As a result of the work reported in this paper, the overall coefficients of heat transfer for the work of Logan, Fragen, and Badger (8) on the evaporation of sucrose solutions were correlated within *10 per cent by the use of a comparatively simple equation involving only the velocity of the liquid entering the heating tubes, the visc o s i t y of t h e l i q u i d b e i n g evaporated, and the over-all t e m p e r a t u r e drop from the condensing steam to the liquid. The viscosity and temperature drop were based on a temperature of the liquid corresponding to the boiling point of the solution a t the pressure existing in the vapor space of the evaporat o r ( a p p a r e n t boiling point corrected for boiling point elevation). It was necessary to use this apparent temperature because the liquid is heated as it passes through the tubes, and its a v e r a g e true temperature cannot be predicted by any known methods. The apparent boiling point is readily obtained, and data for making the correction for boiling point elevation Held under the auspices of the Division of Industrial and Engineering Chemistry are usually available. of the American Chemiortl Society a t Yale University, The same equation was apNew Haven, Conn., December 30 and 31, 1935. plied to data reported by Badger (2, 3) for the e v a p o r a t i o n of sulfite waste liquors and impure sugar solutions. The experimental data for these tests were within * 15 per cent of the values predicted by the equation. The a p p a r a t u s used in these tests contained tubes of nearly the same dimensions as in the work of Logan, Fragen, and Badger. Over-all coefficients of heat transfer for the e v a p o r a t i o n of distilled water were measured by Kleckner and Badger N SPITE of the wide use of evaporators (7) in a vertical-tube forced-circulation evaporator containing tubes of the same length as, but of different diameterfrom, and the large number of tests that, have been run on commercial evaporating equipthose in the evaporator used by the authors. Other coefment, no satisfactory general equation has been proposed for ficients were measured by Hebbard and Badger (5) in an predicting the coefficients of heat transfer in any particular apparatus of the same type but containing one tube of a greater length than the tubes in the authors’ apparatus. A type. One type of evaporator in common use in the chemical industries is the vertical-tube forced-circulation evaporator. revised equation was derived that included the effects of tube Badger (1, 3) measured, in a semi-commercial forced-circulalength and diameter. This revised equation is presented with tion evaporator, over-all coefficients for the evaporation of some hesitation and should be more rigidly established by sulfite waste liquor and caustic soda solutions. Additional further experimentation. However, the size of the tubes used experiments (results not published) by the authors is that generally used were made a t the University of Michigan NATHAN FRAGEN in commercial evaporators. Standard oil Company (Indiana) A detailed description of the apparaChemical Engineering Laboratory and tus and procedure was previously realso by the manufacturers of such equipInd., Whiting, ment. No general correlation of these ported by Logan, Fragen, and Badger data has previously been reported nor (8). Only a brief description will be W. L. BADGER given : have any of the c o r r e l a t i o n s of film University of Michigan, coefficients of heat transfer been usefully The apparatus used was a S w e n s o n applied to this problem. Ann Arbor, Mich. semi-commercial forced- c i rc uls, t i o n
SYMPOSIUM on
HEAT
TRANSMISSION
HEAT-TRANSFER C O E F F I C I E N T S IN
VERTICAL-TUBE FORCED-
CIRCULATION EVAPORATORS
534
MAY, 1936
INDUSTRIAL Ah-D ENGINEERING CHEMISTRY
535
/' I
1200
I
I100
"'o
~
-
,
OVERALL COEFFICIENTS P-&~8"OD,X16 GAGE COPPER TLBS5 EVAPOPAiION OF PORE SUGAR WLUTIONS
/
0 /D
'
0
/'
,
.P
,,
FIGURE 2
I
FIGURE 1
OVERALL COEFFICIENTS a-dXJh"MXl6GAGE NICKEL T U E S EVAPORATION OF W e T E SULPHITE LIOUOR
evaporator having twelve copper tubes (8 feet long) in the heating element. Eleven of these tubes were 7/8 inch o.d., 16 B. W. G. (Birmingham wire gage) wall, and one tube was 1 inch 0 . d. and had an 11 B. W. G. wall. Solution was pumped through the tubes and steam was condensed on the outside of the tubes. I n the experimental procedure, the principal operating variables and the ranges covered were: concentration of sucrose in solution, 22 to 65 per cent; apparent boiling point of the solution, 160' to 210' F.; velocity of the liquid entering the tubes, 7 to 17 feet per second; apparent over-all temperature drop, 9" to 65" F. The system of changing these variables was such that in any one set of experiments three of the variables were held constant while the fourth was varied over the entire range. The heat input was measured by determining the volume of the condensed steam. Heat balances checking within 10 per cent were obtained by using steam that was slightly superheated and by adequately insulating the outside of the steam chest from its surroundings. Hence, the heat lost by the condensing steam was a true measure of the heat transferred through the walls of the tubes. Steam and liquid temperatures were obtained by pressure measurements and were checked by the use of thermocouples. Concentrations of the solution were determined by taking the gravities of the samples a t frequent intervals. The viscosities of the solutions, taken from the data reported in the International Critical Tables (6) by the Bureau of Standards (4), were fitted into an equation which was used to interpolate and extrapolate the reported data.
