ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT less than is possible with alternate methods. This makes it possible to investigat,e true surface temperatures of glass and quartz substrates. The authors are of t'he opinion that' the method will not prove to be applicable to other electrically nonconductive substrates, since any materials having vapor pressures greater than glass or likely to release gases during the deposition of the films markedly increase the electrical instability of the films. Another adrant,age resuking from the negligible thickness of the films in their effectively zero heat capacity, which should permit sufficiently accurate measurements of transient fluctuat,ions of surface temperat,ure. It should be possible to apply this method to the determination of thermal conductivities and work along this line is in progrese. If such films are applied to either side or incorporated in sandwichlike constructions of material of known thermal conductivit,ics, such as quartz, it should be possible to use one film as a source of heat and another for surface temperature measurements. If this can be done, a relatively simple heat met'er could be made that should prove very useful in many heat transfer studies.
Literature cited (1) Appleyard, E. T. (2) (3) (4)
(5) (0)
(7) (8)
(9)
(10) (11) (13)
Acknowledgrnenf
Grateful acknowledgment is made to the Eastmsn Kodak Co. and to The Texas Co. for financial aid received under their fellowship programs.
Heat Transfer Design Data
(13)
S.,Proc. P h y s . Suc. (London). 49, S o . 274, 124 (1937). Baker, E. M., and Tsao, V.,Trans. Am. Inst. Citem. Engrs., 36, 531 (1940); IND. ENG.CHEM., 32, 1115 (1940). Baus, B. V., P h . D . thesis, Cornell University, I t h a c a , S . Y., 1960. Bendersky, David, Mech. Eng., 75, 117 (1953). Colburn, A. P., Inst. M e c h . Engrs. ( L o n d o n ) , Proc. 164, 445 (1951). Colburn, A. P., and Hougen, 0.A , , IND.EXG.CHEX.. 22, 5 2 2 (1930). Jeffrey, J. O . , Cornell Unireraity, Eng. Expt. Sta., Bull. 21, 1930 Peck, R. E.. and Reddie, W. A., ITD. E m . CIAEM., 43, 2926 (1951). Strong, J., "Procedures in Experimental Physics," PrenticeHall, Xew York, 1941. Topper. L., P h . D . thesis, Cornell Uniyersity, Ithaca, ! i Y. ., 1952. Weale, R. A., PTOC. Phgs. SOC.( L o n d o a ) ,62A, 135 (1949). Wenner, F., a n d Smith, A , , S a t l . Bur. Standards (U.S.),Sci. Paper 481, 1942. Williams, R.C., and Backus, R. C., cJ. AppZ. Phys., 20, 98 (1949).
RECEIVED for review May 18, 1954.
ACCrPTEO
October 8, 1934.
/
...
Inclined Falling Films LEO GARWIN'
AND
EMERSON W. KELLY,
JR.~
Oklahoma A. & M . College, Stillwofer, Okla.
P
RESENT-DSY commercial falling film heat cschange equipment is generally of two types-the trombone cooler, in which the liquid in film form f l o m dovn the outside surface of horizontal tubes in a bank ( I , I J ) , and the vertical yetted-wall heater or cooler, in which the liquid film flows down along the inside (or sometimes the outside) surface of a vert,ical tube. The well-known ammonia cooler and the recently developed sulfuric acid concentrator (4)are examples of the latter. A vertical tube film evaporator which utilizes rotating blades to induce turbulence in the film is commercially available ( 1 4 ) . The main objective of the falling film cooler is to obtain a high rate of heat transmission with a low water consumption. Advantages over the conventional tube and shell exchanger reside in the fact that, with the trombone cooler, no shell is required, giving a lower initial cost, per square foot. Also, higher coefficients are obtained n-ith film coolers, resulting in lower heat transfer requirements and further reducing the investment. Lower maintenance costs arc achievcd because of t,he ready accessibility of the tubes for cleaning; no removal of heads is required. Finally, large overloads can be handled by pumping more cooling water, with very little increase in pressure. Where evaporation takes place under vacuum as in sulfuric acid concentration, pressure drop becomes an important consideration, and the film-type heater offers a decided advantage in this respect. Too, the high fluid velocity in the falling film not only provides high heat transfer coefficients but, also reduces the residence time, so crit,ical with heat-sensitive materials. McAdams and coworkers studied the heating of n-ater in turbulent flow in a falling film vertical tubular heater (19). Data for the viscous region have been obtained by Bays and McAdams ((7). 1 Present address, Kerr-McGee Oil Industries, Inc., Oklahoma City, Okla. 2 Present address, D o u Chemical Co., Texss Dirisioii, Freeport, Tex.
