INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1948
in t,he same tank, for higher power inputs. The slope of the line for the 16-inch turbine is 0.33 and for the 12-inch turbine is 0.24. Thus, for the 16-inch turbine h h i , t t is proportional to (or h 3 is proportional to P ) ; kiencca to double the coefiicirnt would require an eightfold increase in power. On the other hand, t o double the coefficirnt, using the arrangement ivith the 12-inrh turbine requires that po~verbe increased 16 times. The v a l u e s of the film coefficient of licat transfer for the outside i r f the v e r t i c a l hcating pipes can he rr>asonably high (Table 11). These coefficients are for 1 square foot of outside pipe heating *urface and it, is expected that coefficients of the same magnitude c~)ultibe ohtainrd for a t least four hanks of heating pipes, arranged in a mixing tank as herein described, ina.qmuch as the samt' flow pattern would result ad in these experimrntal operations. ACKNOWLEDGMENTS
NOMENCLATURE
11 = inipeller diameter, feet h = film coefficient of heat transf'rr (on outside of pipes:? l3.t.u. per hour, square foot, F. .\- = inipcller rotational speed, revolutions per second S B=~ Reyriclds nurnbrr, diniensionli For an impeller = lPA Yp -~ . ~ . il
P = po~ver,horscpoiver, 1i.p. t = temperature, F. ?' = tank diameter, f w , ~ A f J p : = log-mean temperature ilifi'tirt~iict~, ' E'. I - = orcr-all heat, transfer r~oefficic~nr,f3.t.u. per hour, squarci
LITERATURE CITED
I3iss~II.E. 3.. ISD. Esc..
\Vork on this arrangeiiicliit of vertical surface heating i n a niising tank \vas first undertaken at the Cniversity of T-irginia ivith the help of the Mixing Equipment Company, Rochester, S . I-. D. C. Reams, C. D. Quarforth, arid A . 0. Mooneyhan sot up a jacketed mising tank 4 feet in diameter and used vertical haffles consisting of 2- and 3.75-inch iron pipes as heating and cvoling units. Results of this first, work were encouraging hut insufficient haffling was obtained to give good mixing conditions togrther with high heat transfer coefficients. The outgrowth of this early work has led t o the present, invrstigatioir. S. G. Sourelis assisted in the experiments and calculations and Claus F:rmiark helped in construcation of the equipmrnt.
1082
CHEli.,
36. 497 I 1944).
13issell. E. S.,Everett. H. J., Hesse. H. C , , and Hushton, -1. H.. ( ' h c m . Eng. Progrcsa, 43, ti49 (19471. ('hilron, T. H., Drew, T. B.,arid Jehens, 13. H . , IND. 1Ch-i:. (?HEX., 36, 510 (1944). Hixson. A. IT,, a n d Bauni, 5 . J.,Ihiri., 33, 1433 -9 (1941). McAldanis. IT. H.. "Heat T r a n s n i i ~ s i ~ ~ n2nd . " ed.. 249%Sen. Tork, iIcGraw-Hill Book c'o., 194%. Rhodes. F. H.. ISD. ESG.CHmr., 26, 9 4 4 6 (1934). R u s h t o n , J. H.. Costich, E. W., and E v e r e t t , H. < J . , paper yi'esented before .Im. Inat. C'hem. Engrs., Detroit, S o v e m h e r 194i. ( 8 ) Rushton, J. H., Mack, D. E., and E r e w t t , H. .T.. 7 ' m ~ i s .d r n . Irial. C ' A c v r i . Efzgrs., 42, 441 !194H). K s c k i \ - k u .January 19, 1948.
Mass and Heat Transfer in Tube Banks C. C. W I N D I N G
AND
A. J. C H E N E Y , J R . ~
CORNELL U N I V E R S I T Y . I T H A C A . N. Y .
A
new experimental technique has been developed t o o b t a i n h e a t transfer coefficients in t u b e banks. N a p h t h a l e n e tubes are cast in any desired shape a n d t h e n inserted i n t o v a r i ous positions in a d u m m y t u b e bank. Mass transfer coefficients are obtained f r o m t h e loss i n weight a n d change in dimensions. H e a t transfer coefficients are calculated by t h e use of C h i l t o n a n d Colburn's analogy ( I , 2) for t h e transfer of heat a n d mass. Resultsobtained by t h i s m e t h o d are compared w i t h available d a t a for b o t h single tubes a n d banks. T h e results appear t o be well w i t h i n t h e l i m i t s of accuracy of other d a t a a n d compare favorably w i t h recommended average correlations of such d a t a . Some new i n f o r m a t i o n is presented for single streamline tubes and flat plates and for staggered round a n d streamline t u be banks.
T
HE tiesign of heat transftsr equipnit,iit t o heat or cool lai,gt. volumes of gas i+ usually a conipromiw ht~tneerithe ~)ressurc, drop through the apparatus and the rate of heat transfer. The most coninion type' of heat exchangrr is composed of hanks of tube sthrouph which a hixating or cooling medium can he circulatcd tvhile thcl pas is moving normal t o thcse tubes. Ilthougli rouud tuhes arc' perhaps most commonly used, other cominerciallj~ availahl(, .shapt's of tubes have been tested to w d u c e the preswrr clrol) or incwa.yt>tht. heat tran.sfcr area. These include flat plates, w i t h the roun(1etl narrow edges facing the clirc,ction of air flow, .~tr~~amlineti tubes, oval tubes, arid many rarierie.5 of finned tubes. .iny bcrrefits ohtainecl from shape> othcr than round mu.d bc great enough t o cover inc.reawtl coiistruction costs for both the tuhcs and thtd h m t cxchanger. In ordrr to pcrniit coniplete evaluation of tht, p t ~ i ~ f o r m a n cofr tubes of 5.prcial shapes. tlata 1 Present adrlrpss, E. I. dit N. J.
I'oiit
d e S e n i o i i r . a n d C'onipxny, .\rlingtoiL,
inust l ~ eavailable o n the coefficients of heat ~ransferiiir these tubes. Becauni, liquids and condensing vapors are usually eniploytd as the heat-transfer medium inside the tubos, f he outside gas film resistancc is controlling, and it is possihlr to carrj- out design calculations ii information is arailahlr legatding these coeffic.it,nts. ,Iconsiderable amount of inforinat ion is available in thv litimture on heat tran3fer coefficients ior gases flowing outsitlr single t u h w and baiikn. Previous work has hren adcquatrly eummai,izcil by Grimison (4),Hatcher (.5), lIcAklams( I O ) , arid T7aiider\vaart (1.3). I n gmeral, thcl reported cxpc~iinientalwork ronsistcd of isolating a m e a u i i n g tube, eithcr as a ,single tub(' or as x nirmbcr of :I tuhe hank, supplying heat at n iiiea+umblv ratc by rondensiirg c ~ t ' a n r 01' electrical resistors, and measuring tuhe wall teinperatiirt~~ by imhedcied thermocouples to ohtain a ge trmperaluw i i i f ferentials. The aciuracy of tho rsprriniental n.oi.l; usuully dcpenclb OII t t i c
1088
Vol. 40, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
Blower
Pitot Tube
Thermometer
Tube
Bank
_-
and no expensive instruments nere needed. This article describes the rather exhaustive comparison tests t h a t have been carried out to compare this method with previously reported work; some new data are also included.
DIAGRAM OF 4PPARA‘US
EXPERIMENTAL PROCEDURE
‘\
\ %
_ _ .
”
11”
. - I
’-
-
b
DUCT ELEV.4T O N
DUCT CROSS SECTION
Apparatus. The equipment used for these experiments consisted of a carefully constructed rectangular duct, part of which housed a ten-row tube bank, connected to a bloTTer by a series of reducers and a round duct. In addition to the regular tubes in the tube bank, a special measuring tube of the sani(1 dimensions was cast from naphthalene and used tri uhtsin the variation of unit conductances around the i:ircumference. The duct was very carefully constructed r o minimize variations in dimensions and was so designed tliat alterations ere easily made without reducing the Jc4ied accuracy. The arrangement of the equipment is elloivn in Figure 1. -Air n-as forced through the system by a blower having a 1,att.d capacity of 1200 cubic feet per minute against a head of 30 incht,s of water. The flow m-as regulated by an intake damper. A 6.G25-inch round duct 80 inches long was connected to the outlet. Attached to the discharge of the blower and concentrically located inside the round duct n-as a smooth conical nozzle 11.5 inches long n.ith a 3.5-inch discharge orifice. This nozzle effectively prollured a uniform, flat flovi front. h Pitot tube, arranged PO that both vertical and horizontal traverses could be made, m s installed in the round duct 75 inches from the blower. The G.O%inch duct was connected t o the rectangular duct by means ( J f a galvanized iron reducer 65 inches long. This extreme length provided very gradual espansions and conversion from a round to a 1,ectangular duct so that the turbulence created by the enlargement x a s held to a minimum.
Figure 1
eiaboratcness of the equipment employed to minimize ani1 average out inherent errors. As is well known, the localized coeficients, as well as the heat flux, vary considerably around the tuhw from front to back in relation to the cross f l o ~of gases. Thc variation is large, usually of the order of magnitude of t7T.o- to fourfold, and if there is any appreciable resistance in the tube wall or inside film, it n-ill cause some variation in point temperatures around the tube. Such a situation throws some doubt on the advisability of employing single thermocouples for temperature measurements, although the use of several couples located a t different points would, of course, tend to minimize these errors. Radiation is anot,her source of error when hot measuring tubes are uaed and can result in both inaccurate temperatures xiid heat flux measurements. If additional heated tubes, n-alls: or sections are employed t o minimize radiation errors, it is necessary t o calculate some average main-stream temperature for the gas in order t o obtain heat transfer coefficients. If elaborate equipment such as that used by Huge (8)and Pierson (11) is employed, error5 w e minimized and good accuracy is obtained. Hon-ever, such equipment is expensive and extremely time-consuniing to ronstruct.
F I O ~ Plate
hbout 1934 Klein ( 7 ) reported a novel method for dctt,riiiining both average and localized heat transfer coefficients directly. He placed a cylinder of ice in a transverse stream of warn1 air and studied t,he change in shape of the tube as the ice melted. As the temperat,ure of the melting ice was tmhesame over the entire surface of the tube, t,he total heat transferred m s proportional to the JTeight of melted water and the heat transfer coefficient, at any point, depended on the ice melted at that point. The defornied cylinder was molded in Plasticine and a reproduction made in plaster of Paris. The changes in dimensions were then studied from this model. The humidity of t,he air had to be low to prevent n-ater vapor f r o m condensing on the ice cylinder and giving up heat. Other sources of error were the amount of heat radiated to the cylinder and the heat conducted through the tube itself. The length of runs was limited by the change in shapc o:^ the tube because t,his influenced the flow of air ahout the tube. This work suggested a possible modification that would .simplify the determination of both average and local coefficicnts of heat transfer for tubes. It appeared t.hat t,he same technique could be applied by utilizing solids of relatively high vapor pressure but having nielt’ing points above the temperature of the gas stream SO that the difficulties of handling ice could be avoided. The , course, be caused by actual deformation of such a tube ~ o u l dof sublimation of the solid a t different rates as affected by the variQUS factors involved in mass transfer. The mass transfer coefficients could be easily calculated from the change in dimensions and the heat transfer coefficient.s obtained by t,he equations of Chilton and Colburn (1, 2 ) relating heat and mass transfer coefficientsto t h e j function. Preliminary experiments indicated that cast naphthalene tubes wuld be used and would give good results without any auxiliary equipment except an experimental tube bank and blower. KO services were required except electricity to operate the bloww.
