0 KETTLE
.tf
@THERMOCOUPLES
RECEIVERS
@VAPOR SEPARATOR
@)CONDENSATE
BVAPOR ENTRANCE @ P R I N C I P A L CONDENSER
@WEIGH C A N @CONSTANT SUPPLY TANK
BAUXILIARY CONDENSER
@ R E T U R N LINE
FIGURE 1. DRAWING OF APPARATUS
Condensation of Mixed Vapors JOHN L. WALLACE1 AND ALBERT W. DAVISON Rensselaar Polytechnic Institute, Troy, N. Y.
T
HE chemical engineer is frequently called upon to design condensing equipment for handling mixed vapors. Although the bibliography on heat transfer film coefficients for condensing pure liquids is quite complete, there is very little information available on these values for condensation from mixtures of two or more condensable components. Bray and Sayler (6) and Kirkbride (7) established values for comercia1 petroleum products and similar systems; although their results are of unquestionable value in the design of equipment for handling these particular products, they contribute little to the general theory of condensation from mixed vapors, because the compositions of the systems and the physical properties of the substances condensed are too indefinite. Kirkbride ( 7 ) , Patterson, Weiland, Reeburgh, King, and Huntington (IC), and Mueller and Baker (16) reported investigations on the condensation of mixed vapors of immiscible liquids and presented empirical equations for the film coefficients. Betten and Rhodes (1) investigated coefficients for the systems benzene-toluene and acetonechloroform. With this single exception, very few data have been presented on condensation from mixtures of simple miscible liquids for which information is available on the physical properties of the pure constituents and on the various equilibrium data for mixtures. 1
Present address, Yale University, New Haven, Conn.
948
The present investigation was undertaken to determine
fdm coefficients of heat transfer for the liquids condensing from mixed vapors in the case of a simple binary system, as a preliminary step in a series of investigations. It is hoped that this series will contribute to the development of a theory and the establishment of equations for condensation of such systems as will be of value in the design of condensing equipment. I n the present case the system selected was ethanol-water, and condensation was effected on the outside of a horizontal brass tube.
Mixed Vapor Treatment The subject of mixed vapor condensation requires attack from the standpoint of dynamic rather than static equilibrium, as was formerly believed. Recently, Colburn and Drew (4) developed a mathematical treatment of several aspects of the subject. The equation for the coefficient may be expressed as: &/e = hAAT In the case of pure vapors AT would be represented by the difference between the temperatures of the vapor stream and the tube surface. I n a mixed vapor system, however, there exists, between the main vapor stream and the condensate Hm, a layer of vapor which produces a blanketing effect. As
AUGUST, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
the mixed vapor approaches the cooling surface, there is a drop in temperature across this vapor film. I n order to determine the temperature drop across the condensate for calculation of its film coefficient, the temperature of the vapor-liquid interface must be evaluated. A principal assumption in the study of diffusional processes is the absence of a resistance a t the interfacial boundary of a gas and liquid film. T h a t is, if the composition of the liquid phase a t the interface is specified, then the vapor composition is exactly the same as it would be if it were in equilibrium with the liquid phase for an indefinite period. Under this assumption, if zpis the interfacial mole fraction of the more volatile component on the liquid side, then ti is the boiling point of that solution and yi is the corresponding equilibrium vapor a t the interface. For temperatures of cooling water infinitesimally below the main vapor stream (as no heat transfer is approached), static equilibrium exists. The condensate corresponds in composition to the vapor stream on a liquid-vapor equilibrium diagram. The Drew-Colburn theory predicts that a t large condensation rates the liquid produced approximates the main vapor stream in composition. For such a case the net composition of the liquid can be employed as the interfacial liquid composition to determine the interfacial temperature and interfacial vapor composition. The method adopted to find the interfacial temperature and thus obtain the temperature drop across the liquid film was to collect the condensate from the tube and determine its molar composition. By referring to the compositionboiling point diagram of the binary mixture under investigation, the boiling point or interfacial temperature would be B obtained.