I
//"
FIGTJRH 3
Derived Equation The empirical equation derived may be expressed as :
A large number of over-all heat transfer coefficients in forced-circulation evaporators were correlated by the equation:
Several hundred determinations on distilled water, sucrose solutions, molasses, and sulfite liquor were correlated by this equation. Terms for tube length and tube diameter were also included but are based o n too few determinations to have much weight.
435uo.45 U = -p0.Z6 At0.1
where U
over-all coefficient of heat transfer based on arithmetic mean area of heating surface, B. t. u./sq. ft./hr./" F. u = linear velocity of liquid a t tube entrance, ft./sec. p = viscosity of solution being evaporated, lb./hr./ft. = (2.42) (centipoises) At = over-all apparent temperature drop corrected for boiling point elevation-i. e., difference between temperature of saturated steam and temperature of liquid boiling a t pressure existing in vapor space of evaporator =
The experimental range was:
U
= 302 to 1143 u = 7.1 to 17.0 p = 1.05 to 20.6 At = 8.9 to 64.8
INDUSTRIAL AND ENGINEERING CHEMISTRY
536
The agreement b e t w e e n the derived equation for the heat tmnsfer coefficients a n d the experimental results is shown in ~i~~~~ 1. T h e d e v i a t i o n of the experimental data was no g r e a t e r than the accuracy with w h i c h t h e heat balanceswere made.
VOL. 28, NO. 5
cometer. The viscosities at various temperatures and concentrations of solids in the solutions are shown in Figure 4.
Coefficients in Evaporator with Small-Diameter Tubes Kleckner and Badger (7) measured over-all heat transfer coefficients for the evaporation of distilled water in an evaporator of the same type as used by the authors. The heating element of this evaporator contained thirty copper tubes, 0.5 inch 0 . d., 20 B. W. G. wall, 8 feet long. These data were correlated by a n equation similar to Equation 1. However the Constant was different. These two equations were expressed as one in the following manner: 490 =
~ 0 . u~ ~ 7. 4 ~
p0.25
At0.l
(2)
where D = arithmetic m e a n diameter of tubes, in. The greatest portion of the data could be correlated by this equation with a deviation no greater than the accuracy of the heat balances, *10 per cent. The agreement is shown in Figure 5.
Coefficients in Evaporator with Longer Tube
EXPERIMCNTAL
F I G U R5 ~
FIGURE 4
Hebbard and Badger (6) measured over-all heat transfer coefficients for the evaporation of distilled water in a s i n g l e - t u b e , forced-circulation e v a p o r a t o r containing one copper tube, 1 inch 0 . d., 11 B. W. G. wall, and 12 feet long. These data were s u c c e s s f u l l y correlated by a n equat,ion similar to Equation 2. except f o r t h e e x p o n e n t of velocity :
Application of Derived Equation to Other Data Badger (2) measured over-all heat transfer coefficients for the evaporation of a solution prepared from pure sugar and cane molasses. His apparatus was similar to the experimental evaporator used by the authors but contained eight nickel tubes, '/* inch 0.d., 16 B. W. G. wall, and 8 feet long. The derived equation was applied to those data, and the resulting agreement was within 1 1 5 per cent. This agreement is shown in Figure 2 . The range of the variables was:
U
= u = p = At =
whereL = tube length, ft. The agreement of this set of data and Equation 3 is shown in Figure 6. Equation 3 will successfully correIate all of the
400 t o 1000 7.6 to 14.1 2.0 t o 21.6 11.3 to 50.9
Badger (1) also measured over-all heat transfer coefficients in this same apparatus for the evaporation of neutralized, sulfite waste liquors. The derived equation also applied to these data with a fair degree of accuracy. The agreement is shown in Figure 3. The range of the variables was:
u
= u = p = At =
200 t o 900 2.7 t o 11.1 1.2 t o 242 19.6 to 63.3
The data of Moore (9) was used to determine the boiling point of the sulfite solutions, and the viscosities were determined experimentally by the use of a MacMichael vis-
FIQURE 6
MAY, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
experimental data obtained from the evaporators having heating tubes of various lengths and diameters. Equations and are presented with Some hesitation because of the lack of additional experimental verification for the effects of tube length and diameter. However, it was proved that Equation 1 applies to the evaporation of a variety of aqueous solutions under a wide range of operating conditions in a n evaporator containing tubes of a size frequently employed in commercial evaporators.
