[j K

T : l t T .)' T! T T t :T i1T I t ri " r • TI l f l 1f 1m •'T i ! fi T. TI

ROW.

."3^?

V A R IA T IO N

OF

A p p a re n t

N J o s & Ie lt

N u /^ a e R

w ith

A k ig l e

f

art Svv. R o w T u b e

R OW

(b) Two and Three Rows of* Tubes;

The decrease in mean heat

!

transfer rate to first row tubes when two or more rows are present ; is due to the reduction in the heat transfer taking place at the

I

sides and rear of the first row tubes. The point of minimum

'i

heat transfer is nearer the rear of the tube as also is the point I j

of minimum temperature. Thus we see that the heat supplied to

|f

the front of the tube is the same as for a single tube, "but due

|

to the different air flow conditions less heat is given to the

I

rear of the tube.

j'

"

k

The higher mean value of Num for second row tubes

l i

compared with the first row

is fully explained Toy the transfer

at the upstream point which

falls to

front than in the case of a

single row of tubes. There is also a

pronounced increase towards

the rear again. The mean heat transfer^

jj

a minimum value nearer the' I jll

rate for the second row is only slightly reduced "by the addition

i

of the third row, Fig. 25(h) and (c), this small reduction "being due to the point of minimum heat transfer shifting nearer to the front of the tube.

J y irj

f The rapid fall in N u 1 from front to side of a second

i

row tube and the rapidly changing tube temperature curve is

jj

evidence of the very high rate of neat transfer to the outer

£

surface at the upstream point of this tube.

j-j *u

;l (c) Six Row Bank of Tubes: The points regarding circumferential heat transfer distribution in the previous

section apply .equally to the curves for the first three rows in

; '•j

the six row "bank. of Nu

1

In the fourth and succeeding rows the curves

to angle Fig. 31 show a similar form to the temperature

^

curves for these rows, that is, a gradual fall from a maximum

{

at 0° to a minimum at 180°.

i

In Fig. 32 are shown the approximate curves of Nu to tube angle, i.e., the true Nusselt Number for the outside

j

of the tube to angle around the tube for a tube in each of the

^ 1 l i

six rows, the Reynold’s Number "being 18300. These values are

|

obtained "by the application of equation k, page 1».1 . The values j; 2 & t were •obtained by graphical methods. A similar series of , deC2 j curves for Re equal 8330 are shown in Fig. 33• ’

-

From these curves it may be seen that the variation > in heat transfer rate around the second row tube is greater than " that around any other and the maximum value of heat input for any-^ point in the bank is obtained at the front of the second row tube.-y

The trend is for the variation in the heat transfer distribution to be smaller, the further the tube is from the front of the bank/ The heat transfer variations around a fifth row tube o f -a bank of staggered tubes as obtained by Winding and Cheny

17

are

shorn in Fig. 3* These curves indicate a rapid rise to a

" ;

maximum value of heat transfer at about 120° from the upstream point. From the results of the present tests, where the value of Nusselt Number is approximately constant over the rear part of the/

5

NMB££L-VUlti. E'ANK.

57.

fifth row of tubes, there is no indication of this peculiar variation*

58. C - CONCLUSIONS

The experimental techniques followed in this investigation have been specially devised to study heat transfer variations around a tube subjected to heating by a cross-flowing fluid, but the mean transfer coefficients, easily deduced from the results, agree well with the values established by previous investigators who were concerned only with mean values. The.correlation established between the inner and outer heat transfer variations and the temperature variation around a tube leads to a clearer impression of the local conditions around a tube in cross-flow and emphasises the magnitude of the variations to be expected. With temperature variations around the tube known, the circumferential heat flow is approximately calculable.

Probably in this work it has been somewhat

overestimated because of the use of external wall temperatures but the order and significance of the effect is clear. A noticeable feature of the results obtained is that although the general temperature level or mean temperature of the tube is affected by both the gas temperature and the Reynolds number yet the variations around the tube are dependant only on the Reynolds Number.

59

The influence of the latter on the variation of the heat transfer coefficients and also on the circumferential temperature and heat flow variations is graphically shown in Fig.34. The rear portion of a tube in cross flow appears to "be particularly responsive to the increased intensity of flow that is measured "by higher Reynolds Numbers. The curve in fig. 20 shoY/s very clearly the greater effectiveness of the rear with increasing Re. I

.This fact explains the increase in heat transfer rates from the first to the third rovi in a tube hank.