Streamlined Figure 2.
Tube
Dimensions of Special Tubes
Small arrows indicate distances measured
Tile rectangular duct was 8 feet long and 12 inches high, nith widths tliat varied t o provide for differmt spacing betaeen the vertical tubes. The entire structure nas rigidly supported b l means of a framework of 1-inch angle iron. The framework was composed of four longitudinal members set at the four corners of the duct to support the 0.25-inch Insulite which formed the walls. Vertical uprights n-elded to the longitudinal members a t the ends and the center so spaced them that all ducts had a fixed height of 12 inches. The n i d t h of the duct was fived by horizontal cross members bolted to the vertical uprights above and below the duct. Plates yere R-elded to the vertical members below the duct, and t n o bolts vere used on either side in bolting the cross members to ensure that a 90’ angle was alm ays maintained. This construction ensured rigidity mtirely independent, {of the durt walls and permitted very close tolerances in the duct
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1948
ness oi 0.065 inch. End plates carrying 0.125-inch pipe nipplrs were soldered into the ends of each tube. The round tubes had arl outer diameter of 1.5 inches and the other tubes had the dimensions indicated in Figure 2. The sizes of the streamlined and Hat tube were such that they had the same circumference as tlir round tube and therefore the same heat transfer area. For single tubes and the streamline tube bank, the rectangular duct was 8 feet long, 12 iuches high, and 6.25 inches wide. The single tubes mere located in the center of the duct, 58 inches from the front to allow the flow fiont to become as uniform as possible The round tube bank required a width of 11.25 inches and the tubes were spaced on 2.25-inch centers with the r o w 3 inches apart. I n the streamline bank the tubes were on 1.25-inch centers and the r o w were 2.375 inches apart. Casting Tubes. The split brass mold used for casting round tubes was 1.49 inches inside diameter by 10.5 inches long hcld together by end prrces that scren-Pd on with a tapered thrcatl. 5.
005
0 04
0 b3
In c u 0)
= -
002
I
001
"l
30 01
120
60
90
-
Degrees
150
1089
180
-0
--LJ 270
300
1
I
Figure 3. Inches of N a p h t h a l e n e Removed f r o m Round T u b e in R u n 6 0.015
0.010
j
0.007 0.005
0 003 5000 7000 10000
20000
30000
50000
Reynolds Number Figure 5.
1 = C h i l t o n and Colburn ( 7 ) ; 0 = single r o u n d = single streamlined tubes; A = single tubes; f l a t plates
,
1
I
40000
70000
Reynolds Number
F i g u r e 4 . Change in Mass or H e a t Transfer Factor w i t h R e y n o l d s N u m b e r f o r SingleTubes
dimensions as the steel franie\s-ork eliriiinated *light variations due to warping of the Insulite. T h e tube banks were located near the far t.iid of the duct, so that the last row of tubes \vas approximately 10 inches from the end. This location provided a calming section in front of the bank Lvhich varied in length, dependiiig on the specific bank being used, but 11-as approximately 5 feet long. Each baiik consisted 01' ten rows containing alternately five and four tubes arranged with a fixed distance, a. betireen centers. The five-tube rows were placed so that the distance from the walls to the centers of the outer tubes was 0 . 5 ~ . The four-tube r o w had the same spacing betis-een centers, but each tube n-as offset from the tubes in the preceding roiv so that the center of the tube coincided with the center of the space betm-een the tubes in the adjacent rows. This arrangement is usually known as a staggered tube bank. Dunimy half-tubes of the proper shape were affised t o the walls in the four-tube ron-s, making each row, in effect,, an accurate segment of a larger bank. The tubes were made from seamless, drawn S.A.E. 1010steel tubing, with a Jvall thick-
, 20000
Nusselt N u m b e r vs. Reynolds N u m b e r for Single T u b e s
1 = McAdams (70); 2 = Vanderwaart (13); 0 = single round tubes; 0 = singlestreamlined tubes; A = single flat plates
C
30
60
90
I20
150
c(
Figure 6.