949
It was originally planned to hold the cooling water a t a constant low value and to vary the rate of condensation by changing the rate of water flow, to make a number of runs on a given molar composition of alcohol-water at controlled water rates, and then to use the same cooling water rates (and initial temperature) on all other compositions. With such a procedure it was hoped to show variations of film coefficient
Film coefficients of heat transfer are presented for condensation from the mixed vapor system ethanol-water outside a horizontal tube at low condensing water temperatures. Results are given for variation of the coefficient with velocity of the cooling water and with composition of the mixed vapor, and the nature of the temperature gradients and compositions is shown. Data are given for the relation between the composition of the vapor and that of the condensate. Differences between actual and apparent film coefficients ’are demonstrated. For pure benzene and toluene the film coefficients deviate but slightly from the Nusselt value.
Procedure For the purpose of standardizing the experimental technic and of checking data obtained from the equipment against accepted data by other investigators and against values predicted by the Nusselt equation (IS),a series of runs were first made upon the pure vapors, steam, benzene, and toluene. Before each run the apparatus was thoroughly steamed out and completely drained and dried in order to avoid contamination by liquids previously used. Following these series, the alcohol-water system was investigated, starting with alcohol of 95 volume per cent and increasing the water content by dilution with that liquid. Observations taken a t the outset of the work showed the usual inconsistency (6) and necessitated continual condensation of vapors in order to “standardize” the tube. KO data were utilized during this “standardization” period. On beginning a data run, a tune-up period of 30 minutes was allowed for the attainment of equilibrium conditions throughout the system. Actual measurements were made during a 15-minute interval following this initial period. The readings included temperatures of entering and leaving cooling water, together with its weight, six tube-surface temperatures, four vapor temperatures, weights of condensates from the test section and from the final condenser, total pressures within the test section (these were approximately atmospheric and were later neglected), and samples of the vapor entering and leaving the test section and of the condensate leaving the test section. Readings were taken a t least three times during the course of a single run. Thermocouple 6 on the condensing surface was found to give abnormally high values, and its readings were rejected. It is believed that these high values were due to heat conduction along the thermocouple wires from the hot vapor. The heat transferred across the tube was calculated from the rise in temperature of the cooling water and from its weight.
with composition of condensate on the same chart with reasonable accuracy. Four series of runs were made in this manner; but as the molal per cent of water in the vapor increased to about 50, extreme difficulty was encountered in maintaining a vapor composition of constant percentage during a n entire series of runs. Consequently a change in procedure was necessitated. Cooling water was supplied a t constant temperature and rate, and the composition of the vapor was allowed to vary of its own accord or by dilution. Two cooling water rates were employed-1440 and 1456 pounds per hour. The average temperature of the tube surface was taken as the arithmetical mean of the five thermocouple readings and of the vapor as the mean of the four mercury thermometers in the vapor space. For evaluation of the mean interfacial temperature, the sample of condensate was assumed to represent the average mean composition of the condensate along the entire length of condensing surface and would thus give the mean t i .
Apparatus The equipment developed in this investigation is shown in Figures 1 and 2:
A 15-gallon galvanized iron boiler was thermally insulated by 2 inches of commercial magnesia covering and was heated by an internal copper steam coil. Vapor was conducted from the top of the boiler, through an entrainment separator, and into the experimental condensing section. In this series of investigations from 70 t o 90 per cent of the total vapor entering the test section was condensed in the average run. Uncondensed vapor8 from the
test section were passed into a glass auxiliary condenser, where they were totally condensed. A vent was provided at the end of the auxiliary condenser for the elimination of fixed gases from
the system.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Calibrated glass condensate receivers, in duplicate, were provided beneath both the test condenser and the total condenser for collecting samples and for determining rates of condensation. 'These receivers were sufficiently small to minimize the possibility .of materially changing the composition of the system, b withholding a large amount of condensate from the system. %stead of receiving all the condensate in a single receiver and thereby materially altering equilibrium conditions, small quantities were collected and measured and immediately returned to the system. While one receiver was filling, the other was being drained back into the boiler.
flowed by gravity through the brass pipe of the test section to a calibrated weigh tank for determining rates of flow. The water lines, together with all vapor and condensate Iines, were Iagged with magnesia covering. Six copper-constantan thermocouples were imbedded at 5inch intervals along the test surface, numbers 1 and 6 being 2.5 inches from the ends of the tube. In attaching a couple to the tube, slots were cut on opposite sides of the pipe at right angles to its axis. In one of these, the copper element was soldered; in the other, the constantan element. About 1 inch of wire was imbedded in each slot. This was done to minimize the conduction of heat along the wire from the vapor space into the tube. Potential readings were obtained with a Leeds & Northrup student's potentiometer, cold junctions being maintained a t 32' F. (0' C . ) by means of a vacuum flask containing ice and water. The couples were calibrated in place by means of a reference couple, and this calibration was checked at the boiling point of water by passing steam through the condenser, without having any water in the brass pipe. After about 100 hours of operation, couples were rechecked at the steam point. Mercury-in-glass thermometers reading to 0.01" C. were employed for obtaining the temperatures of the entering and leaving
I
600
7
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D
1000
,
I1
I.?
I3
14
IXK)
I
FIGURE 2. PHOTOGRAPH OF APPARATUS
I n order to determine the initial and final compositions of the vapor undergoing condensation, small quantities of vapor were FIGURE 3 (Above). FILMCOEFFICIENTS FOR CONDENSING continually withdrawn from the main stream just ahead of the STEAM test section and immediately downstream from it. These were FIGURE 4 (BebW). FILMCOEFFICIENTS FOR CONDENScompletely condensed in ordinar glass condensers. Condensates ING BENZENE AND TOLUENE VAPORS from these condensers were coocd and normally returned to the boiler. Provision was made for withdrawing small samples of these condensates for analysis. Molar compositions of these samples, and of samples from the test TABLE I. CONDENSATION OF PURE VAPORS section, were ascertained from density --Condensate-determinations made a t constant tempera,-----Cooling Water Av. Av. Tube A T Princi- Auxilture by means of a Westphal balance. Run Te,mp. Temp. Temp. Weight Vapor Surface across pal con- iary conIn designing the test section, particular NO. in out rise flowing Temp. Temp. Film denser denser h attention was paid to two considerations: C. C. ' C . Lh./hr. C. C. C. Lb. per hr. (a) I n order to prevent heat from being Benzene conducted along the tube wall past the 268 5.0 80.1 38.0 .. .. 1238 42.1 17.50 12.50 ends of the test section, fiber insulating 264 .. 1224 42.3 .. 5.0 80.1 37.8 16.10 11.10 269 4 2 . 3 5 . 2 2 8 0 . 1 3 7 . 8 .. . . 1196 18.10 12.88 blocks were carefully fitted at the ends 272 80.1 36.5 .. . . 1220 4 3 . 6 5 . 3 3 1 6 . 1 3 10.80 of the condensing tube, as shown in Fig271 8 0 . 1 3 6 . 6 .. . . 1200 4 3 . 5 5 . 4 0 16.30 10.90 ure 1. (b) In order to minimize the effect 276 44.0 .. .. 36.1 7.30 80.1 750 19.00 11.70 289 . . 3 1 . 3 8 . 7 5 8 0 . 1 4 8 . 8 . . 588 20.45 11.70 of vapor impingement on the condenser 271 . . 4 0 . 4 5 . 9 7 8 0 . 1 3 9 . 7 .. 1006 18.37 1 2 . 4 0 tube, vapor was introduced tangentially, Toluene in such a manner as to create a swirling 226 44.6 .. .. 6.16 110.6 66.0 1328 19.61 13.45 motion around the exchange surface as it 9 229 110.0 47.4 6.40 1288 .. .. 63.2 18.20 11.8 10 passed through the condenser. 241 1 1 0 . 6 4 6 . 7 6 3 . 9 1296 .. .. 6 . 5 5 1 8 . 1 5 1 1 . 6 11 The test condenser was a horizontal 238 110.6 .. .. 85.9 54.7 9.63 744 22.35 12.72 12 243 110.6 4 4 . 5 .. . . 5 . 8 6 6 6 . 1 1512 17.96 1 2 . 1 brass pipe 30 inches long, 0.840 inch 0 . d., 13 202 110.6 .. 39.0 71.6 1516 .. 5.28 19.75 14.08 14 and 0.622 inch i. d., mounted in the 206 110.6 .. 38.7 71.7 1556 .. 5.28 18.90 13.62 15 center of a standard 3-inch iron pipe. 193 110.6 .. 38.7 71.7 1544 5.0 18.90 13.90 16 212 110.6 .. 4.98 70.6 1556 40.0 15.70 10.72 The latter was insulated with 2 inches of 17 magnesia pipe covering. Vapor passed Rteam through the annular space between the 17.54 35.37 17.m 1460 100 88.9 11.1 43.1 4.3 4260 18 89.9 10.1 40.4 5.4 4130 17.47 37.40 19.93 1152 two pipes, condensing on the outer wall 100 4 . 0 3860 19 1 7 . 9 0 4 0 . 7 3 2 2 . 8 3 845 100 9 0 . 9 9 . 1 2 7 . 8 of the brass test section. Cooling water 20 18.58 43.0 24.42 738 100 91.4 8.6 22.3 3.6 3810 21 from the city mains was fed to a 4-gallon constant-level supply tank, from which it
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INDUSTRIAL AND ENGINEERING CHEMISTRY
AUGUST, 1938 condensing water and the vapor. These were checked against one another and against a calibrated copper-constantan thermocouple, and were corrected where necessary.
TABLE 11. COEFFICIENTS AT VARYINGWATERVELOCITIESFOR CONSTANT COMPOSITIONS
of the film coefficients are plotted against cooling water rates for steam, benzene, and toluene. The values obtained from benzene and toluene check those predicted by the Nusselt equation closely; but the steam values are high, possibly because of dropwise condensation. In the case of benzene the film coefficients were also determined by means of a Wilson reciprocal plot (IO), and the values were found to be in substantial agreement with calculated results. I n the following table the results of the investigation are compared with those of other authors and with those predicted by the Nusselt equation : Wallace and Davison
Wilson Plot
Benzene 264-289 193-241 Toluene Steam 3810-4260
276
.. ..
Temp. in
Cooling WaterTemp. Temp. out rise
Nusselt Rhodes Betten McAdams Equa and and and tion Younger Rhodes Frost 270 250 2500
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Av. AT -CondensateCorrected Av. Tube Vapor Princi- AuxilAT Weight Vapor Surface to pal con- iary con- acroa8 Actual flowing Temp. Temp. Surface denser denser Film h O c. c. Lb./hr. C. C. C. Lb. p e r hr. C. Mole % Ethanol in Condensate, 81.9; Vapor In, 77.6: Vapor Out. 81.9: Interfacial Temp., 78.4O C. 17.58 4.85 1468 78.7 47.8 30.9 34.2 2.9 424 30.6 16.73 5.44 1312 78.7 49.3 29.4 35.0 4.4 29.1 446 17.38 6.42 912 78.7 52.4 26.3 30.4 4.6 26.0 465 18.60 7.70 752 78.7 56.5 22.2 29.3 4.9 21.9 481 17.93 7.77 768 78.7 56.4 22.3 29.0 5.2 22.0 490 18.60 9.05 572 78.7 59.6 19.1 24.5 4.6 18.8 500 19.00 10.80 416 78.7 64.4 14.3 22.7 5.3 14.0 583 16.83 12.94 277 78.7 67.6 11.1 17.9 7.3 10.8 603 Mole % Ethanol in Condensate, 56.7; Vapor In, 57.6; Vapor O u t , 60.4; Interfacial Temp., 79.6' C. 7.87 1134 80.4 9 19:IO 26.97 58.1 22.3 4.6 31.7 21.5 750 10 19.40 27.20 7.80 1148 80.4 58.1 22.3 35.1 4.2 21.5 755 60.7 19.7 11 17.62 27.50 9.88 796 80.4 31.9 2.6 18.9 755 61.1 19.3 27.50 9.97 895 80.4 12 17.53 31.0 3.7 18.5 765 13 18.56 28.30 9.74 62.2 18.2 808 80.4 31.6 1.9 17.4 820 27.83 11.23 652 80.4 63.5 16.9 14 16.60 29.3 2.6 16.1 826 28.17 11.37 63.8 16.6 15 16.80 656 80.4 28.8 4.2 15.8 830 11.45 64.1 16.3 16 16.55 28.00 624 80.4 29.1 2.6 15.5 840 Mole % Ethanol i n Condensate, 52.0: Vapor I n , 53.0; Vapor Out, 58.6: Interfacial Temp., 80° C. 24.35 7.58 1448 81.3 59.0 22.3 41.3 4.2 17 16.77 2i.O 950 1448 81.3 59.2 22.1 24.60 7.60 40.2 4.4 18 17.00 20.8 960 1308 81.4 60.5 24.52 8.25 20.9 19 16.27 40.4 5.0 19.5 970 1024 81.6 25.53 9.63 63.5 18.1 20 15.90 36.0 5.8 16.5 1090 1024 81.7 9.66 21 16.27 25.93 63.5 18.2 36.8 5.8 16 5 1090 28.38 11.88 67.5 14.2 22 16.50 704 81.7 31.1 5.1 12.5 1220 10.34 64.6 17.4 23 16.53 26.87 980 82.0 35.2 4.9 15.4 1200 64.5 17.8 26.68 10.35 984 82.3 24 16.33 15.5 1200 Mole % Ethanol in Condensate, 46.7; Vapor I n , 51.4: Vapor Out, 56.0: Interfacial Temp., 80.3' C. 10.20 15.82 26.02 1120 83.1 65.1 25 18.0 40.0 3.8 15 2 1360 12.22 832 83.3 68.7 15.95 28.17 14.6 35.5 3.6 26 11.6 1590 15.90 28.70 12.80 764 83.8 70.1 13.7 33.9 27 5.1 10.2 1750 14.72 568 28 16.28 31.00 83.8 72.4 11.4 27.1 5.6 7.9 1920 7 -
Run No.
Vapors of Pure Liquids I n Figures 3 and 4, values
Vapor
95 I
412 382
353 364
306-366
c.
Kirk-
bride
342-381
Mixed Vapors of Alcohol-Water Variations in film coefficients with condensing water rate for four different compositions of condensate from mixtures of alcohol-water are shown in Figure 5 and Table 11. As was to be expected, the film coefficient decreases with increasing velocities of condensing water. This effect becomes more pronounced as the composition of mixed vapor deviates from pure alcohol. It is therefore unsatisfactory to apply the Wilson repiprocal plot, which assumes the coefficient for the condensing film to be independent of water rate, to systems of mixed vapors.