392
The earlier literature on the hydrodynamics of mater flowing horizontally in liquid layer form under isothermal conditions has been reviened by Cooper and coworkers ( 6 ) . Later measurements of the thickness of vertical liquid films in the viscous range have been reported by ICirkbiide (10) and by Friedman arid Miller (8). Recently, Dukler and Bergelin ( 7 ) used a capacitance technique for making such measurements in the vijcous and low turbulent ranges. Chew ( 6 ) , using an optical procedure, obtained viscous range data for several angles of inclination. There may be inetances where head room limitations make the use of a vertical falling film heater impractical, and mhere inclination of the film heater would eliminate this difficulty. Data are lacking, however, on the effect of such inclination on the heat transfer coefficient. I t was for the purpose of establishing this relationship that this study n-as undertaken. The work is limited to the case of water flowing in the turbulent range. Studies are made on flat plate aver wide range of angles of inclination and flow rates
A flat plate, 8 inches wide, 30 inches long, and 3/4 inch thick, \\as used in this study. The angle of inclination of the plate vas capable of adjustment over the entire range (Figure 1). The plate was made of half-hard engravers brass (61.5% copper, 37% zinc, 1.5% lead), with a thermal conductivity of 68 B.t.u. per (hour)(foot)(O F.) a t 68" F. (2). Flanged to the underside of the plate was a steam chest. The width of the heating surface proper was 6a/4 inches. To measure the temperature drop across the flowing liquid film, four 24-gage co per constantan thermocouples were located approximately inch below the top surface of the plate at various points along the liquid flow path. These couples were located approximately 2 inches from the eides of the plate, as shown in Figure 2. For each couple, R 0.1-inch hole was drilled into the plate from the side for a distance of approximately 1 3 / p inches. Another hole was drilled from the top surface of the
INDUSTRIAL AND ENGINEERIRG CHEMISTRY
Vol. 47, No. 3
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT plate a t an angle of approximately 30" to meet the hole from the side. The purpose of offsetting the hole ffom the top surface was to minimize as much as possible distoruon in the pattern of heat flow through the plate normal to the heating surface. The couple was inserted through the side. The bead of the couple wag positioned just barely below the plate surface and then softsoldered to the plate. A typical installation is shown in Figure 2. To achieve uniform liquid distribution on the plate, a multiplenozzle spray distributor was used. The liquid flow was directed onto a calming section, 4 inches long, attached to the upper plate by two flat head screws. At the discharge end of the plate was located a triangular receiving and directing trough. Vertical retaining sides were provided. The calming section, its retaining sides, and the collecting trough were all constructed of light gage galvanized sheet steel. The plate retaining walls were of brass. Variation of the angle of inclination was accomplished by rotating the lower end of the plate about a rod which passed through a pair of brackets located near the u per end of the assembly. Flexible hose was used for the distriEutor and steam chest connections. The thermocouples were connected through a double pole selector switch (to avoid a common lead) to a potentiometer. Measurements could be made to approximately 0.5' F. The thermocouples were calibrated in place. For this calibration, a t the lower temperatures, isothermal water was allowed to flow through the steam chest and over the plate. At the higher temperatures, steam a t constant pressure was admitte&U&gsteam the chest and the plate was alloxred to reach equilibriuill ~>+h air. For an air film coefficient of 1.0 to 1.5 B.t.u. .fp (hour) (square foot)( O F.), the temperature drop between tht. Bteam and the thermocouple was calculated to be less than 0.5" F. Since this was roughly the experimental error in the thermocouple measurement, the steam temperature, as measured by a calibrated thermometer, was taken as the thermocouple temperature.