The

increased turbulence at the rear of the third row brought about by the presence of the first two rows does in fact correspond to a Reynolds Number virtually higher than the actual. It can also be deduced from fig. 20 that, for Reynolds Numbers above 40,000, the rear of the tube would become so effective that the maximum heat transfer rate would occur at the rear point instead of at the front point as with lower numbers. It is seen that the second row boiler tube failures are to a fair extent explained by the uniqueness of the second row conditions established by the results of the investigation. Reference to figs. 27 -3 2 shows that the second row tubes are

60

subjected to both the maximum rate of convective heating and the maximum circumferential temperature gradient. Hydrodynamic tests by previous workers have also established the unique nature of conditions around the second row. The investigation has shown the close relationship existing between heat transfer characteristics and the features of the flow pattern.

The following points serve to link the

two types of investigation. (a)

The vortex sheet leaves the side of a first row tube at a point nearer to the rear of the tube than in the case of a single tube;

the point of minimum heat

transfer is also nearer the rear in a (b) In the second row, the flow breakaway

front row tube. point and the

point of minimum heat transfer both take place nearer to the front of the tube than for a first row tube (c) In third and succeeding rows there is

again agreement

in the position of points of flow breakaway

and minimum

heat transfer (d)

The area at the rear of a tube, often referred to in hydrodynamic tests as the "dead-water" area, is seen, in relation to heat transfer, to be a zone of very real activity

The implications of circumferential heat flow on tube temperature stresses are obvious.

The results show that

considerable temperature stress relief will be accorded the tube at the upstream point where normally due to both convection and radiation effects the local heat input will be a maximum. The. temperature stress will also be a maximum there, but at the inside tube surface, and will obviously be decreased by any circumferential heat flow. In view of the present demand for higher allowable tube stresses and greater heat inputs much more detailed work should be carried out on tube temperature condition, in particular on the shape of the tube isothermals.

The existing

apparatus, however, will have to be very considerably altered as the thin walled tube is quite unsuited for this type of investigation.

PART

IV

-

APPENDIX

62. \

BIBLIOGRAPHY 1.

KEENAN, J.H. and KAYE, J.: Air (1945)

2.

HUGHES, J.A.; Philosophical Magazine (6 ) 31, (1916), p.118

3.

HILPERT, R.;

4. 5

Thermodynamic Properties

Forschung aug dem Gehiete (1933)> P*215

' SMALL, J,; Philosophical Magazine, Vol*19 (1935) p.251 GRIFFITH, E, and AWBERY, J.H.; Proceedings of Inst, of Mech. Eng. Vol. 125 (1933) P.319.

6.

KING, L.V.; Transactions of Royal Society (London), A.214> (1912+), p.373

7

REIHER, H.; Mitt. Forschungsarbeiten, (1925) P*269

8.

FISHENDEN, M. and SAUNDERS, O.A.: The Calculation of Heat Transmission (1932)

9.

SCHACK, A.; Industrial Heat Transfer (1933)

10.

McADAMS, W.H.; Heat Transmission, 2nd Edition (1942)

11.

SINELNIKOV, A.A. and CHASHCHIKHIN, A.B.; Zurnal Technicheskoi Fiziki, Vol.II No.9-10 (1932)

12.

KRUJILIN, G. and SCHWAB, B.* Technical Physics, U.S.S. R. Vol. 2. (1935), P.312

13.

FAGE, A. and FALKENER, V.M.; R. and M. No. 1408 April 1931

14*

SMALL, J. ; Engineering, Vol. 132 (1931) p.569

15.

KIRPITCHEV, M.V.; Communication of Leningrade PhysicalTechnical Lahoratories No. 2. (1926)

16.

LOHRISCH, W.; Mitt. Forschungsarheiten, (1929) p.322

17*

WINDING, C.C.; and CHENEY, A.J.; Industrial and Engineering Chemistry (1§48) p.1087

18.

KLEIN, V.; Archiv fur Warmewirtschaft, (1934)» P.150.

19.

DREW, T.B. and fiYAN, W.P.; American Institute of Chemical Engineers, (193^)> P«118

63

20.

KRUJILIN, G.; Technical Physics, U.S.S.R., Vol. 5*> (1938) p.289.

21.

SCHMIDT, E. and WENNER, K.; Forschung auf dem Gehiete, (1941) P.65.

