No. 3128: July 22, 1931 
HEAT TRANSFER IN A COMMERCIAL 
HEAT EXCHANGER 

By 
B. E. SHORT and M.M.HELLER 
Eneineering Research Series No. 29 
Bureau of Engineering Researc.h 
Division of the Conservation and Development of the Natural Resources of Texas 

PUBLISHED BY 
THE UNIVERSITY OF TEXAS 
AUSTIN 

Publications of The University of Texas 
Publications Committees: 
GENERAL: 
FREDERIC DUNCALF MRs. C. M. PERRY 
J. F. DOBIE C.H. SLOVER 
J. L. HENDERSON G. W. STUMBERG 
H.J. MULLER A. P. WINSTON 
OFFICIAL: 
E. J. MATHEWS KILLIS CAMPBELL 
C. F. ARROWOOD J. A. FITZGERALD 
E. C. H. BANTEL BRYANT SMITH 
The University publishes bulletins four times a month, so numbered that the first two digits of the number show the year of issue and the last two the position in the yearly series. (For example, No. 3101 is the first bulletin of the year 1931.) These bulletins comprise the official publica­tions of the University, publications on humanistic and scientific subjects, and bulletins issued from time to time by various divisions of the University. The following bureaus and divisions distribute bulletins issued by them; communications concerning bulletins in these :fields should be addressed to The University of Texas, Austin, Texas, care of the bureau or division issuing the bulletin : Bureau of Business Research, Bureau of Economic Geology, Bureau of Engineering Research, Interscholastic League Bureau, and Division of Extension. Communications concerning all other publications of the University should be addressed to University Publications, The University of Texas, Austin. 
Additional copies of this publication may be procured from the 
Bureau of Engineering Research, The University 
of Texas, Austin, Texas 

THE UNIVERSITY OF TEXAS PRESS 
..... 

No. 3128: July 22, 1931 
HEAT TRANSFER IN A COMMERCIAL 
HEAT EXCHANGER 

By 
B. E. SHORT 
and 
M. M. HELLER 

Ensineerins Research Series No. 29 
Bureau of Enslneering Researab 
Division of the Conservation and Development of the Natural Resources 

of Texas 

PUBLISHED BY THE UNIVERSITY FOUR TIM BS A MONTH, AND ENTERED AS 
SECOND·CLASS MATTER AT THE POSTOFPICE AT AUSTIN, TEXAS, 
UNDER THB ACT OP AUGUST 24, 1912 

The bene6ta of education and of useful knowledge, generally diffused through a community, are essential to the preservation of a free govern· ment. 
Sam Houston 
Cultivated mind ia the guardian renius of Democracy, and while guided and controlled by virtue, the noblest attribute of man. It is the only dictator that freemen acknowledge, and the only security which freemen desire. 
Mirabeau B. Lamar 
CONTENTS 
PAGE Introduction -------------------------------------------------------------------------------------5 Apparatus and Method ---------------------------------------------------------------------8 Method of Computing Results___________________________________________________________ 14 
Tabulated Data and Results____________________________________________________________ 17 Discussion of Results_______________________________________________________________________ 2 6 Comparison with Results of Morris and Whitman____________________ 27 Comparison with Results of McAdams and Frost________________________ 27 Experimental Heat Transfer Equation_____________________________________ 34 Diameter of Shell Passage_____________________________________________________ 35 Effect of Length of Path of Flow_______________________________________________ 37 
Effect of Heat Short-circuiting through Metal of Shell and Baffie ---------------------------------------------------------------------------------------38 Fluid Friction in Single-Pass Flow versus Fluid Friction in Doub le-Pass Flow-------------------------------------------------------------------41 Experimental Pressure-Drop Equations_____________________________________ 43 Relation of Heat Transfer Rate to Pressure-Drop____________________ 44 
Cone1usions ---------------------------------------------------------------------------------------4 7 Bibliography ---------------------------------------------------------------------------------48 

HEAT TRANSFER IN A COMMERCIAL 
HEAT EXCHANGER 

I. INTRODUCTION 
·Scope.-This bulletin presents the results of tests made on a horizontal shell-and-tube type heat exchanger having a heating surface of about twenty square feet. Heated fluids with viscosities ranging from 0.44 to 40 centipoises were pumped through the shell; water in the tubes served as the cooling medium. The overall coefficient of heat transfer was determined for several velocities of each fluid while the velocity of the cooling water remained constant. 
Purpose.-The investigation was not undertaken for the purpose of establishing new theories or equations, but to determine the practicability of correlating the results of tests on a commercial (multiple-tube) heat exchanger with results obtained from laboratory data on single-tube experi­mental exchangers and, also, to establish a basis by which a rational analysis could be made of data obtained from tests on any heat exchanger. 
Acknowledgments.-The tests were made in the labora­tory of the Department of Mechanical Engineering in con­junction with the Bureau of Engineering Research, The University of Texas, Austin, Texas. 
The authors are indebted to Professors H. E. Degler, A. Romberg, E. P. Schoch, and A. Vallance for their valuable suggestions relative to the preparation of the manuscript of this bulletin. 
Theoretical considerations.-It is generally recognized that the rate of heat transfer from a fluid to the wall of the containing vessel varies: 
directly with 
(1) 
the velocity 

(2) 
the heat capacity (specific heat) 

(3) 
the heat conductivity 

(
4) the density 
and inversely with 


(1) 
the absolute viscosity of the fluid 

(2) 
the diameter of the containing vessel. 


This theory, based on mathematical dimensional analysis, has been substantiated by physical tests on laboratory appa­ratus. Newton's law implies that 
-Q 
= U A T__ _
___ _
________ _
_____ _
_______________ _
__ _ 
(1) t 
where 
Q =quantity of heat transferred in the time-(t) 
U = constant for given conditions 
A = transfer surface 
T =average difference in temperature between 
the two substances. 
The constant U is the "coefficient of heat transfer" which permits all of the variables named in the first paragraph to be considered in Newton's equation. This constant is also governed by the multiplicity of mediums through which the heat must flow. By maintaining constant conditions on one side of the containing wall, it is possible to show the variation in the "overall coefficient" with the different factors. 
Summary.-In this bulletin the "overall coefficient" is shown to be a function of the velocity and viscosity and, since the friction loss is a function of these variables, the "overall coefficient" is shown to be a function of the pres­sure drop. The relation of the rate of heat transfer to the power required to move the fluid along the transfer surface is the fundamental factor in the design of such apparatus. 
The effect of increasing the diameter of the passage and 
the effect of decreasing the length of the path through the 
exchanger is shown by the relation of the transfer rates for 
"single-pass" and "double-pass" flow for equal linear shell 
fluid velocities. 
Shell fluid velocities between 0.30 and 5.5 feet per second were used in these tests, while the viscosities of the fluids ranged from 0.44 to 40 centipoises. 
The resulting "overall coefficients" were approximately ten times as great for the least viscous fluid as for the most highly viscous fluid for the same linear velocity. 
II. APPARATUS AND METHOD 
The various tests were performed on a commercial hori­zontal shell-and-tube type heat exchanger having a heating surface of about twenty square feet. Figure 1 shows a diagrammatic sketch of the exchanger. 
Description of exchanger.-A cylindrical one-quarter inch steel shell having an inside diameter of six inches encloses a bundle of thirty % -inch tubes which are five feet one inch in length. The tubes terminate in tube sheets at each end. One tube sheet is held rigidly to the shell while the other terminates in what is known as a floating head. 
The flow of cooling medium through the tubes is divided in two passes of fifteen tubes each by the baffle K. The flow of fluid through the shell is divided by a longitudinal baffle J at the center of the shell. To this longitudinal baffle are fastened narrow rings or semi-circular baffles H; these rings decrease the effective cross-sectional area of the shell fluid passage, and result in a flow practically parallel to the length of the tubes. 
Explanation of fiow of fiuids.-The piping, Fig. 2, to the two-inch inlet and outlet nozzles of the shell passage was so arranged as to allow flow to take place in what is termed in this bulletin as "single-pass" or "double-pass." For double-pass flow the fluid entered the shell at nozzle E and was discharged at nozzle D. For the single-pass flow the fluid was allowed to enter the shell through nozzles E and D simultaneously and was discharged from the shell through a single nozzle B. It may be noted that the cross­sectional area of the shell passage in single-pass was twice that for double-pass flow, but the length of the path of flow of the shell fluid in single-pass was but one-half that for the double-pass arrangement. 
/j 0 F 

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7-Lo11~ilvd!/Ja/J)Je/I fividBa/'t7e. 

