INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
1226
Vol. 43, No. 5
6 = fraction voids (dimensionless) d,,
=
Up = g = G = h, = h,,, = k =
k’ = L = h = = AP =
X
=
G ’ f
Q = p =
7‘ =
U
=
geometric mean diameter of closely screened particles, feet average particle diameter, feet gravitational constant, feet/hour squared mass velocity, pounds/(hour)(square foot) heat transfer coefficient for gas film average gas-film heat transfer coefficient thermal conductirity, B.t.u./(hour)(square foot)( F./ foot) constant (dimensionless) length, feet particle shape factor (dimensionless) mass, pound preswre drop, pounds/square foot pressure drop at point of fluidization, pounds/square foot quantity of heat transferred, B.t.u./hour density, pounds/cubic foot time, hour over-all heat transfer coefficient, B.t.u./(hour)(square foot)( F.) viscosity, pounds/(hour)(foot) O
p =
Subscripts o = over-all .f = fluidizing fluid g = gas p = particle ACKXOW LEDGMENT
Figure 14. Copper Transport Tube Electrostatically Charged by Fluidized Solid Particles
Silicon carbide and aluminum oxide did not build up a charge in the copper tube or in the bottles to any appreciable extent, although a very slight attraction for the pith ball did exist. The difference in the behavior of the solids may be due t o different dielectric constants or, more likely, t o the nature and characteristics of the surfaces of the materials. Also, absorption of a monomolecular film (such as alumina) on the surface of the solid may alter the picture entirely. As a result of the observations it may be said that electrostatic charges can be built up within a fluid process, and may give erratic results in heat transfer or mass transfer studies. Some of the factors which may affect the magnitude of the charge may be (1) dielectric constant of the material used, (2) contact potential difference, ( 3 ) ratio of fluidized solids to gas, (4) properties of the gas, ( 5 ) temperature of the solid-fluid system, and (6) nature of the surface of the solid particles.
Thanks are due to C. F. Priitton for advice, to J. Lukes of the Diamond Alkali Co. for suggestions on the construction of the heat transfer apparatus, and to the Glenn L. Martin Co. for providing the funds which made these investigations possible. LITERATURE CITED
Baerg, A , , Klassen, J., and Gishler, P. H., “Heat Transfer in a Fluidized Solids Bed,” submitted for publication in Can. J . Research.
Boucher, D., IND. ENG.CHEM.,40, 32 (1948). IXD. ENG.CHEM.,41, 1098-250 (1949). Leva, M., Ibid., 42, 55-9 (1950). Leva, M., Grummer, &I and .,Weintraub, M., Chem. E n g . Progress, 44, 511 (1948). Leva, M., Weintraub, hl., and Grummer, M., Zbid., 45, 563 (1949). Logwinuk, A. K., thesis, Case Institute of Technology, 1948. Mlckley, H. S., and Trilling, C. -4., IND. ENG.CHEM.,41, 1135 (1949).
Norton, F. H., “Refractoiies,” Kew York, McGraw-Hill Book Co.. 1931.
Wilhelm, R. H., and Kn-auk, M., Chem. Eng. Progress, 44, 201 (1948).
NOMEBCLATURE
RECEIVED M a y 23, 1950. Presented before the Division of Industrial a n d Engineering Chemistry a t t h e 117th Meeting of t h e AMERICASCHEMICAL SOCIETY, Detroit, Mich.
A = heat transfer area, square feet C, = specific heat a t constant pressure, B.t.u./(lb.)(” F.)