FIGURE 6. VARIATIONOF FIGURE 7. VARIATIONOF ACTUALAND APPARENTCON- ACTUALCONDENSATE FILM DENSATE FILM COEFFICIENTS COEFFICIENTWITH COMWITH COMPOSITION POSITION FOR COOLING WATER RATE OF 1440 POUNDS PER HOUR
h I600
800
Li
OO
400
800
I
I200
IS00
WATER RATE, LB./HR
FIGURE 5 . VARIATIONOF CONDENSATE FILMCOEFFICIENT WITH COOLINGWATER VELOCITY FOR ETHANOL-WATER MIXTURES
Table 111gives the principal data and calculated values for the investigation. Figure 6 illustrates the dependence of film coefficient upon concentration of condensing mixture for one water rate (1456 pounds per hour), and Figure 7, the same dependence a t another water rate (1440 pounds per hour). At these rates the following empirical equation shows the relation in a satisfactory manner for mole fractions of ethanol above 0.10:
+
h = ( M - 0.008)e("~4'350 where h = condensate film coefficient, B. t. u./(hr.)(sq. ft.)(" F.)
952
INDUSTRIAL AND ENGINEERING CHEMISTRY
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VOL. 30, NO. 8
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OF ACTUAL COEFFICIENTS FIGURE8. CORRELATION BY REVISED NUSSELT PLOT
If the condensation of mixed vapors is considered in the same manner as that of single component vapors, the temperature drop across the liquid film would be the difference between the temperatures of the vapor and of the tube surface. The film coefficient computed in this manner might be called an "apparent" coefficient. Data presented in next to the last column of Table I11 were calculated in this manner. Those given in the last column, "Actual h," were calculated on the assumption that the true temperature at the liquidvapor interface is the boiling point of the condensate and not the actual vapor temperature. I n order to illustrate the differences between apparent and actual coefficients, the two values are plotted on the same graph, Figure 6. There is little deviation for 4igh mole fractions of ethanol, but when the water content in the condensate increases above about 50 per cent, the difference becomes increasingly greater.
Nusselt Correlation A check on these actual heat transfer coefficients might be made by correlation with the theoretical curve based on a revision of Nusselt's theory, allowing for turbulence in the condensate film (3, 8 ) . This involves plotting the function 417 h '3 against --1 the Reynolds number for the condensing layer. Such a correlation is shown in Figure 8. Taking the Reynolds number equal to 2100 for the value a t which turbulent flow develops, as suggested by Cooper, Drew, and McAdams ( 5 ) , all the data p?ints fall far into the viscous region, Any marked deviation from the theoretical
(Gg)'
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I I 20 IS 10 5 DISTANCE FROM VAPOR ENTRANCE
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FIGURE9. TEMPERATURE GRADIENTS ALONG CONDENSING TUBELENGTH
INDUSTRIAL AND ENGINEERING CHEMISTRY
AUGUST, 1938
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953
ratic, and it is presumed that dropwise condensation may have caused the irregularities. Vapor stream temperatures and tube surface temperatures (entrance, exit, and average) are plotted in Figure 10 against condensate compositions. Inasmuch as the data were available (having been recorded for other purposes), film coefficients on the water side were calculated with due consideration to the small temperature drop through the walls of the tube. They are shown in Figure 11. The results are in satisfactory agreement with the McAdams equation for heating water (9). The line shown in Figure 11 may be represented by the formula :
MOLE FRACTION ETHUKK.
FIGURE 10. VARIATION OF SURFACE AND MEAN VAPORTEMPERATURES WITH COMPOSITION OF CONDENSATE
curve in the viscous region of data for which the composition of the vapor a t entrance and exit and of the condensate approached each other might be attributed to the uncertainty in evaluating the interfacial temperature. The dots on Figure 8 represent data for which there is but slight variation between the three compositions in question. It was noticed that the greater the variation in composition, the greater was the deviation from the Nusselt curve. The crosses apply for data for which there is a difference of a t least 5 mole per cent ethanol between any two of the compositions. For the case where the condensate and entrance and exit vapor compositions are nearly equal, the data can be correlated rather satisfactorily by the revised Kusselt plot. For varying composition between vapor and condensate the interpretation is more difficult. All of the runs were made a t a time when the temperature of the city water supply was comparatively low, and for this reason these data represent high condensation rates. The data seem to show that the composition of the condensate approximates that of the entering vapor. This is in agreement with the Colburn-Drew prediction that, a t high condensation rates, the combined mass transfer and bulk flow of the vapor towards the condensing surface will produce a condensate approaching the composition of the main vapor stream. In a later investigation it is planned to utilize warmer condensing water in order to secure smaller temperature differences between vapor and condensing surface and to ensure smaller mass transfer towards the condensing surface. Figure 9 presents surface temperatures along the tube, with the various compositions studied. For mixtures containing more than 50 mole per cent of alcohol, the differences are slight but, as water content increases above this value, the differences increase progressively. The steam curve is er-
xloo
3
4
FIGURE 11.
