Rate of Heat Transfer between Condensing Organic Vapors and a Metal Tube -
vapor. Of these three r e s i s t a n c e s , HE rate of transfer of F, H, RHODES .IVD K. only that of the t u b e w a l l c a n be heat between a vapor Cornell University, Ithaca, N. m e a s u r e d independently a n d a c c u c o n d e n s i n g on the * rately. It has been found, however, that outer surface of a horizontal cylindrical the thermal resistance between the inner wall of a cylindrical tube and the surface of the tube is usually computed from tube and water, a t about constant temperature, flowing by the Nusselt equation (f, 7 ) : turbulent flow through the tube varies exponentially with h = 0.725 [ k 5 d 2 g Q L / D pAt)]O ( 25 the reciprocal of the velocity, V , of the cooling water. The most probable value of the exponent appears t o be 0.8. Thus This equation has not been adequately tested by experiment. Most of the work on the condensation of vapors has been done we may write: w i t h s t e a m , w h i c h often, if not R = r, rm a/V".3 (1) usually, condenqes in separate drops where a = a constant and not i n a c o n t i n u o u s film, as assumed by Kusselt in his derivaThe thermal conductances If we a s s u m e t h a t rv is independtion. Only a few experiments have between several condensing ent of the rate of flow of cooling been made to d e t e r m i n e the rate vapors a n d a h o r i z o n t a l water, this is a linear equation beof heat transfer from condensing ormetal tube have been meastween R and 1/Vo.8. If, in a conganic vapors. The results generally ured. In general, the experiappear to confirm the equation, ald e n s e r w i t h a c o o l i n g t u b e of though the agreement between the known dimensions, made of material mentally determined values of known thermal conductivity, we observed and the calculated values agree satisfactorily with the is not always c l o s e . M c A d a m s measure the over-all thermal resistvalues computed from the and Frost (5) found, f o r b e n z e n e , ance a t known rates of flow of coolNussel t equation. film c o n d u c t a n c e s of from 306 to ing w a t e r a n d p l o t the values of 366 B. t. u. p e r s q u a r e f o o t p e r R a s o r d i n a t e s against the corres p o n d i n g v a l u e s of 1/Vo.8, the hour per O F. difference in temperat u r e b e t w e e n t h e v a p o r and the Doints should lie on a straight line. surface of the tube; carbon tetrachloride gave a value of 283. The intercept of this link represents the value of (T, rm). These results were obtained with a tube 0.675 inch in exterFrom this intercept and from rm, which can be calculated nal diameter. Kirkbride (2), using a tube 1.313 inches in independently, the value of rv may be computed. diameter, obtained values of 242 t o 381 for benzene and 174 In Equation 1 two tacit assumptions are involved: T h e to 361 for Cleaners' Naphtha. Bray and Sayler (4) report value of a remains constant in all of the individual measurea film conductance of 625 to 1300 for 95 per cent ethyl alcoments of a series of determinations, and the value of rv rehol, and of 374 to 547 for benzene. mains unchanged as the rate of flow of cooling water is varied. The first of these assumptions is justified if the average temperature of the cooling water is about the same in all of the Experimental Method individual experiments of the series. The assumption t h a t In all of these experiments, the temperature of the surface the value of rv is independent of the rate of flow of cooling of the condenser tube was measured by thermocouples set mater is certainly not correct. As the rate of flow of the water into the wall of the tube. Measurements made in this way is increased, there is an increase in the drop in temperature indicate the temperatures at, isolated points only; the average through the film of condensate and a decrease in the average wall temperature can be computed only by making certain temperature of the condensate. Both of these changes affect assumptions that may or may not be valid. Moreover, when the thermal resistance of the film. I n applying Wilson's a thermocouple is inserted in the wall of the tube, the flow of method, as outlined, to any series of experiments made with heat a t that point may be more or less disturbed so that therthe same vapor and with cooling water a t the same average mal conditions there are no longer normal. temperature, we are, in effect, assuming that Complications of experiment and interpretation may be avoided by the use of the indirect method originally suggested r,, = ru0 b/VO,S (2) by Wilson (8) and subsequently discussed by McAdams (3) where ru0 = vapor film resistance when velocity of cooling water and by McAdams, Sherwood, and Turner (6). The overis infinite all thermal resistance, R, between the vapor outside of the b = aconstant cooling tube and the water within the tube can be measured accurately and directly. It is the sum of the 6h-1resistance, Equation 1 thus becomes: rl, between the cooling water and the inner surface of the tube, the resistance, rm, of the tube wall itself, and the film resistance, ro, between the outer surface of the tube and the (3)
QT
+ +
+
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
958
There does not appear to be any exact theoretical basis for Equation 2 ; its justification is strictly empirical. If, in any series of experiments made with the same vapor and with
FIGURE 1. DIAGRAM OF APP.4RATUS T. Thermometer well S. Condenser tube P . Packing nut VI. Vapor inlet
co.
Outlet for oondenaate
cooling water a t about the same temperature, the measured values of R are found to vary linearly with l / V o 8, the approximate accuracy of Equation 3 would appear to be demonstrated, and the use of Wilson's method for the measurement of vapor film resistances would appear to be justified. Experimental evidence in support of the validity of the equation is afforded by the present results.
Apparatus and Procedure The apparatus used in these experiments (Figure 1) consisted essentially of a still in which the vapor to be condensed was produced, a measuring condenser, and a final condenser t o condense any vapor passing through the measuring condenser: The still was a steam-jacketed kettle, whose working capacity was 2 gallons, and which was made of glass-enameled cast iron. The jacket of the measuring condenser was a horizontal brass cylinder 1.375 inches in diameter and exactly 12 inches in internal length. Axially within this condenser was a cylindrical cooling tube of copper, 0.373 inch in external diameter and 0.044 inch thick. The inlet end of the cooling tube was extended horizontally 3 feet from the condenser to provide a calming section. At the outlet of the cooling tube was a mixing chamber. Two thermometer wells were inserted in the water line at the inlet to the calming section; in one of these wells was inserted a thermometer graduated to 0.1' C., in the other was placed a Beckmann thermometer set so that at the temperature of the entering water the reading on the thermometer was about + l o C. Similar thermometers were placed in the outlet line just beyond the mixing chamber. The discharge line was provided with a swing elbow so that the water could be diverted to a tared container for weighing.
FIGURE 2. VARI.4TI03 1. 2.
3.
Benzene Toluene Pentane
4.
5.
OF
VOL. 27, NO. 8
The vapor from the kettle passed upward through a half-inch line terminating in an inverted U-bend and was discharged into the top of the condenser through two ports near the ends of the jacket. The condensate was returned, through a trap, to the still; the uncondensed vapor passed through a side tube to an ordinary glass (Liebig) reflux condenser in which it was completely condensed. The condensate was returned through a trap to the kettle. All lines carrying vapor or hot liquid were thoroughly insulated, as was also the kettle. A heavy layer of thermal insulation covered the calming section of thelinlet water line, the measuring condenser, and the mixing chamber. In making a determination of the rate of heat transfer, about 2 gallons of the material to be distilled were boiled at such a rate that some of the vapor passed through the measuring condenser and was condensed in the reflux condenser. The velocity of the water through the measuring condenser was set at some constant value, and the distillation was continued until equilibrium was established and constant temperatures were attained. When the difference between the temperature of the inlet water and that of the outlet water was small, the rise in temperature was measured by the Beckmann thermometers. (After each setting, the Beckmann thermometers were compared and the difference in reading when the bulbs were at the same temperature was applied as a constant correction.) When the difference between the temperature of the outlet water and that of the inlet water was more than about 4' C. (7.2" F.), both temperatures were measured by the ordinary thermometers. When equilibrium was established, simultaneous readings were taken of (1) the temperature of the vapor, (2) the temperature of the inlet water, and (3) the temperature of the outlet water. After several consistent sets of readings had been obtained, the rate of flow of cooling water was measured by diverting the outlet stream to a tared container: collecting the water for a definite period of time, and weighing the water thus collected. The rate of flow of water was then changed and a similar set of observations was made at t'he new rate. No experiments were made with rates of flow of water less than about 230 pounds per hour, since at lower rates there is a possibility that true turbulent flow may not be maintained. The materials used were: Distn. Range
c. Benzene Toluene Pentane Hexane Octane Acetone, pure
(0
1.2 ( 2.16) 1 . 2 ( 2.16) 3.0 ( 5.4 ) 2 . 2 ( 3.96) 5 . 8 (10.44) ,
..
