I
EUGENE 1. MOTTE' and LEROY A. BROMLEY Radiation Laboratory and Department of Chemistry and Chemical Engineering, University of California, Berkeley, Calif. i-.
Film Boiling of Flowing Subcooled Liquids Heat transfer coefficients across the vapor film can be markedly increased by subcooling the liquid, so that they approach those of nucleate boiling
FILM
6
boiling is that type of boiling phenomenon wherein the heated surface is separated from the liquid by a continuous vapor film. Banchero, Barker, and Boll (7) have investigated film boiling of liquid oxygen outside single tubes and wires over a wide range of temperatures and pressures. This work reported the correlation suggested by Bromley (2) to predict correctly the effects of temperature and pressure but only approximately the effect of tube diameter. In 1950, Bromley, LeRoy, and Robbers (3) proposed a theory for forced convection film boiling of saturated liquids. The prediction of heat transfer coefficients to any liquid was found possible through the use of two pairs of equations developed from this theory. At values of U / d g T less than one, where U is the velocity, g is the gravitational constant, and D is the outside diameter of the tube, heat transfer coefficients were found to be predicted by the correlation (2) for free convection film boiling. h = h,,
+ 0.75 h,
(1 1
where h is the heat transfer coefficient for film boiling, h,, is the heat transfer coefficient for convection if there were no radiation, h, is the heat transfer coefficient for radiation, D is the diameter of the tube, At0 is the temperature difference across the vapor film, pv is the viscosity of the vapor, k , is the conductivity of the vapor, and A' is the effective difference in heat content between the vapor at its average temperature and the liquid at its boiling point. At values of U / & j greater than 2, 1 Present address, Union Oil Co. of California, Rodeo, Calif.
forced convection film boiling occurs, and the heat transfer coefficients are predicted by (3) h = h,, -k 7 / 8 h,
fluid which is moving upward a t a uniform velocity of U. If q o is the rate of heat transfer from the heated surface by conduction into the vapor film, then
(3) Po = Pr
The nature of the vapor film in both natural and forced convection film boiling has been described (3). Heat is transferred across the vapor film by conduction and radiation in forced convection film boiling. The amount of heat transferred by radiation is determined by the temperatures, emissivities, and absorptivities of the heated surface and of the vapor-liquid interface, while the amount of heat transfer by conduction is determined by these temperatures and the vapor film thickness. An increase in velocity of the liquid decreases the vapor film thickness and will therefore increase the heat transfer rate across the vapor film. If the liquid is below its boiling point, some heat will be transferred from the liquidvapor interface, which is near the boiling point, into the bulk of the liquid. Because this heat will not be available for vaporization Of the liquid, the vapor thickness be less, and the rate of heat transfer across the vapor film will be increased.
+ 41
(5)
where q. is the net heat flow into the vapor stream and ql is the heat flow into the liquid stream. If the depth of penetration of infrared radiation into the liquid is not appreciable, heat transferred by radiation will only affect q. since qEwill be constant for any liquid a t set values of the velocity and the amount of subcooling of the liquid below the boiling point. 40
(6)
= hmA At0
where h,, is the heat transfer coefficient across the vapor film if there were no radiation, A is the area of the horizontal tube from which heat is transferred, and Ato is the temperature difference between the heated surface and the boiling liquid, that is, across the vapor film. If there were no subcooling of the liquid then from Equation 4, eliminating
At,,
The numerical constant is probably accurate to only a few tenths (and from the present work should probably be somewhat smaller to eliminate negative values on Figures 5 through 14). I t is now postulated that this equation will hold for q, even though there may be subcooling. This may be at least partially justified by the following argument. From a material balance of the vapor in the vapor film the following expression isobtained v
Film Boiling Theory Heat is transferred through the vapor by conduction and radiation as it has been shown (7)> at least for tubes not over 0.75 inch in diameter, that the vapor film is in laminar flow. I t is assumed that no heat is conducted along the tube. Because most of the heat is transferred across the film on the bottom half of the tube, the theory is developed to fit the mechanism on this part of the tube. The tube is immersed in a body of
Wep,aLV
(8)
where W is the weight rate of the liquid evaporated, a is the average vapor film thickness, L is the length of the tube, and Vis the vapor velocity. VOL. 49, NO. 1 1
0
NOVEMBER 1957
1921
4 00
1-1
L I
This is the same as Equation 7 except for the numerical constant. The development of Equation l l , however, is not restricted to any liquid temperature. Substituting 6 and 7 into - Equations . Equation 5 and multiplying through by
dAtoz,,,,,,
the following equation is
obtained:
.