Literature Cited (1) Badger, M;. L., IND.ENG.CHEM.,19, 677-80 (1927). (2) Badger, W. L., "Sugar Juice in Forced-Circulation Evaporators," unpublished data.
537
(3) Badger, W. L., Tmns. Am. Inst. Chem. Engrs., 18,237 (1926). (4) Bingham, E . C., and Jackson, R. F., Bur. Standards, Sci. Paper 298 (1917). (5) Hebbard, G. M., and Badger, W.L., IND.ENG.CHEM.,26, 420 (1934). (6) International Critical Tables, Vol. V, p. 23, New York, McGrawHill Book Co., 1929. (7) Kleckner, and Badger, T.V. L., "Heat-Transfer Coefficients in Small-Tube Forced-Circulation Evaporators," unpublished data. (8) Logan, L. A . , Fragen, N., and Badger, W. L., IND.ENG.CHmf., 26, 1044 (1934). (9) Moore, Trans. Am. Inst. Chem. Engrs., 15, Pt. 11, 245 (1923). RECEIVED February 11, 1936.
A HORIZONTAL FILM-TYPE COOLER FILM COEFFICIENTS OF HEAT TRANSMISSIONS F. W. ADAMS, G. BROUGHTON,' AND A. L. CONN School of Chemical Engineering Practice, Massachusetts Institute of Technology, Cambridge, Mass.
F
ILM-TYPE heat exchangers offer certain advantages for heating and cooling liquids and for the condensation of vapors on account of the high coefficients of heat transmission which they afford. I n this type of apparatus the tubes may be arranged vertically with the liquid passing down through the inside of the tubes, or they may be arranged horizontally in banks with the liquid flowing over the outside of the tubes and falling from one tube to the next below it. This latter arrangement is common in the so-called trombone cooler in use by the heavy chemical, coke, brewing, dairy, petroleumrefining, and refrigeration industries. It has the distinct advantage of lower cost due to the use of only one set of tubes without the necessity of surrounding tubes or shell to confine the liquid. It may be constructed to fit any desired floor arrangement and is readily accessible for cleaning, alteration, or replacement of tubes. When used as a cooler, the water requirements of such an exchanger are extremely low. T h a t the importance of the horizontal film type of liquid heat exchanger has not been generally appreciated is evident from the dearth of design data covering its operation, particularly as regards the outside film coefficient. The uncertainty in the value of this coefficient is further accentuated in many cases by the presence of scale and dirt. Hence little attention has been paid to the inside film coefficient, which frequently is the major resistance to heat flow and is readily calculable. As a result, many of the present installations operate in efficiently. I
Fellow of the Salters' Institute of Industrial Chemiatry, London.
Fundamental data were determined in a study of the factors affecting film coefficients of heat transmission for water films on the outside of a horizontal pipe cooler in an experimental set-up. These data cover the commercial range of operating conditions for a type of cooler on which no adequate design data were previously available. Water velocity and pipe diameter are the major factors controlling the magnitude of the outside water film coefficient. Over a range in cooling-water temperature of 52" to 177" F., corresponding to film temperatures of 146' to 196' F., no variation in the value of the film coefficient is apparent. The results are correlated by the equation, ho = 24.4 (C0.39/D0.g1), for 2-inch and 4-inch pipe. One-inch pipe yields values of the coefficient which are 80 per cent of those calculated by the equation.
Van der Ploeg (6),working on a trombone cooler composed of twenty-four tubes of a flattened, irregular cross section, determined outside film coefficients for the top sixteen tubes by measuring outside wall temperatures. He obtained values of the water film coefficients from 470 to 695 B. t. u. per hour per square foot per F. for water velocities of 1000 to 2100 pounds per hour per foot and cooling water temperatures of 50" to 104' F. He gives an empirical equation for calculating water film coefficients, which recalculated to English units becomes : C0.27
ho
=
53.4
(1
+ 0.0099t)
Davis (2) worked with small single wires, electrically heated, which he moved through water and several hydrocarbons a t various velocities. His results were expressed by MoAdams (4) as follows:
