Page 461 - Bird R.B. Transport phenomena

§14.5 Heat Transfer Coefficients for Forced Convection Through Packed Beds 441

|14.5 HEAT TRANSFER COEFFICIENTS FOR FORCED
CONVECTION THROUGH PACKED BEDS
Heat transfer coefficients between particles and fluid in packed beds are important in the
design of fixed-bed catalytic reactors, absorbers, driers, and pebble-bed heat exchangers.
The velocity profiles in packed beds exhibit a strong maximum near the wall, attribut-
able partly to the higher void fraction there and partly to the more ordered interstitial
passages along this smooth boundary. The resulting segregation of the flow into a fast
outer stream and a slower interior one, which mix at the exit of the bed, leads to compli-
cated behavior of mean Nusselt numbers in deep packed beds, 1 unless the tube-to-parti-
cle diameter ratio D/D p is very large or close to unity. Experiments with wide, shallow
t
beds show simpler behavior and are used in the following discussion.
We define ft loc for a representative volume Sdz of particles and fluid by the following
modification of Eq. 14.1-5:

dQ = h (aSdz)(T 0 - T ) (14.5-1)
b
]oc
Here a is the outer surface area of particles per unit bed volume, as in §6.4. Equations 6.4-
5 and 6 give the effective particle size D p as 6/a v = 6(1 — s)/a for a packed bed with void
fraction s.
Extensive data on forced convection for the flow of gases and liquids 3 through shal-
2
low packed beds have been critically analyzed 4 to obtain the following local heat transfer
correlation,
2/3
j = 2.19 Re~ + 0.78 Re' 0 3 8 1 (14.5-2)
H
and an identical formula for the mass transfer function j D defined in §22.3. Here the
Chilton-Colburn j H factor and the Reynolds number are defined by
2/3
(14.5-3)

D G _ 6G
p 0 0
(1 )ф п(лф (14.5-4)

In this equation the physical properties are all evaluated at the film temperature T =
f
\{T - T ), and G = zv/S is the superficial mass flux introduced in §6.4. The quantity ф is
b
o
Q
a particle-shape factor, with a defined value of 1 for spheres and a fitted value 4 of 0.92 for
5
cylindrical pellets. A related shape factor was used by Gamson in Re and j ; the present
H
factor ф is used in Re only.
For small Re, Eq. 14.5-2 yields the asymptote
j H = 2.19 Re~ 2/3 (14.5-5)
or
Nu 1/3
ioc = 77, T " = 2.19(RePr) (14.5-6)
k{\ - е)ф
H. Martin, Chem. Eng. Sci., 33, 913-919 (1978).
1
2
B. W. Gamson, G. Thodos, and O. A. Hougen, Trans. AIChE, 39,1-35 (1943); C. R. Wilke and O. A.
Hougen, Trans. AIChE, 41, 445-451 (1945).
L. K. McCune and R. H. Wilhelm, Ind. Eng. Chem., 41,1124-1134 (1949); J. E. Williamson, К. Е.
3
Bazaire, and C. J. Geankoplis, Ind. Eng. Chem. Fund., 2,126-129 (1963); E. J. Wilson and C. J. Geankoplis,
Ind. Eng. Chem. Fund., 5, 9-14 (1966).
4
W. E. Stewart, to be submitted.
B. W. Gamson, Chem. Eng. Prog., 47,19-28 (1951).
5