K.-Lom;Jfvofi?o//Vbefiv1i:IBaffle. \0 
FIG. 1. SKETCH OF HEAT EXCHANGER 

FIG. 2. LAYOUT OF EQUIPMENT AND APPARATUS FOR HEAT 
EXCHANGER TEST 

TABLE I. HEAT EXCHANGER DATA 
Size__________________________
______________ 20.5 square feet Type_______
________________________________ Shell and tube, horizontal 
Manufactured by__________________Westinghouse Electric and Manufac­turing Company, Pittsburgh, Penn­sylvania 
SHELL 
Diameter inside____________________ 6 inches MateriaL__________________________
___Steel 
Thickness_______________________________ 14 inch Number-major passes______ One or two Inlet nozzles__________________________Two 2-inch diameter Outlet nozzles__________
____________ Two 2-inch diameter 
Working pressure____________ _____l50 pounds per square inch 
TUBE CHANNEL 
MateriaL______________
__________
_ 
Steel 
Inlet nozzle___
___________
___________ One 11h-inch diameter 
Outlet nozzle____
______
___
_______
_One 11h-inch diameter 
Working pressure___
_
_________lOO pounds per square inch 

TUBE BUNDLE 
Diameter_____________ 
_
___
___ 51h inches 
Size of tubes_________
___________ 
_ 
% inch (O.D.) 
Tube thickness_____
____
_
________ 0.049 inch-No. 18 B.W.G. 
Tube metaL_________ 
_
__________ 
,Admiralty 
Length of tube__________
_
_
____ 
5 feet 1 inch 
Number of tubes_
______
_______
_30 
Number of passes____
________ 2 
Tubes per pass _____ 
_
___ 
_ 
15 

Tube pitch ----------------------------· %, inch 
Tube sheets.___
_________________
_ 
1h inch-steel 
Longitudinal baffie__
____
_
____ One 3/ 32 inch-steel 
Half-circle baffles__
_____ 
_ 
·----Thirty 3/ 32 inch-steel 
The cooling water entered the exchanger through nozzle F and was discharged through nozzle G. This resulted in counter-flow arrangement of the fluids passing through the exchanger when double-pass flow existed in the shell. In the single-pass arrangement counter-flow existed in one pass of the exchanger and parallel flow in the other. The two possible paths of the shell fluid through the exchanger may be traced by referring to Fig. 2. 
The cooling water was circulated by city water pressure through the tubes of the exchanger to the weighing tanks and then discharged to waste. 
The shell fluid to be cooled was circulated by a centrifugal pump belt driven by a direct-current motor. The fluid passed into the pump from the pump receiver and dis­charged into the line leading to a vertical closed heater, where it was heated to the desired temperature before entering the exchanger. From the heater the fluid passed through the exchanger and then back again to the pump receiver to complete the shell fluid cycle. 
Quantity measurements.-In the first series of tests the quantity of shell fluid passing through the exchanger was determined by weighing the fluid in tanks after it had 
passed through the exchanger. In order to facilitate a greater range of quantities of flow, the shell fluid was metered by use of an orifice in the line as shown in Fig. 2. The orifice was calibrated in place by direct weighing of the fluid passing through the orifice at different orifice pres­sure drops. The calibration curve for the orifice is shown by Fig. 3. 
FluUi velocity regulation.-The velocity of the shell fluid passing through the exchanger was controlled by varying the speed of the pump and by adjusting the valves which 

FIG. 3. ORIFICE CALIBRATION CURVE 
controlled the discharge from the exchanger. The velocity of the tube fluid was varied by regulating the inlet valve V 5 to the tube passage. 
Temperature measurements.-The temperatures were measured by long-stem mercurial thermometers which were read at least every five minutes. The thermometer wells, the positions of which are indicated on Fig. 2, were placed in ells or tees so as to assure a condition of turbulence about the stem of the wells. 
Pressure measurements.-The pressure drop across a single-pass or double-pass of the exchanger and across the orifice used for metering the shell fluid was measured by the use of mercury-filled U-tube manometers as indicated by Fig. 2. The manometers were read at the same intervals as the thermometers. Manometer P2 was used to measure the pressure drop across the exchanger when single-pass flow existed in the shell, while manometer P3 measured the pressure drop when double-flow existed in the shell. Ma­
nometer P4 was used to determine the pressure drop across the tube passage and particularly to check the uniformity of flow of the cooling water. 
Time of tests.-The time of each test varied from fifteen to thirty minutes, and was determined by the constancy of the indications of the apparatus. 
As may be noted from the data and result sheets, the fluid being cooled (the shell fluid) was first heated, in each case, to a predetermined temperature which was kept as nearly constant as possible after conditions of thermal equilibrium were established for each test. The amount of time neces­sary to establish thermal equilibrium varied and depended upon the changes made and upon the steam pressure in the line. There was no control of the incoming temperature of the cooling water; however, this temperature did not vary appreciably. 
Shell fluid samples.-Samples of each oil used were taken shortly after the run, and determinations of the specific gravity and viscosity were made of each sample (except for the viscosity of the kerosene1 ) by the use of a hydrometer and a Saybolt Universal viscosimeter. 
1The viscosity of the kerosene was obtained from a temperature­fluidity chart given in Hamor and Padgett's "Examination of Petro­leum Oils," Fig. 38, page 85. 
III. CALCULATIONS AND DATA 
Series I of the tests was performed to study the relation of the velocity of the shell fluid to the overall heat transfer coefficient. Series II of the tests was performed to study the pressure loss of the shell fluid and its relation to the overall heat transfer coefficient in addition to similar data taken in series I of the tests. 
Overall heat transfer coefjicient.-The overall heat trans­fer coefficients were computed from the following equation: Q = U A T___
__________
__________________________
__
_____ 
(2) 
where 
Q =heat transferred in B.t.u. per hour 
U =overall heat transfer coefficient in B.t.u. per 
hour per square foot per degree Fahrenheit 
mean temperature difference 
A = transfer surface in square feet 
T = mean temperature difference in degrees Fah­
renheit. 
The overall transfer coefficient was computed on the basis of the tube surface, which has an area of 20.5 square feet. 
The heat passing through the transfer surface was taken as that absorbed by the cooling water. This value was checked by the heat given up by the fluid being cooled. Radiation from the shell was not considered, since this por­tion of the heat did not pass across the transfer surface. 
Specific heat.-In the case of oil, the amount of heat given 
up or absorbed was calculated by using a value of specific 
heat determined from Fortsch and Whitman's equation.2 
2Morris and Whitman, "Heat Transfer for Oils and Water in Pipes," Industrial and Engineering Chemistry Vol. 20 p. 236. 
(T +670) (2.10 -S)
c= -------------------------(3) 
2030 
where 
C = specific heat 

T =temperature in degrees Fahrenheit S = specific gravity of the oil at 60 degrees Fahrenheit. 
Mean temperature difference.-The arithmetic mean tem­perature difference was used in all computations where the error involved was less than 0.1 per cent. 
Properties of oils.-Designations of the oils with the gravities at standard conditions and absolute viscosities at average conditions are given in Table II. 
TABLE II 
Properties of Oils Used as Shell Fluid 
Oil 
A ________________________________ B__
____________________
_
______ 
c ________________________________ D ________________________________ E ________________________________ F ________________________________ G___________________________ 
_
_ 

Degrees 
Baume 
60°/ 60° F. 

38.0 
24.7 
19.6 
18.8 
27.8 
23.8 
41.4 Specific Gravity 60°/ 60° F. 
0.835 
0.906 
0.936 
0.941 
0.888 
0.911 
0.814 Absolute Viscosity at Average Temperature in Centipoises 
0.90 
4.65 
8.30 
11.60 
10.40 
5.60 
0.90 
The variation for the different oils of the relative vis­cosity (seconds Saybolt Universal) with temperature is shown by the curves in Fig. 4. 
C?OOO .J <( l/'J1000 ~ w >600 z :'.)400  
'.J300 0 a'.l zoo  
~  
({)  
U) Q z 1008  
~ 80  
I 70 .J i5 60 u.. 0 T BO t 48 If) 460 \) 44 <I) :; 4G  
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FIG. 4.  RELATION  OF  OIL  VISCOSITY TO  TEMPERATURE  

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REMA1ii?.K..S 
Tests I to 9 incJ. Double Po.ss
{ 
.Shell Fluid Ve!ocity Vorioble 
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Shell Fluid Velocity Vor-ioble 
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Double Fbss 
'"-3
34 585 80.0 152.\ 131.6 75.l'o 3.~50 0.85 0.1% 1.e.3 0.80 0.0352 0.1265 7908 ZZ.1130 \.'55 3.29 \\0.0 
She 11 Fluid Velocity 
~ 
35 5'8.4 77.9 152.0 13~3 76.0 z...4 0.84 0.\% 1.29 0.63 0.0352 0.1059 7.908 1911.0 l55 2.16 99.8 
~
Variable. 
36 58.0 74.7 151.6 \34.0 76.4 1.502 0.87. 0.196 0.85 OM 0.035\ 0.0784 1880 14,150 \.55 2.05 85.4 
c::::::
31 58.0 71.9 152.0 132.0 17.\ 0.767 0.81 0.19G 0.50 0.25 0.035\ 0.0552 1.900 9950 I.SS 1.44 69.4 
;:l 38 58.0 69.8 159.3 m.1 av; 0.402 0.80 0.1% 0.30 0.\5 0.0351 0.0390 7,896 1,030 1.55 1.02 55.1 
~· 
~
39 59.0 89.3 1520 140.0 11.8 12.020 0.86 0.1% 3,SO \.12 0.0350 0.2320 "!890 41,900 1.54 3.0'1. 162.5 
....
40 59.1 88.4 150.9 139.1 11.3 '.;l.{190 0.86 0.\96 3.01 1.48 0.0350 0.210G 7888 3aoso 1.54 2.14 159.0 
~­
41 59.5 87.5 \51.5 139.0 11.8 am D.86 0.196 Z.b4 /.30 0.0352 0.\964 1,928 35450 1.55 2.56 151.0 
{Tests 39-lo45incl. 
~ 
4Z 59.5 86.3 151.4 13B.3 1\.9 7,402. 0.86 0.196 Z.36 1.\6 (10354 0.182Z 7.95G 32,900 l.5G 2.31 145.0 	5in9le. Po.s.s 
.5nel1 Fluid V• loclty 

~
43 59.7 84.3 1510 138.2 13.6 S:Ob4 0.86 0.196 1.71 0.84 0.0354 0.1509 1968 17.250 /.'56 1.% 130.0 
Variable
44 59.7 8o.4 150.4 134.7 72.5 3.0"4 0.85 0.196 I.I(; 0.57 0.0355 0.1160 1972 20,~ZO 1.51 1.51 111.2 
'"-3 
~
45 59.7 77.0 \50,4. 132.1 7Z.9 1.602. 0.82 0.1% 0.76 0.37 0.0353 O.OB09 7.932 14,610 l.'55 I.OS 92.0 
~ 
.. 
~ 
Tube Fluid -Water" Snell Fluid -Oil ;;>: 
~ 
i;:
Sp.Gr. ·0.804 o+­
......
Averoqe Temp. Ab~Vi,,. -0.9 c..p. o+ 
~ 
Avero9e Temp. 
;:;· 
WATER. COOUNG
IABLE ""SL. DATA AND RE.SULTS -OIL •e,• SE.,IES ][ 
TEMD""R.ATVR.E$ l.~LOW' OlhF"IClEI Pl:.ES3\Jll.I!: OR.OP I FLUID ~I.OWING I FLUIO llELOC.ITY OVE•ALL 
,:~~:tt ~~~b ~~~~ ~~~~. ~~t~ ~~: ~::~~ F~~.;T L:~::lt ·=~=~~ ~:~~~"-c:~=~ t~sr~~ L:~::. l:~:~ ..:~::"-::.:~~ i:$~f£~ litEMARK~ 
OEG, . f'". O~G.F. DEG-~-ot:-.11: OE<t. r: ~-~.IN.. ~-.s~. IN. Pellt UC. . ~1(11. $1'.C . tt()l.)2. HOVtrt.. ~EC. sec.. Pflt..,.-""T.O. 
4IO 59.5 85.'3 199.7 18&.8 120.5 7457 0.86 0.1% 2.79 1.31 0.0352 0.1177 191G 33900 1.55 Bl 84.8 
4-1 59.5 84-8 200.0 180.7 121.Z '.320 0.86 0.\% 2.30 1.13 0.0353 0.1(,32. 7.936 31.100 I.Sb 2.13 81.0 r. + 4 <0tosi· I t
4e 59.7 83.b 200.b _ 187.1 122.2 5.195 O.&E. 0.1% /.87 0.92 0.0352 O.\<lro 7.920 28.!ZO 1.55 1.93 75.1 { 5~~q~e Pa» inc · 
49 GO.O 81.3 l'00.4 18&.4 122.8 3.982 0.85 0.196 l40 0.{,') 0.0~58 0.1284 &048 24.500 1.58 l.{,1 66.3 ~hell Fluid Velocity 
~ 
50 60.0 79.5 200.9 185.(, 123.5 2.520 QM 0.1% 1.\0 0.54 0.0348 0.1010 1816 19.260 1.53 1.)2 G0.4 variable 
51 59.5 11.6 19ao 176.0 122.4 0.732 0.80 0.1% 0.57 0.28 0.0364 0.0518 8184 9870 I.GI O.E.7 39.S 
52 59.0 83.& 199.5 186.0 122.4 7.962 0.86 0.1% 3.~ 1.92 0.0349 0.183G 1.848 35,000 IS4 4.71> 11.0 


i..,
53 56.b 82.0 196.8 186.8 122.5 7.Z{,5 QBE. 0.1% 3.4.(, 1.70 0.0355 0.1141) 1914 ')3,350 1.57 4.?S 74.5 
54-sac 82.0 zoo.a 186.0 124.0 6.232 0.8' 0.1% 3.15 LSS 0.0348 O.IE.ZO 7828 30,900 1.53 4.ZI 14.1 
s· 
55 58.0 79.9 Z00.0 188.0 115.1 SIB'l 0.86 Q.19(; 2.71 l33 0.03'IB 0.1479 71>16 ZB.ZZO 1.53 3.~S IOb.I> { Tests SZ fl> 61 in.cl. 
51i> 56.0 78.1 200.5 189.3 12b.O 3.882. 0.85 0.196 2.14 LOS 0.0350 O.IZ69 1.BbO 24220 1.54 3.30 Gl.0 Double Pu4 s 
l=l 57 58.0 75.0 Z00.4 18C.3 126.8 Z.781. 0.84. 0J% ~70 0.64 O.D355 0.1~ 7, 990 20740 L51 2.16 53.1 Shell Flvld Velocity 
~ 
58 5 6.0 73.0 200.9 186.0 128.0 1-101 0.S3 Q.1% LIO 0.54 0.0354 00821 7,940 15680 l56 2.14 45.4 Varloble c 
;:i
59 ss.o 69.o 196.2 1eo.e. 1259 neoi MO o.m . o.w 0.30 00354 0.0545 7.~ 10,1120 1.s6 1.42 33.9 
;:i
G.O 585 69.5 201.7 184.5 12a9 0.832 0.80 D.1% o.60 0.79 0.0~ 0.0553 '776 10550 1.53 1.44 33.6 Test _5inqle Pnss
62..,
!;.I 58.6 73.4 199.S 184.I 125.8 1.782 Q83 0.""-/.IS 0.57 0.03118 0.0840 !824 16,010 1.53 Z.19 45.2 [ ~hell Fluid Velocity "' <") 62 SB.1 67. / 197.5 IG?.7 \19.7 0.232 0.79 0.1% O.lS 0.11 0.0351 0.0288 (87Z 5490 1.55 0.38 21.0 -{ Voriable 
~ 
63 58.6 GZ9 201.3 184.5 129.7 0.532 0.80 0.1% 0.43 0.21 0.0355 0.0443 7,980 8450 l51 \.IS 28.C ) { Test <03ond 64 
64-58.8 ~2.5 202.0 172.8 12C.7 0.231. 0.79 ().1% 0.?L> 0.10 0.0355 0.0288 7,980 5,490 LS1 C>.75 II.~ l Double Pass 
::i::: 
5hel I Fluid Veloc.ity Vorioble. ~ 
Tube Fluid -Wote'I'"" 
~ 
Shell f\oid -Oil ·e,~ ;;:.­
Sp. qr. · 0. 85 ot 
A veraqc. Temp. 
Abs. Vi~. -4.~5c.p. at ~ ..,
Averoqe Te.mp. 
t--' \0 
TABLE 3Zl DATA AND RE..SULT.S WATER. COOLING OIL "c." SERIE"~ II Pe:KA"TU~£.S !'"LOW OltrFICe PPF: .. 4'URF OEOP FLUID FLnW1NG FLUID VELOCITY 0Vf'.12'ALL 
~ ~~!~2 ~~-~~ts ~~t~ ~~:: ~~Wf; ...~~,;T ::~ 1==~~ ~:~~~2 :v~~-:~~,.~~ L:~:=~ L:~=~~ p-:~:2 :;:~~ ~~~=~=:t REMARK~
~ 
E~. F. Ofl!q. F" C>e'Q.F. O'EG·"'· H~. S~,IN. \-\(ii. 5q.11-t. ~llt~EC. PE'lt:.EC.. \-\OUR. HOUR. 5£C. SEC. P£C 0 F.1"'1:'f.O. 
65 r;,;.s 83.'l wo.o 190.0 119.1 4.21 o.894 0.1% 2.10 t.oJo _9.0345 ~_]750 27,100 1.51 3.54 49.& 
GIO 67.5 82.8 WO.O 190.0 119.B 3.70 0.892 0.1% 193 0.950 0.0355 0.12~9 7972 25,250 1.% 3.30 49.1 
r;,1 !07.5 81.1 199.3 189.3 119.7 3.04 0.885 0.1% 1:53 0.748 0.0347 0.1150 1.BOO 229!0l52 Z.99_,~ I 
GB 1>7.4 80.5 199.3 189.1 IZO.Z 2.45 0883 oJ96 (.5 0.614 0.03430,\023 7.736i0'4o0--r.so-2.66 41. 2 

~69~ 78.~-~_!_87.9 IZO.I ~O.BGO 0.196 -08£ _Q:437 0.0347-O.OB22 : 7.808 TG'.380 l.S'Z 2.14 36.4:_ 70 67.S 17.0 200.0_ 187.5 121.5 097_ 0833 0.1% _Q.GQ_ 0.295 0.0341 O.Oo\2 _2812 12,200___1,.52_ _1,59 29.9 { Te>b ros +o11 incl. 11 65.2 83.4 Z03.G 193.4. IZ4.Z 5.51 0.894 0.1% 2.89 1.420 0.0352 0.1%2 lo/24 31.100 1.54 4.01 5!0.7 Double Poss ~ 
Cb
7Z,_65.0 81.'.l 199A 189.8 121.2 4.80 0.8~4 0.196 -2.50 1.228 0.0345 0.1450 hh8 28,9001.$1-3.17-1-53.0 .Shell Fl_uidVelocity 73'--'Gs.z 81.3 200.3 190.I 121.9 ~0.894 0.1%Z\S\.07o 0.0350 Q:i346 7,880 26800 1.53 3.50 50.9 Vanoble c::: 
;::!
74 <;;S.2 '78.':l 201.5 190.2 123.8 24') 0.883 01% 1.45 0.111 0035'2. 0.1032 1928 20.540 L54 2.69 43.1 
~· 
75 i;5,5 75.B 199.\\ IS7.5 123.0 1.30 0.860 0196 0.80 0.393 0.03'.il 0.0732 7,916 14,570 1.54 1.91 32.b Tube Fluid -Wate< Cb ,__]L_GS.5 74.8 199.\ IB&.O 122.4 0.90 0.833 0.1% 0.60 0.'295 _Q.0352_ 0.0590 491'2 11730 1.54 1.S4 29.3 Shell Fluid -Oil 'C' ;:: 77 GS.3 73.0 200.0 186.0 !23.9 0.55 0.633 0196 0.35 0.112 0.0351 0.04&1 7,904 9,180 1.54 1.1.0 24.0 Sp.G" -0.886 at ::::.· 
~
lB C.S.5 84.0 ZOLi 1905 I'll.I 5.40 0894. 0.19f, 2.Z5 \.\OS -0.0354 0.\539 >-7,960 30,C.OO 1.55 2.00 56.G A Av~n>q~ Temp. 
1 
79 65.5 83.0 200.0 190.0 120.8 4.C.O 0.894 01% 2.00 0.98'2 0.0354 ,_Q.1420 1,980 ZB,2b0 1.55 L85 59.5 ~;,,~~~~. -~.'.;;~. 0 
~ 
BO GS.5 82.0 ZOO.O 190.0 IZl.8 4.23 0.694 0.1% 1.81 0.859 0.0354 0.13GI 7954 27.100 I.SS 1.11 5'2.7 
81 G5.3 79.0 200.5 189.5 122.8 2.15 0883 01% 1.35 0.661 0.0351 0.0958 7904 1~100 1.54. 1.25 43.0 

82. G5.2 76./ 198.'l 186.0 121.5 I.OB 0.8GO 0.196 095 0.461 0.0354 O.OGl;.5 795(, 13,250 I.SS 0.81 34.G { Te.oh 18to88 incl. ~ 83 65./ 10.2 1984 115.0 119.I 0.10 0.80S 01% 035 0.112 0.0354 0.0190 7,964 3,170 I.SS 0.25 16.9 Sinqle Po.s..s. ~ 84 65.0 75.4 201.Z 186.8 123.8 0,60 0833 0.1% OID5 0.319 0.0354 0.055& 7%0 II Of,~ \.SS 0.12. 32.6 Shell Fluid Velotity 
~
Y,_~;.~ ~:~ ~:~ :~~~ :i~'.~ ~~ ~:; ~\~ ~~ g.!4~ ggi~~ ~~~~"i~;: :~;: :.·~; ~:i~ !~:; -b:I 
. Variable 
~,.. G4.9 so~ 20091961 122.1 3.sz ·o.es3 0}%' -1.18 0.814.-0:03G5 o.122G-8z2s 7 4350 1.GO 1.&o sv;. I ~ 88 G4.8 82.2 20o.8 190.I IZl.'l 4.IDO 0.8'34 0.1% 2.lf3 1.010 0.0354 0./420 7,968 Z8,200 1.55 i.B5 55.5 ;;· 



~~~~~=--J 

r 

'--3 
.... 
~ 
~ 
.... 
..... 
;:i 
~ 
("') 
c
;:; 
;:; 
Cb 
ci 
i 
~ 
a Cb ~ 
£. 
§ 
~ 
.... 
t,J 
...... 
TABLE  Jl11I-­ DATA  AND­ RE.SULTS  WATE~  COOLING  WATER.  5ERIE.S I  l.',J  
TEMP1!:R.ATUlil.I!-"  I FLOW'  OQIF'IC•I  PRE~~UR:E  O~OP  F'LUIO  F"LOWINQ  ,.LUIO  VELOCITY I OVl.aALL.  ~  
Tl!5T TU.Sli ,.L.UIO NUM&Ul -IN­~"­...  TUl!U!' l'LUIO -our­011:q.,.  .5Hl!'LL ..LUIO -IN­O'l.:4. F.  .SHf.LL f'L.UID -OUT-Ol'q,. ...  MfAN TEMP. 01..... Ol"G.,.;  MANO. COl!'Fr TU9C. .SHf.LL "-'AD1NG P'ICll!MT ·~HI!~ LB. Pll!llt INCHl[.S HG,. .SQ. IN, Hef.  .!>M'ltLL L8. Pe'R. 6Q. IN.  TUBE cu. FT. PER. ~cc.  .SHELL c.u. PT. P!:i;t .SEC.  Tuel! Le.. Ptlt. HOUA..  .SHELL LI&. Pl!R. HOUR.  TU8e'. ..T. pelt ~·C.·  .sHeLt.. PT. P•• .sec;.  Tl2AM5"rlt COC~&NT a.T. Jq.''C l"IR •,: :r.o.  R.EMA.e.K,.S  
103  86.0  101.0  124.9  115.4  26.6  0.0259  0.0419  581Z  940Z  1.14  1.09  ll00.5  )  
104  86.0  103.9  125.0  117.6  26.0  O.o25&  0.0{,09  5,752  13b84  1.13  1.59  194.0  '{ Tesb I03h:>I01incl.  
105 106 107 108 109 110 Ill  8G.G 86.6 86.6 78.0 78.0 78.0 79.0  104.9 106.6 108.1 106.6 100.0 96.5 93.Z  124.3 124.8 IZ5.I 123.7 IZ3.7 124.7 1n1  117.9 119.l> IZO.~ 116.8 114,0 113.I 111.1  24.9 24.9 24.4 26.4 29.3 31.G 31.G  0.0255 0.0256 O.OZ53 0.0104 0.0189 0.0284 0.0~67  0.0756 0.0955 0.1132 00448 0.0446 0.043 0.0446  SJfO. 5,760 5f.8Z l.33Z 4,236 6,365 8,B4  16,990 Zl,418 25444 10,050 /0,004 9b'ILI­/0014  l.IZ 1.13 I.If 0.46 0.83 1.15 1.62  1.'n 2.49 2.94. 1.11 I.lb 1.IZ 1.16  Z06.0 l.27.0 24SO 124.3 155.4 181.0 182.0  Double Puss .'.>hell Fluid Velocity VariableI { Tesb 108h:>ll2 ind. Double Poss Tube Flu'od Velocity  ~ "' ~  
llZ  79.5  92.1  IZ3.6  111.3  3l6  0.0443  0.0440  9,940  9873  1.95  1.15  192.0  Vorloble Tube Fluid -Water  ~·  
Snell Fluid -Water  "'  
A~.Vis. -0.44c.p.ot  ~  
Averoq• Snell Temp.  ~­ 
c- 
'"-3  
~  
l:l  
"'  
t:ti  
i;:........  
~  
;:;·  
~ 
- 


COOLING OIL 'E" !!ERIES t • 
FLUID VELOCITY OVEf!ALL TUee: HELL ,~m~~~~ t""T. PEit. FT. PU!. &J'.u/H~/.,q.i:r .51!'.C.. sec.. ,..e. •F. f'\."tD. 
1.23  I.I/  t.b. /  
l.ZZ  1.62  32.1  
1.23  2.02  37.Z  
1.22  2.40  4/.6 - 
1.22.  2.BZ  46.8  
"""'123-z.95  49.6  
1.22  0.65  18.1  
1.21 1.21  176Z.17  37.4­43.ro  
1.22  2.57  49.4  
/.19  3.11  55.4  
1.17  3.33  58. 7  

REMAW!.1<...S 
) ~~:~. 1:;,,~~IBoncl 
~hell Flu;dVel.Vor;oblc 
{ 5p.Gc·O.e64alA,.Temp Ab>. Vi>.· I0.4 c.p. al AveroqeTernp. 
119 '° 124
l { Te>b ,ncl. 
~~~~1:;i;~eLV.riobl• 
Sp.<;< ·Q649otAve.Temp. Ab;, V• >.·5.kp. ol Averoqe Te"'~ 
Tube Flvid -Water 
.5hell fluid -Oil "E" 
~ 
~ 
'"'-3 
~ 
~ 
., 
s· 
~ 
~ 
c 
;i 
;i 
., 
('!> (") ~· 
...... 
~ 
~ 
~ 
f., 
1:-.:1 
CJj 
TABLE WATER. OIL "F"

~ 
~ 
(l> 
~ 
~· 
(l> 
;-,;: 
~­~ 
i 
b:i 
i;:
..... 
~
-;:;· 
~ERIES 1
IABLE XI DATA AND RESULTS WATER. COOLING 01 L "G' ­

::i:: 
~ 
"'-3 
~ 
... ;:;· 
~ 
('") 
0 
;:i ;:i 
~ 
;; ~ · 
...... 
~ 
~ 
w 
~ ~ 
~ 
... 
I:',:) 
CJ> 
IV. DISCUSSION OF RESULTS 
Mechanism of heat transmission.-In open vessels where a gas or a vapor separates the warmer substance from the cooler substance heat is transmitted largely by radiation; but in vessels where the heat must pass through a liquid or a solid, the kind of transmission is principally that of conduction. 
Ifthe fluids were quiescent, heat would be transmitted by conduction alone and the rate of heat transmission would be dependent upon the conductivity and the thickness of the substance. If, however, the fluids are in motion, as is the case in a commercial heat exchanger, heat will flow not only by conduction but also by convection. 
The particles of the fluid do not move at the same rate through the vessel. That portion of the stream nearest the wall moves at a slower rate than the central part. The variation of the velocity across a section of the path is gov­erned by the viscosity of the fluid and the width of the path. The thickness of the layer of the slow-moving particles near the wall of the vessel is also governed by the viscosity of the fluid and the width of the path. 
Since the heat transferred in an exchanger is principally by conduction and convection, the rate at the point of trans­fer will be governed by the thickness of the slow-moving film at the surface of the fluid. The rate at which the heat is conveyed to the point of transfer will be controlled by the average velocity of the stream, its density, and its heat capacity. Also, the total amount of heat transferred will be governed by the relation of the width of the path to its length. 
From a summary of the foregoing statements it may be noted that the transfer of heat in the case of a moving fluid in a closed vessel is governed by the diameter (width) of the vessel, the length of the path, the heat capacity (spe­cific heat) of the fluid, its conductivity, density (specific gravity), velocity, and viscosity. 
Heat Transfer in a Commercial Heat Exchanger Transfer relation developed by Morris and Whitman.­
Morris and Whitman3 have presented data on a single tube experimental heat exchanger which shows that a relation 
exists between the groups of the variables DV --. z hD That is, ( ;;:--)0.37 is a function of n;  hD , K  CZ , and K  
K  
where  
h =  film coefficient  

D = diameter of the containing vessel in inches 
K =conductivity of the fluid in B.t.u. per hour per square foot per foot of thickness per degree Fahrenheit m.t.d. 
C = specific heat of the fluid Z = absolute viscosity in centipoises V = mass velocity in pound per second per square 
foot of cross-sectional area. 
These men, however, did not consider the relation of the length of the path to its diameter (width). A replot of their data is shown by Fig. 5. 
Transfer relation developed by McAdams and Frost.­
Messrs. McAdams and Frost4 have presented data that show the relation of the rate of heat transfer to all of the variables given above. 
A replot of their data with interpolation and extension for 
different values of c: to cover the range encountered in 
these tests is shown by Fig. 6. 
aMorris and Whitman, "Heat Transfer for Oils and Water in Pipes," Industrial and Engineering Chemistry, Vol. 20, p. 232. 4 McAdams and Frost, "Heat Transfer," Journal of Industrial and Engineering Chemistry, Vol. 14, No. 1, p. 13. 
-

..... 
"' ;,..,..... 
N\Y. 'COO 
~ 
~o 

4 

FIG. 5. REPLOT FROM COOLING DATA OF MORRIS AND 
WHITMAN TESTS 

CZ
These curves show that for a given value of K' 
hD 
"]( is a function of DV _
_______________ 
_ 
(5)
(1+5~) z 
where r = ratio of the length of the pass to its diameter. (The other symbols have the same meaning as given above for the Morris and Whitman data.) 
The group c:_ shows the ratio of the product of the 
specific heat and absolute viscosity (in centipoises) to the conductivity of the fluid in B.t.u. per square foot per hour 
per foot of thickness per degree Fahrenheit mean tempera­ture difference. Both Morris and Whitman's and McAdams and Frost's data point to a relation existing between the overall heat 
transfer coefficient and DUS . Since the diameter (D) is 
z 
constant for a given vessel, there exists a relation between the linear velocity of the fluid (U), the specific gravity (S), and the absolute viscosity (Z) with the overall heat transfer coefficient. Such a relation is shown by Fig. 7. 
Film coefficients versus overall coefjicients.-Overall 
transfer coefficients computed for the fluids under the con­ditions of these tests from the data of McAdams and Frost were found to vary approximately 5 per cent from the average values found experimentally. 
As an example: 
Oil "A" (Shell Fluid) flowing in Double Pass 
Water (Tube Fluid) as cooling medium. 
(Data taken from test number 29.) 

Shell Side 
CZ 0.51 X 0.9 
--= =5.9 
K 0.078 

DV 3.59 x 5.59 x 62.4 x 0.804 = 1117 z 0.9 From the curve, Fig. 6, the corresponding coordinate G DV CZ 
at --= 1117 and --= 5.9 equals 5300 
Z K 
and 
h.D 3.59h. !"{ 0.078 
G= =5300 50 1 50
1+­
+ 10 x 12 e3oo x 2.495 ft 
r 
h. = = 288 B.t.u. per hour per sq. . per 46 degree Fahr. m.t.d. 
e.o,ooo 
10,000 
apoo 
0000 
4000 
~000 
e.ooo 
r---,---, 

~'""1000 
+ 800 
---=:_, 
+ 600 
,----..500 
~400 
0 
~.300 
eoo 

w 
~ 
C1) 
~ 
~· 
C1) 
;:;: 
~· 
~ 
~ 
"-3 
~ 
r ~ 
;;· 
Tube Side 
CZ = 1 X 0.96 = 2.
6 
K 0.37 

DV 0.527 X 1.53 X 62.4 X 1 
--= =52.4 
z 0.96 From the curve, Fig. 6, 
DV CZ 
G = 390 at --= 52.4 and --= 2.6 
Z K 

or 

0.527ht 
0.37 l.505ht 1 50 
1.22 
+ 10 x 12 
0.527 
h = 316 B.t.u. per hour per square foot per degree Fahrenheit m.t.d. 
The overall transfer coefficient U then becomes equal to 
1 
-------------------------------------------------(6)
1 L 1
-+-+­
h. h0 ht 
where 
h
h. = film coefficient on the shell side ht = film coefficient on the tube side 0 = conductivity of the tube metal in B.t.u. per 
hour per square foot per inch of thickness per degree Fahrenheit m.t.d. L = thickness of tube wall in inches. 1 
U = ------.------= 149 B.t.u. per hour
1 0049 1
+ + per square foot per 288 660 316 degree Fahr. m.t.d. 
The experimental coefficient for the same shell and tube velocities was 145 B.t.u. per square foot per hour per degree Fahrenheit mean temperature difference. 
A second example: 
Oil "A" (Shell Fluid) flowing in Single Pass Water (Tube Fluid) as cooling medium. 
(Data taken from test number 39.) 
Shell Side 
CZ 0.51X0.9 
--= -----= 5.9 
K 0.078 
DV = 5.07 X 3.02 X 62.4 X 0.804 = 853 
z 0.078 From the curve, Fig. 6, 
DV CZ 
G = 4220 at --= 853 and --= 5.9
Z K 

0. 3 o.5 0.7 1.0 z. .3 s 7 10 zo 40 80 RATIO OF VISCOSITY TO SPECIFIC GRAVITY 
FIG. 7. RELATION OF OVERALL TRANSFER COEFFICIENT TO RATIO OF VISCOSITY TO SPECIFIC GRAVITY 


5.07 h. 0.078 65 
----= --h. = 4220 1 50 5.22 
+ 5 X12 
5.07 
h. = 339 B.t.u. per square foot per hour per degree Fahrenheit m.t.d. 
Tube Side 
CZ = 1 X 0.96 = 
2.6 
K 0.37 
DV = 0.527 X 1.54 X 62.4 X 1 = 

53.8 
z 0.94 
From the curve, Fig. 6, 

DV CZ
G = 400 at --= 53.8 and --= 2.6 Z K 

0.527
----ht __o_.3_7__= 400 
1 _L 50 
I 
10 x 12 
0.529 ht = 325 B.t.u. per square foot per hour per degree 
Fahr. m.t.d. 
1

Then U = = 164 B.t.u. per hour
1 0 049 1 
__ + _._ +__ per sq. ft. per de­339 660 325 gree Fahr. m.t.d. 
The experimental coefficient as calculated from test number 39 was found to be 163 B.t.u. per hour per square foot per degree Fahrenheit mean temperature difference. 
Film transfer coefficient equation.-The equation 
50) 	co.2Ko.8 so.184 vo.184 
h=374 1+-D z ________ 
(7)
( r 0.216 o.584 
is satisfied, approximately, by the experimental coefficients. In this equation the symbols are: 
h = 	film transfer coefficient on one side of the container in B.t.u. per square foot per hour per degree Fahrenheit m.t.d. 
r = 	ratio of the length of path to its diameter 
K =conductivity coefficient of the fluid in B.t.u. per square foot per hour per foot of thickness per degree Fahr. m.t.d. 
C =specific heat v = linear velocity in feet per second S = specific gravity Z = absolute viscosity in centipoises D = diameter of the vessel in inches. 
Applying the above equation to the data of test number 29, the calculations are as follows: 
Oil "A" (Shell Fluid) flowing in Double Pass 
Water (Tube Fluid) as cooling medium. 
The Shell Fluid coefficient would be 
50 
h. = 374(1 2 x 5 )(0.51) 0·2 (0.078)0.8 (0.804)0.784 (5.59)0.784 
+ 	3.59 (3.59) 0.216 (0.9) 0.584 12 
h. = 277 B.t.u. per hour per square foot per degree Fahr. m.t.d. and the tube fluid coefficient would be 
2 ~5) (1.0)0.2 (0.36)0.8 (l)o.784 (l.53)o.784
ht=374 1 + 	---~---,-.,.,.---­
( 0.527 (0.527) 0.216 (1) 0.584 
-i-2­
ht= 323 B.t.u. per hour per square foot per degree Fahr. m.t.d. 
The overall coefficient then becomes 
1 
U = ---0-.-----= 147.6 B.t.u. per hour
1 049 1
+ + per square foot per277 660 323 degree Fahr. m.t.d. 

Ae.50LUTE V\5C051TV, CENTIPOl5E..5 
FIG. 8. RELATION OF WATER VISCOSITY TO TEMPERATURE 
The experimental value for this test was 145 B.t.u. per hour per square foot per degree Fahrenheit mean tempera­ture difference. 
At stated before, the values of specific heat were calcu­lated from Fortsch and Whitman's equation. The conduc­tivity of water at various temperatures is shown by Fig. 8, and the conductivities of oils and that of brass at different temperatures are given by the curves in Fig. 9. 
Diameter of shell passage.-In making a comparison with the data of Morris and Whitman and with that of McAdams and Frost, it was necessary to set a value for the diameter of the passage through which the fluid moved during the heat exchanging process. The true equivalent diameter of a passage of this kind is questionable, for the hydraulic relations would depend upon the wetted perimeter of the pass, while the conduction of heat would depend upon the radial distance from the cool surface to the point from whence the heat comes. Heat will pass from any point to another if there is a difference in temperature, and the amount of heat flow will depend upon the resistance of the path and the thermal head. 
c ci 
2~ 
-11)\,:' 
::> ·~ 
~~.2 
~·it 

ot::o 
0
l.L.. 04 

~u:. 
i.J ~0.'3 
o~ 

v .to,2
>-.. 
!:~ 
~t._ 

b~o. 
::>Ii
oo. 
~3.o6
v It) 30 50 10 100 200 400 700 TEMPERATURE OF OIL, OEG. FAHR. 
FIG. 9. RELATION OF HEAT CONDUCTIVITY OF LIQUIDS AND SOLID~ TO TEMPERATURE 
The circle marked B, Fig. 10, represents the area equiva­lent to the gross area of one-half of the exchanger cross­section. The diameter of this circle was used as the diame­ter of the shell passage in the double-pass "set up" for all of the calculations involving this factor. The diameter of a circle of twice the area of circle B was used for the single­pass "set-up." 
The external circle marked A represents the equivalent perimeter equal to the wetted perimeter of the tubes in one pass (fifteen tubes) of the exchanger. The circle marked C represents an area equal to the shell passage area of one pass divided by the number of tubes in that pass. 
It appears that the heat conducted from the fluid in the shell to the tube would be governed by a diameter approxi­mately equal to that of circle C. That is, that the variation of the velocity across the passage would be controlled by the "free" space between the tubes; but, when it is consid­ered that the shell of the exchanger is the only true containing wall, it should be seen that the diameter of the shell area would be more nearly that with which the velocity would vary. Then, too, some heat is probably conducted from the remote portions of the passage to the centrally 

located tubes, which would infer that the diameter as used would be more nearly the true equivalent diameter. 0 
Effect of length of path of fiow.-The factor(1 + 5r ) as given by McAdams and Frost in their equation for heat transfer across a film of fluid, is substantiated by the results of these tests, since there was a greater overall heat trans­fer rate shown by the single-pass flow than was shown by the double-pass flow for the same oil flowing at the same velocity and entering the exchanger at the same tempera­ture. The length of the path for single-pass flow was one­half of the length for double-pass flow; and, since the 
diameter of the passage was based on the gross cross­sectional area in each case, the ratio, r, of the length to the diameter was 5.22 for the single-pass and 2.495 for the 
DV h" h 
double-pass. With the same fluid, the value of -Z' w ic 
is used as the abscissa for the curves of Fig. 6 for single­pass flow, would be 1.41 times the value for double-pass flow for the same shell fluid velocity. This would give a 
hD 
K
value of G = ----for the single-pass 30 per cent 1+50/ r greater than for the double-pass. And, with a value of G 30 per cent greater, the film coefficient h for the single-pass would be, approximately, 90 per cent greater than for the double-pass. Taking the tube side of the film into consid­eration, the ratio of the overall transfer coefficients as determined experimentally in these tests, and as shown in Fig. 11, uphold this relation. The relative positions of the single and double-pass curves, Fig. 14, make the above dis­cussion evident. On the other hand, a shortening of the length of passage of the fluid would decrease the time allowed for the heat exchange. This would indicate that the time necessary for the heat exchange to take place between the hot and cold fluids is less than the time necessary for the fluid to pass the length of the double-pass and that the efficiency of heat transfer is reduced because of too long a path of flow. The lack of consistency in the relation of the experi­mental results with that as calculated using Morris and Whitman's data may be attributed, principally, to the omis­sion of the length of the pass from their data. 
Effect of hea,t short-circuiting through mefol of shell a,nd baffie.-Some heat will pass from the fluid in the shell on one side of the central baffle across the baffle to the fluid on the opposite side, thereby decreasing the overall transfer rate in the case of the double-pass flow. And, too, some heat will pass from the fluid on one side of the baffle through the metal of the shell to the fluid on the opposite side, which also decreases the transfer rate for the double pass. The heat transferred across the baffle, however, affects the overall transfer rate by approximately 1 per cent, while the heat transferred through the metallic shell affects the rate to a lesser degree. 
In the interpolation and extension of the curves of 
. 	CZ
McAdams and Frost for different values of~· a curve, 
Fig. 11, was plotted showing the relation between CZ 
K 
and G for a constant value of DV. The results obtained 
z 
were then used in replotting the curves of Fig. 6 for values 
of CZ for the fluids used in these tests. The consistent 
K relation between the results of the replotting and the results of these tests give evidence that the interpolation and exten­sion of these curves is plausible. 
~ 800 
J... 




IOOO ~!~~!ml~~i§E~El~EEl--~-1-al
~600 
+ f--1f--+-+-l==*-'IH'f='F--+--+--+-+-++++++--+-+--lf-+-+++1-H 
~4oo~i--.,:::.-+....-+-l-+-l++---l--+-+--1--+++++1f--+--f--+--+-+-+-++H Cf. ~OO~l--+-+-+-+-11-+++--+--+--+--+--+-+-+-+++--+--+---il--l-+-++-H-t 
.E_, 
eoo o.z o.3 o.5 o.7 	LO / z. .~ 6 s 10 eo 40 60 100 CZ K o.t D'1 z.= IOO 
CK 	DV 
FIG. 11. RELATION OF --AND G FOR A CONSTANT VALUE OF -­K Z 
Factors affecting fiuUl friction.-In considering the pres­sure drop through the exchanger it is necessary to refer to the general layout of the apparatus, as shown in Fig. 2, to justify the results that were obtained. 
It is considered in hydraulics that the drop in pressure caused by the friction of the path of a fluid through a vessel 
is proportional to the square of the velocity. Such a pro­portionality does exist in a symmetrical vessel, but it is doubtful whether this theory can be applied to a container of the type used in these tests without considering the indi­vidual losses that cause a reduction in pressure. 
For the double-pass set-up the fluid enters the bottom half of the shell at one end, passes the length of the tubes, is reversed in direction, and then returns through the upper half to the outlet on the same end as the inlet. Since the inlet and outlet connections are of the same size, the velocity will be the same at these points and, consequently, the pressure drop due to the sudden enlargement and contrac­tion would be the same. 
When the single-pass set-up is used, the fluid enters both sides of the shell at one end; that is, it enters through both the inlet and outlet connections for the double pass. In this case it leaves the shell at the opposite end after having passed the length of the exchanger. Since the outlet con­nection for the single pass is the same size as each of the other connections, the velocity in the out.let will be twice that in each of the other connections; thus increasing the pressure drop due to the exit of the fluid from the shell proportionally to the entrance as the square of their respective velocities. 
A second cause for friction in the shell fluid passage is the reversal in direction of the fluid after it has passed through the lower half of the exchanger. Comparing the single-pass flow with the double-pass, it may be thought that, since the fluid is turned through an angle of 90 degrees in the single-pass set-up, while it is completely reversed in direction in the other type of set-up, the resulting friction due to flow would be less in the first case than in the second. To assume that the loss produced at this point is as large in one case as in the other is not likely to be appreciably in error, because the two parallel streams join at this point in the case of the single-pass flow and, as a result, addi­tional turbulence, which is not present in the double-pass set-up, is produced. 
The third cause for a loss in pressure by the fluid flowing through the exchanger is fluid pipe friction. In long pipes and similar containers this item is usually the largest; but in this, a short vessel, it is much smaller comparatively than the other losses which have been considered. This loss in the single-pass set-up would be, approximately, 40 per cent of the same loss in the double-pass set-up. 
Fluid friction in single pass versus fluid friction in double pass.-If, then, it is assumed that the pressure loss due to reversal of direction in the shell is the same in each type of set-up, and that the pipe friction is comparatively negligible, the total drop across the exchanger in the case of the single-pass flow will be approximately 230 per cent of the total drop for the double-pass flow for the same shell fluid velocity. That is, there are two losses at entry in the single-pass, each of which is equal to the loss at entry or exit in the double pass, and in the single-pass flow there is a loss at exit which is 400 per cent of each of the losses at entry because the velocity in this outlet is twice that of the velocity in each of the inlets. Since in the single­pass set-up there are two inlets and one outlet, and in the double-pass set-up one inlet and one outlet of the same size, the experimental data should show that the pressure drop across the exchanger in the single-pass set-up is approximately twice that in the double-pass set-up. 
Calculating the pressure drop for the single-pass flow from data taken for the double-pass flow, the above discus­sion may be made more clear. 
Example for Oil "D" at a velocity of 2 feet per second: 
DVS = 3.59 X 2 X 0.892 = 
0.551 
z 11.6 From standard pipe friction curves, f = 0.0114. From the standard equation for pressure drop in straight pipes, 
0.323 fLSv2 p = ------------------------------------------( 8)
D 
where 
p = pressure drop in pounds per square inch 
f = friction factor 