~
The equipment has been described in detail (9). Procedure. Vater from a constant head elevated tank flowed through a calibrated orifice to the distributor. A 30-inch manometer containing carbon tetrachloride was used to measure the orifice differential. A pump, equipped with a by-pass, was used in the feed line to provide additional pressure for the higher flow rates.
Figure
-A_-
-?-
Figure
March 1955
2.
-.
Details of thermocouple location and installation
1.
Heater plate assembly
The distributor nozzles were inclined about 10" to 15" downward with respect to the plate. Since the entire plate assembly was rotated from run to run, no adjustment had to be made to keep the distributor-plate inclination unchanged. At low to moderate water rates, the entire heating area was covered by the flowing water, and the complete surface was used in the calculations. At the very high flow rates, the water sometimes hit the plate a little downstream of the calming section, and a correction for the actual heating area used was made in such cases. The hot water leaving the collecting trough was received in a drum, from which it flowed to the drain. The water was not weighed; its rate was obtained from the orifice calibration. Steam a t 5 to 10 pounds per square inch gage was used in the steam chest. Its pressure did not vary more than 0.5 pound during a run. The chest was provided with a steam trap. Although the steam chest was insulated, the amount of steam condensate was not used for checking the quantity of heat transferred because of significant heat losses from the under side of the assembly. It required almost 30 minutes for steady-state conditions to be established. Inlet and outlet water temperatures were measured from time to time with two thermometers placed directly into the stream of liquid. A complete range of flow rates was studied a t each angle of inclination; the angle was then changed to a new value. Measurement of the angle was made with a protractor and plumb line.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
393
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT I n order to ensure an absolutely clean heating surface, the plate was polished with No. 1 emery paper before each experimental operating period. Calculations. The amount of heat transferred to the flowing water was obtained from its weight rate of flow and its temperature rise. The average temperature of the plate surface was calculated by subtracting from the average of the four thermocouple temperatures the drop in temperature taking place in the metal between the couple and the surface (0.038 inch). Since this temperature correction for thermocouple depth was lese than 3" F., the metal thermal conductivity a t 68" F. ?$as used in the calculation, even though the actual temperature of the metal in the correction zone was close to 130' F. Negligible error (roughly 0.2" F.) is introduced as a result of this approximation. The water film coefficient was calculated from the average metal surface temperature and the teiminal bulk n ater temperatures, using a logarithmic mean driving force. The experimental data cover the follonring ranges:
point is low. This deviation from Equation 2 mag indicate a tendency for laminar or incompletely developed turbulent flow to persist a t low angles of inclination. K h e n Equation 2 is substituted into Equation 1, there is obtained the final correlating equation
h = 87 (sin 0 j 0 . 2 ( ~ ) 1 ' 3
(3)
A log-log plot of h versus (sin +)o.z(r)lia is presented in Figure 4. The dashed line represents Equation 3 . The average deviation of the experimental points from the line is 7%; the maximum deviation is 17%. Correlating equation i s consistent with results of previous turbulent film studies
The general equation for estimating heat transfer coefficients in vertical film turbulent flow was given by blcAdams (11). h
(4) Angle of inclination Flow rate, Ib./(hr.)(ft. of breadth) Reynolds number Inlet water temperature, F. Outlet mater,teinperature, F. Q u a l ~ i t ~ ; ~ .at transferred; B.t.u./hr. MeSms,rfhe temperature, F. Heat transfer area, sq. ft. Logarithmic mean temperature difference, F Film heat transfer coefficient,B.t.u./(hr.)k Q.ft.)!' F.)
90-900
1850-10,100
2800- 12,800 40-13
57-117 70.600-105.600 94.b-147.4 1.219-1.825 42.5-67.5
817-1912
Complete data are available (9).
Slope 0.26 0.25 0.35 0.39 0.38 0.33
56
67 Average
The number of runs made a t angles of inclination of 9' and 90' was insufficient to establish an accurate slope in these cases. The data tend to shorn an increase in slope with increasing angle of inclination, but the change is rather small. Because the average slope obtained in this work is essentially the same as the value reported by McAdams, this rounded-off figure was adopted for the subsequent correlation. Through the points on each angle of inclination plot, including those for 9" and go", was drawn the best straight line of slope Such a line is represented by the equation: l/3. h, =
c (ry3
Q)o.2
(2)
Equation 2 represents well all of t h p ppinti: of Figure 3 except the one for Q = 9". This
394
=
70
(r)1/3
(6)
h = 87
(7)
(r)l3
T h e agreement between Equations 6 and 7 is quite satisfactory, considering the approximate nature of Equation 4 and its sensitivity to minor changes in mean film temperature, Equation 3 can be shovm to be consistent with available data on the properties of flowing liquid films. Cooper and coworkers ( 6 ) , in their correlabion of the work of previous investigations in this field, concluded that the Fanning friction equation, togcther with the conventional friction factor-Reynolds number curve for smooth circular pipes, could be used to describe approximately the behavior of liquid layers in turbulent isothermal flow. The Fanning friction equation may be written
Fmg f = 2 -2 Lv2
I n the case of a fluid flowing on a flat plate, the hydraulic radius,
m, defined as the cross-sectional area of the stream divided by the wetted perimeter, becomes the thickness of the liquid film. F. in this instance may be replaced by sin 4, the usual aesumption
being made that variations in film thickness are negligible. Equation 8 thus becomes (9)
(1)
where C is a function of the angle of inclination. Because the hydrodynamic properties of a fluid flowing down an inclined plane are related to the sine of the angle of inclination, C was plotted versus sin 4 on log-log paper. A straight line x a s obtained, as shown in Figure 3. T h e slope of this line is 0.1Y: it may be rounded off conveniently to the value 0.2. The equation of the line is, C = 87 (sin
Equation 4 reduces to Equation 5 a t a mean n-ater film temperature of approximately 190' F. I n the work reported in this article, the mean liquid film temperature was approximately 93" F. Equation 4 reduces, at this film temperature, to Equation 3, obtained in this study, gives, for a vertical surface,
The results of Xc-iidams and coworkers on vertical film-type heaters operating in the turbulent flow range ( 1 8 ) showed h t o vary as the power of r. For each angle of inclination in this work, therefore, h was plotted versus r on log-log paper. Straight lines were obtained in each case, v i t h the following slopes: e
(51
h = 120 (r)1/3
h
Heat transfer coefficients vary with mass flow rate and angle of inclination
Angle of Inclination, 18 28 42
McAdams and coworkers found, for the case of m,ter in turbulent flow down the inside of wetted-wall columns,
100 90 80
o m 60
so
ai
02
SIN
Figure 3.
a4
Q3
0.5
OB
a7
0.8
os
IO
I
C versus sin
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
+ Vol. 41, No. 3
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT which becomes, after making the substitution, m =
r
and
-
Vd
simplifying
v
01
(sin 4)1/3(r)0.40
(15)
Equation 15 is identical with Equation 12. The excellent correspondence of the equations obtained by these two entirely different methods provides strong support for the extension of the Fanning friction factor equation to falling liquid films in the turbulent .range. Both approaches give results that are entirely consistent with the heat transfer coefficients obtained in the present study. Because the Dukler and, Bergelin data are limited to Reynolds numbers up to 3000, additional film thickness measurements well in the turbulent range are desirable for further substantiation. 20
30
fi)'.' ( r Y 3 Plot of correlating equation, Equation 3 (SIN
Figure
4.
= specific heat, B.t.u./(lb.)(' F.) C = dimensional constant, defined by Equation 1
c
A good approximation to the turbulent range portion of the Fanning friction factor plot for smooth pipes is (1.2) I
1
f = - 0.046
a
Re0.2
Oi
(r)o.z
since r is directly proportional to Re. 9 and 10, v2 a
Since m
r = -, VP
(Y.
c(r)o.2
(11)
01
(sin 4)1/3(r)0.4
(sin
#)0.27(r)o.32
(12)
(13)
The exponents of Equation 13, particularly that for r, show very good agreement with those of Equation 3. Dukler and Bergelin (Y), using the von KBrmBn velocity distribution theory, developed equations for calculating m that are applicable to the entire Reynolds number range. Their results show that for a vertical liquid film, in the absence of forced flow of the gas phase, $(m) = m g1j3
(;)
is a continuous function of the Reynolds number. Chew (5) quantitatively verified the relationship for the viscous flow of water on inclined plates. For this case, $(m) was represented by m g1/3
F
= Fanning friction factor, dimensionless = frictional head loss, ft.-lb. force/lb. mass
g
= acceleration of gravity, 4.17 X 10*ft./(hr.)(hr.)
h k
= film heat transfer coefficient, B.t.u./(hr.)(sq.
go = conversion
constant,
32.2 lb. mass-ft./(sec.)(sec.)(lb.
force) = thermal conductivity, B.t.u./(hr.)(ft.)(' F.)
ft.)( F.)
m = hydraulic radius, ft.
Re
=
v
=
(Y.
=
r
I n the turbulent range, the heat transfer coefficient, h, is proportional to the 0.8 power of v. Thus,
h
f
L = length, ft.
By combining Equations
Equation 11 becomes
v '
m sin
Nomenclature
(i)2'3 (sin in order to take into account the angle
of inclination. Dukler and Bergelin pointed out that the transition Reynolds number between the viscous and turbulent ranges is approximately 1100. Their log-log $ ( m ) verms Reynolds number plot can be represented by two straight lines, one for each flow region. The viscous range portion possesses the theoretical slope of Their turbulent range data lie above the line predicted by their equations. If a straight line is passed through their turbulent range data, it is found to possess a slope of 0.60. Thus, their turbulent range results msy be represented by
=
p
=
p
= = =
#
$
4r Reynolds number, dimensionless; equal to -P linear velocity, ft./sec. proportionality sign flow rate per unit breadth, lb. mass/(hr.)(ft.) viscosity, lb. mass/(ft.)(hr.) density, lb. mass/cu. ft. angle of inclination with respect to horizontal function
Subscript ,f refers to film Literature cited
(1) Adams, F. W-.,Broughton, G., and Conn, A. L., IND.ENG.
CHEM.,28, 537 (1936). (2) American Brass Co., Chemical Engineering Catalog, pp. 186-7,
Reinhold, New York, 1953-54. (3) Bays, G. S., Jr., and McAdams, W. H., IND.ENG.CHEM.,29,
1240 (1937).
(4) Chambers, F. S., and Peterson, R. F., Chem. Eng. Progr., 43, 219
(1947). (5) Chew, Ju-Nam, Ph.D. dissertation, University of Texas, May 1953. ( 6 ) Cooper, C. M., Drew, T. B., and Rlchdams, W. H., IND. ENG). CHEM.,26, 428 (1934). (7) Dukler, A. E., and Bergelin, 0. P., Chem. Eng. Progr., 48, 557 (1952). (8) Friedman, S. J., and lVliller, C. O., IND.ENG.CHEM.,33, 885 (1941). (9) Kelly, E. W., Jr., M.S. thesis, Oklahoma A. & 1%. College, 1951. (10) Kirkbride, C. G., IND.ENG.CHEM.,26, 425 (1934). (11) McAdams, W. H.. "Heat Transmission," p , 203, RiIcGraw-Hill, New York, 1942. (12) Ibid., p. 119. (13) McAdams, W. H., Drew, T. B., and Bays, G. S., Jr., Trans. Am. Soc. Mech. Engrs., 62, 627 (1940). (14) Rodney Hunt Machine Co., Orange, Mass., "Turba-Film Evaporator," Catalog 253, 1953. (15) Thompson, A. K. G., J . Soc. Chem. I n d . ( L o n d o n ) , 56, 380T (1937). RECEIVED for review June 28, 1954. ACCDPTED November 12, 1954. Presented before the Tenth Southwest Regional Meeting of the A h r s R I C A N CHEMICAL SOCIETY, Ft. Worth, Tex., Deo. 2-4, 1954.
March 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
395