5
6
788oooo
20
The constant 0.0166 compares with the value of 0.0225 formulated by McAdams.
Acknowledgment The authors wish to express their appreciation and thanks to T. B. Drew and H. C. Carlson of the du Pont Experimental Station for their valuable suggestions in considering the manuscript, and to C. C. Furnas of Yale University for valuable assistance in determining the empirical equations.
Nomenclature A C
= area of heat transfer surface, sq. ft. = specific heat, B. t. u./(lb.)(” F.)
= inside diameter of condensing tube, ft. G = weight velocity, Ib./(hr.)(sq. ft.) g = acceleration due to gravity, 4.18 X lo8 ft./(hr.)(hr.) h = individual film coefficient of heat transfer, B. t. u./(hr.) . . (sq. ft.)(” F.) k = thermal conductivity, H. t. u./(hr.)(sq. ft.)(‘ F.)/ft. QJ = amount of heat transmitted, B. t. u./hr. = mean mole fraction of ethanol in condensate = mean temperature difference, O F. = temperature at interface between vapor and condensate
D
films
= interfacial mole fraction of more volatile component in =
condensate interfacial mole fraction of more volatile component in vapor
=
= =
mass rate of flow, Ib./(hr.)(ft. of wetted periphery); for a horizontal tube, periphery is twice the length of the ipe density, lf./cu. ft. viscosity, lb./(hr.) (ft.) = 2.42 centipoises
Literature Cited Betten and Rhodes, paper presented a t Symposium on Heat Transmission held under auspices of Div. of Tndustrial and Engineering Chemistry of A. C. 8. a t Yale Univ., New Haven, Conn., Dec. 30 and 31, 1935. Bray and Sayler, S. M., thesis in chem. eng., Mass. Inst. Tech., 1923. Colburn, Trans. Am. Inst. Chem. Engrs., 30,187-93 (1933-34). Colburn and Drew, Ibid.,33, 197-215 (1937). Cooper, Drew, and McAdams, Ibid., 30,158-69 (1933-34). Drew, Hottel, and McAdams, Ibid., 32, 271-305 (1936). Kirkbride, IND.EA-G.CHEM.,25,1324-31 (1933). Kirkbride, Trans. Am. Inst. Chem. Engrs., 30, 170-186 (1933-34). McAdams, “Heat Transmission,” p. 169, New York, McGrawHill Book Co., 1932. Ibid., p. 264. McAdams and Frost, J. IND.ENG.C H E ? ~14, . 13 (1922). Mueller and Baker, Ibid.,29, 1067-72 (1937). Nusselt, z. v e r . deut. I n g . , 60, 541-6, 569-75 (1916). Patterson, Weiland, Reeburgh, King, and Huntington, Trans. Am. Inst. Chem. Engrs., 33,216-41 (1937). Rhodes and Younger, IKD.ENG.CHEW,27, 957-61 (1935).
.moo0
CORRELATION OF DATAox HEATINGWATER
RECEIVED February 7, 1938. This paper is abstracted from a thesis presented by John L. Wallace a t Rensselaer Polytechnic Institute a8 partial requirement for the degree of master of chemical engineering in June, 1937.