I80
0
30
60
90
12.0
150
180
- Degrees
V a r i a t i o n of Local H e a t Transfer Coefficients for Single Round T u b e s
(1)G = 12,000;
(2) G = 9500; (3)G = 7720; (4) G = 5100; (5) G = 3860; (6) D a t a of Vanderwaart (73)G = 4900
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
1090
t
I
Vol. 40, No. 6
Krurhilin
I
30(
250
20c
I50 L 0
a
--5 z
C
Q
3 io0 2
-
Inches
I
-FC\ =
O
d
f i g u r e 8. Variation of Local H e a t Transfer Coefficients for Single Streamlined T u b e ( 1 ) G = 25,100. (2) G = 19,600; (3) G = 16,100; (4) G' = 12,300; (5) G = 8150
50
0
20
40
60
80 o(
Figure 7.
-
IO0 120 Degrees
140
160
180
Comparison of Authors' Results for Single Round Tubes w i t h Results Obtained by Others
C
-w
- Inches
7
-0
G
7
2.359
Figure 9. Variation of t h e Local H e a t Transfer Coefficients for a Single F l a t P l a t e (11 G = 20,800; (2) G = 16,030; (3) G = 13,500; ( 4 ) G = 9900; (5) G = 6400
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1948
II
I
Reynolds
I
/
1 ;
1091
/ ~
Number
Figure 10. V a r i a t i o n of Mass or H e a t Transfer Factor in Staggered T u b e Banks I = C h i l t o n and Colburn; 0 = row 3, round b a n k ; 0 = row 5, round b a n k ; A = r o w 3 , s t r e a m l i n e d bank; A = r o w s , streamlined bank
nas allowed to dry and the mold was ready to be used. The -wo halves were clamped together and one end plugged with Plasticine. Kaphthalene, at just above its melting temperature, r a s poured in and the top covered to prevent the napht'halene 7apors from escaping. The cast. tube was removed any time rfter 1 hour. Apparently there were tn-o reasons for t,he naphthalene adherng to the plaster of Paris: either the mold dried out and tiny -avities were formed into which the naphthalene could penetrate w after considerable usage, the naphthalene picked up a good n a n y impurities which increased its tendency to st'ick to the mold. The life of a mold could bc increased by keeping a naphthalene tube in the mold, but when sticking occurred, a new mold had -0 he made. Procedure. The cas1 naphthalene tube was cut approximately the right length and weighed to the nea.rest 0.01 gram. The ends were wrapped in Scotch cellulose tape and the effective esoosed lengt,h between the tape was measured accurately. Dummy Jnds were attached and the tube was placed in the duct. The iamper on the intake to the blower was adjusted and the blower itarted. Readings taken a t uniform time intervals viere velocity nead on the Pitot tube, static pressures in the round and rectanguar ducts, and the temperature of the air. At the end of the run, -he tube was immediately removed and weighed. The length i f the run was controlled 1~:- the amount of naphthalene that n-as -o be removed. The change in dimensions of the round tubes was deteriiiined -iy the use of a feeler gage. The ends of the naphthalene tube., rhich were wrapped in tape during the run, did not change shape. When the tape was removed, the tube could be put nack into half of the mold and the naphthalene removed was mdicated by the clearance b e t w e n the tube and the wall of the ,iioId. The direction of air flow had been marked on the tube hefore the run and n o v 10-degree sections were marked off on ine of the unchanged ends, starting from the zero mark. The .ube was then rotated in the mold to each of these mark? and the blearance determined by a feeler gage. Kith the streamlined tubes and flat plates, the feeler gage was sirjed in the same way to find the change at 0" and 180". The -ube was then cut into several sections and a posit,ive picture of *he cross sect,ion taken on Ozalid paper. Measurements 17-ere nade a t uniform distances about the circumference and all measuring n-as done as marl?- as possible perpendicular to the urface. Preliminary runs indicated that escellent uniformity was being obtained along the axes of the tubes, so that only one sec-ion needed to be measured. The uniformity was undoubtedly h e to an extremely flat flow front and the special end supports -hat kept the naphthalene away from the walls. The arrows on
Number
Reynolds
Figure 11. Nusselt N u m b e r vs. Reynolds N u r n b e r f o r Staggered T u b e Banks
-
1 = Hatcher ( 5 ) ; 2 = McAdams (70); 0 = row 3, round; 0 r o w 5 , r o u n d ; A = r o w 3 , s t r e a m l i n e d ; A = row5,streamIined
rhr ,-pc.cial shapes in Figure 2 indicatr, the artual distances that w r p measured on the shadow prints. SAMPLE CALCULATIONS
Tht: tollorring tquations n-ere used: Heat iransfrr I X ) : 3 =
-
Data of run 6 for a 4rigltb round tube.
:ir
IV = 00488 pounds 0
= 4 hours
A = 0.2375 square foot. bloleculrtr aeight naphthalene = 128 C D
= 3.2 X 10-4 rttrri.
K
=
0.0488
__~
128.2
x
4
x 0.2375 x 3.2 X
p
=, - 4 760 1t1.
G
= 12.000
0 993
(A)' The value 1.84.
id
10.'
1 250
=
3 84
'
thic group \\a- found to he practically constant at 1.250 X 0.998 X 29 X 1.84
=-
12000
n,oo.ij8
C, = 0.245
The value of this gruup v a s found to vary so slightly that a constant value could be assumed without introducing an appreciable error. n ---r
0.00593 X 0.245 X 12000 0.776
il
= 0.0454
Re
1.49 X = __-.
k
=
0.0158
Nu
7
20.Q X 1.49 0,0158 X 12 =
12000 12 X .0454
= 32,800
"*"
20,1r
Vol. 40, NO. 5 '
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
1092
thalene, The use of an average driving force would have changed the results by less than 270. I n addition, most experimental work on heat transfer to small single tubes also employs the initial temperature difference so that the data should shop- a better correlation on this basis. RESULTS
-4s this experimental method can be readily employed for both average heat transfer coefficients and point values around thr tubes, comparisons have been made with other data for single tubes on the basis of average results as \yell as local coefficients. Reproducihility of the data is good, as is shown in Figures 5, 10,11,and 13. Round tubes show the bcst agreement for duplicate runs partly because measurements are more easily made. The actual change of dimensions of the 1.5-inch round tube is illustrated in Figuie 3. lieasurements were made for the full 360" around the tube but are plotted only for 180" as the symmetry was \\-ell within the accuracy of the measurements. The average mass or heat transfer factor for single tuhes ie correlated by the following equation (Figure 4): j = 0.174 Re'."
All values are above the recommended curve as given by Chilton and Colburn ( 1 ) but are Tell within the total spread of data used by these authors to establish their preferred curve. The average heat transfer results for single tubes are compared n-ith other data in Figure 5 . The curve dran-n through the data gives the folloxing relationship between Susselt, anti Reynolds numbers:
Figure 12. Variation of Local H e a t Transfer Coefficient for Row 5 of a Staggered Round T u b e Bank (1) G = 20,800;
(2) G = 15,000; (4) G = 4560
Nu = 0.16 Reo."
(3) C = 9200;
For single round tubes, the local coefficient of heat transfer varies smoothlv from a maxinium at the front of the tube to a
Local Heat Transfer Coefficients. Local coefficient 3 were found by plotting I versus oi (Figure 3) and determining the area under the curve. This area was equal to half the w-eight removed [from 0 " to 180"). The jveight proportional to any ordinate could then be found and h calculated the same as above. The average coefficient, hav, is the arithmetic average of the local coefficients.
For streamlined tubes and Hat plates I is plotted against C and the same procedure followed as under round tubes. The equivalent diameter is found as follows: For streamlined tubes: Area = 1.36 square inches Circumference = 4.71 inches Hydraulic radius = 1.36/4.71 0.288inch de = 4 X 0 288 = 1.152 inches
-
For flat plates: Circumference = 4 . i l inches Area = 1.11 square inches Hydraulic radius = 1 , 1 1 / 4 , i l = 0.235 inch de = 4 X 0.233 = 0.94 inch
The initial driving force vas employed to calculate niass transfer coefficients. This is a good approximation, because even a t the lowest rates of air flow, the partial pressure of naphthalene in t.he exit air was only a little over 3y0 of the vapor pressure of naph-
C
-
Inches
C
-
=
O
U
9
Figure 13. Results of Duplicate Runs i n Row 3 of a Staggered Streamlined T u b e Bank
0 ( R u n 8) G
-
28,800;
0 ( R u n 10) G
- inches
= 28,200
Figure 14. V a r i a t i o n of Local H e a t Transfer Coefficients in Row 3 of Staggered Streamlined T u b e B a n k (1) G = 37,200;
(2) G = 28,500; (4) G = 12,100
(3) G
20,100;
1093
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1948
minimum betlveen 80' and 90 O and then increases until it reaches value at the rear of the tube t h a t is of the same order of niagnitude as the frontal maximum. Actual data are presented for several rates of flow in Figure 6. h comparison with data available in the literature is given in Figure 7 . I n this case the results are presented as Susselt numbers because they w e most frequently used to correlate heat transfer data in tube banks. It should be remembered, however, that Reynolds and Nusselt numbers are calculated by employing the single-tube diameter, so that the velocity across the tube is not the same for the same Reynolds number if the tube diameter is different. The data obtained by the various investigators were for single tubes varying from 1 to 12 inches, so that the velocity across the tube had approximately a tenfold range. This accounts for most of the differencesin numerical data. A comparison of the actual shape of the curves is all t h a t is n-arranted. The data obtained by the use of a naphthalene tube appear to be well within the range obtained by previous workers. The fact that the minimum is more sharply defined is to be expected, since it is possible to obtain a larger number of point values by this method. About a single streamlined tube the local heat transfer coefficient is a maximum a t either side of the front and a t the rear (Figure 8). The greatest rate of heat transfer is over t,he front half of the tube but the maximum rate is not exactly a t the front. The only apparent effect of air velocity indicates that an increase in velocity moves the maximum at the rear forward along either side of the tube. As the velocity is increased the air flow breaks away from the surface of the tube farther from the rear and increases the violence of the swirls and eddies to cause an increase in the rate of heat transfer in this region. About a single flat plate, the local coefficient,is a maximum a t the front and side (Figure 9). There is a great difference between the values over the front, but those to the rear are more uniform. Velocity seems to change the absnlute values over the front of t,he tube without having much effect, on the rates towards the rear. The maximum at the side decreases as the velocity decreases. For staggered tube banks of either round or streamline tubes the data (Figure 10) are best, correlated by:
IE
j = 0.554
Re****
This agrees very well with the curve recommended by Colburn ( 2 ) . The calculated Xusselt numbers can be expressed by the Following equation (Figure 11): Nu
-
0.55 Re0.65
These data fall a little above the line recommended by MChdams (IO) but are in excellent agreement with the data of Hatcher ( 6 ) v h o worked viith the same tube bank and obtained average over-all coefficients between condensing steam and the sir stream. The local coefficient of heat transfer about a round tube in the hank is a maximum a t the front (Figure 12); drops to a minimum at about 95' (almost 10' more than for single tubes); rises rapidly to another peak at 120"; drops again, and then increases until the back of the tube is reached. As would be expected, all these values are greater than those obtained for a single tube a t the same velocity. The greater variation is also due to increased turbulence and the effect of the tubes in the follon-ing r o x on the magnitude and shape of the m i r l s and eddies formed behind each tube. The accuracy obtained with streamlined tubes in staggered banks is illustrated by the approximately duplicate runs presented in Figure 13, Although the results cannot be duplicated as closely as with round tubes, the data agree \vel1 over most of the tube. Figure 14 gives the results obtained with a streamlined tube inserted in row 3 of a streamlined tube bank. I n general, although the absolute values are much higher than for a single
tube a t a corresponding velocity, the variation around the tube is not affected as much as with round tubes in going from a single tube to a bank. As was the case with round tubes, however, the minimum is shifted farther back on the sides of the tubes. Lack of tubing of the proper shape prevented a corresponding study of flat tubes in a tube bank. CONCLUSIONS
This nicthod of obtaining experimental mass and heat transfer coefficients for gas f l o gives ~ results that compare favorably with other methods. Very inexpensive experimental apparatus is all that is required. Equipment may be built out of wood or any other material commonly used for dummy construction and the measuring shape itself is relatively easily cast. The method is particularly useful in those cases where conditions vary greatly in one or more directions, so that single point measurements (as with thermocouples) may be in considerable error. Some limitations are readily apparent. Thin sections cannot be used and shapes must be such that they can be molded in a split mold. Experimental work must be carried out undpr steady temperature conditions below about 50" C. The artual rates of mass transfer must be considerably higher than those existing in still air, so t h a t normal losses of material by sublimation are negligible NOMENCLATURE
A
= effective original outside area of naphthalene tube, square feet
c = original circumferential distance flat plate, inches c, = specific heat, B.t.u. per pound,
on streamlined tube or
O F .
D = diameter of round tube, feet D, = effective diameter of streamlined tube or flat plate, feet d = diameter of round tube, inches de = effective diameter of streamlined tube or flat plate, inches G = maximum mass velocity of the air, pounds per hour, square feet h = heat transfer coefficient, B.t.u. per hour, square feet, F. I = change in a dimension of the naphthalene tube, inches j = heat or mass transfer factor K = molar mass transfer coefficient, pound moles per hour, square feet, atm. k = thermal conductivity, B.t.u. per hour, square feet, O F. per foot kd = diffusion coefficient of naphthalene L = length of streamlined tube of flat plate, inches Ji = molecular weight
hD hD s u = Susselt number - or -' k k P = total pressure, atm. P = vapor pressure of naphthalene, atm. or DeG Re = Reynolds number,
s, /
TV f
1
P
= change in Tveight of naphthalene tube during run, pounds f
angle from direction of air flov, degrees absolute viscosity of air flowing, pound per hour, feet density of air, pounds per cubic feet = time of run, hours =
/ 1 = P =
e
LITERATURE CITED
(1) Chiltori, T. H., a n d Colburn, A. P., IND. ESG.CHEM.,26, 1183 (1934). (2) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29,174 (1933). (3) D r e r , T. B.. and Ryan, W.P., Ibid., 26, 118 (1931). (4) Grimison, E. D., Trans. Am. SOC.M e c h . EILQTS., 59, 583 (1937). (5) H a t c h e r , J. E., thesis, Cornell Univ., 1940. (6) H u g e , E. C . . Trans. Am. SOC.Mech. Engm., 59,573 (1937). 17) k l r i n . T.. A r c h . T n r m e w i r t . . 15. 150 (19311. (8; Kruzhilid, G. H., J . Tech. h h y s . , 8, '123 (19.38). (9) Lorisch IT., J l i t t . Forsch., 322, 1 (1929). (10) M c l d a i n s . IT, H . , " H e a t Transmission," New York, McGrawHill Book Co.. 1942. (11) Pierson, 0. L., Trans. Am. SOC.Illech. Engrs., 59,563 (1937). (12) Small, J.,Phil. Mag., 19,251 (1935). (13) Vanderwaart, C. XI., thesis, Cornell Univ., 1940. RECEITED J a n u a r y 14, 1948