L = length of pass in feet S = specific gravity of fluid v = velocity of fluid in feet per second D = diameter of c0ntainer in inches Z = absolute viscosity in centipoises. 
0.323 x 0.0114 x 10 x 0.892 x (2) 2 
P= 
3.59 
= 0.0366 lb. per square inch. 
The remaining pressure drop is then divided equally among the losses due to entry, exit, and reversal of direc­tion, or, each is equal to 
0.68 -0.0366 . . 
-----= 0.1878 lb. per square mch. 3 
0.68 may be found to be the total pressure drop across the slhell fluid, Oil "D" flowing in double pass at a velocity 
of 2 feet per second, Fig. 12. The total losses for the single-pass flow should then be 
Shell friction (0.0366)0.4 = 0.0146 
Reversal of flow = 0.1878 
Two entries = 2 X 0.1878 = 0.3756 

2 
Exit = 0.1878 ( : ) = 0.7512 
Total = 1.3292 
The curve for Oil "D," Fig. 12, for single-pass flow at a velocity of two feet per second shows a pressure drop of 
1.32 pounds per square inch. 
Pressure-drop equations.-An analysis of the curves for all of the oils shown by Fig. 13 reveals two equations which 
are satisfied, approximately, by the data from which these curves were plotted. For single-pass flow, 
0.3 v1•5 
p = ----------------------------------------------( 9) ( ~ )0.159 
while for the double-pass flow, 

0.15 v1•5 
p = ------------------------------------------( 10)(~)0.159 
where the symbols have the same meaning as given for equation (8). 

VELOCITY OF OIL IN 5HE.LL-FT. PE.R !)E.C. 
Equations (9) and (10) show the pressure drop varying as the three-halves power of the linear shell velocity instead of with the square of the velocity. Since the total drop is given in the data, the above relation between the pressure drop and velocity is justified, due to the different factors that make up the total pressure drop. 
~ 
cj U'l 
t!
11.1.l.O 
CL 
di_. 08 
I 
0. 06 
8 

Ill 04 b'. 
~o.a 
II') 
w 
b'. 
Q. o.z 
0.1 

VELOCITY OF' SHEL.I.. FLUID-FT. PER SEC.. 
FIG. 13. LOGARITHMIC PLOT OF PRESSURE DROP TO SHELL 
FLUID VELOCITY 
Relation of transfer coefficient to pressure drop.-The heat transfer coefficient is not a direct function of the pres­sure drop across the exchanger, but it is a function of the velocity. Since the pressure drop is also a function of the velocity, the coefficient may be plotted as a function of the pressure drop. Because the velocity of the water which passed through the tubes was maintained approximately constant, the overall transfer rate was plotted against the shell fluid velocity and, also, against the pressure drop across the shell. The curves are shown by Figs. 14 and 15, respectively. 
The design of heat-exchanging apparatus should be such that the pipe friction losses are a minimum and the transfer rate a maximum. The pressure drop through the various types of exchangers will vary widely with different designs. Therefore, it is not considered that the data for the pres­sure drop nor the equations derived from the data will hold for any other type of exchanger. The data show, however, that the principal losses with baffling parallel to the tubes 
Cl 
I-' 
~ 
" 
..t: 
~ 
IOo:z 0.3 o.4 o.& o.e 1.0 2 3 4-.!) 6 s 10 VELOCITY OF SHELL FLUID -FT. PE.R SE.C. 


are those of entry and exit and the loss due to the reversing of the direction of flow. 
The curves of Fig. 15 show the rate of heat transfer for the single-pass flow to be higher for the same total drop in pressure than that shown for the double-pass flow. Since both the pressure drop and transfer rate have been defi­nitely shown to be functions of the velocity, it should be expected that the transfer rate would increase with an increase in pressure drop. However, from an analysis5 of the two types of flow, it may be seen that the pressure drop over the transfer path of the single-pass flow would be 
ssee example on pressure drops on page 41. 
approximately 40 per cent of that of the double pass for the same linear velocity of the shell fluid. 
It has already been stated that the film transfer rate for the single pass should be, approximately, 90 per cent greater than that of the double pass for an equal shell velocity, which, if considered in conjunction with the pres­sure drop along the transfer surface, would indicate that the overall transfer rate for the single pass would be five times that of the double pass for the same pressure drop. 
In this particular set-up, the pressure drop across the entire exchanger was nearly 100 per cent greater in the case of the single-pass flow than it was in the case of the double-pass flow for the same linear velocity of the shell fluid. For this reason there is not the wide divergence in the single and double-pass curves of Fig. 15 that theoretical consideration indicates. 
CONCLUSIONS 
The results obtained from the data in this bulletin point to general conclusions which may be briefly stated: 
(1) 
A definite relation exists between the overall heat transfer coefficients and the velocity of the fluid being cooled within practical limits of the velocity. 

(2) 
The overall heat transfer coefficients may be esti­mated from overall pressure drops of an exchanger. 

(3) 
The variation of the experimental transfer coeffi­cient was 5 per cent above and below the coefficients com­puted from McAdams' and Frost's data. 

(
4) An increase in overall heat transfer coefficients 


. L 
may be effected by a decrease m the value of ­
D 
where 
L = length of pass of the fluid being cooled 
D = diameter of the pass of the fluid being cooled. 
(5) By replotting McAdams' and Frost's heat transfer data with interpolation and extension for different values 
of 	CZ to cover the range of fluid used, the overall heat K 
transfer coefficient of any exchanger may be estimated to 
a fair degree of accuracy. 
BIBLIOGRAPHY 
Badger, W. L., Heat Transfer and Evaporation, The Chemical Cata­log Company, New York, 1926. 
Cox, E. R., "Heat Transfer Formulas," Mechanical Engineering, Vol. 49. 
Day, D. T., A Handbook of the Petroleum Indmtry, John Wiley and Sons, New York, 1922. 
Hamer and Padgett, Examination of Petroleum Oils, McGraw-Hill Book CompatJ.y, New York, 1920. 
Heilman, R. H., "Transmission of Heat Through Insulation," Mechan­ical Engineering, Vol. 52, July, 1930. 
McAdams, W. H., "Heat Transmission Between Fluids and Solids," Mechanical Engineering, Vol. 52, July, 1930. 
McAdams and Frost, "Heat Transfer," Industrial and Engineering Chemistry, Vol. 14, January, 1922. 
Morris and Whitman, "Heat Transfer for Oils and Water in Pipes," 
Industrial and Engineering Chemistry, Vol. 20, March, 1928. 
Walker, Lewis, and McAdams, Principles of Chemical Engineering, 

McGraw-Hill Book Company, New York, 1927.