EngE;ri
Dittus-Boelter Equation for Heati ooling liquids
ng
pocess development
I
T
JOHN F. HEISS’ UNIVERSITY
HE calculation of the film coefficients of heat transfer is
necessary in the design of liquid-liquid heat exchangers. McAdams ( 2 ) recommends the following equation to be used in calculating the film coefficients for fluids having viscosities not more than twice that of water, for Reynolds numbers exceeding 2100: 1 Present address, m’estvaoo Chemical ~ Chemical Corp., South Charleston, W. Va.
i
~
i ~~~d ~ i hIachlnery ~ ~ , and
AND
JAMES CQULL
OF PITTSBURGH, PITTSBURGH, PA.
h_o k
= 0.023
(F)”’” c2)0.4
(1)
This equation with consistent units may be called a modification of the Dittus-Boelter equation, where the coefficient 0.023 is such that safe design values are obtained for the film coefficient, h . The coefficients determined formerly by Dittus and Boelter ( 1 ) were 0.0243 for heating and 0.0265 for cooling, with the esponents of the Prandtl number, c , ~ / k ,respectively, 0.4 and 0.3.
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1951
1227
TEMR,t
KEY
DC.
t-x,v-($t -30
@t-R-V
-30
R-h-D -2 0
-I
0
eo
c
'
I
WITH
CONSISTENT
X WHERE
F h:;:
UNITS
N10.4 FOR HEATING N 1 0 . 3 FOR COOLING
e,5
Figure 1. Nomograph of Dittus-Boelter Equation for Heating and Cooling
A nomograph of Equation 1 with a coefficient of 0.0243 for liquids being heated has been prepared , b y Ryant (3). The range of the variables, especially viscosity, appears t o be excessive, so that this chart might give incorrect h values for fluids of high viscosities. I n order t o make a more simplified type of nomograph (Figure l), which be nonviscous liquids, Equation 1 was written as h = C
(g)
(2)
c
(g)
(3)
+(t)~ for heating
and h =
+(t)cfor cooling
For heating,
+(t)H
=
k0.6 P~ 0o' 8.c,4 0.4
For cooling, +(t)c = 1.056
(4)
k0.7,,0.8~,0.3
/.o.6
(5)
If the mixed units given in the noInenr]ature are used, therl C = 286.3. A line-coordinate chart relating + ( t ) t o t h e temperature was desired where log +(t) would vary linearly with some function of t. It was found that for the 22 substances treated, the log + ( t ) varied linearly with the reciprocal of the absolute temperature, or with the log of the temperature in degrees Fahrenheit. The semilog type of relation ~
H
T h e Dittus-Boelter equation is generally used for calculating film coefficients of heat transfer for nonviscous fluids flowing i n turbulent motion through tubes. A rapid method for solving this equation for the film coefficient is presented here, where the physical properties of the substances can be expressed as functions of the temperature and be represented individually by a grid coordinate; system on a nomograph. For the 22 nonviscous liquids selected a t random, the logarithm of the temperature function for the physical properties was found to vary linearly with the reciprocal of the absolute temperature. The Y coordinates for each substance were then determined from each linear relationship, The value of the film coefficient for any of the substances listed can be determined if the average bulk temperature of the fluid, t h e average linear velocity of fluid through the tube, and the inside diameter of the tube are known. For additional substances not listed here, the grid coordinates can be easily obtained if the physical properties are known over the necessary ranges in temperature.
x,
waa chosen, where the various
sets of values of A and B for heating and cooling were determined from plots on semilog paper as shown in Figures 2 and 3. The values of X and Y necessary to fix + ( t ) for 22 different nonviscous l i q u i d s are given in Table I. The temperature ranges for which the line coordinate system was developed are listed here for e d substance. I f h values are to be determined at slightly
1228
INDUSTRIAL AND ENGINEERING CHEMISTRY 040
04 0
Vol. 43, No. 5
n -PARAFFINS,C,H,,
TO GH ,,
0.30
MA, 0 20
0.15 0.60
0.50
c IO 0 63
040
0.30
@(t), 0.20
I
I .8
I .6
Figure 2.
I
2.2
2.0
2.4
Effect of Temperature on Physical Properties Function, & ( t ) x
I,O 0 0 higher or loner values of' temperature than are included in the range listed, slight errors in h may 1.x expect,ed. For t8he tcmperature ranges listed, h may be detcrmined within an accuracy of at' least, *5%. To locate the X'and I* (soordinates for a liquid other than that given, the + ( t ) in either Equat,ion 4 or Equation 5 is evaluated at several different temperatures and these respective points arc
TAB LE
XUO.
I. X, Y
C O O R D I N A T E S FOR ~ O I I O G R A P J I
Liquid
Benzene Bromobenzene n-Butyl alcohol Carbon tetrachloride n-Decane iothane
Temp. R ~ 0 F. O t o 150 80 t o 2 0 0 32 to 170 32 to 120 -10 0 32 -40 0 0 0 0 -20 0 0 n
1Y
20 21 22
n-Y'ropyl alcohol Isopropyl alcohol Toluene Water
to to to to to
to
to to to to to A-
f70 150 150 4-90 150 150 140 140 f70 140 120
onn
32to200 32tol50 32to180 32 to 212
~Heating~ X Y
~ Cooling , X Y
5.6 4.1 6.4 4.0
8.8 7.7 10.2 8.9
5.4 3.6 5.7 3.2
7.6 6.3 9.2 8.1
8 8 6 7 7 7 7 6 9 6 4
8 4 2 2 9 2 4 6 1 4 6
10.0 12.0 8.6 11.2 9.9 9.0
9.1 7.9 6.3 6.8 6.9 6.6 9.6 7.0 11.4 6 . 3 13.3 8.9 12.1 6 . 1
8.9 11.1
4 3 6 4
4 5 3 3
8 0
6.R 10.3 9.1 8.0 8 6 10.1 12.9 11.1 8.0 7
8 7
8 3 3 0 9 3 6 3 15 8 3 7
7
b 7
7 1 8 1
14 1
(t+46O)OF Figure 3.
Effect of Temperature on Physical Properties Function, + ( t ) c
connected by straight lines. If these intersections are nearly at a common point, this point may be taken as t'he X, Y locus, since Equation 6 therefore applies for that particular liquid. The difficulty of obtaining data on the physicaI properties of various liquids over a wide rangc in temperature has limited this grid system to 22 different liquids. If data on the physical properties are available, it' is probable tlmt Equation 6 will apply for most other nonviscous liquids, so that these substances niay l w represented on this nomograph, also. - If the h values obt,ained from the nomograph are considered to be too conservative because of the coefficient 0.023, they may be easily increased by multiplication with a factor of the desigli engineer's choice. EX4MPLE
The average film coefficient of heat transfer, it, is to be calculated for liquid benzene which floivs into a heat exchanger at 70' F. and leaves a t 110' F. The average fluid velocity through the bank of 1-inch inside diameter tubes is 5.0 feet per second Condensing steam is used in the shell as the heating medium. Therefore, the average bulk temperature of the benzene is 90" F and its X, I' coordinatw are 6 4 9.4. I3y following the key givcri on the nomograph. a value of h = a i 0 is ol,tained, as cvmparcd to 7i = 347 1 1 , numrricsl ~ computntioii
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1951
1229
If the benzene is to be cooled from 110” to 70” I?. by passing / ? P = Reynoldq nutnhri = ( D V p ) / p , dimensionless with concold water through the shell, an average bulk temperature of sistent units = average bulk temperature o,f liquid a t which physical 90’ F. is again used, with the A’, Y coordinates of 6.0, 8.3. 1 3 ~ ~ t the previous method, h = 282 from the chart as compared with properties are determined, F. V = average linear velocity of liquid, feet per second h = 290 by numerical methods. p = absolute visrosity of liquid, centipoises = density of liquid, grams per ml. ACKNOWLEDGMENT = density of liquid, pounds per cubic foot The aid of C. W. Hurley, 111, A. F. Bentz, €I. F. Wyatt, and kO.6 0 8 0 4 ~0.6(p’)0.8(cp’)0.4 +(t)ic = = 0.0650 F. S. Glessner in collecting data on the physical properties of ,,o.~ these liquids is gratefully acknowledged.
-:;&
NOMENCLATURE
specific heat of liquid, joules/(grani)( O (7.) specific heat of liquid, B.t.u./(lh.)(’ F.) I> = inside diameter of pipe, inches h = film, $o$Iicient of heat transfer, B.t.u./(hour)(sq. foot)
cp
= cp’ =
~
thermal conductivity of liquid, B.t,.u./(hour)(sq. foot) ( F. per foot) Pr = Prandtl number = (c,p)/Ic, dimensionless with consistent units k
*
t.)
-
=
LITERATURE CITED
(1) Dittus, F. W., and Boelter, L. M. K., l i m a . CuW. ( B e r k e l e y ) Pubs. Eng., 2, 443 (1930). (2) MoAdams, W. H., “Heat Transmission,” 2nd ed., p. lG8, Sew
York, McGraw-Hill Book Co., 1942. (3) Ryant. C. J., Jr., IND.ENG.CHEM.,35,1187 (1943). RECEIVED Augost 28, 1950.
Thermal Conductivity of Granular Beds Filled with Compressed Gases
Engjrnediring Process development I
JOSEPH L. WEININGER’ McGlLL UNIVERSITY, MONTREAL, CANADA
WILLIAM G. SCHNEIDER NATIONAL RESEARCH COUNCIL, OTTAWA, CANADA
*
x
T h e present measurements were undertaken to obtain information on the heat transfer in granular beds filled with gas, and more particularly to investigate the possibility of deriving from such measurements the pressure coefficient of thermal conductivity of the gas contained in the powder. Measurements of thermal conductivity on granular beds of aluminum oxide and powdered borosilicate glass when filled with helium, hydrogen, or nitrogen at varying pressures yielded linear relations between thermal conductivity and pressure; carbon dioxide in the same beds gave rise to a parabolic relation. Except for the measurements with helium and hydrogen, the measured values of the thermal conductivity were much greater than would be predicted from calculated values of the pressure coefficient of thermal conductivity of the gas in question. This behavior is attributed to increasing gas adsorption on the solid granules with increasing pressure. While the system employed in the present measurements effectively eliminates heat transfer by convection in the compressed gas, because of a possible gas adsorption (particularly the heavier gases) it ,does not appear very promising as a method for measuring the pressure coefficient of thermal conductivity of a gas. It may, however, be useful for measuring the thermal conductivity of liquids where the convection problem is also encountered. Finally, the gas-granule systems used i n the present meaeurements bear a close resemblance to granular catalyst beds used industrially.
T
HIS report concerns the experimental measurement of the
thermal conductivity of granular aluminum oxide or borcsilicate glass, when filled with gases at varying pressures u p t o 100 atmospheres. Although such measurements yield valuable information regarding the heat transfer in granule-gas or powdergas systems, i t appeared worth while also t o investigate the possibility of deriving from the data the pressure coefficient of thermal conductivity of the gas itself. It is extremely difficult t o measure the pressure coefficient of gas conductivity by the ordinary methods, owing t o the experimental difficulty of completely eliminating convection at high gas pressures. T o date, the only reported measurements are those of Varhaftik (16) and Keyes (10). I n the present work a modification of the Schleiermacher hot wire &ell (12)was used; the cell space was filled with the granular material, into which the gases t o be studied were compressed. With this arrangement the space available t o the gas is broken u p into a large number of minute cells, and convection is effectively eliminated. This method gave reliable measurements of heat transfer in the granule-gas systems, but attempts t o derive the pressure coefficient of conduction for the individual gases from t h e data were not too successful. With possibly two exceptions, the derived pressure coefficient was too high. This behavior was attributed t o increasing gas adsorption on the granules with increasing pressure. The systems investigated here are in many respeots similar t o a reacting system employing a granular c a t s lyst bed. Some thermal conductivity measurements on gas-filled powPresent address, University of North Carolina, Chapel Hill, N. C.