Distn. Range
c.
F.)
...
Ether, pure anhydrous E t h y l alcohol, 95% E t h y l alcohol, abs. n-Propyl alcohol n-Butyl alcohol sec-Pentyl alcohol
F.)
i:S ( 2 : s ~ ) 4 . 2 (7.56)
3 . 7 (6.66)
In all of the experiments except those made with octane, the cooling water was drawn directly from the main. With octane, the rate of condemation was so high when very cold water was circulated through the cooling tube that it was impossible to keep the measuring condenser filled m-ith vapor and to maintain a continuous flow of vapor into the secondary condenser. For this reason, in the experiments made with octane, the cooling water was warmed before it was admitted t o the condenser.
OVER-ALLRESISTANCE R I T H RATEOF FLOW OF COOLING WATER
Hexane Octane
( 0
.. .. .. .. ..
1. Acetone 2. Ethyl alcohol, 95 per cent Diethyl ether Ethyl alcohol, absolute
3. 4.
5. n-Propyl alcohol 6. n-Butyl alcohol
7. sec-Pentyl alcohol
AUGUST. 1935
INDUSTRIAL AND ENGINEERING CHEMISTRY
959
DATA TABLEI. EXPERIMENTAL Run
NO.
Ti F.
To-Ti
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
49.06 48.61 49.91 49.68 51.98 50.36 50.90 52.34 52.00 49.17 49.69 50.81 51.24 51.62 52.03
3.14 3.39 3.529 3.735 4.25 4.545 5.35 5.272 6.02 6.24 7.36 8.40 9.02 9.80 11.38
1 2 3 4 5 6 7
53.82 52.16 51.62 54.93 55.21 57.20 57.56
5.69 7.74 7.80 9.54 10.80 14.41 13.33
1 2 3 4 5 6
42.08 42.35 42.08 42.08 42.44 42.92
1.405 1.835 2.097 2.70 3.51 4.46
1 2 3 4 5 6 7 8
40.28 40.55 41.36 41.90 42.26 42.92 43.0i 43.52
2.99 3.385 3.91 4.86 5.12 6.21 6 87 7.56
1 2 3 4 5
6
40.55 40 28 41 00 41.27 41.30 41 63
F.
3.33 3.78 4.335 5.29 5.81 6.48
T" F.
'T
Lb./hr. B . Benzene 175.6 1417 5 175.6 1247.5 175.6 1172.5 175.6 1125 0 175.6 950.0 175.6 890.0 175.6 732.0 175.6 722.0 175.6 618.8 175.6 609.0 175.6 490.0 175.6 407.5 175.6 367.5 175.6 324.0 175.6 267.5 Toluene 229.6 952.8 229.3 671.3 229.3 667.5 229.6 510.0 229.4 435.0 229.4 292.5 229.4 325.0 Pentane 95.72 1083.8 95,90 770.0 96.44 679.0 96.35 502.5 96.67 365.0 96.62 257.0 Hexane 154.04 1016.3 154.29 905.0 154.22 753.8 154.4 570.0 154.4 475.0 154.4 412.5 154.4 357.5 154.4 315.0 Octane 239.18 922.5 239.5% 705.0 239.9 476.3 139.36 425.0 239.72 372.5 239.15 321.0
Run
Q
NO.
4440 4240 4140 4215 4050 4050 3905 3820 3730 3805 3610 3430 3325 3180 3040
0.0282 0.0296 0,0299 0.0295 0.0300 0.0304 0.0312 0.0316 0.0324 0.0325 0.0339 0.0352 0.0361 0.0374 0.0388
0.00300 0.00333 0.00351 0.00364 0.00417 0.00435 0.00510 0.00515 0.00581 0.00695 0.00704 0.00820 0.00886 0.00980 0.01150
5430 5200 5205 4870 4700 4215 4340
0.0318 0,0330 0.0331 0.0348 0.0357 0.0392 0.0382
0.00415 0.00549 0.00549 0.00685 0.00775 0.01063 0.00980
1523 1413 1424 1356 1280 1147
0.0347 0.0372 0.0372 0.0390 0.0403 0.0448
0.00374 0.00492 0.00543 0,00694 0.00892 0.01175
3040 3060 2950 2770 2670 2560 2460 2380
0.0370 0.0366 0,0376 0.0398 0.0410 0,0423 0,0438 0,0450
0.00392 0.00428 0,00500 0.00625 0.00726 0.00812 0.00900 0.01010
0 0264 0 0277
0.00384 0 00435
0 0298 0 0314 0 0318
0 00620 0 00699 0 00781
4060 3940 3775 3670 3490 3410 3500 3370 3235 3040 2870 2790
Ti
To-Ti
I".
F.
t. u./hr.
Experimental Results The results obtained in these experiments are shown in Table I. From the corresponding values of R and 1, VO.' obtained with each vapor, the slope and the intercept in Equation 1 were calculated by the method of least squares. The results for the various individual vapors are shown in Figure 2. In every case the separately determined values lie very close to the graph. The greatest discrepancies are observed with the paraffin hydrocarbons. That slightly more erratic results were obtained with these vapors is probably due to the fact that the paraffins were slightly less pure than most of the other materials, and also to the fact that with materials of low boiling point-for example, pentane and hexane-a small amount of impurity in the vapor had a greater effect upon the measured rate of heat transfer than it would have had if the condensation temperatures were higher. That the measured points do fall so closely on straight lines is evidence that this method of measuring the individual film resistance between the vapor and the surface of the tube is valid and that the assumptions upon which it is based are a t least approximately true. The various graph?, except that for octane, have about the same slope. Since the slope of the line depends upon the temperature of the cooling water and upon the nature of the vapor that is being condensed, it is to be expected that the graphs for different vapors and with cooling water a t slightly
1 2 3 4 5
48.05 48.97 49.24 49.46 48.47
2 3 4 5
1
6
48.74 48.92 49.10 48.92 49.28 47.93
1 2 3 4 5 6 7
41.18 41.0 41.0 41.72 41.72 41.72 42.26
1 2 3 4 5 6 7 8 9 10
51.08 51.62 52.16 52.79 53.5 54.46 54.74 54.70 55.84 54.76
1 2 3 4 5
51.85 52.25 52.25 53.42 54.32
1 2 3 4 5 6 7 8
50.54 51.11 52.14 49.64 51.94 49.80 53.33 48.47
Tv
F.
V
R
Q
~/vQ.=
Lb./hr. B. 1. u . / h r
Ethyl Alcohol, 95 Per Cent 172.04 1050.0 4370 172.04 827.5 4180 172.04 630.0 3960 172.04 495.0 3745 172.04 417.5 3620 Diethyl Ether 1.405 94.56 1020.0 1413 1.80 93.56 772.5 1390 2.305 558.0 1285 93.65 2.81 93.56 435.0 1222 2.825 93.74 420.0 1187 3.33 94.4 357.5 1190 E t h y l Alcohol, Absolute 3.67 i70.6 1087.5 4000 4.69 170.6 805.0 3770 4.956 170.6 746.3 3710 5.8 170.6 635.7 3685 6.84 170.6 517.5 3540 7.74 440.0 3410 170.6 8.82 170.6 367.5 3245 n-Prowl .. Alcohol 3.78 205.16 1147.5 4340 4.50 205.16 941.3 4235 4.86 205.16 865.0 4200 5.58 205.16 727.5 4165 7.16 205.16 551.3 3945 7.81 205.16 482.5 3770 8.67 205.16 422.5 3665 10.00 355.0 3550 205.16 11.16 205.16 299.0 3340 3210 12.60 205.16 255.0 n-Butyl illcoho1 4.3555 241.52 1147.5 5010 5.31 241.52 912.5 4845 6.21 241.52 761.3 4725 8.64 241.52 517.0 4470 10.6 241.52 395.0 4200 sec-Pentyl Alcohol 3.96 244.76 1182.5 4685 4.805 955.0 4585 244.76 5 88 244.76 768.8 4520 6 69 660.0 4420 244.76 7.41 244.76 585.0 4345 244 76 515.0 4325 8.38 10.70 944.76 381.2 4080 11.06 244.76 368.0 4075 4.15 5.06 6.28 7.56 8.67
0.0279 0.0302 0,0316 0.0329
0.00384 0.00465 0.00574 0.00699 0.00806
0.0311 0.0314 0.0338 0.0353 0.0362 0.0374
0.00392 0.00490 0.00633 0.00781 0.00800 0.00908
0.0390
0.0338 0.0342 0.0342 0.0354 0.0366 0.0382
0.00373 0 00476 0.00505 0.00571 0.00671 0.00763 0.00885
0.0351 0.0357 0.0358 0.0368 0.0374 0.0387 0,0398 0.0410 0.0427 0.0446
0,00357 0.00417 0.00450 0.00513 0.00640 0,00714 0,00793 0,00917 0.01061 0.01190
0.0374 0.0386 0.0394 0.0412 0 0433
0.00357 0,00429 0,00497 0.00780 0.00840
0.0410 0.0116 0.0420 0.0135 0.0137 0.0442 0.0455 0.0467
0,00348 0.00415 0.00495 0.00561 0.00613 0.00680 0.00854 0,00885
0.0288
different temperatures should not be exactly parallel. The small slope of the graph for octane is explained by the fact that the cooling water in the experiments made with this material was warmed. Many more points were obtained with benzene than with any other liquid. After almost every series of experiments with a single vapor the apparatus Kas cleaned, benzene was charged into the kettle, and one or two points were obtained with this material. This was done to insure that no corrosion or fouling of the tube, or other change that might affect the accuracy of the results, had occurred. The experimental results are summaraized i n Table 11. TABLE11. FILMCOXDUCTANCES BETWEEN METALAND CONDEXSING VAPORS Vapor Benzene Toluene Pentane Hexane Octane Acetone Ethyl alcohol, 95% Ether Ethyl alcohol, abs. n-Propyl alcohol n-Butyl alcohol see-Pentyl alcohol
Slope 1.255 1.139 1.253 1.137 0.390 1.297 1.182 1.292 1.070 1.136 1,206 1.040
Intercept 0.0250 0.0270 0.0302 0.0327 0.0391 0.0218 0.0234 0.0256 0.0284 0.0308 0.0332 0.03i2
h. B. t. u./sq. it./hr./O F. 412 382 341 315 263 473 442 403 364 335 310 276
In computing the resistance of the wall of the tube, the thermal resistance of copper was assumed to be 220 B. t. u. per square foot per hour per O F. per foot. Within each homologous series of compounds the t h e r m 1 conductance decreases by an about constant amount 8s we
INDUSTRIAL AXD EKGINEERING CHEMISTRY
960
pass from one member of the series to the next. vidual increments are as follows:
The indi-
-30
Benzene t o toluene Ethyl alcohol t o propyl alcohol Propyl alcohol t o butyl alcohol Butyl alcohol t o sec-pentyl alcohol Pentane t o hexane Hexane t o octane (two steps)
-29 -25
-34 -26 -52
This change is due, in part a t least, to the increase in the temperature of the vapor and in the rate of condensation with increase in the number of methyl groups.
Comparison with Values as Computed from Nusselt Equation The values for the thermal conductance that n-ere obtained in these experiments are for the limiting condition at which the rate of flow of the cooling water is infinite. Under these conditions the average temperature of the cooling water and the temperature of the inner wall of the tube should be the same as that of the incoming cooling water. Since the resistance of the wall of the tube is less than 0.5 per cent of that of the film on the vapor side, the drop in temperature through the film a t the limiting rate of flow is approximately equal to the difference between the temperature of the vapor and that of the incoming cooling water. From the Kusselt equation it is possible to conipute the theoretical thermal resistance when the drop in temperature through the film and the various physical properties of the material a t the average temperature of the film are known. These theoretical values have been computed for all of the liquids for which information concerning the physical properties a t the average film temperature are available (Table 111). In most cases the agreement between the observed and the calculated values is fairly satisfactory. I n every instance the calculated value is the lower, although the discrepancy is usually less than 10 per cent. With benzene and toluene, however, the discrepancy is considerably larger, without any evident reason. The data for toluene appear t o be even more consistent that those for most of the other liquids; with benzene a very large number of points were determined, all of which fall fairly close to the average line. It is true that the values for the thermal conductivity of benzene that have been determined by different investigators differ considerably among themselves, and that the value taken here may be
VOL. 25, NO. 8
cooling surface varies, since any change in this difference results also in a change in the average temperature of the film and in a variation of each of the controlling physical properties of the condensed liquid. Most liquids show an increase in thermal conductivity, k , with decrease in temperature ; the change is not large, but it may affect the value offsignificantly, since k enters into this function as the 0.75 power. The density also changes with the temperature, although the change of density with temperature does not markedly affect the value off. The viscosity increases rapidly as the temperature is lowered, but the effect upon the value off is relatively small, since p enters into f t o the 0.25 power only. The net effects of the changes in the physical properties of the liquid with change in temperature tend to cancel, and the value of f o , * 6 , for most liquids at least, changes only slightly with change in the temperature of the film. For example, for benzene we have the following values of j a t 30 O and60"C. (86"and 140°F.): Temp.
c.
30 60
k 0,0888 0.0877
d
54.2 51.3
P
f
(fSo/f30)0.2~
1.357 0,942
1.52 1.88
1:055
Thus, for any one vapor, we can write the approximate equation : h(D' X At)'.'' = K where h = thermal conductance between outer surface of tube and vapor, B. t.u./hr./s ft./'F. difference in temp. D' = external diam. of tube, inctes
The values of K for the various liquids are as follows: Acetone Ethyl alcohol, 95% Ether Ethvl alcohol. abs. Propyl alcohol Butyl alcohol
1150 1095 820 961 920 900
see-Pentyl alcohol Benzene Toluene Pentane Hexane Octane
806 1053 1085 723 800 732
The values of K given in this table were computed from experimental data obtained under such conditions that the average temperature of the f ilm of condensate was somewhat less than it would normally be under actual operating conditions. They are probably somewhat lower than would obtain under normal plant conditions, although the discrepancy is mobably not more than about 5 per cent. On the other {and, under normal operating conditions the drop in temperature between the vapor and the cooling water TABLE111. COMPARISON OF COMPUTED AND ACTUAL is considerably greater than the drop in temperature VALUES FOR FILMCONDVCTANCES Tav. Qo h Obsvd, h', h,h, between the vapor and the outer surface of the tube. Material O F . O F . In design calculations it would probably be perBenzene 113 125 0.0883 53.2 1.14 169 303 412 0.735 missible to use the values of K as given, and to Pentane Toluene 'g": ::$:: : : :E substitute for At the average difference between the Hexane 98 112 0.0790 40.2 0.654 150 282 315 0.896 temperature of the vapor and the temperature of 263 0.925 128 243 Octane 160 160 0.0816 41.8 0.80 .4aetone 88 94 0.102 48.6 0.726 223 412 473 0.870 the cooling water. 403 0.947 45 0.0797 44.3 0,556 151 382 Ether 71 In this work no special study was made of the 364 0.935 106 129 0.104 48.2 1.98 368 340 Ethylalcohol (abs.) Butyl alcohol 147 O.0953 48.6 2.59 254 Z47 310 0.798 effect of the velocity of the vapor upon the rate of heat transfer. Among the individual experiments there was some variation in vapor velocity, but the design of somewhat incorrect; but it does not appear probable that this value is sufficiently in error to cause the discrepancy. the condenser was such that the vapor had only a small comAdditional experiments with benzene and toluene have been ponent in the direction parallel to the surface of the condensing tube. Under such conditions the effect of even considerable made in this laboratory by other investigators, employing the same general method but using a different apparatus, variations in the velocity of the vapor should have little or no effect. In the condensation of a single pure vapor, turbulence and have given results that agree quite satisfactorily with within the vapor itself can have no direct effect upon the those listed in the foregoing. coefficient of heat transfer. With very high vapor velocities Application of Results i n Condenser Design the impact of the vapor on the surface of the condensate may decrease the thickness of the film and thus increase the rate of The Nusselt equation may be written: heat transfer. In a condenser with a single horizontal tube, h ( D X At)'.'5 = 0.725 ( k 3 ~ P & ? ~ / p )= ~ . 0~ .~7 2 5 j 0 . 2 5 this effect should be slight; if the cooling tube is inclined o r vertical, the effect of the velocity of the vapor may be more With any one vapor, the value off does not remain constant marked. In a large multitube condenser with closely spaced as the difference in temperature between the vapor and the ~
!g'
3":;
::: gii
3:
AUGUST, 1933
horizontal tubes, the rapid flow of the vapor past the tubes of the upper banks should increase the rate of heat transfer. Our results apply directly only in the case of a condenser with a single horizontal tube. In a large condenser with several banks of tubes, one above the other, the surface of each of the lower tubes is more or less blanketed by the drip from the upper ones, so that the average rate of heat transfer is decreased. It has been suggestjed that in a condenser of this type the vapor film resistance varies as the 0.25 power of the number of individual tubes in a vertical row.
