Engineerin S:O : ,p
development
'
Heat Transfer Coefficients for Vapors Condensing on Horizontal Tubes R. E. PECK AND W. A. REDDIE
ILLINOIS INSTITUTE OF TECHNOLOGY, CHICAGO 16, ILL., AND ARMOUR AND CO. AUXILIARIES, CHICAGO, ILL.
T h e Nusselt equation has been used to calculate film coefficients for a vapor which is condensing filmwise on a horizontal tube. Experimental results have shown considerable deviation from calculated values. Two of the assumptions upon which this equation is based have been shown to be invalid. A correlation has been developed, which corrects a great deal of the discrepancy found in the results calculated by the Nusselt equation. Experimental results of the authors and sixteen other investigators showed that heat transfer around the tube did not account for the deviations from the Nusselt equation. With the application of the proper dimensionless group, as given in the correlation, i t is possible to predict film COefficients with much greater accuracy.
I
N T H E derivation of the familiar Nusselt equation (1) which gives the condensate film coefficient for a single saturated vapor condensing filmwise on a smooth surfaced horizontal tube, two basic assumptions vere made-the temperature drop across the condensing film is constant around the tube and the condensate film is not subject to acceleration forces. It has been shown by many investigators that the experimentally determined condensate film-heat transfer coefficient is in practically every instance either less or more than the coefficient calculated from the Nusselt equation. In order to investigate this variance between experimental and theoretical results and its relationship to the assumptions mentioned above, it was decided to derive equations giving a value of the heat transfer coefficient a hich was independent of these assumptions. Experimental condensate film coefficients have been obtained for the organic liquids butyl alcohol, carbon tetrachloride, isopropyl alcohol, methanol, methyl ethyl ketone, and nitromethane. Selection of these liquids was based on their availability in commercial quantity with adequate purity, the mildness of operating conditions required in their use, and certain physical properties, such as viscosity, which were believed to be important in determining the nature of the condensate film coefficient. Prior to 1916 some experimental work ( 1 , 8, 11, 12, 17, 26, 27, 34, 36, 38) had been done in order to obtain over-all heat transfer coefficients for the case of saturated steam condensing on a horizontal tube, but no mathematical expression was available by means of which a condensate film-heat transfer coefficient could be predicted once a definite condensable vapor and specific operating conditions were chosen. A comprehensive mathematical development dealing with the filmwise condensation of saturated vapors on a cold surface was presented by Nusselt (26) in 1916. Many later investigators
(2-6, 7 , 9, 14,16, 20, 28, SO, S7,40) used the equation for the case of a horizontal tube as the basis for comparison of experimentally determined results with predicted valueE. Parr ( S l ) has calculated steam film coefficients on somewhat different assumptions than Nusselt, but he uses the same general idea. A brief comparison of the theories of Nusselt and Parr is given by Jakob (13). Monrad and Badger (IS) briefly reviewed in English the theoretical contributions of Nusselt t o the subject of vapor condensation. Condensate film coefficients for both single and mixed saturated vapors of many chemical types have been obtained by McAdams and Frost (20), Othmer (R8), ilIontillon, Rohrbach, and Badger (24))Kirkbride (16),Baker and Xlueller (W),Wallace and Davison ( 3 7 ) )Gilkison ( 9 ) ) Baker and Tsao (S),Bauermeister (4),Bureau and Cavanaugh ( 7 ) , Othmer and White (SO), Bisesi (j), Young and Wohlenberg (do), Bromley (6')) and Othmer and Berman (29). The phenomenon of temperature variation around the perimeter of a horizontal condenser tube has been investigated by Jakob, Erk, and Eck (14), Langen (16))Baker and Mueller ( 2 ) )Gilkison (9), Bauermeister ( 4 ) ,Bureau and Cavanaugh ( 7 ) ,Bisesi ( 6 ) )and Bromley (6). McAdams (19) gives a summary of film coefficients for vapors condensing on both horizontal and vertical tubes. Rhodes and Younger (38) approximated the condensate film coefficients of a large number of vapors from over-all coefficients by using an indirect method originally suggested by Wilson (39) and subsequently discussed by Mcildarns ( 18) and by -McAdams, Sherwood, and Turner (81). THEORETICAL DEVELOPMENT
For a single horizontal tube, condensate forming on the external surface and dripping off, Nusselt (26) has developed the expression given below in order to predict the heat transfer coefficient for a condensing vapor.
