ENVESTIGATION OF HEAT TRANSFER. 2
FROM A TUBE TO AN AIR STREAM '
FLOWING NORMAL TO ITS AXIS.

THESIS FOR THE DEGREE M M s. _ .' ‘
G. E. Gollwitzer * '
1934

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Thesis for Degree of 3.0.
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9 E; Gollwitzer

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193

2- H 5513

 

I wish to egress my appreciation
to Professor L. G. xiller as director of
my problem land to the, many members of the
mechanical and Electrical I'hzgh'zeering
degmtgzcnts for their assistamco in

obtainim and baililing apparatus.

96426

C 0 N T E N T 8

Introduction . . . .
Review of Relevant Data .
Mechanical Apparatul . o 0
Electrical Apparatus o .
Procedure . . . . .
Computations . . o o
Tabulation of Data and Results
Discussion of Results . .

Literature Cited 0 o o

INTRODUCTION

With the ever increasing use of warm air under forced
circulation as a means of heating homes and other buildings, the
problems of forced convection become more important. One of the
many problems is how to design the heated surface so that it will
give up the most heat with the least resistance to air flow. In
fact one might say that forced convection is a method of employ-
ing high grade energy to make a heating surface more effective.
Thus it is evident that in such a system the over-all efficiency
will include the power consumed to further heat transfer in addi-
tion to the usual factors considered in computing the over-all
efficiency of a heating system. Hence with this thought in mind,
some companies have adopted stream-lined tubing for forced con-
vection since that form of tubing does give a higher ratio of heat
transferred for the amount of resistance it offers to the flow of
air past it. It does not follow, hoaever, that that type of tube
is the best type.

In order to ascertain what effect the behavior of the fluid
around a tube has on the heat transferred from the tube, it seems
logical to start with the round tube in order to arrive at some
general theories which might help to guide in the design of the
best type. The purpose of this paper is, therefore, to find the
relative amounts of heat removed from the various portions of a

tube by a stream of air moving past it, and to prOpose reasons

for this distribution. Thus for this particular problem it is
desirable to keep all important factors as nearly constant as
possible. To this end an attempt is made to obtain a measure of
heat loss from as small a portion of the tube as is practicable
and to have the air which removes this best not be preheated by
any of the up-steam portion of the cylinder. In other words,
only a minute part of the tube is to be heated. This is at
variance with most similar investigations as will be shown.

While few investigators seemed willing to advance any reason
for their results, one does find a variety of explanations for
the increase of heat transferred by forced convection over that
by free convection. most of these explanations make use of
boundary films or layers which surround any object in a fluid.
Since the fluid used in this work is air, it will be used in this
discussion as the surrounding medium. While in still air this
boundary film is a very good heat insulator, so it is natural to
suppose that the introduction of a blast of air does in some way
remove a part of this insulation. Hence there are the following
possibilities: (1) That the increase in heat transferred by
forced convection is due to the sweeping away of the layers of
films which act as insulators. (2) That this increase is due to
the impact of the particles of air which hurl themselves into the
boundary film in exchange for heated particles which come out to
join the air stream. (5) That the increase is due to the increase

in the velocity of the outer layers until these layers are moving

at a velocity which exceeds Reynold's number for laminar flow
conditions and hence gives a thinner laminar film and less
insulation. (4) That the increase in heat transfer by forced
convection is greater than that for still air due to a combi-

nation of two or more of the above possibilities.

REVIEW OF RELEVANT DATA

Most of the investigation that pertains to round tubes has
shown only the total heat transferred and not that removed from
the various portions of the pipe. In addition to this work much
has been done toward determining the behavior of a fluid near a
solid in a fluid stream. By use of minute pitot tubes, thermo-
couples, hot wire anemometers, and the camera it has been shown
that there is no slip between the fluid film and the surface but
rather a velocity gradient beginning at zero at the surface and
increasing, finally, to the velocity of he stream as the distance
from the surface becomes large. By similar means it has been shown
that eddy currents appear behind the cylinder and seem to come first
from one side and then the other with a definite frequency depend-
ing on the value of Reynold's number (1) (2).