All of the results given were obtained with a cooling tube of which the external surface was clean and free from dirt and scale. In the course of the work, a few experiments were made with a vapor that attacked the copper slightly and caused the tube to become coated with a thin layer of finely divided material, apparently copper oxide. With this fouled tuLe the apparent thermal resistance of the external film was from 10 to 20 per cent higher than the value obtained TTith the same vapor condensing on a clean tube: h,
Dirty Tube 396 366 343 292 269 257 326
even a slight fouling or roughening of the surface should hold more liquid on the metal and thus increase the film thickness.
Nomenclature d
= density, lb./cu. ft.
9
h k
= gravitational constant = 4.18 X 101, (ft./hr.)/hr. = thermal conductance, B. t. u./hr./sq. ft./’ F. = thermal conductivity, B. t. u./hr./sq. ft./(” F./ft.)
Qu
=
D = external diam. of tube, ft. D’ = external diameter of the tube, in.
Q
=
R
Effect of Fouling of Tube Surface
Vapor -4cetone Ethyl alcohol, 95% Ether Propyl alcohol Butyl alcohol Amyl alcohol Benzene
961
INDUSTRIAL AND ENGINEERING CHEMISTRY
h
Clean’Tube 473 442 403 335 3 10 276 412
In this respect the present results differ from those of Kirkbride ($) who states that he observed no marked difference between the results obtained with a clean tube and those with a slightly fouled one. It seems reasonable to assume that the presence of scale or dirt, even in slight amounts, on the surface of the tube should increase the film resistance, since
=
rv
=
rm
=
roo =
Ti
=
T, Tsv.
= = =
To
total amount of heat transferred, B. t . u./’hr. latent heat of vaporization, B. t. u./lb. over-all thermal resistance between vapor and cooling water thermal resistance between vapor and outer surface of cooling tube thermal resistance of wall of condenser i ube thermal resistance between outer surface of tube and vapor when velocity of cooling water is infinite temp. of cooling water a t inlet, O F. temp. of coolingTater at outlet, F. temp. of vapor, F. av. temp. of film of condensate, O F. difference in temp. between vapor and outer surface of cooling tube velocity of cooling water through tube of dimensions used, lb./hr. viscosity (in English units), centipoises X 2.42 O
Literature Cited Badger and Monrad, I N D .E N G .C H E X . 22, , 1103 (1930).
Kirkbride,Ibid.,25, 1324 (1933).
McAdams, Chem. & M e t . Eng., 3 4 , 5 9 9 (1927). McAdams, “Heat Transmission,” p. 261, New York, McGrawHlll Book Co., 1933. Mcddams and Frost, I N D .E N G .CHmf., 14, 13 ( 1 9 2 2 ) . McAdams, Sherwood, and Turner, Trans. .4m.SOC.Mech. Engrs., 48, 1233 (1926). Nusselt, 2. Ver. deut. Ing., 60, 541, 569 (1916). Wilson, Trans. Bm. SOC.Mech . Engrs., 3 7 , 4 7 (1915).
RECEIVED.4pril 5 , 1935
Courtesy, Carrier Engineering Carp.
INTERIOR VIEWOF CARRIER PLANTSHOWING LOW-TEMPERATURE CENTRIFUGAL REFRIGERATING MACHINE BUILTFOR SPECIAL APPLICATIOKIN THE CHEMICAL INDUSTRIES
