INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1949
silver pentachlorophenate had unusually high resistance t o deterioration in soil burial compared to the other treatments. LITERATURE CITED
(1) Am. Soo. Testing Materials, “Standard General Methods of
Testing Woven Textile Fabrics,” Designation D 39-39. (2) Am. SOC. Testing Materials, “Tentative Methods of Test for Resistance of Textile Fabrics to Microorganisms,” Designation D 684-42T. (3) Armstrong, E. F., Chemistry &,!ndustry, 60,668 (1941).
(4) Assoo. Official Agr. Chemists, Methods of Analysis,” 5th ed., p. 409 (1940).
1789
(6) Barghoorn, E. S., Office of Quartermaster General, Teztile Beries Rept. 24 (1946). (6) Dean, J. D., Strickland, W. B., and Berard, W. N., Am. Dyestuff Reptr., 35,346 (1946). (7) Dean, J. D., and Worner, R. K., Ibid., 36,405 (1947). (8) Fargher, R. G., J.Soc. Dyers Colourists, 61,118 (1945). (9) Goldsworthy, M. C., and Green, E. L., Phytopathologg, 29, 700
(1939).
(10) McFarlane, W. D., Biochem. J . , 26,1022 (1932). (11) Thaysen, A. C., Bunker, H. J., Butlin, K. R., and Williams, L. H., Ann. Applied Biol., 29,750 (1939).
(12) Zuck, R. K., and Diehl, W. W., Am. J . Botan?~, 33,374 (1946). RECEIVED August 11, 1948.
Film Coefficient of Condensing Vapor JU CHIN CHU, R. K. FLITCRAFTI, AND M. R. HOLEMAN2 Washington University, S t . Louis,M o .
A
modified method of measuring the heat transfer coefficient of a condensing organic vapor on a single horizontal tube is presented. The method of Wilson is not fundamentally sound in t h a t i t assumes t h a t the heat transfer coefficient is independent of the rate of heat transfer. It is shown theoretically t h a t the heat transfer coefficient is a function of the rate of heat transfer; therefore, the correlation of data obtained a t a constant value of rate of heat transfer will place Wilson’s method on a rigorous basis. This involves a major modification of the Wilson method. Experimental conditions of rate of water flow and over-all temperature difference are varied 80 t h a t data are obtained a t a constant rate of heat transfer under two or more conditions. The value
of the heat transfer coefficient a t a constant value of t h e rate of heat transfer is calculated according to the modification of the Wilson method. The over-all temperature difference is varied by changing the vapor system pressure. The experimental values of the heat transfer coefficient obtained a t low rates of heat transfer check those calculated from the Nusselt equation. The deviation of the experimental values from the calculated values increase as the rate of heat transfer increases. This may indicate turbulenoe i n the condensate flow a t high rates of heat transfer. The theoretical derivation of the relationship of the heat transfer coefficient and rate of heat transfer is confirmed by experimental data obtained on ethyl acetate and benzene.
T
the wall. The thermocouples measure only isolated point temperatures, and then i t is necessary t o make certain assumptions in calculating the wall temperature. Baker and Mueller ( 1 ) later proved that there is no point at which a thermocouple can be located in a tube wall and obtain the true surface temperature of the tube wall. Rhodes and Younger (12) avoided the use of an embedded thermocouple by applying Wilson’s method. Checked experimental values with Nusselt’s equation have been obtained with the exception of benzene and toluene. I n an effort to obtain further information on the subject of film coefficients of condensing organic vapors and to determine, if possible, the reason for the discrepancy in the values of toluene and benzene, i t was proposed t h a t a modification of the Wilson method (12, 1 4 , based on a rigorous theoretical analysis, be employed. Wilson’s method (14) has been well discussed by Mchdams (6, 7) and by McAdams, Sherwood, and Turner (9). It is based on the following equation of over-all thermal resistance for the transfer of heat from condensing vapor t o cooling water through a tube surface when the flow of water is inside a tube in turbulent region.
HE Kusselt equation (7, 10) is usually used in predicting
the rate of heat transfer between pure condensing vapor and a colder surface. The Nusselt equation for a single horizontal cylindrical tube is
ho
x
=
0.725(K,33;2gX/D#,
(11
The equation assumes t h a t streamline motion exists throughout the continuous film of condensate and that gravity alone causes the flow of condensate over the surface. The possible effect of vapor velocity upon the film thickness is neglected. The theoretical equation is based on the assumption that the total thermal resistance is in the condensate film. The film coefficients for benzene and toluene have been investigated previously by using an embedded thermocouple (6,8, la). The data do not check well among themselves, and in some cases the agreement between the theoretical ho value and the observed value is not good. There appear to be no previous experimental data on the film coefficient for ethyl acetate on a horizontal tube. Rhodes and Younger (1%’)pointed out that the use of thermacouples embedded in the tube to obtain the wall temperature had several disadvantages. There is likely t o be disturbance of the fluid film on the tube surface due to irregularities; however, with the present advanced techniques i t is probable t h a t the surface can be smoothed properly. The introduction of a foreign metal in the tube wall will be likely t o disturb the flow of heat through address, Monsanto Chemical Company, St. Louis, Mo. 1 Present address, Fouke Fur Company, St. Louis, Ma. 1 Present
ZR
=
Re
+ R w + CL/VO.’
(2)
where a = a constant. It was then assumed t h a t if R, R , was independent of the cooling water flow rate, a linear equation would result between R and 1/Vo.8. Using a condenser with a tube of known thermal
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
1790
R
R
Vol. 41, No. 8
The value of the group in Equation 1 (K,~{,?Q/ t o be a constant from results of calculation made ( 4 , 1 2 ) for most organic solvents, especially benzene, toluene, and ethyl acetate which are used in the present work. Therefore, for a given coriderisirig tube of definite dimensions, Equation 1 can be simplified into ~ 1 1 appears ~ ' ~
1
I
HI
where K represents a constant. Substituting Equation 6' into 5 and simplifying one obtains
Figure 1.
Heat Transfer from Condensing Vapor -4pparatus
corrduct,ivit,yand dimensions, t,lie over-all thermal resistance can be measured a t known water rates. A plot of the values of R as ordinates versus the corresponding values of 1/Vo.8should result in a straight line. The intercept of this line rcpresents t h e value of R, R,. The value of R, can be calculated independently; thus the value of R, can be determined. This equation assumes that the value, a, remains constant in a series of det,erniinat,ionsand t h a t changes in water rate have no effect upon R,. Rhodes and Younger ( 1 2 ) have pointed out t h a t the latter assumption is not correct. I n applying Wilson's method to any series of experiments as outlined, they assumed in effect that,
+
IZ,
=
R,o
+ b/I'O.'
(3)
where Z, = a constant. Substituting Equation 3 into Equation 2
R
'
=
R,G
+ R w + + b)/Vo.S (U
where K' is another constant which is equal t o
AK. A log log plot of ho versus p should give a straight line with the slope of minus one third. I t has been shoivn in Equation 7 that at a single value of q,
ho is constant no matter what the over-all temperature difference or rate of water flow. Therefore, it appeared desirable t o obtain experimental data such that a conetant value of q could be obtained a t different water flow rates. This can be done by varying the over-all temperature difference between the vapor and the water which in turn can be accoinplished by varying pressure maintained in the vafior space. If the simplified expression for heat transfer coefficient of water inside a pipe (7') is substituted into lhe usual expression of over-all tliernial resistance from one side to the other of a tube, the overall thermal resistance l/UOAo, wiiich is also equivalent to A?'/q, froin the condensing vapor t o the cooling water side can be represented by:
(4)
The justification for Equation 3 is empirical, as there is no theoretical reason for setting R, up as a function of R,, and the water flow rate. The final treatment of the experimental data is exactly the same as the Wilson method. Beatty and Katz (2)in their rvorli on condensing organic vapors on finned tubes maintained constant over-all temperature differences and presented their data in the same manner as that, of Rhodes and Younger ( 1 2 ) . They modified the expression for cooling water t o allow for changes in the water temperature and its effect upon the water film resistance. It appeared t h a t the method of Wilson was not fundamentally sound without modification. The equipment setup used by Rhodes and Younger ( I d ) was satisfactory in t h a t no thermocouples were embedded in the tube wall and t'hat t h e effect of vapor velocity was kept to a minimum. Therefore, the decision was made t o assemble equipment similar t o t h a t of Rhodes and Younger ( I d ) , with minor modification, and t o correlate the data in a manner which would be a modification of Wilson's method. As pointed out previously, the assumption t h a t R,o is constant is incorrect. According t o Equation 7, at a single value of q, the value of R, or ho (ho = 1/R,Ao) is constant, no matter what the value of the over-all temperature difference between the vapor and the cooling water, A T , or the rate of water flow. For a steady state heat t,ransfer through a condensing film, the rate of heat transfer, q, is by given (5) q = h4At
At constant values of q, ho is constant. The thermal resistance due to the tube itself is negligible, compared t o the other values. Therefore, for a given condenser tube all values in Equation 9 are constant except t h e rate of water flow, V, t , and the value of l/Uo. A plot of l/Uo& versus 1/(1 0.011 t ) W 8should yield a straight line a t equal values of q . A4fterthe plot is made as indicated above, the ho value can be
+
Figure 2.
Condensing Vapor Apparatus
August 1949
1791
INDUSTRIAL AND ENGINEERING CHEMISTRY
calculated from the intercept where (D)Oa2/A1150(1 equals zero; thus
+ 0.011 t)VOJ
or
From the above, it appeared that if several sets of experimental d a t a were obtained so that each set maintained a constant over-all temperature difference but varied the flow rate of the water, and these data were plotted as q versus the water flow, it would then be possible t o obtain two or more sets of conditions in which q was equal. The variation in the over-all temperature difference between the sets of experimental data would be obtained by operating the system under reduced pressure. When q was equal, the ho value would be equal. A plot of l/UoAo versus the rate of water flow at constant q would give a straight line. The value of ha, a t the constant value of q, could then be calculated from the intercept. DESCRIPTION O F APPARATUS
The apparatus used in this work (Figures 1 and 2) consisted essentially of a still pot, 1, in which the vapor to be condensed was produced, a measuring condenser, 2, a final condenser, 3, to condense vapor passing through the measuring condenser, a rotameter, 6, t o measure the water flow, and a vacuum pump, 11, to allow work under reduced pressures. The still pot, formerly a desiccator, was of aluminum construction and was 7.5 inches in inside diameter and 6 inches deep. About 25 feet of 0.125-inch copper tubing were coiled inside the vessel. The capacity of the still pot was 2500 ml. of liquid. The top contained connections for the vapor outlet, condensate returns from the measuring condenser and the secondary condenser, a charging openin and the steam inlet and exit lines. The jacket of t f e measuring condenser was a horizontal brass cylinder 1.5 inches in diameter and 12.7 inches long. A cylindrical cooling copper tube was contained axially within the jacket. The tube was sealed from the atmosphere by a stuffingbox type of construction at the inlet and outlet of the condenser shell. The tube was 0.374-inch outside diameter, 0.295-inch inside diameter, thus giving a wall thickness of 0.0395 inch. The length of the tube exposed to condensing vapors was 12.47 inches. From the above data, i t was calculated that the outside surface of the tube contained 0.1018 square foot of area. The inside tube area was 0.0805 square foot. The inlet end of the cooling tube was extended horizontally 4 feet 4 inches from the condenser to provide a calming section. The inlet water passed through a strainer and a calibrated rotameter, 0 to 20 gallons per minute range, and then by two thermometers before entering the calming section of the cooling tube. One thermometer, 7, graduated in 0.2" C., waB placed directly in the water stream. The second thermometer, a Beckmann (3), was placed in a thermometer well, 8, containing a small amount of mercury. The Beckmann thermometer well was located just ahead of the inlet t o the calming section. A similar thermometer setup, 9 and 10, was employed in a mixing chamber on the water outlet of the cooling tube. The vapor from the still o t passed upward through a one-half inch line and was discharges horizontally into the measuring condenser through two ports near the ends of the shell. A thermometer, graduated in 0.2' C., was placed in the vapor line just ahead of the condenser. The condensate was returned to the still pot through a liquid seal trap, 4. The uncondensed vapor was passed into an ordinar glass, water-cooled condenser, 3, where it was completely congnsed and returned through a liquid seal trap, 5. The steam entering the system was controlled by means of a pressure reducer valve (Spence, S-52-C, 0.25 inch, range 0 to 80 pounds per s uare inch gage) and a manually operated needle valve, locatedzetween the reducer valve and the still pot. The pressure in the system was controlled by means of a vacuum pump, 11. The pump was connected into the system at the exit of the secondary condenser. A vacuum gage, 12, indicated the pressure in the system. A liquid collecting trap, 13, and a n activated carbon scrubber were located between the vacuum gage inlet and the vacuum pump. Lines carrying organic vapor and cooling water were heavily insulated as was the condenser proper.
.
o
P
I (1
+
3 1 0.01 1t)V0.8
4
5
O'
Figure 3. Variation of Rate of Heat Transfer w i t h Rate of Water Flow for Ethyl Acetate
EXPERIMENTAL RESULTS AND TREATMENT OF DATA
The experimental results are presented in Table I, together with the calculated values for the expression of (1 X loa)/ (1 0.011 t)Voas,a representative plot of which versus the rate of heat transfer in the case of ethyl acetate is presented in Figure 3. DETERMINATION OF HEATTRANSFER COEFFICIENTOF CONDENSING VAPOR,ho. A number of straight lines were placed parallel t o the z-axis in Figure 3. Over-all temperature drop, AT, and the value of the expression (1 X 10a)/(l 0.011 t)Ve-8 at the equal rate of heat transfer were read. The value of 1/UoAo was then plotted versus (1 X loa)/( 1 0.011t)V*.8. This plot should yield a straight line and the value of the heat transfer coefficient of condensing vapor, hp,
+
+
+
0.0230
0.0210
4 .
0.0190
0.0170 d
0.01 50
0.0130
0
1
P
3
.1x (1
+
4
5
6
103 0.OlIt)Vo.'
Figure 4. Relation between Over-all Thermal Resistance and Rate of Water Flow for Benzene 0, A,
-
5 600 2600 B.t.u./hr.; 0, 3200 B.t.u./hr.; B.t.u./hr.; 0 , 3800 B.t.u./hr.; and
X 3400 B t u /hr . 4500 B.i.G./hi:
1192 can be calculated from the intercept. The plots of these data for benzene are in Figure 4. The toluene data plots are in Figure 5. Figure 6 contains the plots of the ethyl acetate data. The values of the heat transfer coefficient of condensing vapor, ha, a t the various constant rate of heat transfer, p, values were then calculated by means of Equation 9. DISCUSSION OF RESULTS
INDUSTRIAL AND ENGINEERING CHEMISTRY TABLE I. Run
Name of
No. 1 2 3
Compound
Benzene
Inlet Water Temp., ' C. 8.06 8.00 8.02 8.03 8.01 8.15 8.23 10.42 12.27 .44 7.31 8.13 9.83 9.90 9.50 9.49 9.56 7.70 7.69 7.70 7.75 7.89 7.32 7.51 7.39 9.19 8.74 9.65 8.48 8.64 8.83 7.98 8.12 8.10 8.17 8.20 7.58 7.69 7.48 10.14 10.08 9.70 10.02 9.42 5.14 4.92 4.78 4.90 5.53 6.23 6.50 6.20 5.90 6.50 6.80 6.90 5.26 5.11 5.12 5.03 6.25 6.40 6.40 7.20 6.95 6.91 5.02 5.24 5.00 5.24 6.42 7.31 7.33 6.90 6.80
,
It was found that the value of ho varies with p on the three compounds investigated; therefore, ho is a function of y. The ho values for benzene varied from 377 to 422 with y varying from 4500 t o 2600. The q values on toluene ranged from 6000 t o 2600 and the ho varied from 369 to 319. With ethyl acetate, q va.ried from 4800 t o 1900, and ho varied from 405 t o 458. These values (ho) were obtained from a plot of a minimum of two points and a maximum of four. The majority w e r e o b t a i n e d from three points. Additional points for p l o t t , i n g w o u l d h a v e been highly desirable. However, owing to the slope of the curves in the original plot, as in Figure 3, it would have been necessary t o make a series of experiments whose o v e r - a l l temperature difference varied from one another by only 5 " C. Inasmuch as the usual variation in the over-all temperature difference from run to run was *0.3" t o 0.5" C., there might be a tendency for some overlapping of t'he data. It is believed that the value of q shown in the original plot as in Figure 3 is correct within a range of *5%, The average deviation of the points from the curve is 2% of the average value io p. The Beckmann thermometer readings were estimated to the nearest 0.002" C. The average temperature rise was 1.5'; thus the percentage error involved in the Beckmann thermometer readings is negligible. The water flow rate varied a maximum of 5 %, and the average was much lower. It was shown in the introduction that the relat,ion of ho and p was such that a log log plot of ho and q should give a straight line with a slope of minus one third. This plot is shown in Figure 7 . The data for benzene are a littfe erratic. The data on toluene line up fairly well, but the slope of the line is positive. The data on ethyl acetate confirm the theoretical relationship of ho and q. The reason or reasons for the nonconformance of the data on toluene are unknown a t this time. There may be some unknown factors affecting the experimental results. It has
Water Temp. Rise, O C . 0,640 0.783 0.779 1.007 2.290 2.916 3.949 0.852 0.646 4.039 4.134 1.563 0.639 0.815 1,201 1.512 2.157 0,507 0,628 0.802 1.065 1,807 2.637 3.399 3.426 0.484 0,548 0.753 0.905 1,188 1.722 0.496 1.165 1.675 1.975 2,854 3.031 2.401 2.380 2.538 1.344 0.385 0.607 0.715 0.873 1.361 3.081 5.74 2.143 1.028 1.371 2.41 2.950 3.720 4.780 5.290 0,803 1.178 2.836 5.393 1.235 2.013 5.285 0.946 3.59 4.47 0.760 1.252 2.458 4.789 0.840 0,760 1.726 1.249 3.753
EXPERIRlEXTAL
Vapor Temp., 0
c.
79.4 79.4 79.4 79.4 79.4 79.4 79.4 80.6 80.6 79.9 79.9 79.4 78.8 78.8 78.8 78.8 78.8 68.6 68.5 68.6 68.8 69.2 69.0 69.5 69.5 59.8 69.0 59.6 59.2 58.8 59.2 58.1 58.5 58.9 58.9 59.4 58.8 49.0 48.8 52.0 50.5 50.1 50.3 50.3 109.5 109.5 109.4 109.5 109.5 110.7 110.5 110.4 110.0 109.2 110.1 110.0 101.1 101.3 102.2 103.0 102.2 102.2 103.3 102.5 102,6 104.1 91.2 91.8 91.7 92.2 92.3 92.3 93.2 93.5 93.0
RESCLTS
Over-all Temp. Difference between Water and VEpor,
AT,
Vol. 41, No. 8
C.
71.08 71.07 71.04 70.90 70.23 69.78 69.16 69.83 70.07 70.42 70.50 70.49 68.72 68.52 68.72 68.56 68.15 60.62 60.53 60.53 60.53 60.33 60.35 60.28 60.41 49.87 60.04 49.59 50.27 49.58 49.50 49.83 49.82 50.03 49.69 49.79 49.68 40.06 40.01 40.57 40.45 40.29 40.05 40.56 103.9 103.9 103.1 101.7 102.9 103.7 103.0 103.2 102.2 100.5 100.8 100.0 95.4 95.6 95.5 95.3 95.5 98.7 94.5 94.9 94.1 95.3 85.8 86.1 85.5 84.9 85.7 84.7 85.0 85.1 84.5
Water Flow U ,
Lb./Hr. 3887 3100 3150 2380 930 680 463 2900 3900 460 450 1435 3775 2875 1925 1450 965 4125 3100 2450 1825 935 660 475 475 4113 3360 2358 1975 1450 880 3600 1501 935 750 2455 440 440 460 160 975 3875 2425 2000 3913 2392 990 470 1475 3470 2520 1304 1023 780 334 500 3922 2803 965 445 2500 1463 475 3400 750 587 3905 2408 983 465 3102 3350 1450 747 583
q (ZZ), 1 x lo3 B.t.u./Hr. (1 0.011t) V ? . 4480 0.89 4370 1.09 4410 1.06 4305 1.30 3830 2.73 3565 3.50 3285 4.73 4490 1.09 4560 0.85 3340 4.77 3350 4.84 4030 1.94 4350 0.87 4225 1.13 4165 1.50 3950 1.90 3740 2.62 3770 0.73 3520 1.09 3540 1.29 3500 1.62 3150 2.84 3135 3.61 2910 4.68 2940 4.69 3360 0.83 3310 0.99 3200 1.29 3220 1 .so 1.92 3100 2740 2.84 3185 0.96 3150 1.86 2820 7.74 2670 3.23 2455 4.58 2405 4.96 1900 4.96 1925 4.88 2100 4.54 2360 2.61 2690 0.87 2650 1.25 2580 1.49 6207 0.92 5877 1.36 5512 2.67 4875 4.79 5710 1.97 6460 0.99 6240 1.06 2.15 5670 5460 2.59 5200 3.17 4880 4.14 4780 4.44 5715 0.96 5342 1.32 4935 2.76 4325 4.96 5575 1.31 5300 1.96 4520 4.68 5800 0.99 4860 3.26 4740 3.95 5355 0.92 5043 1.35 4383 2.73 4015 4.82 5120 1.01 4600 1.01 4540 1.96 4210 3.26 3940 4.00
+
been suggested that subcooling of the condensate might have been occurring. It is believed that this did not occur to any great ext,ent,as excess vapors were present a t all times. It was noted in the plots of q versus 1/(1 0.011 t ) V o . 8as in Figure 3 that the slope decreased as AT decreased. This is to be expected, as p will equal zero when A T is zero, no matter what the rate of water flow. A comparison of the observed values of ho with the theoretical values (Nusselt equation) is given in Table 11. Fouling of the condenser tube surface plays an important role in the film coefficients of condensing organic vapors. Rhodes and Younger ( 1 2 ) found that the apparent thermal resistance of the condensing film was 10 t o 20% higher on an oxidized surface than that of the same vapor condensing on a clean tube. The ratio of observed heat transfer coefficient to the value
+
r~ RESULTS (Continued) TABLE I. EXPERMEST!
Run No. 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149
Nameof Compound Toluene (Contd.)
Ethyl acetate
Over-all Temp. Difference Inlet Water Water Water Temp. Vapor between Water and Vapor, Flow U , ~ ( 1 1 ) Rise, Temp., Temp,, A T , C. Lb./kr. B.t.u./Hr. ( I + ' C. ' C. 4252 3780 74.7 80.4 0,622 5.47 3996 2380 75.1 80.7 0.928 5.12 3780 1005 26.2 82.5 2,086 5.26 3266 478 (5.4 82.4 3.813 5.39 3430 480 74.5 82.7 3,973 6.15 3555 558 74.3 82.1 3.551 6.15 3870 1400 75.1 82.7 1.512 6.90 3750 770 74.5 82.7 2,701 6.93 3780 633 73.8 82.6 3.304 7.09 2962 475 65.2 72.4 3.488 5.43 3207 992 65.5 71.7 1.794 5.32 3517 2450 65.0 70.9 0,794 5.49 3460 4003 64.9 70.9 0.476 5.74 3125 568 65.3 74,l 3.023 7.22 3170 760 64.7 73.3 2.309 7.39 3275 1433 65.4 73.3 1.267 7.30 3585 3467 64.7 73.4 0.574 8.01 3550 4306 64.8 72.9 0.457 8.00 2710 4052 54.7 62.6 0.371 7.73 2790 2357 55.0 62.7 0.657 7.39 2680 1038 55.0 63.2 1.431 7.43 2630 465 54.6 64.4 3.140 7.56 4807 3920 67.5 76.3 0.680 8.49 4740 3290 67.4 76.3 0.796 8.55 4550 2430 67.4 76.3 1.037 8.43 4390 446 67.3 76.6 1.686 8.43 3950 1018 66.6 76.2 2.155 8.43 3770 765 66.4 76.2 2.739 8.45 3615 558 66.2 76.4 3.503 8.45 3430 465 65.9 76.4 4.095 8.46 4025 4050 60.2 72.6 0.553 12.19 4075 3450 60.5 72.6 0.657 11.85 3950 2502 60.4 72.6 0.877 11.80 3720 1556 60:l 72.6 1,327 11.83 3450 980 59.9 72.8 1.954 11.85 3065 558 59.9 73.4 3.051 11.93 2995 468 60.0 73.8 3,579 11.94 4260 3333 60.2 72.2 0.710 11.60 3740 1418 60.1 72.3 1.461 11.45 3260 775 59.5 72.3 2.477 11.50 3050 580 59.0 72.0 2.916 11.45 3620 3943 54.8 65.2 0,509 10.21 3575 2500 55.1 65.3 0,794 9.97 3250 1003 55.4 66.3 1.800 9.98 3745 3500 55.2 67.2 11.70 0.599 3820 3915 55.2 67.2 0.542 11.75 3410 1425 55.2 67.5 1,330 11.62 3035 750 55.2 67.9 2.249 11.60 2780 468 55.2 68.5 11.62 3.304 3310 3478 55.2 65.2 0.528 9.80 1423 3150 55.1 65.2 1.221 9.50 763 3040 54.6 65.3 2.183 9.55 3010 630 54.3 65.2 2.649 9.53 3383 3080 45.0 56.9 0.505 11.73 1433 2910 45.0 1,129 57.3 11.69 3813 3235 44.9 54.2 10.13 0.472 2525 3090 45.2 55.4 9.88 0.679 2855 45.2 978 1.621 56.0 9.98 470 2315 54.8 56.2 2.737 10.01 3388 2980 45.0 55.1 0.488 9.96 793 2715 45.0 55.3 9 . 3 5 ' 1.771 633 2615 45.1 55.7 2.484 9.40 3935 2640 35.1 47.3 12.05 0.373 3433 2600 35.2 47.1 11.83 0.421 2448 2540 35.2 47.4 0.576 11.80 1558 2395 35.2 47.4 0.854 11.73 2270 1075 35.3 47.7 1.174 11.74 760 2125 35.3 47.9 1.551 11.80 565 1905 3 5 . 3 48.1 1.875 11.83 468 1840 35.2 48.2 2.186 11.88 3380 2360 3 4 . 7 44.5 0.385 9.70 1383 2130 34.7 44.5 0.849 9.35 755 2050 34.2 44.3 1.509 9.30 592 1995 33.9 44.3 1.874 9.45
c.
BETWEEK OBSERVED AND C A L C T L ~ T E U TABLE 11. COMPARISON HEATTRANSFER COEFFICIENT OF COXDENSISG VAPOR
q
Temperature Difference acrosy ho Condensing Vapor, Observed Theoretical At, F. Benzene
O.O1lt)VO.* 0 93 1.37 2.74 4.66 4.69 4.18 2.03 3.20 3.76 4.81 2.72 1.33 0.89 4.04 3.23 1.99 0.98 0.83 0.87 1.34 2.58 4.76 0.89 1.01 1.29 1.94 2.54 3.17 4.04 4.68 0.83 0.93 1.22 1.74 2.49 3.89 4.46 0.96 1.90 3.12 3.78 0.86 1.24 2.51 0.93 0.84 1.88 3.14 4.49 0.95 1.95 3.13 3.66 0.95 1.88 0.88 1.24 2.52 4.61 0.97 3.04 3.67 0. 0.94 1.23 1.75 2.36 3.03 3.89 4.52 0.98 1.99 3.19 3.84
w
calculated from the Xusselt equation approaches unity as the rate of heat transfer decreases. As the rate of heat transfer increases, more turbulence will be developed in the condensate flowing over the tube and the condensation deviates from a film type. The larger deviation of experimental heat transfer coefficients of condensing vapors from values calculated from the Nusselt equation is expected therefore, as the latter was derived on the assumption of streamline flow of condensate on the tube surface. The physical property values are important in the calculation of the theoretical film coefficient and the available data on some values, particularly thermal c o n d u c t i v i t y values, may be of limited accuracy. The value of At used in calculating theoretical value of ho may be slightly in error, as it was necessary t o use an average water temperature during the various runs on the three compounds in the calculation of Ai. The water temperature varied during the runs as follows: 7.3" t o 10.8" C. (benzene), 4.7" to 8.0' C. (toluene), and 8.4" to 12.0" C. (ethyl acetate). The experimental data were treated in the same manner as t h a t used by Rhodes and Younger ( 1 2 ) . A straight line may be drawn through the data obtained with any one over-all temperature difference. The experimental value of ho c a l c u l a t e d f r o m t h i s plot checked that obtained by Rhodes and Younger within 5%. This indicates that the Berformance of the equipment fs the same as t h a t -used by Rhodes and Younger ( 1 2 ) .
CONCLUSIONS
Ratio of Observed ha to Theoretical ha
A modified method of measuring the heat transfer film coefficient, based on a rigorous theoretical analysis, has been presented This method has the following advantages:
43
1.14 1.10 1.04
The use of thermocouples in the tube wall, which disturb the flow of heat and may disturb the fluid film, is avoided. Rhodes and Younger (12) used Wilson's method for correlation after introducing a new interpretation which is highly empirical. The proposed method is based on the following equations: ho = C4p-o.333
4500 3400 2600
377 402 422
330 365 405
6000 5000 4000
369 359 319
286 301 311
99
145 122 108
1.29 1.19 1.03
405 420 458
Ethyl Acetate 324 80 345 61 402 33
1.25 1.22 1.14
65
Toluene
4200 3600 2600
1793
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1949
X _1 _-- -1 UoAo hoA" + K T ,
(0)O.Z
+
A1 150(1 +
T
O
T
The values of l/UoAo can be obtained with different water rates a t the same value for the rate of heat transfer, 9, by varying
INDUSTRIAL AND ENGINEERING CHEMISTRY
1794 0.0240
Vol. 41, No. 8
8 SE
= d 500 UO
0.0220
ka
i:
9 0.0200
u 62
‘=
%
I/
s
EZ
0.0180
400
300
-0
4
?”
200
0.0160
2000 3000 4000 5000 6000 RATE OF H E A T TRANSFER, B.T.U./HR.
1
0
Figure 5.
2
3
4
1 x loail + 0.011t)V’.S
7
6
5
0 , Benzene, A, toluene; and @, ethyl acetate
Relation between Over-a11 Thermal Resistance and Rate of Water Flow for Toluene
0 , q = 3500 B.t.u./hr.;
0, 4000 B.t.u./hr:
@, hOO.B.t.u./hr.;
add
X, 4500 B.t.u./hr.: B.t.u./hr.
8,6000
A, 5000 B.t.n./lir.;
0.0220
3 0.01 80
=
= gravitational constant, 4.17 X lo8ft./(hr.)z
ho
= film coefficient of condensate outside
q
=
10 T i.
! ,
\
r
R
II
=
0.01 60
4
t = at = AT =
0.0140
U
0.01 20 1
0
2
4
3
1
(1
x
5
6
103
+ O.Ollt)Vo.*
3600 B.t.u./hr.;
0 : 3800 B.t.u./hr.;
ahd
6,4200
B.t.u./hr:
the pressure in the vapor space. This technique is new. Correlation of the data obtained a t a constant value of q places Wilson’s method on a rigorous basis.
=
X
=
h
= = =
r/ pf
Figure 6. Relation between Over-all Thermal Kcsistance a n d Kate of Water Flow for Ethyl Acetate C p = 2600 B.t.u./hr: 0 3000 B t.u./hr: x 3200 B.t.u./hr:
a’,
inside diameter of a tube, inches
D g
of a tube, B.t.u./’ (hi-.)(” F.) (sa. ft.) I
