Condensation of Vapors on a Horizontal Tube Heat Transfer Coefficient for Condensation of Vapors of Water and Nonmiscible Organic Liquids EDWIN M. BAKER AND UTAH TSAO University of Michigan, Ann Arbor, Mich.
Coefficients of heat transfer from vapor to a horizontal tube were determined for the condensation of mixed vapors of water and nonmiscible organic liquids. This work is an extension of the research previously published by Baker and Mueller ( I ) . In the present work a much wider range of vapor compositions was studied for systems of water vapor mixed with vapors of benzene, toluene, chlorobenzene, trichloroethylene, or tetrachloroethylene. The data were correlated into the following relatively simple equations :
ht
-1-- 0.0167
1
500 vol.
- 0.0085
% HzO
+ 80
D
$
where D
0.0284
- 7) 1.67
366 . (l \ h - 1 - 0.0085 vol.
% ' HlO
+
%-
= outside diameter of tube, ft.
h, = coefficient of heat transfer, based upon AT calculated from saturation temperature of mixed vapor, B. t. u./ (hr.)('F.)(sq. ft.)
The value of ht given by either of these equations is independent of A T .
T
vapors is almost a virgin field. Little previous work has HE condensation of mixed vapors of nonmiscible liquids on a horizontal tube may seem a narrow and unimporbeen done. Kirkbride (6) established values of heat transtant problem. But the extent of theuse of steamdistillafer coefficients for benzene and commercial petroleum products with water. Patterson et al. (9) worked on the tion in the organic and petroleum industries indicates the imheptane-water system in a vertical condenser. Baker and portance of the problem. The mechanism of this type of Mueller (1) reported data on the nonmiscible liquid SYScondensation is very complex. If two liquids wetted the condenser tube equally well, they would probably form films of tems benzene-water, toluene-water, heptane-water and tric h l o r o e t hyleneliquids side by side on the tube. If water. neither of them wetted the tube, Apparatus they would probably form drops The condensation of the vapors of liquids side by side on the tube. of n o n m i s c i b l e liquids is usually If o n e l i q u i d drop-film type. wetted the tube The readings of better than the other, the former thermocouples are erratic, and i t was would form a film realized t h a t on the tube, and the latter would t h e r m o c o u p 1e s were not ideal for form drops on the film. The last case this type of work. A method which is encountered will give an when water and water-immiscible average temperature of the whole organic liquids are tube was adopted. condensed on a This method was copper tube. The condensarecommended by FIGURE1. DIAGRAM O F APPARATCS Jeffrey (4). The t i o n of m i x e d 1115
INDUSI'IIIAI. AND ENGINEERING C H E & l I S ' ~ l ~ Y
1116
copper tube itself \vias used us a resistance thermometer. The total resistance of even a thin-walled copper tube is so low that special methods for measuring its resistance have to be used. The apparatus is shown in Figure 1 :
~~
~~~~
~
~
.
~~
YOL. 32, NO. 8
Tho total rcsistnnms of thP Irtd wires. m , M , y, and z are so small, compared \rith the 1000-ohm r~sistaiicrsA , B , a, and b, thnt they can be neglected. \Then the Kelvin hridga circuit is balanced, the reiiistnnce o i tire tiibe can be ealcol;ited by the following equation:
.~ ~~..~ .. ~ ~ Jeffrey
condenser (Figure 2) is provided xith three windows ior the observation of the conditions of condensation. Rubber &omem
is provided to 'eollect the condeisate iormed'between the fins. Thc excess vapor having the main condenser is completely condensed in a total condenser, on which a vent is provided to e x p d the noncondensablr gases. Two Liebig glnss condensers are attached to the main condenser to collect and condense for analysis sam ler of inlet and outlet vapors. The pressure in the main eon&& is measured by R morcirry mnnometw.
~ that, ~ ~ ~tilbo with ~ the valrte of strowed fW a tlrin-nnllcd 17 = r* / T < = 1.23, the ternporntiire a t any point in the tube wail is proportional to the railitis at that goiiit; and the relation between the mean temperature and resistance is as follows:
J d r e y also showed that for a tliin-~~-alled tube, wit,h the variations of temperatures around and along the tube, the measured resistance of the tube provides a direct measure of its average resistivity and hence its temperature. (This method does not give t,he variat.ion of temperature dong the tube, which was shown by Mueller and Baker to be small if the cooling wator was circulated at irigh idocity.)
All conilrnsnte is sent to BLI nut,omtLiic sepnrator which separates the nonmiseible liquids and sends each hack to the corresponding still. The condensate collected in the trough is sent to the separator under ordinary conditions. It can also be sent to a small receiver for the determination of the rate of condensation by turning B three-way cock. A part of the pipe nhich carries away the condensate from the trough is made of Pyrex .glass ....~.~~ ..~~~.~I ~
from a 3-inch Pyrex glass cylinder. Any leakage of the threeway cock leadine to the receiver c&n be quickly discovered. The
weighing. The cooling water for the rnnin condenser is recirculatod by a centriiugal pump from a reservoir tmk, whlch is provided with a steam .~ heatine device and an overflow connection. A city water lino is connezed to tho suction side of the prim A small bypass line is attached across the valve regulating t t e city wuter in order to facilitate close adjustment of tho temperature of the cooling water. The inlet and outlet water temperatures are measured by ordinary mercury thermometers. The velocity of cooling water is measured by B calibrated orifice with a mercury mnnometer. For measuring the resistance of the eondenscr tube, tuo copper wires itre soldered around the eondensor t,ube close to the fins. They are led to an electric circuit as shown in Figure 3. 0 is IL direct-current generator which delivers 150 a,mpeeres a t 3 to 4 r.olts. R is the condcnser tube. S is a shunt in a bath a t conatnnt temperature. The temperature coefieient of the shunt is so low that its resistance remains ractically constant within ordinary temperature variations of t i e bath. Ga LS x sensitive gslvanometer. A , B, a,and b are resistances of 1000 ohms. A' and a' are variable-resistance bores. One resistance box is chosen as a standard, and against it d l the others are calibrated. I n the bridge circuit only the ratio of the resistances are important; thereiore no absolute standard resistance is required. Jeffrey set A, B and a, b a t a definite ratio and adjusted S to balnnce the bridge. The resent equipment is a slight modification. S is a fixed standarfresistance, but A ' and a' are adjusted to balance the bridge. ~
Aftor the a w a g e temperature i3 obtained, the outside surface temperature of the tube call be calculated from AT across the tuhe. The AT across the tube can be calculated from the following equation:
(3)
Figure 4 is a plot of the temperature difference betreen the center of the tube (or average tube temperature) and the outside surface tcmperat,ure of the tube, against &/O (E. t. u. transferred per hour). T h i s plot is more convenient than Equation 3 and also indicates the small magnitude of this correction for thin-walled tubes wiili small or moderate coefficients of heat transfer. The heating effect of a current 5s large as 150 amperes is entirely negligible in the present experiments. The total resistance of the tube is around 400 micro-ohms for the 20-gage/Iinch tube and 650 micro-ohms for the %-gage/
AUGUST, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
5/ginch tube. The amount of heat produced by a current of 150 amperes is 8.4 B. t. u./hour per foot of the 1-inch tube, and 13.6 B. t. u. for the 5/s-inch tube. Usually the rate of heat transfer in the present experiment is around 10,000 B. t. u./hour/foot of tube, and then the heating effect amounts to only about 0.1 per cent even if the current is left on continuously. During the experiment only a few seconds are required to observe any swing of the beam of light on the scale of the galvanometer, and the current is flowing only when necessary for measurements of tube resistance. The present equipment was set up without any inductance effect in the circuit to disturb the galvanometer when the circuit was intermittently connected. The current of 150 amperes goes through an “idle” condenser tube in the iron casing of the main condenser in one direction and returns in the test condenser tube in the opposite direction. The copper tube, with its inner wall previously dried, was calibrated in place with benzene vapor and also with steam a t different temperatures. It was found that the temperature coefficient of the copper tube checks with the value given in the literature for copper; that is,
+
Rt = R, (1 0.0041181 2 - 0.0000019988 t Z ) where t = temperature, C. Rt, R, = resistances at t o and 0” C., respectively
(4)
O
The mean value of R, calculated from different values of Rt does not deviate from the individual values of R, more than 0.1 per cent. For temperatures below 80” C. the relation between temperature and resistance was obtained by extrapolation of Equation 4 and checked by circulating water through the tube a t different temperatures where there was no vapor in the condenser. The temperature of the water was measured by a mercury thermometer previously calibrated against a standard thermometer. The resistance of the tube was checked frequently and was found to vary little or not a t all from day to day, unless some vapor which attacks copper was introduced ; nevertheless, the calibration was checked frequently. The sensitiveness of the equipment is about 0.1 O F.
1117
There are two orifices on the two steam lines leading to the two vapor generators. The relative amount of heat supplied to each generator can be maintained constant by keeping the same reading on the manometers in the steam lines; thus the composition of the vapor to the main condenser is kept constant. The vapor temperature is a good indicator of the vapor composition. The thermocouples in the vapor phase indicate almost instantaneously any change of vapor composition.
Physical Properties of Binary Systems of Nonmiscible Liquids When the pressure and the composition of the vapor of a binary system of nonmiscible liquids are fixed, the temperature for equilibrium is definite. The temperature a t which only one vapor is saturated-i. e., is in equilibrium with its liquid-is defined as the dew-point temperature of the vapor mixture. The dew-point temperature a t fixed pressure will vary with vapor composition, and the lowest dew-point temperature, sometimes called the “pseudoazeotropic temperature”, is defined as the eutectic temperature. At the eutectic temperature the relative concentrations of the two components in the vapor are proportional to their vapor pressures at that temperature. This vapor mixture is defined as the eutectic mixture. Thermodynamically the eutectic mixture is the most stable mixture, because if any partial condensation of the mixture occurs, the noneutectic mixtures always tend to change into the eutectic mixture. 1.8,
I
I
I
I
I
I
I
I
I
1
Procedure Before a run was started, all cooling water was turned on and then steam was sent to the stills. For several hours the apparatus was thus heated thoroughly. The cooling water was maintained at a temperature and flow rate as constant as possible. The temperature of the cooling water controlled the temperature drop for each run. During a run readings were taken of the thermocouples in the vapor phase, the inlet and the outlet temperatures of the cooling water, the temperature of the condensate, the Kelvin bridge readings, the rate of flow of cooling water, and the pressure in the main condenser. When these readings remained constant for 5 minutes, a sample of condensate was collected within a short interval of 30 seconds to 2 minutes, depending upon the rate of flow of the Condensate. All readings were checked in the beginning, in the middle, and a t the end of collection of a sample. The condensate was cooled and weighed. For the nonmiscible liquid systems the analysis was carried out simply by separating the two components in a separatory funnel and weighing the separated parts. The condensates collected from the auxiliary condenser during the run were also analyzed for their compositions. After analysis all the condensates were returned to the apparatus through a funnel connected to the automatic separator. From the amount and composition of the condensate the heat transferred through the section of the tube between fins can be calculated.
FIGURE 4. TEMPERATURE DIFFERESCEBETWEEN SURFACE AND CENTER OF TUBE us. &/e
The vapor mixtures led to the main condenser were in the dew-point state or eutectic state under all experimental conditions. For low-temperature drops in the condenser the vapors of noneutectic mixtures change composition during condensation, owing to the partial condensation of the excess component in the mixture. The eutectic mixture will condense even a t very low temperature drops without any change of the vapor composition.
Calculation of Heat Transfer Coefficient for Condensing Film The organic liquids under investigation all have better adhesion tension with copper than does water. Therefore the organic film wraps the entire tube, and water drops float on or rather are immersed in the organic film. The vapor next to the condensing film must be of eutectic composition, because a t this point a three-phase condition of two nonmiscible components exists. Therefore the true temperature gradient across the vapor film is the difference between the temperature of the surface of the tube and the eutectic vapor temperature of the mixture under the existing pressure. For all the
INDUSTRIAL AND ENGINEERING CHEMISTRY
1118 1
1600)
I
I
I
I
I
VOL. 32, NO.8
calculations of the vapor-film heat transfer coefficient, h, from the experimental data this temperature difference is used for the temperature drop AT in the equation:
I
ht =
0
v
T
A A 1.314-IN. X
+
1.0
1.2
16001
1.4
1.6
1.8
2.0
2.2
I
I
I
I
I
TOLUENE CHLOROBENZENE TRICHLOROETHYLENE MUELLER d BAKER BENZENE TOLUENE
2.4
2.6
2
&/e
~
AT X A
(5)
To calculate the heat transferred through the tube between the fins from the amount of the condensate collected in the trough during a certain time interval is rather simple. Since the two liquids are nonmiscible, they can be treated separately as two individual liquids. The total amount of heat transferred can therefore be calculated as the summation of the weight of each component multiplied by the latent heat of vaporization of each component a t the eutectic temperature, plus the heat of cooling the vapor from the dew-point temperature to the eutectic temperature. The latter usually amounts only to a fraction of one per cent of the former. The total outside area of the condenser tube between the fins is 0.96 square foot for the 1-inch tube, and 0.60 square foot for the 5/a-in~htube. The time intervals in the experiment were measured by an electric clock with a long second hand.
Correlation of Data and Explanation of Results
-’ I
600
400
Kusselt’s equation for condensing pure vapors is as follows: 0
I
0 0
I
d
A
I
BENZENE TOLUENE CHLOROBENZENE TRICHLOROETHYLENE
I
I
Krkbride presented an equation for the condensation of binary systems of nonmiscible liquids as follows: h =
hwQw Qw
+ +
(7) &a
where the individual film coefficients were determined by the Kusselt equation. Baker and Mueller pointed out that Equation 7 is unsound mathematically. Baker and Mueller presented an empirical equation for several mixtures,
where p , C, and X of the mixtures were determined according to the weight of each component present and k was weighted on the basis of the volume of each component in the liquid phase. The viscosity, p , was not weighted, but the viscosity of the component forming the film in the drop-film type condensation was used. Baker and Mueller tested a narrow range of &./& and warned against using their equation for a wider range than was covered experimentally. This research shows that the warning was justified. This research has also confirmed the finding of Baker and hlueller that the temperature drop AT
FIGURE 5. CORRELATION OF DATAWHEN TUBE TEMPERATURE Is BELOW THE DEWPOINT OF BOTHCOMPONENTS F I G ~ R6.E CORRELATION OF DATA WHEN TUBE TEMPERATURE Is ABOVETHE DEWPOINT OF ONE COMPOWENT FIGURES 7 AND 8.
C O R R E L A T I O N O F DAT.4 B Y
EQUATION 12
AUGUST, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
has little or no effect upon the heat transfer coefficient, h, and further showed that the coefficient decreases with a decrease in the diameter of the tube. Both of these findings indicate that the Nusselt equation for the condensation of a single vapor on a horizontal tube will not apply to the condensation of mixed vapors of nonmiscible liquids. This is perhaps surprising, since the tube is covered with a film of organic liquid, which preferentially wets the tube. Unfortunately, values of the group (k3p2X/p)‘/4 for all of the organic liquids tested do not differ by more than 10 per cent of the mean value. Hence, even if some modification of the Susselt equation could be applied to the resistance of heat transfer of the organic liquid film, the different systems of liquids tested would not reveal with certainty any effect of the change in value of this group of physical properties.
Mechanism of Condensation I n the experiment the mater forms drops which are immersed in the organic film. These water drops roughen the surface of the film of the organic liquid and embed the film with a material of relatively high thermal conductivity. This will improve the thermal conductivity of the organic film, which is the controlling film. The higher the percentage of water in the condensate, the rougher is the organic film. Hence an empirical factor such as 1/(1 - C X vol. % H20) might well be expected to apply to an equation for the film coefficient for drop-film condensation. This group really represents the roughness of the organic film. For each tube diameter, plots were made of h, against 1/(1 - 0.0085 X vol. yoHzO). These are shown in Figures 7 and 8. While not perfect, the correlation is relatively good and a t this stage of our knowledge may be considered satisfactory. The actual mechanism of condensation was studied for some indication of the effect of tube diameter on heat transfer coefficient. According to the Nusselt equation for the condensation of single vapors on horizontal tubes, smaller tubes should have higher heat transfer coefficients than the larger tubes, but the present experimental results on the vapors of nonmiscible liquid mixtures indicated the opposite effect. The explanation of this lies in the roughening effect of the organic film next t o the tube by embedded water drops. Also, during the condensation of vapors of nonmiscible liquids large drops of organic liquid hang on the bottom of the tube before they grow large enough to drip off the tube. The organic film on the bottom of the tube is therefore very thick. The water drops which form on the organic film may leave the film by the combination of centrifugal and gravitational forces before they reach the very bottom of the tube. For these two reasons there is not much roughening effect of water drops on the film on the bottom portion of the tube. This part may be considered inert to the roughening effect. The extent of this “inert” part of the tube surface depends upon the physical properties of the liquid covering that part and is about the same for large and small tubes. The proportion of the surface which is inert is naturally greater for small tubes than for larger tubes. The heat transfer coefficient for large and small tubes, therefore, should be capable of correlatjon by multiplying each with a proportionality factor. The empirical factor found was 1/ 1 With this factor, results for s/g-, 1-, and 1.313-inch tubes can be correlated very well. A plot of
(
h i / ( l - 0’0167 7) against 1/(1
1119
partial pressures in the vapor mixtures. This plot is shown in Figure 5, and from i t an equation was derived, as follows: h,
0.0167 1-D
-
500
1
- 0.0085 v01. % HzO
+ 80
(9)
From this equation the values of hLwere calculated and compared with the values of ht observed in the experiments. The maximum deviation for different vapor mixtures does not exceed 15 per cent except for the tetrachloroethylene-water system, and for a few runs where the tube temperatures were below the dew point of only one component. The tetrachloroethylene-water mixture attacked the copper condensing tube used, and the experimental data were rather erratic. Therefore no data mere plotted on the tetrachloroethylene-water system. The observed values of h, for this system were generally high and rather indifferent to the composition of vapor mixtures. The changing surface condition of tube resulting from chemical reaction caused water drops to attach directly to the tube and to be held on the tube rather firmly. These water drops roughen the tetrachloroethylene film from inside. The extent of this kind of roughening depends entirely upon the size and number of water drops, which are determined much more by the nature of tube surface than by the proportion of water in the condensate. TUBETEMPERATURE ABOVE DEW POINTOF ONE COMPONENT. When the temperature of the condensing tube is above the dew point of only one component of the vapor mixture, partial condensation occurs on the tube. The data do not correlate well on any basis, but a fair correlation was obtained by using the average composition of inlet and outlet vapor in place of composition of the condensate collected from the condensing tube. The results of this correlation are plotted in Figure 6, but the corresponding data are not given in the tables.
Alternate Correlation Equation 9 is subject to the criticism that for a tube diameter of 0.0167 foot the calculated value of ht is 0, and for smaller diameters ht is negative. It is a simple relation which showed satisfactory results for tube diameter of about ‘/2 to ll/z inches. An equation free from these objections can be developed by assuming a constant width at the bottom of the tube blanketed by thick drops of organic liquid, and computing the mean coefficient, h, as a weighted average of the coefficient on this blanketed portion of the tube and the coefficient on the part of the tube roughened by the water drops. Thus
where ht
=
coefficient of heat transfer for entire tube
The value of h, should be affected by the roughening effect of the water drops and should also respond to the amount of condensate formed on the tube. Therefore ha, according to the Kusselt concept, should be proportional to (l/D)l ’4. Therefore,
y).
- 0.0085 X
vol. % H20)
was made for all the data obtained when the tube temperatures were below the dew point of both components a t their
where C is a constant. Evaluation of the constants, from the data of this research gives ht =
366
%
0.0284
(l
- 7)1.67 (12)
1 - 0.0085 vol.
70 H,O -k 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
1120
VOL. 32, NO. 8
TABLEI. EXPERIMENTAL AND CALCULATED DATA"
.
Run No.
,
,
Wt. of Pres- ,Temperature, ' F. Rate of Consure, ConCooling denhfm. hlean Satura- hlean den- Cooling Water Water, sate, BQt!:./ Hg tube tion AT In Out sate In Out Lb./Hr. Lb./Hr. Hr.
11 18 34 49 51 127 128 132
746.5 747.3 741.9 741.7 741.7 745.0 749.0 750.0
109.4 139.5 106.8 123.2 114.8 107.1 106.4 116.5
155.9 156.0 155.6 155.6 155.6 155.8 156.1 156.1
46.5 17.5 48.8 32.4 40.8 48.7 49.7 39.6
162.5 163.3 184.3 193.6 197.1 170.3 167.7 156.4
157.8 159.3 178.3 190.6 193.5 169.3 166.7 156.4
63 71 73 79 95
740.9 744.5 744.7 742.4 743.3
133.8 138.2 157.7 128.5 126.1
183.0 183.3 183.3 183.2 183.2
49.2 45.1 25.6 55.7 57.1
202.8 183.7 183.9 200.7 187.4
201.0 183.7 183.9 199.3 186.4
111 115 121 122 124 126
744.9 741.5 749.4 749.2 741.0 752.9
138.5 142.5 135.1 138.2 129.7 127.1
194.8 194.5 195.0 195.0 194.5 195.2
56.3 52.0 59.9 56.8 64.8 68.1
200.9 205.3 197.7 199.0 219.7 230.4
200.5 204.7 196.9 195.6 205.1 220.4
142 145 148 174 177 189
742.0 742.0 742.0 743.5 744.5 765.4
112.2 112.2 111.5 113.5 117.9 125.6
162.0 162.0 162.0 162.0 162.1 163.5
49.8 49.8 50.5 48.5 44.2 37.9
172.2 168.3 164.9 183.1 196.7 166.4
170.8 166.9 163.7 178.7 193.3 165.8
193 198 199 203 205 207 208 209 211 212 213
743.0 64.1 155.6 748.4 101.4 156.0 748.4 124.2 156.0 749.0 109.8 156.1 745.0 96.6 155.8 744.0 69.4 155.7 744.0 98.1 155.7 743.0 71.6 155.7 743.0 72.7 155.7 743.0 74.6 155.7 741.0 76.6 155.5
91.5 54.6 31.8 46.3 59.2 86.3 57.6 84.1 83.0 81.1 78.9
158.4 157.2 156.8 166.4 183.3 192.3 194.2 198.3 200.0 202.7 203.8
157.6 156.8 156.4 164.0 179.3 189.1 188.8 195.1 196.8 199.1 200.8
219 221 224 225 227 228 229 230 238 240 243 244 245 246
748.0 65.6 748.5 127.9 753.0 69.2 747.5 76.6 749.5 69.5 748.5 80.8
162.4 162.4 162.7 162.4 162.5 162.4
96.8 34.5 93.5 85.8 93.0 81.6
249 252 253 254 256 258 259 260 261 265
749.5 750.0 745.0 743.6 741.5 743.0 742.5 744.5 742.5 742.0
73.4 135.6 130.8 130.9 170.7 83.6 88.8 94.5 98.8 138.4
195.0 195.0 194.7 194.6 195.0 194.6 194.5 194.7 194.5 194.5
121.6 59.4 63.9 63.7 24.3 111.0 105.7 100.2 95.7 56.1
0
Bensene-Water, 1-Inch Tube , 76.5 80.2 7,150 86.7 131.5 133.0 7.150 30.4 15i:O 59.0 62.6 7,410 69.1 152.0 85.1 88.7 7,050 39.4 153.0 39.0 64.4 7,050 52.8 149.0 56.8 60.3 7,210 117.5 156.0 57.2 60.8 7,210 110.5 154.0 77.0 80.1 6,930 75.5 Toluene-Water, 1-Inch Tube 55.1 178.0 77.0 82.9 7,050 177.5 104 0 107.6 7,050 78.6 35.9 178.0 140.0 142.7 7,050 178.0 59.9 66.2 7,050 65.0 87.0 176.5 68.0 73.4 7,000 Chlorobenzene-Water, I-Inch Tube 75.8 189.0 68.0 74.3 7,070 60.6 190.0 68.0 74.8 7,070 88.8 190.0 62.6 68.5 7.030 90.5 189.0 77.0 81.9 7,030 117.2 188.0 60.8 66.2 7,200 128.5 193.0 60.8 66.2 7,200
..
755.2 128.1 183.9 55.8 208.5 207.1 753.0 70.2 183.8 113.6 191.4 188.6 753.8 70.6 183.8 113.2 183.4 183.6 751.8 74.8 183.7 108.9 194.0 192.4 745.8 78.6 183.4 104.8 200.0 198.2 87.3 183.5 96.2 205.9 204.1 747.8 746.8 89.2 183.5 94.3 207.1 205.3 744.8 82.8 183.3 100.5 204.0 202.6
Trichloroethylene-Water, 1-Inch Tube 160.0 57.2 61.2 6,910 178.4 161.0 159.0 57.4 61.3 6,910 148.7 159.0 57.4 61.3 6,910 159.0 55.4 58.6 6,910 100.1 68.9 161.0 55.4 58.3 6,910 159.0 86.0 88.7 6,930 99.9 Benzene-Water, E/a-Inch Tube 102.0 151.0 47.7 52.2 6,270 53.3 153.5 95.0 97.7 5,060 33.5 154.0 122.0 123.8 5,060 40.9 152.0 104.0 106.7 5,060 40.8 152.0 86.0 90.0 5,060 52.7 152.0 47.7 54.1 5,060 34.7 153.0 86.0 90.0 5,060 50.4 153.0 46.9 54.1 5,060 49.2 152.5 46.8 54.5 5,060 47.1 153.5 46.8 55.0 5,060 5,060 46.9 153.0 46.8 55.6 Toluene-Water, s/a-Inoh Tube 66.5 188.0 122.0 125.1 5,060 5,060 105.0 176.0 46.4 53.1 88.1 176.0 45.9 53.6 5,060 72.0 177.0 45.9 54.0 5,060 66.6 178.0 46.4 55.8 5,060 64.6 179.0 46.4 58.5 5,060 64.8 179.0 46.4 59.0 5,060 63.5 179.0 45.9 56.3 5,060
171.4 163.9 182.9 200.7 193.3 203.9
172.2 163.5 179.7 198.7 190.1 202.3
222.1 196.1 229.8 213.3 194.0 197.8 203.2 205.4 206.6 202.0
214.7 193.9 220.2 207.3 193.5 197.0 202.0 204.4 205.6 200.6
Compn., Wt.
Out
In
23,100 8,500 25,400 19,410 28,450 21,500 21,650 17.300
13.0 14.7 11.2 11.2
.. ..
..
32,500 21,360 12,100 35,200 30.400
50.0 24.6 20.3 43.6 24.1
36,600 37,850 37,400 32,500 34,400 33,400
39.1 37.8 56.5 49.0 33.7 30.6 27.8
5% Hz0 Condensate
1/(1 0.0085 hi Vol. % ' Calcd. Obsvd. Hs0) ht
.. .. ..
10.76 12.43 22.20 36.8 42.1 0.56 2.25 6.60
509 518 563 655 695 472 475 495
517 505 542 624 726 460 454 455
1.09 1.11 1.21 1.41 1.50 1.01 1.02 1.06
44.6 20.7 22.1 38.3 22.2
50.8 18.76 21.10 45.1 22.3
760 540 548 705 540
688 492 492 658 555
1.65 1.16 1.18 1.53 1.19
39.9 56.8 33.0 25.5 16.7 11.8
710 907 656 601 550 522
677 759 650 596 554 510
1.54 1.98 1.42 1.30 1.18 1.12
487 500 510 566 697 527
500 513 495 537 645 527
1.04 1.07 1.09 1.22 1.51 1.13
..
..
37.4 30.0 41.4 34.0
.. ..
.. .. ..
..
..