0
0
r
0 10
0
20
40
30
50
&%tSC
Figure 1 .
60
70
80
, "F-
Film boiling of ethyl alcohol
Tube diameter, 0.387 inch
Afo = 800-1800° F. Approximate velocity
a
x
3 ft./sec, 5 ft./sec.
0 8 A
ft./sec.
1 1 ft./sec.
13 ft./sec.
As forced convection film boiling occurs at high liquid velocities, it is assumed that the average vapor velocity is proportional to the liquid velocity. The heat transferred into the vapor is equal to the weight of the vapor multiplied by the effective heat of vaporization or
Because only the heat that is transferred across the vapor film by conduction is of interest, we may write he, = k./a
(10)
Substituting Equations 9 and IO into Equation 8,
qs = W X '
0
0
IO
eo
30
40
Atsc
Figure 2.
,
I
I
50
60
"E
Film boiling of benzene
Tube diameter, 0.387 inch At0 = 800-1200° F. Approximate velocity
a
x
0 A
1922
3 ft./rec. 5 ft./rec. 8 ft./sec. 11 ft./sec. 1 3 ft./sec.
INDUSTRIAL AND ENGINEERING CHEMISTRY
~
70
BO
90
Equation 12 reduces to the correlation proposed for forced convection film boiling of saturaTed liquids (3) when q r is equal to zero. Only the heat transfer rate from thr vapor-liquid interface, q L , remains to be determined. This heat transfer rate is dependent upon the mechanism by which heat is transferred through the liquid : either by thermal conduction or by eddy conduction. Three cases involving these mechanisms have been solved ( 4 ) to determine ql. The cases considered and the resulting equations are: Case 1. Heat is transferred by thermal conduction in tha liquid,
K I was incorrectly reported (4) to be 0.136. It has not been numerically evaluated. This is equivalent to saying that the Nusselt number for heat flow into the liquid is proportional to the Peclet number raised to the 0.5 power. Case 2. Heat is transferred by eddy conduction in the liquid.
where Ki is a constant of proportionality. I t is assumed that eddy conductivity is proportional to eddy viscosity. Case 3. Heat is transferred by eddy conduction, but the time of contact is small compared to the ratio of the scale of turbulence to the intensity of turbulence. I n this case the eddy conductivity is independent of the scale of turbulence and proportional to the time of contact multiplied by the square of the intensity of turbulence. The intensity of turbulence is assumed to be proportional to the velocity of the fluid.
41 = A
KI Atsc CPZP i
u
(15)
Since neither the surface area of the vapor-liquid interface nor the velocity distribution of the liquid around the top half of the tube can be defined, the rate of heat transfer into the liquid from the vapor film around the top half of the tube
has been assumed to be proportional to that around the bottom half. Summary. For forced convection film boiling in which the heat is transferred into the liquid by thermal conduction, Equations 12 and 13 can be combined:
A
For forced convection film boiling in which the heat is transferred into the liquid by eddy conduction, two situations are possible. If the contact time is large compared to the ratio of the scale of turbulence to the intensity of turbulence Equations 12 and 14 give :
1
250
50
F I L M BOILING
9’
’ 8
I
I
0
0
20
IO
40
30
*’Sc
Figure 3.
50 J
70
60
80
“E
Film boiling of carbon tetrachloride Tube diameter, 0.387 inch
Afo = 500-900° F.
If the contact time is small compared to the ratio of the scale of turbulence to the intensity of turbulence, Equations 12 and 15 give :
The only significant difference between Equations 17 and 18 for a particular piece of equipment is that Equation 18 shows a dependence of the rate of heat transfer into the liquid upon the diameter of the tube in the last term, Equations 16, 17, and 18 may be expressed by the single Equation 19:
Approximate velocity
4 ft./sec.
0 A
8 ft./sec. 1 1 ft./sec. 1 3 ft./sec.
Screens were mounted on the nozzle beneath the tube for some runs to produce a higher intensity of turbulence. Two different screens were used. Because of time limitations, the tubulence level was not measured.
Film boiling was produced by passing an electric current through the graphite heating tube mounted in a 6-inch glass cross. Graphite was chosen for its high thermal conductivity and moderate electrical resistance. The tubes were 8
I
CY = kt is used if heat is transCPZ Pl ferred in the liquid only by thermal conduction and E , the eddy diffusivityfor heat, is used if eddy diffusion is controlling. T h e total coefficient, h, including radiation, is approximately related to h,, by Equation 3. These equations are used as a basis for correlation only and are not to be considered as exact equations.
where
w
Equipment T h e equipment used to carry out the experimental work is essentially that used by Bromley, LeRoy, and Robbers (3). I t was modified, however, to allow continuous control of the circulating liquid temperature.
0 0
IO
20
30
I
1
I
I
I
40
50
60
70
80
90
NOVEMBER 1957
1923
Atsc
Figure 4.
,
Film boiling of hexane
Tube diameter, 0.387 inch At0 300-800’ F. Approximate velocity 0
0 A
3 ft./sec. 8 ft./sec. 1 1 ft./sec. 1 3 ft./sec.
x1
VOL. 49, NO. 1 1
lo
I-
I
-I
c
I
1 O
Figure 5 .
I
I
I
I
I
I
I
0.4
0.8
1.2
1.6
2.0
2.4
2.8
I
I
3.2
3.6
I 4.0
4.4
Film boiling of ethyl alcohol outside of 0.387-inch outside diameter tube Approximate liquid velocities 0
x
3 ft./sec. 5 ft./sec.
0 8 ft./sec. A
1 1 ft./sec.
13 ft./sec.
inches in length, from about "8 to 5 / 8 inch in diameter and tapered at both ends to fit supp3rting steel inserts. The tubes were supported in position over the nozzle by steel inserts tapered to form a seal with the ends of the tube. The inserts, in turn, fitted into copper rods. Two coil springs mounted in the packing unit of one of the brass end
Table 1.
plates on the glass cross provided for the thermal expansion of the tube. The voltage was measured by using a porcelain-covered tungsten voltage pro be lvhich was bent at one end so as to contact the inside surface of the tube when inserted down the hole of the tube mounting. The voltage drop across a known section was measured by reading the
voltage a t each end of the section. Two General Electric high internal resistance a.c. flux voltmeters were used to read the voltage. One voltmeter had a double scale range of 0 to 5.0 volts and 0 to 30 volts, and the other had a scale range of 0 to 40 volts. The amperage was read on a General Electric a x . ammeter which had a double scale range of 0 to 2 . 5 amperes and 0 to 5.0 amperes. A current transformer with the rating of 800/S was used to reduce the current to the measuring ammeter. These measuring instruments were calibrated to within 0.5y0of the total scale reading. Chrome1 us. Alumel thermocouples were used to measure temperatures. Flow rates were measured by means of a calibrated orifice. Experimental Data Experimental data were taken for four systems: benzene, carbon tetrachloride, ethyl alcohol, and hexane. These four systems were chosen for their physical properties, Jvhich vary over a fairly wide range. Three tube sizes of 0.387, 0.496, and 0.638 inch outer diameter \vere used to study the effect of the tube diameter. Liquid velocities were varied from 3 feet per second to approximately 13 feet per second a t the nozzle and the amount of subcooling was varied from 20' to approximately 80' F. The intensity- of turbulence was varied by inrrcducing screens directly above the nozzle below the graphite tube. The
Experimental and Calculated Data on the Film Boiling of Ethyl Alcohol from an 0.387-Inch Outside Diameter Tube without a Screen B.t.u.,
Run No. 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
ti I
Volts 3.89 6.14 5.25 4.47 6.94 5.67 6.71 7.80 7.76 6.03 9.06 7.65 7.05 8.75 5.17 4.46 6.11 6.45 5.52 7.77 7.74 6.48 8.99 8.25 7.55 9.41 8.90 8.10 6.23
Amp. 238.2 362 326.5 280 398.2 352 415 450 481 382 504 476 422 546 320 281 411 388 344 435 480 399.2 499 505 424 585 559 486 342.3
hto,
F.
F.
669 1828 1383 698 1906 777 1508 2001 1232
448 I631 1193 515 1704 588 1308 1791 1028 561 1938 761 568 1121 1343 662 1652 1561 692 1885 1046 664 2037 963 680 2045 1025 716 1513
O
751 2161 962 763 1335 1533 846 1852 1760 880 2096 1250 857 2260 1170 877 2280 1239 918 1703
(Hr.) h
6's. Ft.) (" F.)
153.2 108.9 115.8 197.1 131.3 280.0 172.8 158.8 294.0 335.0 190.9 389.5 424.0 345.0 98.9 153.2 122.9 129.5 222.2 145.2 284.0 312.5 178.9 350.0 380.5 217.6 392.0 446.0 114.1 D
1 924
INDUSTRIAL A N D ENGINEERING CHEMISTRY
hc,
U, Ft./Sec.
At,,, F.
149.7 89.6 104.7 193.4 110.1 275.8 159.9 135.7 285.3 331.0 163.9 383.7 419.9 335.0 85.4 148.3 103.1 111.2 217.1 119.7 275.7 307.6 149.0 342.1 375.5 187.4 383.3 440.7 97.3
3.68 3.68 5.12 5.12 5.12 8.00 8.00 8.00 10.93 10.93 10.93 13.98 13.98 13.98 3.52 3.52 3.52 5.20 5.20 5.20 8.04 8.04 8.04 10.85 10.85 10.85 13.13 13.13 3.65
40.2 41.0 40.2 40.3 40.5 41.3 39.8 40.2 40.9 40.2 40.2 40.8 40.8 40.2 60.3 61.1 59.7 59.6 61.9 60.4 58.2 60.3 59.6 59.1 62.1 59.6 58.9 61.6 80.4
Athe A 5.61 4.48 3.04 6.18 3.04 6.99 3.85 2.86 6.04 7.10 2.78 7.32 7.94 6.14 3.16 6.02 3.60 3.26 7.11 3.25 7.05 8.30 3.10 7.83 8.75 3.36 7.61 9.31 3.46
4.48 0.74 1.19 5.21 0.87 6.31 2.20 0.63 5.26 6.54 0.60 6.94 7.60 5.20 0.86 4.81 1.57 1.02 6.08 1.02 6.02 7.45 0.74 6.90 7.92 1.18 6.65 8.52 1.35
CslPl kl
yi
3.13 0.85 1.26 3 .OO 0.79 2.67 1.11 0.72 1.48 2.70 0.64 2.02 2.68 1.30 1.63 3.68 1.22 1.33 3.48 1.02 2.12 3.54 0.88 2.47 3.17 0.87 2.12 3.29 1.93
i
R 306 84 144 344 91 460 156 102 250 443 104 371 489 240
155 348 116 149 390 116 294 490 39 378 575 44 316 575 177
F I L M BOLLING “small” screen had a 0.1033-inch mesh and a 0.0250-inch wire thickness, and the “large” screen had a 0.2435-inch mesh and a 0.0466-inch wire thickness, Extensive data were taken with ethyl alcohol in order to determine the effect of turbulence on the rate of heat transferred into the liquid.
>
Typical data are included in Table I. All data have been recorded (4). The run number is taken directly from the laboratory notebook and is used only as a means of listing the data in the correct columns. Volts refer to the voltage difference across the 5-inch test section a t the center portion of the tube. The values represent the difference of two readings from the current flux voltmeter. Amp. refers to the total current flowing in the graphite tube. The ti is the recorded average inside temperature of the tube a t the center point. T h e values were measured in millivolts with a precision potentiometer and were converted to ” F. The At, is the temperature difference across the film-that is, between the outside tube surface and the boiling liquid. The temperature a t the surface of the tube is calculated from the knowledge o f t , and the thermal conductivity of graphite. The h is the over-all coefficient of heat transfer which has been corrected for losses due to conduction along the tube. The h,, is the coefficient of heat transfer due to convective heat transfer. The U is the velocity of the liquid a t the nozzle opening below the graphite tube as measured by the calibrated 3inch square-edged orifice. The At,, is the amount of subcooling of the liquid, which is the temperature difference between the liquid temperature and its _boiling - point. The h,,
3
,/us
l9o
3 I
$:V 20
0
0
-‘ t I 0
Figure 6.
IO0
200
300
400
500
600
700
Film boiling of ethyl alcohol outside of 0.387-inch outside diameter tube Approximate liquid velocities 0
x
0 A 0
l9 o
3 ft./sec. 5 ft./sec. 8 ft./sec. 1 1 ft./sec. 13ft.fsec.
L
e
is the dimension-
less parameter which has been used to correlate data in forced convection film boiling to saturated liquids. The A is the dimensionless parameter
7 6 5 4
t
The B is the dimensionless parameter
3
2
I
Discussion of Results The values of the heat transfer coefficient h,, across the vapor film are shown plotted as a function of the amount of subcooling of the liquid with the velocity of the liquid as a parameter in Figures 1 through 4. At liquid velocities above 8 feet per second at the nozzle, the heat transfer coefficients h,, are increased approximately foui-fold by subcooling the liquid approximately 80” F. These heat transfer coefficients thereby approach numerically the values of the heat trans-
0
-’
8 0
130
300
200
Figure 7.
400
500
600
700
Film boiling of ethyl alcohol Diameter of tube
X 0
0.387 inch 0.496 inch 0.638 inch
VOL. 49, NO. 1 1
NOVEMBER 1957
1925
10
I
4
9 i 8
7
tI-
Figure 8.
Film boiling of benzene Diameter of e 0.387 X 0.496 i3 0.638
tube inch inch inch
It
-1.
0
100
200
330
700
600
500
400
800
Figure 9. Film tetrachloride
boilhg
Diameter of a 0.387 X 0.496 0 0.638
of
carbon
tube inch inch inch
I
-1
c
9
I
1
Figure 10.
5
0 -I
0
1926
Film boiling of hexane Diameter of tube e 0.387 inch X 0.496 inch 0 0.638 inch
100
I
I
I
I
I
200
300
400
500
600
INDUSTRIAL A N D ENGINEERING
CHEMISTRY
700
F I L M BOILING
A
b Figure 11. Forced convection film boiling of subcooled liquids Diameter of Tube, Inch Liquid Benzene Ethyl alcohol Hexane Carbon tetrachloride
0.387 0.496 A 9
r
e
b
@
4
0.638 X
+ * ++
0
0
Figure 12. Film boiling of ethyl alcohol using screens to increase turbulence
S
Tube Diameter, Inch
0.387 0.496 0.638
Large
A
0
+0
X
200
300
400
500
10 ‘I
700
600
.
12
Screen Small
100
t
A
I
%
9
cl
b
8 7
6
fer coefficients in nucleate boiling, and the heat fluxes are becoming much higher than in nucleate boiling. Because it was not possible to estimate accurately the eddy conduction in these experiments, the results a t high degrees of subcooling should be used only for very qualitative estimates. The dimensionless parameters, which are plotted in Figure 5, are proposed in Equation 16 to correlate the data when the mechanism of heat transfer into the liquid is thermal conduction. The data in Figure 5 show that the dimensionless group A,
i
increases markedly with increasing velocity. This indicates that eddy conduction is more important than molecular thermal conduction. Figure 6 shows the same data for ethyl alcohol as are shown in Figure 5 plotted as predicted by Equation 17 for heat transferred into the liquid by eddy conduction. The systematic variation with velocity noted in Figure 5 is now no longer apparent. The length dimension, lo, used is the width of the passages in the straightening vanes in this equipment. This length, lo, was further corrected for the effect of the nozzle contraction (4). These graphs should not be used for prediction of heat transfer coefficients, since this correction is only a rough approximation.
5 4
3 2 I
L
0 0
IC0
200
300
There is only one significant difference between the equation for long and short contact times. There is an additional dependence of the dimensionless group A upon the diameter of the tube for the case when the contact time was short enough to be smaller than the ratio of the scale of turbulence to the intensity of turbulence. Figure 7 shows that there is no systematic dependence upon the size of the tube and thereby indicates that the time of contact is large compared to the ratio of the scale of turbulence to the intensity of turbulence in this equipment. Figures 8, 9, and 10 show the data for film boiling of benzene, carbon tetrachloride, and hexane, respectively. Figure 11 shows a summary of the data for all four systems. The best line drawn through all the data by eye is shown as a solid line in Figures 6 through 11. The effect of introducing screens
400
500
600
700
above the nozzle upon the dimensionless parameter A is shown in Figures 12 through 14. The solid line in these figures represents the best line that could be drawn by eye through all the data with screens. Because Figure 13 shows the large screen to have approximately the same effect as the small screen, only the large screen was used with the other liquid systems. The screens caused an increase in group A of approximately 3070 over that shown in Figure 11. This seems reasonable as the screens increase the intensity of turbulence markedly but decrease the scale of turbulence. If the time of contact had been short enough so that the eddy conductivity was independent of the scale of turbulence, the screens would have been expected to cause a much greater increase in group A . I n Figures 6 through 14, the best line drawn through the data is found to be an VOL. 49, NO. 1 1
NOVEMBER 1957
1927
IS
t-
:t
-1
0
dl
1
1
I
I
1
I
I
E
l 0
100
I
I
I
I
1
1
200
300
400
500
600
700
A t , , C P , 4dA=
cy)-' O5
Figure 13. Film boiling of benzene using large screen to increase turbu!ence Diameter of tube 0
0
0.387 inch 0.638 inch
S-shaped curve instead of a straight line which was theoretically predicted. This deviation from the theory can be explained by the numerous inexact assumptions made in the derivation.
C,
=
D g h
= = =
h,,
=
h,
=
k
=
Conclusions T h e heat transfer coefficients h,, across the vapor film in film-type boiling can be markedly increased by subcooling the liquid. Values of this heat transfer coefficient have been found to approach numerically those of nucleate boiling. Heat is transferred into the liquid by eddy conduction, and the effect of thermal conduction is small in forced convection film boiling to subcooled liquids. I t is possible to use the dimensionless parameters
K
=
1 10
= =
L
=
qo = = q q% = 1
Re
and
t
T At,
to correlate the data for heat transfer in upward flow forced convection film boiling to subcooled liquids from a horizontal rod. Nomenclature a
-4
= film thickness, ft. = heat transfer area, sq. ft.
= = = = =
At,, = C'
=
WO = V W
= =
01
=
specific heat a t constant pressure, B.t.u./(lb.) ( " F.) outside diameter of tube, ft. acceleration of gravity, (ft./hr.2) film coefficient of heat transfer, B.t.u./(hr.) (sq. ft.) ( " F.) film coefficient if there were no radiation, B.t.u./(hr.) (sq. ft.) ( " F.) radiation coefficient of heat transfer, B.t.u./(hr.) (sq. ft.) ( " F.1 thermal conductivity, B.t.u./ (hr.) (ft,) ( " F.) constant of proportionality scale of turbulence, ft, length dimension of Reynolds number of the fluid flowing in a conduit, ft. length of tube, ft. heat flow from tube, B.t.u./hr. heat flow into liquid, B.t.u./hr. net heat flow into vapor, B.t.u.f hr . radius of tube, ft. Reynoldsnumber temperature, " F. absolute temperature, O R. temperature difference across film, " F. temperature difference between liquid and its boiling point, " F. incident velocity of liquid on tube, ft./hr. velocity of liquid in conduit where level of turbulence is determined, ft.,'hr. velocity ofvapor, ft./hr. weight rate of liquid evaporated, 1b.fhr. molecular diffusivity of heat (or denotes proportionality), sq. ft./ hr eddy diffusivity of heat, sq. ft./ hr .
.
E
1 928
INDUSTRIAL A N D ENGINEERING CHEMISTRY
=
0
Hexane
X
Carbon tetrachloride
XO
X'
p
= latent
heat of vaporization, B.t .u./l b. = effective (3,6) difference in heat content between vapor a t its average temperature and the liquid a t its boiling point, B.t.u. /lb. = viscosity, lb./(hr.) (ft.) = density, lb./cu. ft.
Subscripts
i
= inside thetube
I u
= = =
1
liquid vapor conditions before nozzle
References (1) Banchero, J. T., Barker, G. E., Boll, R . H., Heat Transfer Symposium,
Annual Meeting, American Institute of Chemical Engineers, St. Louis, Mo., December 1953; Cher>
E n g . Progr. Symp. Ser.. No. 17, 51 21 (19551. --, \ -
(2) Brornley, L. A., Chem. E n g . Progr. 46, 221-7 (1950). ( 3 ) Bromley, L. A., LeRoy, N. R . , Rohbers, J. A.. Universitv of California Radiation Laborator\,' Reat. UCRL1894 (1952); ~ N D . ENC.~ K E M 45, . 2639-46 (1953). ( 4 ) Motte, E. I., M. S. thesis, University of California, Berkeley. Calif., 1954; University of California Radiation Laboratorv Rept. UCRL-2511 11954). (5) Nakagawa, Yuzo, Yoshida, Tetsue. Chem. E n g . ( J a p a n ) 16, 74-82, 10410 (1952). (6) Rohsenow, W. M., Trans. Am. SOC. Mech. Engrs. 78, 1645 (1956). RECEIVED for review July 20, 1954 ACCEPTED June 22, 1957 This work was performed under the auspices of the Atomic Energy Commission.