The terms of this expression and those following are defined under the nomenclature section. In the Nusselt equation ZL,is ordinarily unknown. In order to obtain a solution when complete experimental data are lacking, it is necessary to estimate the value of Kt0j and proceed in a trial and error manner. The data taken in this investigation permit Ato/ to be determined directly. It has been noted that Atcf varies considerably around the tube 2926
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1951
and to a lesser degree along the length. It is necessary, therefore, to determine an over-all mean value for Ato/. A satisfactory method of arriving a t an over-all mean value for Atof is to measure with a thermocouple the temperature at the midpoint of the tube wall for a large number of points around the circumference of the tube and for several positions along its length. Temperatures of the outside surface of the tube, to,, corresponding to corrected thermocouple readings can be obtained from the equation
Equation 9, with the proper values of A‘, B’, Ea,and F,, has been found to give a temperature distribution very similar to the experimentally determined distribution. DERIVATION OF HEAT TRANSFER EQUATION CONSIDERINQ Aicf AS^(@). In the derivation of Equation 1, one of the basic assumptions made was that the temperature drop across the condensing film is constant around the tube. An equation giving a value of the heat transfer coefficient independent of this assumption can be developed. From Nusselt’s work can be obtained the relation X
A plot then can be made of to* us. corrected tube position. Next, with the aid of a planimeter, a graphical average value of toecan be determined for each thermocouple. Finally, a plot is made of (to& us the location of the thermocouple along the length of the tube and another graphical average is taken. This second graphihal average will be a representative average over the entire tube, allowing for both circumferential and longitudinal temperature The over-all mean gradients, and will be designated temperature drop across the condensate film, act, is obtained from the equation
-
Aft, = tm
- (to,),,
2927
Jg
r1I3dr’
=
kroAtojsin1/36’dt?
By definition A t c j = tsv
(10)
- los
(11)
From Equation 9 there can be obtained an expression of the form ios = uo
+
U ~ C O S0
+
U ~ C O S 26
+
W O S
36
+ ..
ne (12)
.U~COS
From a combination of Equations 10, 11, and 12 it can be shown (32) that
(31
Also
If in Equation 13 a2 +.0, the equation reduces to The experimental value for the condensate film heat transfer coefficient can be found from the relation which is the Nusselt equation. The coefficient,a2 = 0 for a symmetrical temperature distribution and at, was found to be very small for all experiments perThe quantity, q, is readily obtained by calculating the amount of formed. Thus the heat transfer around the tube cannot account heat absorbed by the cooling water per hour. for deviations from Nusselt’s equation. Assuming POINT VALUESOF COOLINO WATERTEMPERATURE. DETERMINATION OF HEAT TRANSFER EQUATION INCLUDING no heat flow along the tube, the over-all coefficient, U,around the CONSIDERATION OF ACCELERATION EFFECTS.In the previous perimeter will be the same along the tube from one end to the section it was shown that under certain conditions, Nusselt’s a3other and is given by the expression sumption that the temperature drop across the condensate film is c o n s t a n t around the tube was valid. Having o b t a i n e d By rearranging Equation 6 , there is obtained the general equathis information, it tion was decided to 2rr0LUo derive t h e heat - tw) log ( t J Y - two) 2.303wCp -= log (7) transfer equation in a manner similar to Since t,,, two, U,, ro, and w are known for an experimental test run, Nusselt’s method of it is seen that t, is a function of L and that t, may be calculated a p p r o a c h to‘the for any distance along the tube by substituting in Equation 7 the problem, but, in value of the length of the tube up to the point where the water addition, to include temperature is desired. the effects of acTEMPERATURE DISTRIBUTION IN A HORIZONTAL CONDENSER celeration. TUBE. Consider a relatively thin-walled cylindrical shell in the ’ For condensate form of a condenser tube of length z. If this tube is formed from a Figure 1. Condensation upon an upon an i n c l i n e d homogeneous material and if a saturated vapor is condensed on Inclined Plane plane, the force of the external surface by means of cooling water flowing along the gravity per u n i t inside surface where the heat flow along the length of the tube is volume parallel to the surface is g sin 6, where 6 is the angle with neglected, the temperature a t any point in the tube is given by the the vertical of the normal to the plane, Figure 1. solution of the expression In condensing a pure saturated vapor, the iinterfacial thermal resistance is considered to be zero. It is assumed that, as the condensate forms on the plate; the plate temperature remains constant, the vapor has no velocity relative and parallel to the inThe general equation giving t as a function of r and 6 becomes terface, the vapor is saturated, the heat flows through the conm densate only by conduction, and the condensate flows viscously (Ear,cos a0 ~ ~ r - n c o~ s( e ) (9) t(r, e = A’In r B’ down the plate under the influence of gravity alone. If the veloca=l ity is considered zero a t the wall and a function of z only (Figure It can be shown ( 3 2 )that the quantities A‘, B’, E,, and F a are I), the following relation for a differential element of fluid of unit related by simple equations. area in the z plane may be established:
(5)
-
+ +C
+
Vol. 43, No. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
2928
and
The above expression is arrived at by assuming the fluid element of depth, x o - x, and of unit area is accelerated and is not in equilibrium with the traction caused by the velocity gradient, d u l d z , and the viacosity, p, in the z plane. Blso
I
By combining Equations 24, 25, and 26 and simplifying terme, the following expression is obtained as a first approximation. 3 1
n
n
e =du-d-L = dr
d L dr
From Nusselt's work
u =u u u d- d-
dL
ro dR
(15)
XdI'
since the surface of a horizontal tube is made up of an infinite number of danes of width rode, Figure 2. By combinhg Equations 14 and 15, there is obtained the relation
dx
k
= -
xo
T,deAt,/
(28)
By combining Equations 27 and 28 and separating variablea, there is obtained Figure 2. Condensatiou upon a Horizontal Tube
=
pgsin e(zo - x)
Integration of the functions between the limits corresponding to the top and bottom of the tube gives
From Equation 16 Ju
pdU f
JxLXo E X" dx d x
=
pgsin e(x,
Ae a first approximation, if the effects of acceleration forces are neglected, the following relation is obtained from Equation 30
which reduces to
where E' is a proportionality factor. Solving for u,
Substituting Equation 31 in Equation 30 there is obtained
By definition, The integral in Equation 32 is a function of the dimensionless group ( k / & / p j X ) and. as an approximation, can be reduced to the form which reduces to
and substituting into the
Upon solving Equation 33 for fundamental relation
Also,
r
=
x,,E~
By combining Equations 21 and 22, there is obtained t,he equation
Solving for ze, '
-
-
h,w,At,f
=
XI'B
(34)
there is obtained, after considerable simplification,
Equation 35 can be rem-ritten in the form ^
From Nusselt's work
.
where K and m are variable parameters. The usefulness of Equation 36 lies in the fact that once a value of has been determined for a specified set of conditions a value of E, can be obtained which is, in the majority of cases, a more accurate value than &I,-.
December 1951
I N D U S T R I A L A N D E N G INE E R IN G C H E M I S T R Y APPARATUS
2929
stream was allowed to flow in the annular space of the horizontal tube condenser. The excess vapors were recovered in the small auxiliary condensers. The vapor velocity was maintained a t a mmlmum. Cooling water was admitted to the inner tube from the constant head tank and passed countercurrent to the vapor stream. The condensate and cooling water rates were measured by collecting the streams for certain time intervals and weighing the quantities collected. The first step in making a run was to A. CONSTANT-LEVEL WATER TANK set the desired rates. This accom lished, the 6. MANOMETER apparatus was left undisturbeb) until the C. WATER THERMOCOUPLES system reached equilibrium. This required 0. CONDENSER E. WATER MIXER approximately 2 to 3 hours. A portion of the F. BOILER lagging was then removed from the condenser 0 . VAPOR THERMOCOUPLES in order to make certain that the condensaH. REFLUX CONDENSER I . CONDENSATE THERMOCOUPLE H tion was of the true filmwise type. J. CONDENSATE COOLER A test run was then started. The confl denser tube was set a t the zero position, the tube thermocouples being a t the top. With the tube in this osition, millivolt readings were taken for eac! of the six thermocouples. The tube was then rotated to a new angle and, after a short lapse of time to enable the system to regain equilibrium, the thermocouple readings were taken again. The time required for securing equilibrium conditions between changea of the tube position was approximately 1 minute. This procedure was repeated until the entire 360" were traversed. At selected intervals during the course of the run, thermocouple readings were taken for the inlet and outlet water and vapor streams. These usually wer,e taken at the O", 60°, 120' BO', 240 , 300". and 360' Dositions of the tube. ADh proximately four-+ater and condensate races Figure 3. Diagrammatic Sketch of Apparatus also were taken during the test run. The potentiometer was read to the nearest 0.005 millivolt. The apparatus was essentially a single horizontal Monel metal tube with cooling water flowing through the tube and vapors conLABORATORY DATA densing on the outside. The outer jacket was a pipe made of borosilicate glass. The vapors studied were generated in ti Laboratory data were obtained for technical grades of butyl stainless &eel boiler which used steam as the heating medium. alcohol, carbon tetrachloride, isopropyl alcohol, methanol, methyl Cooling water was supplied from a constant head tank and the ethyl ketone, and nitromethane. These data may be found flow was controlled by means of a needle valve. The condensing tabulated in the thesis (38). section and heaters were heavily insulated. A small reflux condenser waa used as an auxiliary condenser to ensure against CORRELATIONS having the vapor space only partially filled. Arrangement was made to return the condensate directly to the boiler, except durThe experimental resulta of this investigation are illustrated in ing the periods when the rate of condensation was being measured. Temperatures were measured by means of thermocouples. Table I, in which the condensate film coefficientsfor nitromethane All thermocouples were of the chromel-alumel type, No. 22, and the operating conditions are shown. B. & S. gage. Six of these thermocouples were inserted in the In connection with the items listed in this table, the following center of the wall of the Monel metal tube, equally spaced, and notes are offered. in longitudinal alignment. The installation was performed by Bauermeister according to the method described by McCormack ( 2 2 ) and similar to that described by Hebbard and Badger (IO). After releasing the flange bolts, the inner tube may be rotated to any position desired. An angular scale allows the angle of rotation, referred to the top of the tube, to be measured-that is, the thermocouples are on the top of the tube when the angle reading is 0", and at the bottom when the angle reading is 180". Thermocouples were also provided for measuring inlet and outlet water and vapor temperatures. All thermocouples were brought to a selector switch box, and the electromotive force was measured by a Leeds and Northrup portable precision potentiometer, Type 8662. The cold junction was maintained a t 32' F. by insertion in a Dewar flask containing ice. The apparatus used for this investigation has been used by Gilkison (9),Bauermeister ( d ) , Bureau and Cavanaugh (7), Bisesi ( 5 ) )and BromleY (6)for diverse experiments in the field of condensing saturated vapors. It is shown diagrammatically in Figure 3, and by photograph in Figure 4.
EXPERIMENTAL PROCEDURE
Thermocouples for the measurement of water and vapor temperatures were removed from the e uipment and calibrated a t several points against an accurate t%ermometer of the mercury expansion type. The following points were used: melting point of ice; room temperature; boiling point of benzene; and boiling point of water. Data obtained may be found in the thesis (32). These thermocouples were then replaced in the equipment and the thermocouples imbedded in the tube were calibrated against the vapor couples a t room temperature and a t boiling water temperature. Data obtained may be found in the thesis (32). Vapors were generated in the stainless steel boiler and a steady
Figure 4. Photograph of Apparatus
d
INDUSTRIAL AND ENGINEERING CHEMISTRY
2930
Vol. 43, No. 12
data was recalculated using a c c u r a t e v a l u e s of t h e physical properties. There tvere a fex cases where only the published data were used. Given the temperature distribution corresponding to midpoint locations about the circumference of a cylindrical, horizontal condenser tube made of homogeneous inaterial which has saturated vapor condensing on the outer surface and cooling water floning along the inner surfare, the temperature distribution at either interior position3 or on the surface of the tuhe inav be calculated. Figure 5 . General Correlation of Experimental Results, Ratio The point value of temperature drop across the c o n d e n s a t e film can be The water and condensate rates are experinlentally deterrepresented by an expressioa of the for111 mined values. The Reynold's number refers to the water stream flowing within the inner tube. The heat load, q, is the heat absorbed by the cooling water in B.t.u. per hour. Atcf = t,, - a. - U ~ C O S e - wos 28 - a l C 0 ~38. , a , l ~ no ~s The water and condensate rates are experimentally ctetermined values. The Reynold's number refers to the water stream flowing within the inner TABLE 1. COXDENSBTE FILIICOEFFICIEXT, tube. The heat load, q, is the Condensate ' heat absorbed by the cooling _Film_Coefficient _ ~ ~ Condensate Heat Load, water in B.t.u. per hour. The he values for the mean over-all Water Rate, Rate, Reynold's Q, ~te.i, Experii,v temperature d r o p across the R u n KO. Lb. per Hr. Lb. per Hr. Number B.t.u. per Hr. F. mental Susselt' h~ to hN 4.17.42 1695 149.2 9035 37400 42.3 461 488 0 95 condensate film, Ato/, are those 717 113.7 4310 96200 27.0 506 552 0.92 4.18.42 found by the method of 4.21.42 1069 128.3 5900 31500 36.0 456 Z13 0.89 averages described in t h e 4.22.42 1378 149.0 7500 36800 43.9 437 488 0.90 9 9 . 9 3725 21600 6.11.42 495 22.2 608 582 0.87 theoretical development sec900 123.8 6190 26200 6 . 1 2 . 4 2 2 8 . 5 480 545 0 .88 tion. 6.13.42 201 80.8 1970 16700 16.5 528 630 0.84 O
Equation 36 was found empirically by trial and error to be
h,
= $N
b.0206
(k / Atci k''')+ 0.791
TABLE 11. CONDESSING VAPORSOUTSIDESINGLEHORIZOXTAL PIPES (37)
Reference
In Figure 5 there are summarized graphically the calculated values of h,/K?and ( X M , / k / Z e / ) 1 / 2 for the experiments performed in this investigation together with those based upon data obtained by other investigators in this field of heat transfer. The key to Figure 5 is given in Table 11. Figure 5 represents 199 separate experimental measurements of the condensate film heat transfer coefficient for 17 condensing vapors made by 17 investigators over a period of 26 years. In this figure the Nusselt equation for determining the condensate film coefficient is represented by the horizontal line TEC/zv = 1.0.
4
$9
2 9 16 BO 36 37 29
BO
3.9 30 92
40 29 29 6 , 38
20 6,38 80
5 , 30
29
38 29 36 36
COYCLUSIONS
A eemiempirical relation, Equation 37, has been developed which will give more accurate values of the condensate film heat transfer coefficient for the case of saturated vapor condensing on a horizontal tube than the Susselt equation gives, especially for certain values of the dimensionless group ( h p , / k / X dtc/)l/2asshown in Figure 5. The majority of the
96 37 -
36 36 8
6 $8 29 36
Observer Bauermeister Othmer, Berman Baker, Mueller Gilkison Kirkbride BlcAdams, Frost Tsao Wallace Davison Othmer,' Berman Othmer, Berman Reddie McAdams, Frost Reddie Young WohleAberg Othmer, Berman Othmer Berman Bisesi, Reddie Othmer Berman Bisesi Reddie OthmLr, Berman Bisesi, Reddie Othmer, Berman Reddie Othmer, Berman Tsao Tsao Tsao Wallace, Davison Tsao Tsao Baker Mueller Bromiey Othmer Othmer, Berman Tsao
Vapor
Outside D.ameter D i , Inche's
Effective Length Condenser, Lt
Bcetone Acetone Benzene Benzene Benzene Benzene Benzene Benzene Butyl acetate Butyl alcohol Butyl alcohol Carbon tetrachloride Carbon tetrachloride Dichlorodifluoromethane
1,312 1.94 1.314 1.312 1.313 0.675 0,625 0.840 1.94 1.94 1.312 0.675 1.312 0.75
5.58 1.68 3.67 6.58 8.16 3.98 3.67 2.5 1.68 1.68 5.58 3.98 5.68 2.0
Ethyl acetate Ethyl alcohol Isopropyl alcohol Isopropyl alcohol Methanol Methanol Methyl ethyl ketone Methyl ethyl ketone Xitromethane Propyl alcohol Tetrachloroethylene Toluene Toluene Toluene Trichloroethylene
1.94 1.94 1.312 1.94 1.312 1.94 1.312 1.94 1.312 1.94 1.00 0.625 1.00 0.840 0.625 1.00 1.314 1.312
1.68 1.68 5.58 1.68 5.58 1.68 5.58
Trichloroethylene Steam Steam Steam Steam Steam
3.0
1.94
1.00
1.68
5,58 1.68 3.67 3.67 3.67 2.5 3.67 3.67 3.67 5.25 3.9 1.68 3.67
Symbol
December 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY X
The coefficient dz = 0 for symmetrical temperature distribution and a3 was found to be very emall in all experiments performed. Thus the heat transfer around the tube cannot account for deviations from Nusselt’s equation.
p
ACKNOWLEDGMENT
p
The authors are indebted to Carl H. Bisesi, William H. Bureau, and Orville A. Cavanaugh with whom portions of the experimental work were performed and to Harry McCormack for his direction in constructing the equipment. The advice of Michael Sadowsky and Richard Edwards of the Mathematics Department, Illinois Institute of Technology, was also extremely helpful. NOMENCLATURE
The units listed are those of the English Engineering System but any consistent set of units may be used.
A ’ , B’, E, E,, Fa = mathematical constant an = (n = 0, 1, 2 . . . ) mathematical constant C, = spyific heat at constant pressure, B.t.u. per pound X F. Do = outside diameter of condenser tube, feet 0: = outside diameter of condenser tube, inches s_ = acceleration of gravity in (feet per hour)2 = 4.18 X 108 h, = average condensate film heat transfer coefficient given in (6),B.t.u. per (hour) (square foot) ( O F.) hv = average condensate film-heat transfer coefficient given in ( 1 ) B.t.u. per (hour)-(square foot) ( ” F.) K = mathematical constant k = thermal conductivity of condensate, (B.t.u.) (foot) per (hour) (square foot) ( O F.) thermal conductivity of condensate, a t 7, (B.t.u.) (foot) per (hour) (square foot) ( O F.) Lt = length along condenser tube measured from vapor outlet L = a length of arc on circumference of a circle, feet AI = mathematical constant m = mathematical constant q = rate of heat transfer through condenser tube, B.t.u. per hour r = radius of cylinder, feet ro = outside radiusoof condenser tube, feet t = temperature, F. tj = average value of condensate film temperature, O F. tm = measured temperature at midpoint of tube wall, O F. tm = average valu: oi measured wall temperature, t,, around the tube, F. toa = point value of outRide tube surkce temperature, O F. (tos)m = graphical average value of tos, F. (to,),, = over-all mean outside tube surface temperature, F. tsv = temperature of saturated vapor to be condensed, O F. tw = teyperature of cooling water a t a point, L,along tube, F. 1,j = temperature of cooling water at exit from test section of condenser tube, F. lroo = temperature of cooling water a t entrance to test section of condenser tube, ’ F. U, = over-all heat transfer coefficient based on outside surface area of test section of condenser tube, B.t.u. per (hour) (square foot) (’ F.) = point linear velocity of condensate film, feet per hour u, u = average linear velocity of condensate film, feet per hour w = mass rate of flow of cooling fluid, pounds per hour = thickness of condemate film, feet zo 2 = distance along axis of a horizontal cylindrical shell, feet Greek 1 cy = mathematical constant r = mass rate of flow of condensate from any point on condensing surface, divided by the breadth, pounds per (hour) (foot) rs = mass rate of flow of condensate from lowest point on condensing surface, divided by the breadth, pounds per (hour) (foot) At = temperature drop, F. Atm = over-all mean temperature drop across metal wall, O F. At,j = temperatye drop across the condensate film a t the angle 0, F. At,/ = oyr-all mean temperature drop across condensate film, F. k,
=
p.i
pj 7
e
2931
enthalpy change, latent heat of condensation a t saturation temperature, B.t.u. per pound = absolute viscosity of condensate film, pounds per (hour) (foot) = absolute viscosity of condensate film a t t/,pounds per (hour) (foot) = density of condensate film, pcunds per cubic foot = density of condensate film a t t f , pounds per cubic foot = time, hours = angle, measured from top of the tube, of a point under consideration, radians =
LITERATURE CITED
(1) Anon, J. Am. SOC.Naval Engrs., 24, 155 (1912) (2) Baker, E. M., and Mueller, A. C , IND.ENG.CHEM,29, 1065
(1937).
(3) Baker, E. M. and Tsao, U., Ibzd., 32, 1115 (1940)
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