23,850 24,500 24,000 25.050 27,400 19,200
2Q:l 2511 7.6 7.2
3.11 5.28 6.41 15.50 31.4 9.68
22,050 12,900 5,200 11,500 15,900 25,000 18,460 28,900 30,120 32,000 33,700
8.2 8.1 8.8 12.1 22.0 32.9 34.7 43.6 47.3 54.0 58.6
8.0 8.3 8.5 10.5 18.7 27.0 29.4 36.6 40.4 45.1 49.1
4.07 8.20 8.50 12.63 24.9 34.5 41.5 46.2 50.7 58.7 63.2
392 403 405 418 463 510 550 584 620 700 747
402 394 430 414 447 483 534 573 605 657 712
1.035 1.066 1.070 1.107 1.24 1.37 1.49 1.58 1.68 1.90 2.04
12,550 29,400 30,050 33,250 37.100 47,900 50,700 43,600
6.7 13.5 20.7 37.1 47.4 68.9 73.6 63.5
7.6 15.1 19.7 30.6 40.6 57.1 61.0 53.0
3.81 14.55 21.60 35.9 47.0 69.2 74.0 62.5
390 420 444 510 581 822 905 734
375 431 443 509 590 829 897 724
1.030 1.117 1.185 1.37 1.57 2.25 2.48 1.97
Trichloroethylene-Water, &/,-Inch Tube 159.5 45.9 50.9 5,060 145.7 54.4 160.5 122.0 123.8 5,060 99.1 159.5 45.9 52.2 5060 5,060 66.5 160.0 45.9 54.1 79.0 159.0 45.9 52.9 5,060 62.5 161.0 45.9 55.4 5,060
20,000 8,980 24,900 33,500 27,800 39,400
3.8 6.7 15.1 41.1 25.4 51.3
4.5 6.7 12.6 34.6 22.0 43.6
3.31 6.67 15.67 43.00 26.35 56.70
394 410 458 660 522 822
344 434 444 650 499 805
1.045 1.087 1.223 1.790 1.405 2.250
Chlorobenzene-Water, s/a-Inch Tube 118.0 191.0 45.9 53.4 5060 53.3 190.0 122.0 126.3 5:060 68.7 195.0 122.0 125.6 5,060 59.5 192.0 122.0 126.0 5,060 20.1 190.0 167.0 168.1 5,060 84.5 188.0 46.9 56.3 5,060 5,060 75.7 188.0 47.1 57.9 74.9 5,060 190.0 47.1 59.5 74.9 190.0 47.1 60.1 5,060 190.0 122.0 127.4 5,060 41.7
30,300 19,500 16,800 16,750 7,700 37,800 44,000 50,000 54,600 22,150
2?:6 11.1 17.2 29.2 35.0 51.0 60.4 67.3 42.9
15.8 28.1 14.2 19.2 28.4 34.1 46.8 55.3 60.7 41.2
12.63 26.50 9.31 16.00 28.60 36.2 51.8 62.2 69.3 46.0
423 487 411 440 500 545 674 797 908 620
415 548 412 438 528 567 694 831 951 658
1.125 1.305 1.090 1.170 1.340 1.470 1.830 2.180 2.490 1.680
.. ..
..
..
Complete data are given in Utah Tsao's dissertation, filed with the Horace H.Rackham School of Graduate Studies, University of Michigan.
For a 6/8-inch
0. d.
ht =
1
450
tube,
-
350 0.0085 vol.
ht = 1
70 HIO + 32
(13)
- 0.0085 V O ~ .70 HtO + 20
for a 1.314-inch 0. d. tube, 471
for a 1-inch
0. d.
tube,
(14)
ht = 1
- 0.0085
% ' HzO
VO~.
+ 15.2
(15)
AUGUST, 1940
1121
IKDUSTRIAL AND ENGINEERING CHEMISTRY
All of the data for these three tube diameters are plotted in Figures 7 and 8. A few of the data and results of calculations are given in Table I. Heat transfer coefficients for the condensation of single vapors were also determined. Since all the organic liquids used are of technical grade, vapor temperatures instead of theoretical saturation temperatures were used for the calculation of these temperature drops across the film, The observed values of h were compared with the values calculated from Kusselt's equation. They were found to check within 10 per cent except for runs of low temperature drop and may be published later. The quantity of heat transferred, &/e,in Table I is only about 44/51 of that calculated from the rate of flow and the inlet and outlet temperatures of the cooling water, because the quantities tabulated were calculated from condensate collected between the fins 44 inches apart, whereas the total length of condenser tube exposed to the vapor is 54 inches.
Sources of Data All of the latent heats of vaporization and the densities used in the calculation are evaluated a t the saturation temperature of the mixture. The latent heat of water was obtained from Keenan (5), that of benzene from McAdams ( 7 ) , that of toluene from Kesselmann and Dardin (8), and that of trichloroethylene from Churchill ( 2 ) . The latent heat of tetrachloroethylene was obtained from the International Critical Tables ( S ) , and the temperature coefficient of latent heat was assumed as -0.065 B. t. u./" F., which is the experimental value for trichloroethylene. The latent heat of chlorobenzene was taken from Ravenscroft (10). The densities, viscosities, and vapor pressures a t different temperatures of all the materials used were obtained from the International Critical Tables. The thermal conductivities of benzene and tetrachloroethylene were obtained from the International Critical Tables. Those of chlorobenzene and toluene were taken from Smith (11). The thermal conductivity of trichloroethylene was calculated by an equation given by Smith (11). The value found was 0.0737 a t 30" C. Baker and Mueller used a value of 0.127 which was calculated from a n older equation of Smith. From the characteristics of the empirical equation for the calculation of thermal conductivities the values for trichloroethylene and tetrachloroethylene were expected to be close together. The new value calculated is more reasonable, because it is closer to the experimental value 0.0728 of tetrachloroethylene. The temperature coefficient of thermal conductivities for both trichloroethylene and tetrachloroethylene was assumed as -0.00005 per O F. Eutectic temperatures were calculated from gas laws and vapor pressures, assuming no mutual solubility of the liquids. Conclusions The present work satisfactorily overcame the difficulties of measuring the mean surface temperature of the condenser tube. -4t the eutectic temperature both of the two nonmiscible liquids will coexist with their vapors under equilibrium conditions. The eutectic temperature was used to calculate the temperature drops across the condensing film. Satisfactory correlations were obtained on this basis, but not on the basis of the actual vapor temperature less the temperature of the tube surface. Kirkbride studied too narrow a range of composition of vapor mixture to derive a general equation for the condensation of mixed vapors of nonmiscible liquids with justification. Baker and Mueller investigated four vapor mixtures with the composition range limited to eutectic mixtures of each vapor
mixture, and to mixtures not differing greatly from eutectic mixtures, and their empirical equation may not be applied to an extended range of composition. I n the present work an approach based upon an analysis of the mechanism of condensation was tried. A mechanical mechanism of the condensation of the vapors of nonmiscible liquids was discovered. This mechanism overshadowed many of the conventional physical properties of the condensing liquids which influence heat transfer coefficients. From a study of this mechanism, a simple empirical equation was derived. This equation correlates not only the data of four vapor mixtures with extensive variation of vapor compositions and temperature drops for the two tube sizes of the present work, but also the data of Kirkbride and the data of Baker and Mueller for another tube size and another additional vapor mixture. For further investigation of condensation along the same line, different condensing surfaces may be tried. If a condensing surface should be found which is preferentially wetted by water and not by the organic liquid, quite different coefficients may be expected. A B
D F L
=
= =
Nomenclature area, sq. it. width of tube blanketed with thick organic drops, ft. outside diameter of tube, ft.
= ra/ri =
length of tube, ft.
&/e= heat transferred, B. t. ug/hr.
T = tube-wall temperature, F. AT = temperature drop, F. C, = specific heat, B. t. u./(lb.) (" F.) g = acceleration of gravity, 4.18 X lo8 ft./(hr.)(hr.) h = coefficient of heat transfer, B. t. u./(hr.) ( O F . ) (sq. ft.) h, = coefficient of heat transfer for portion of tube roughened O
I
by water drops coefficient of heat transfer for blanketed portion of tube ht coefficient of heat transfer, based upon AT calculated from saturation temperature of mixed vapor, B. t. u./ (hr.)(OF.)(sq. ft.) IC = thermal conductivity of condensate film, B. t. u./(hr.) (sa. ft.)(" F./ft.) r = radiis of'tube,'inch P, = resistivity at mean temperature T,, ohm/(ft.) (sq. ft.) p = viscosity, lb./(ft.)(hr.) h = latent heat of vaporization, B. t. u./lb. p = density of condensate, lb./cu. ft. Subscripts i = inside m = mean value o = outside s = second component ZL! = water hb
= =
Literature Cited (1) Baker, E. XI., and Mueller, -4.C., 1x0.ENQ.CHEM., 29, 1067-72 (1937) ; Trans. Am. Inst. Chem. Engrs.,33, 531-58 (1937). (2) Churchill, J. B . , Refrig. Eng., 26, 85-7 (1933). (3) International Critical Tables, 5'01. 111, pp. 28, 29, 216, 220, 221, 223; T'ol. V, pp. 12, 136, 228; 1'01. VII, pp. 213, 217, 218, New York, McGraw-Hill Book Co., 1928-29. (4) Jeffrey, J. O., Cornel1 Univ. Eng. Expt. Sta., Bull. 21 (March, 1936). (5) Keenan, Steam Tables, Am. SOC.Mech. Engrs., 1930. (6) Kirkbride, C. G . , IND.ENG.CHEM.,25, 1324-31 (1933). (7) McAdams, "Heat Transmission", New P o r k , McGraw-Hill Book Co., 1933. (8) Nesselmann, K., and Dardin, F., Wiss. V e r t f e n t l . SiemanKonrern, 10, No. 2, 129 (1931). (9) Patterson, W. C., Weiland, J. H . , Reeburgh, S. L., King, R . A., and Huntington, R. L., Trans. Am. Inst. Chem. Engrs., 33, 216-41 (1937). (IO) Ravenscroft, E. A., IND.ENG.CHEM.,21, 1203 (1929). (11) Smith, J. F. D., Trans. Am. SOC.Mech. Engrs., 58, 719-25 (1936).
PRESENTED before the meeting of the American Institute of Chemical Engineers, Buffalo, N. Y . Submitted by Utah Tsao in partial fulfillment of the requirements for the Ph.D. degree, University of Michigan.