Elias (5) found indications of a thick laminar film at the
upwstream edge of an object exposed to fluid flow. hotographic
work done by Ray (4) indicates a relatively cool region in the film
at the downstream side of a hot wire. All of these investigations
indicate what may be expected of a flowing fluid near a solid and
give some basis on which to form explanations of he results found
in this work.

The first heat transfer distribution was proposed by King (5).
His work was theoretical and was based on the assumption that the

greatest heat transfer would be at the position on the cylinder

from which the film could be most easily renoved by the fluid
stream. This assumption proved to be incorrect, or at least inade—
quate. At about the same time Stanton (6) reported that the most
heat was given from an electrically heated platinum foil fastened
to an ebonite rod when the foil was faced upstream if the rod were
round, or downstream if the rod were square. This work, which

was carried on hy Jakeman, apparently was not designated to show
the peripheral distribution. It does indicate, however, that the
thick laminar layer at the upstream edge was much larger in the
case of the square rod than when the round rod was used.

Lohrisch (8) took advantage of the similarity of the differen-
tial equations governing diffusion and thermal conduction. He used
hydrochloric acid and phosphoric acid to remove ammonia from dampen-
ed filter paper fastened to glass models placed in the fluid stream.
He obtained the total heat transferred by covering the entire model
with the filter paper. To get the distribution, however, 12 small
strips were used and the ammonia diffused from each was measured
first with hydrochloric acid in the fluid and then with phosphoric
acid. His results indicate a high heat transfer from the leading
edge of the cylinder gradually tapering off for 60 degrees on each
side. The drOp at the sides was rapid and the lowest values were
found at about 50 degrees downstream from the sides, that is 60
degrees upstream from the trailing edge. The heat transferred
from the back was large and increased in almost direct proportion

to the increase in Reynold's number until for large values of

Reynold's number this down stream heat transfer became the maximum.

Reiher's (7) work on the cooling effect of a water cooled
pipe indicated high rates of cooling at the front gradually changing
to low rates at the downstream edge. This gradual change does not
agree with any other experimental work, however.

The work of Drew and Ryan (9) indicated a heat transfer similar
to that of Lohrisch. In this work an eSpecial effort was made to
approximate actual conditions as found in forced convection over
steam pipes. Therefore although the air striking the leading edge
was of known temperature, that striking other points had been pre-
heated by the upstream portions and the resulting temperature dif—
ferential between solid and gas was variable. The reason these results
approach those of Lorisch is, of course, that Lorisch obtained a
similar effect due to the law of mass action. While both of these
experiments show fine corresgonding results for their purpose, they
do not give the downstream portions of the tube a fair chance to show
their ability as heat dissipaters. Hence they give no clue as to
the probable optimum shape of a convector tube.

The most recent work seems to be that of Small (10). This
work most nearly parallels the problem at hand in that it consisted
in a relatively small heating element. The apparatus consisted of a
wooden tube containing an electric heating element placed in a slot
with a piece of fibre covering the element. The fibre contained two
thermocouples at different distances from the center along a radius.

The wood and fibre were turned down together to give a smooth round

surface. Since the conductivity of the fibre was known, as was

the distance between the thermocouples, then the temperatures as
measured by the thermocouples gave the data necessary to compute

the heat flux through the fibre. As the fibre was of appreciable
size the desired effect of heat given off at the measuring point
only was not entirely realized since the air was slightly heated

by the up-stream portion of the fibre. Also this method assumes
radial flow‘of heat since the thermocouples are located radially.

In addition to these objections there is the difficulty of accurate-
ly locating the thermocouples. But in Spite of these objections this
method remains a nice way of handling the problem since the percent
error is probably small.

The results obtained in this expcri ent were comparable with
those advanced in the present paper. The heat transferred was the
greatest at angles between 45 degrees and 60 degrees away from the
leading edge and slightly lower at the leading edge. He records
his lowest points directly at the sides with an increase again at
the down stream portions. {is minimum rate of heat transmission
was from .3 to .4 times that of his maximum.

While much of the above mentioned data seems contradictory
it will be shown that when the particular conditions are considered

in addition to the data obtained reasonable deductions can be made.

MECHANICAL APPARATUS

-10..

The first requisite to an experiment in forced convection
is, of course, a steady, controllable supply of air so confined
that it can be measured readily. The blowers available were, for
purposes of Speed variation, equipped with direct current motors.
Since there were many large direct current motors nearby which
were run intermittently, the direct current supply was of variable
voltage and would, therefore, produce a variable fan and air speed.
This being undesirable it was thought better to use an alternating
current motor at a constant speed and to vary the size of the inlet.
For lack of a synchronous motor a large induction motor was used at
a small fraction of its rated load thus giving a constant fan speed
of 1200 revolutions per minute. Special gates were built for the
purpose of varying the size of fan inlet. The fan was of the for-
ward curved blade centrifugal type with a 14-inch round connection
at the exhaust side.

The wind tunnel was a 14-inch round pipe in 50-inch sections.
The first section was filled with 2-inch pipes for the purpose of
straightening the turbulence set up by the fan and thus assuring as
nearly stream lined flow as possible in the tunnel. Since the
general engineering rule is that air will flow normally past a
point 10 pipe diameters down stream from an irregularity, it seemed
reasonable that the air issuing from 2-inch pipes 20 inches long
would be flowing more nearly stream lined than would be the case if

20 inches of open 14-inch pipe were used. In addition to this

precaution, lO diameters of the 14-inch pipe were passed before
the air arrived at the test section of the tunnel. The entire
pipe was kept straight by use of tight wires stretched one-half
inch from it which were used to check the alignment. This preven-
ted wave formation due to crooked pipe joints. A canvass con-
nection was used near the blower to dampen vibration in the
tunnel.

The test section used was merely a short piece of 14-inch
pipe equipped with machined castings bolted to top and bottom for -
the purpose of supporting the test element to be studied. A draw-
ing of this section complete with the test element is shown on
plate 2, entitled "Wind Tunnel Assembly". The bottom view is a
view as seen from the blower. The two castings bolted to the top
and bottom are identical except that the bottom one has holes
drilled and tapped for adjustable legs and the t0p one has a small
scratch indicating the upstream direction. Both castings are sup-
plied vith reamed holes through which the element is inserted. The
element is so designed that it can be easily removed by merely
disconnecting one wire and lifting it from the tunnel.

A cast iron dial was carefully machined and marked at five
degree intervals over half the circumference by use of a dividing
head. The dial is marked I'D" in the upper view of plate 2 and the
zero position is marked '0”. For simplicity graduations are shown
for 60 degrees only instead of 5 degrees as was the actual case.

The dial measured 7 inches. It was made large so that the element

- 12 -

could be accurately set in position.

-15...

ELECTRICAL APPARATUS

The test element referred to is shown in greater detail on
plate 5 called "Details of Heating Element“. In the full view
shown at the left is a textolite tube with an 8-inch strip of
metal exposed. The textolite was chosen because it had a low
conductivity of known value. The metal is a part of a number 30
hytemco wire. This metal was selected because it has a high tem-
perature coefficient of electrical resistance coupled with a reason-
ably high electrical resistance and non-corrosive properties at
ordinary temperatures. It is a high nickel alloy steel. In the
cross section view at the leftthis wire may be seen to pass to the
interior of the tube and to binding posts at the ends of the tube.
Potential leads are placed to measure the potential drOp over a
three-inch section at the middle of the tunnel. The exposed wire
is continued two and one-half inches each side of the test section
in order to minimize end losses from that section. The potential
leads are fastened to bushings on the Opposite side of the tube,
these bu hinge in turn being connected to binding posts at the top
of the element. These bushings were used merely to facilitate the
assembly of the element. The bottom binding post, partially shown
in the cross section view on plate 5, is faced downward so it will
not interfere with the removal of the element from the tunnel.

The exposed metal strip referred to was made by cementing a piece

of number 50 hytemco wire in a small V groove on the surface of

-15..

the cylinder. The wire was then carefully honed down flush with
the surface of the tcxtolite, the amount honed off being computed
by the change of electrical resistance between potential leads.

Plate 1, the wiring diagram, will be used to show the set up
of the apparatus.

The large rectangle marked "potentiometer" includes all equip-
ment used in a potentiometer circuit and will not be discussed
here. The potentiometer itself is a Leeds & Northrop Student
potentiometer. a sensitive portable mirror type galvanometer is
used. It will be sufficnent to say that a potential applied at
the two connections shown may be readily measured by the instrument.

The heat supplying circuit starts at the storage batteries,
passes through the variable resistances, through the test element,
the fixed resistances and back to the battery. The current flow
in this circuit is controlled by the variable resistances which
are placed in parallel to allow minute adjustments.

By using switch 8 it is possible to measure the potential
drop across either the fixed resistance or the element itself.

It will be well at this point to consider the relationship between
these two.

The element is made of hytemco wire which has the preperty of
changing its resistance appreciably with small changes of tempera-
ture. The relation between temperature and resistance is known in
this case so it may'be shown that a piece of this wire having a

resistance of .4008 ohms at 68 degrees F. will have a resistance

of .4555 ohms at 100.5 degrees F. It will be readily seen that
by using a fixed resistance of .4555 ohms in series with the test
element, the element will be at 100.5 degrees F. when the poten-
tial drOp across the fixed resistance is the same as that across
the element. This condition may be brought about by adjustment
of the current flowing in the circuit and hence the heat supplied
to the element. Furthermore, the value of this potential drop
indicates both the amount of current flowing and the heat given
up by that portion of the element lying between the two potential
leads. The fiied resistance is made of advance wire, the resistance
of which is very nearly constant over the range of temperatures

used. It is immersed in an oil bath.

-17..

PROCEDURE

For each run the setting of tne air inlet gate was mece at
approximately the desired value by use of a blade t;pe aneuometer.
This was, then, the air veiocit, used for the run and its actual
value was determined acc “ateiy b; use of a pitot tube traverse
vith the fihalen gage. Other factors such as hunidity, barometric
pressure, and tenderetures were noted to be used in con uting the.

I

actual air velocit, and the Vaiue of keynolu's number.

with the air suppl; functioning prsaerly the elrncnt was
turned to measure uq—strean heat transfer. The Lot ntial drop
across the three-inch section was pace to balance that across
the fixed resistance by acjusting the current in the circuit to
the proper value. This, 0: course, indicated that the 'ire in the
element was at 100.5 degrees F. and the element was allowed a fee
minutes to obtain equilibrium. Fhen the aspe*.tns hid attained
a constant con itLon, readings were taken. at each yosition
(i.e. 0, 5, 10, 15, 23 degrees etc. from the iosition directly us-
stream) the potential drop across the three-inch section was me e
to baiance that across the fired resistance flat the value in volts
of this drOp was recorded.

P sierically throu_hout the run the tangerdture, huhimity,
and at ospheric pressure were noted.

Thirty-seven reacings were taken for egch air velocity and

seven velocities were used ranging iron 575 feet p.r minute to 1330

- 15 -

feet per minute. The 578 feet per minute run was in the nature of

a preliminary run and was therefore not plotted.

- ho _

COMPUTATIONS

-21...

 

The first computations were made in order to determine the
length of advance wire necessary to give a fixed resistance equal
to the resistance of the element when at about 100 degrees F.

The resistance of the test section was found to be .4008 ohms
at 68 degrees by comparing it with the resistance of a standard
ohm in a low current series circuit.

Data on hytenco shoes that a 55 percent increase in electrical
'resistance corresponds to a temperature rise of 152 degrees F. in
the vicinity of 100 degrees F. Hence an increase of 52 degrees P.
will raise the resistance of the element to .4008 x‘—%§§ x .55
or about .455 ohms.

Since the resistance of number 24 advance wire is given as
.727? ohms per foot then the number of inches of this wire neces-
sary to give .455 ohms is f%%%?»x 12 or 7.18 inches.

when a resistance reasonably near this was made complete with
soldered potential lease, its resistance was found by comparison
with the standard ohm to be .4555. This was found to be an 8.6
percent rise above .4008 so that the hytemco wire will be raised
g-g-é x 132 or 52.45 degrees to give it a resistance of .4555 ohms.
As this is beyond the range of accuracy of the thermometers used,
however, 100.5 degrees F. is the value used in subsequent calcu-
lations.

In order to determine the temperature of the air correSponding

to each reading taken, the temperatures as recorded were plotted

as ordinates against positions of the element as abscissa. An
average curve drawn through these points gave a graph from which
a value for the air stream temperature at any of the thirty-seven
points could be obtained.

Computations for the exact air velocity were made in the
customary way using the formula V equals l/-§—§_E_ in which h
is the head measured in feet of the fluid being used (air in this
case), and 2 g is 64.4. For a more detailed discussion of such
computations, see (11) or any book on air flow and its measure-
ments. The velocity obtained as above divided by the weight of
one cubic foot of air gives the number of pounce of air passing
one square foot of area per second. This is the value often desig-
nated as G in the formula Re =‘%%- for Reynold's number. Values
of Re were also found in each case b, substituting 1/12 for d and
the absolute viscosity of air forat. The results for these
standard computations are shown on the data sheets.

The actual heat transfer computations while simple were not
as usual as the above and will therefore be examined in slightly
more detail. Fran Ohm's law I 3 E/R and watts = 12R, it is seen
that watts also equal Eg/R. Since all measurements have been
made in volts and since the resistance is held constant at .4555,

the heat loss in each case will be

(volts drOp)2 x [factor to change to B;§gU./ hourl .
.4555 Temperature difference

This gives the total heat loss in B.T.U. per hour per degree

difference in temperature. These computations were made by

logarithms. The equation then became Leg B.T.U. : 2 Log voltage

drop plus Log constant - Log temperature difference. The results
of these computations are shown on the following sheets and are
plotted on plates four and five.

The data as computed was merely relative and while valuable
for the purposes of this paper it was thought advisable to so ar-
range it that it might be compared with work of other investiga-
tors as a check. To do this curves were drawn showing the heat
loss for each setting of the element over the range of air veloci-
ties used. Extra polating these to the zero air speed line gave
a point indicating the constant heat transferred independent of
position. Values resulting when this correction was applied

Checked reasonably close to the recent work of Small (10).

f"
at ,1", ‘1. t

TABULATION OF DATA END RESULTS

Air Velocity 3 600 ft. per min. or 45.05 lbs. per min. per sq. ft.

Reynold's number 3 5,100

Column-A.= Position of cylinder in degrees from front or back.

Column B 8 Potential drop in volts.
Column 0 8 Temperature difference in degrees F.

Column D 3 Heat loss per hour per degree difference in B. T. U.

A

0

5
10
15
20
25
50
55
40
45
50
55

60

70
75

85

90

Front

B
.5066
.5167
.5250
.5555
.5421
.5465

.5525

rrrn
. .."K:‘b'—v .

.5585
.5509

.5599

C
27.9
27..
27.7
27.7
27.6
27.5
27.4
27.5
27.5
27.2
27.1
27.0
27.0
26.9
26.8
26.7
26.6
26.6

26.5

D
.0785?
.00152
.0847?
.08755
.09081
.09252
.09491
.09699
.09800
.09914
.10005
.10066
.09991
.03872
.0964?
.08501
.08871
.06271

.07782

B
.4805
.4808
.4791
.4776
.4750

.4750.

.4700
.4660
.4645
.4625
.4590
.4591

.4595

Back

c
25.1
25.1
25.2
25.5
25.4
25.5
25.5
25.6
25.7
25.8
25.9
25.9
26.0
26.1

26.2

D
.07856
.07846
.07760
.07681
.07571
.0745?
.07580
.0722?
.07152
.07065
.06914
.06955
.06918
.06951
.06965
.07125

.07262

.07561

Air Velocity = 800 ft. per min. or 56.5 lbs. per min. per sq. ft.

10
15

25
50
55
40
45
50
55
60
65
70
75
80
85

90

.5556
.542?
.5555

.5645

Front

C
50.6
50.5
50.4

50.5

50.5.

50.2
5051
50.0

50.0

D
.07942
.0822?
.08495
.08955
.09209
.09464
.09540
.09845
.09959
.10070
.10104
.10101

.1010
.09954
.09661
.09250
.08722
.08014

.07491

I
TO

0

J.)

' .5069

.5065
.5057
.5055
.5018
.4990
.4955
.4912
.4885
.4844
.4824
.4811
.4811

.4806

Back

27.8
27.9
28.0
28.1
28.1
28.2
28.5

28.4

28.5

28.7
28.8
28.9
29.0
29.0

29.1

D
.07884
.07854
.07781
.07680
.07654
.07522 V
.07591
.07258
.07153
.07014
.06952
.06871
.06871
.06852
.oseve
.06959
.0715?

.07576

Air Velocity = 1000 ft. per min. or 70.2 lbs. per min. per sq. ft.

10
15

2O

50
55
40
45
50
55
60
65
70
75
80

85

.5596
.5478
.560?
.5714
.5811
.5907
.5975
.6015
.6050
.6100
.6115
.6098
.6086
.6055
.5942
.5800
.5597
.5565

.5186

Front

D

.08891
.09196
.09669
.1005
.1042
.1077
.1105
.1120
.1154
.1155
.1158
.1152
.1147
.1128
.1092
.1042
.09705
.08714

.08552

.5545
.5540
.5540
.5288
.5250
.5205
.5164
.510?
.5060
.5052
.5000
.4968
.4959
.4954
.4964
.4984
.5022

.5089

Back

D
.08851
.08854
.08854
.08665
.08559
.08412
.08261
.08080
.07952
.07844
107745
.07646
.07618
.07618
.07654
.07695
.07815

.07966

Air Velocity 8 1200 ft. per min. or 80.8 lbs. per min. per sq. ft.

10
15

20

50
55
40
45
50
55
60
65
70
75

80

.5075
.5588
.5705
.5815
.5915
.5998
.6065
.6118
.6161
.6195
.6215
.6210
.6186
.6158
.6047
.5891
.5661
.5402

.5211

Front
C
27.9

27.8

D
.07859
.09566
.10000
.1051
.1096
.1155
.1165

.1190

.1194
.1155
.1050
.09599

.08952

Back

D
.10000
.09394
.09920
.09804
.09652
.09441
.09267
.09058
.08865
.08690
.0855?
.08480
.08455
.08425
.08585
.08410
.08484

.08645

Air Velocity = 1600 ft. per min. or 107.4 lbs. per min. per sq. ft.

50
55
40
45
50
55
60
65
70
75
80
85

90

B
.548
.5570

.5700

Front

25.2

25.1'

25.0

.1026

.1070

.1186
.1258
.1277
.1511
.1555
.1576
.1401
.1412
.1408
.1412

.1592

.1280
.1080

.1064

.09992

- 29 -

Back

.1184
.1172
.1161
.1151
.1150
.1120
.1078
.1054
.1027
.09972
.09779
.09725
.09645
.09546
.09421
.09568
.09401

.09510

Air Velocity = 2000 ft. per min. or 150.5 153. per min. per sq. ft.

10
15
20

25

45
50
55

60

80
85

90

.5649
.5752

.5906

.6165
. 251
.6520
.6557
.6400
.6425
.6416
.6456
.6581
.6520
.6200
.5985

.5373

Front

C
20.2
20.1
20.0
19.9
19.8
19.7
19.7
19.6
19.5
19.4
19.5
19.2
19.2
19.1
19.0

19.0

.51?2
.5066
.5056
.5020
.4953
.5000
.5015

.5061

Back

Air Velocity = 400 ft. per min. or 26.05 lbs.

10
15
20

25

50

55
40
45

50

60
65
70
75
80
85

90

Front

B
.7515
.7604
.7719
.7854
.7950
.7997
.8052
.8154
.8167
.8158
.8160
.8160
.8086

.8077

()1
H

.80'
.7921
.7724
.7545

.7554

D
.07674
.07856
.08096
.08559
.08544
.08689

.08809

’.08989

.09065
.09045
.09047
.09047
.08884
.08864
.08765
.08525
.08106
.07755

.07548

1 51 -

B
.6965
.6965
.6962
.6945
.6952
.6911
.6885

.6866

.6840

.6813
.6802

.6820

Back

er min. per sq. ft.

D
.06576
.06576
.06586
.06550
.06529
.06489
.0645?
.06405
.0655?
.06516
.0628?
.06519
.06298
.06415
.06518
.06685
.06824

.07014

DISCUSSION OF RESULTS

-52..

For convenience consider first what might naturally be ex-
pected to occur when an air stream flows past a round tube. The
air must, of course, be parted by the tube yet it is common
knowledge that a sharp point at the leading edge is not necessary
or even desirable for stream lined conditions. The reason for
this is, as has been shown by many investigators (5) (6) (10),
that a relatively stationary film of air exists in front of the
tube to form an effective point and to part the approaching air.
This film is held in place by the force of the moving air, or
more correctly, by the radial component of that force. In the
straight up—strean position this force is entirely radial but as
one considers points around toward the side it is seen that the
tangential component becomes increasingly large and removes the
film rather than holding it in place. This effect will be most
pronounced at the side. Thus did King (5) predict high rates of
heat transfer at the sides.

Continuing back from the side of the tube there is a low
pressure area in which the velocities of the outer film layers are
still too great to allow excessive turbulence (12). This is the
condition which is maintained as nearly as possible by the gradual
curve at the back of a strut or other stream lined object. The
purpose in those cases is to maintain a low pressure area with

resulting reduction in skin friction while at the same time pre-

venting eddy current I by not allowing the pressure to become too
low. In the case of a round tube, however, this condition does not
exist for a great distance back of the side before turbulence is
set up due to the low velocity of the films compared to the high
velocity of the stream and the resulting low pressure behind the
tube. These eddy currents provide a condition in which the air
actually strikes the back of the tube, or more preperly, the film
which surrounds it. Also, it has been shown that (2) the eddys
come alternately from either side of the tube and it is reasonable
to believe that they have a scouring effect capable of removing
outer layers of the air film. Finally the picture is a tube
blanketed in front by a thick relatively stationary film of air
which becomes thinner at the sides. This film probably becomes
thinnest at the sides where the total force is tangential to the
surface but gets large again downstream slightly Just before eddy
currents begin to effect it. The downstream portion is probably
scoured by eddy currents especially at high velocities and the
film there no doubt becomes quite thin at those velocities.

With this in mind, an inspection of the heat transfer distri-
bution curves on plates 4 and 5 will show that the maximum heat
transfer rates do not coincide with the points of smallest film
thickness. This surprised early investigators who eXpected a heat
distribution similar to that predicted by King.

It follows, therefore, that if present ideas about film

distribution are correct, and they'have been established by a

number of methods and for a variety of purposes, there is some
factor entering into the heat transfer other than just that of the
film thickness itself. Also, it may be said that since the largest
heat transfer does not occur at the direct up-stream portion of

the tube, the transfer is not totally dependent upon the impact
and exchange of particles striking the tube. Thus the first two
possibilities mentioned in the introduction must be abandoned.

The third possibility, namely, that the increase in velocity
changes laminar films to turbulent ones allowing greater heat
transfer, cannot possibly explain the effect noted since this
would imply higher heat transfer at the sides than is the case.
Whether the films are transferred from laminar to turbulent or
are entirely swept away is beside the point. Since there are
distinct evidences of a turbulent layer, it is probably true that
an increase in the velocity of air over a pipe results in decreas-
ing the thickness of the laminar film by moving the turbulent
layer nearer to the pipe. Keck (15), by use of sensitive apparatus
shown that these transitions, whatever they are, appear to take
. place periodically with increases of air velocity as though the
ultimate strength of the adjacent film bonds was being exceeded at
these periods. Obviously, from this data, the process is not a
gradual one.

From the above discussion it seems logical to conclude that
the rate of heat transfer in this case is a function of

each of the components of the air stream force against the tube.

The tangential component tends to tear away (or render less effective
by turbulent movement) the insulating film of air surrounding the
tube. The radial component tends to bring the moving air in more
intimate contact with the air of the film, thus improving heat
transfer by conduction or by an actual exchange of cold particles
for warm ones.

That this eXplanation satisfies the actual conditions as
shown by the curves on plates 4 and 5 may be seen. The up-stream
portion is not affected by a large enough tangential component
and hence the transfer is poor due to the thick air layer. The
interval between 45 and 60 degrees from this point is high in heat
transfer due to the favorable combination of the two forces and the
amount transferred varies only slightly over that range where one
force is replacing the other. From the 60 degree point to the side
position the rate of heat transfer drOps rapidly due to the rapid
decrease in the value of the cosine of angles near 90 degrees, hence
the radial component becomes small. The portion Just back of the
side position has the lowest rate of heat transfer since the radial
force actually becomes Opposite in sense. This is the condition
present at the back of the streamlined tube and accounts for the
smaller heat of streamlined tubing compared with round tubes of the
same surface area. Back of this point turbulence is set up and
while this portion cannot be readily analyzed it is probable that
the radial and tangential forces again come into play as the eddy

currents strike the back.

Without further reviewing the data of other investigators
it will be seen that this explanation is in keeping with all data
except, possibly, that of Reiher (7) on the cooling of air which
he himself finds puzzling and explains by supposing eddy currents
in the cooling water inside the pipe used. The works of Drew
and Ryan or of Lohrisch show maximum heat transfer at the up-stream
center, but since isothermal conditions or its equivalent were
approached in each case, the temperature differential was variable
as previously xplained and one would not expect the maximum values
as shown in this paper.

Unfortunately these results show that any attempt to stream-
line a tube used as a convector will result in reducing the heat
transfer rate on the back portion. On the other hand, stream-
lining is desirable since it reduces the wind resistance to heat
transfer ratio. A more Specialized study would show to what extent
streamlining is practicable. A more pronising possibility is that
of replacing the laminar film at the front of the tube with the
tube itself by proper shaping. This should result in higher heat

transfer rates without appreciable increases in wind resistance.

-38..

(1)

(2)

(5)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

LITERATURE CITED

Relf

Philosophical Magazine, Volume 42, Page 175, 1921.
Half and Simmons

Ibid, Volume 49, Page 509, 1925.
Elias, Z.

Mathematical Mechanics, Volume 9, page 454, 1929.
Mathematical Mechanics, Volume 10, page 1, 1950.

Ray

Proceedings, Indian Association for the Cultivation
of Science, Volume 6, page 95, 1920-21.

King, L. v.

Transactions of the Royal Society (London), A 214,
Page 575, 1914.

Stanton, T. E.

Technical Report of the Advisory Committee on

Aeronautics, Great Britain, 1912-15, Page 45.
Reiher

Forschungserbeiten, Page 269, 1925 (Reprint).
Lohrisch

Forschungsarbeiten, Page 522, 1929 (Reprint).
Drew and Ryan

Industrial and Engineering Chemistry, Volume 25,
Page 945.

Small, J 0

Engineering (London), Volume 132, Page 569, 1952.

(ll) Ower, E.
Measurement of Air Flow, Page 55.
(12) Stalker, E. A.
Principles of Flight, Pages 44 and 112.
(15) Keck, W. G.
Investigation of the Heat conductivity of the

Boundary Film Surrounding Hot Bodies. Thesis
at Michigan State College. Presented 1935.

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—-——.- ————..—__

DISTRIBUTION OF HEAT TRANSFERRED
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PLATE 4

 

DISTRIBUTION OF HEAT TRANSFERRED
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PLATE 5

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