22.

J0UK0USKY, V.,-KIREJEN, A., and SCHAMSCHEN, L.; Technical Physics U.S.S.R. Vol. 4, (1935) P-353

23.

HUGE, S.C.; Transactions of A.S.M.E. Vol. 59 (1937) P-573

2i+.

PIERSON, O.L.; Transactions of A.S.M.E. Vol. 59 (1937) p. 5S3 .

25.

GRIMISON, E.D.: Transactions of A.S.M.E. Vol. 59 (1937) p.583.

26.

KUZNETZGFF, N.V. and LOKSHIN, V.A.; Teplo i Sila, No.10 (1937) P.19

27.

LANDER, C.H.; Proceedings of Inst, of Mech. Eng. Vol. 148 (1942) p.81

28.

FISHENDEN, M. and SAUNDERS, O.A.; Journal of Inst, of Fuels (1945) P. 62

29.

WINDING C.C.; Industrial and Engineering Chemistry Vol.30. (1938) p. 9*4.2 .

30.

ORNATSKI, A.P.: Sovietskoye Kotlotorhostroyniye, No.2 (1940) p.48.

31.

LOKSHIN, V.A,: Teplo i Sila, No. 8 (1940) p.20.

32.

Qfl/ER, E.; The Measurement of Air Flow (1932)

33*

American Institute of Physics, Temperature, its Measurement and Control in Science and Industry (1941)

34*

TOFT, L. and McKAY, A.D.D.; Practical Mathematics (1942)

35*

Modern Developments in Fluid Dynamics, Vol II. p.631

36.

WALLIS AND WHITE,

Engineering, Vol. 146 (1938) p.603.

3

NOTATION Specific heat at constant pressure diameter emissivity prefix designating function mass flow per unit area of cross section coefficient of heat transfer between fluid and surface coefficient of convective heat transfer between fluid and surface coefficient of radiant heat transfer between fluid and surface heat transfer per unit area per unit time thermal conductivity length Nusselt Number Prandtl Number

= 4^ ~ k ke = k

Quantity of heat radius Reynolds Number time temperature, bulk temperature of fluid Tube surface temperature film temperature = i (t + t

) sm

duct wall temperature absolute temperature velocity of fluid

oC ' - angle $

- temperature rise

f

- density of fluid

j Ll

- absolute viscosity - temperature difference between fluid and surface

Suffixes other than given, i

- inside

m

- trpe mean

o

- outside

r

- by radiation

1E.STS

Table la.

/Aeam M e a t T r a n s f e r to Single Tube

\.-'2lo

-

lUB£

O.PlA., » 0-74-7"

IMICKRIESS 1 U -Q 5 3 '

Tests ?7-~2>l - Tube o.Dia.-0 -4=01"

Thickness'Oo55’ _

T

est

N

I

umber

P itot S tatic M e a d Air T e m p e r a t u r e P itot S t a t i o n

»n H2o

at

°f

2

ater

-A

(b

5

7

8

9

3-L7 2-31 3LI 3-»4 109 0-79 2-98 1-24 071 108

198 248 207 20L 291

A ir T e m p , at E n t r y 190 2 oo to T e s t S e c t i o n °F A v e r a g e Tu b e . W aul 70 LL Te m p e r a t u r e • °F Av e r a g e D u c t W all 193 190 Tem pe ra tur e °F O v e ra ll W a t e r *2*3*2 2-02 T e m p e r a t u r e R ise -0m *°F To t a l W

5

IO

u

2-40

2-11

12

2-01

lb

14

75

70

LB

398 39L 392 49L 494 490 487 544 540

82

235 284, '283 272 2>75

77

75

372

*7*

82

iU

17

18

19

20

22

21

2

b

0-71 2-57 2-28 2-08 2-37 0-59 0-L9 O L8 0-70 2-99 3-22

250 299 300 297 402 401 398 501 501 502 505 551 73

15

79

90

590 LOO 590 586 675 47L 338 291

24

25

Co 3-3L

1-1

287

-L2

2

28

2

.

}

9 JbO

bl

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194 375 376 375

201

298

202

300

!85 SL 7S 89 80 7b 70 LS L2 L3 LL 7* 70 --480 *7? 470 4L5 502 500 554 555 547 54L 54S 485 575 285 280 234 190 345 341 340 192 287 &7

87

94

3

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