x
= distance from plate
a
=
6 -1
x
(5) Horvay. G.: J . Heat Transfer 82, 37 (1960). (6) Landau, H . G . , Quart. Appl. M a t h . 8, 81 (1950). ( 7 ) Pattle. R. E.; Quart. .Mech. Appi. M a t h . 12, 408 (1959). (8) Stefan. J.. .4nn. Phys. Chem. (Wiedemann) ( N . F . ) , 42, 269 (1891). (9) Zener, C., J . .4,b,bi.Phys. 20, 950 (1949).
growth parameter, Equation 15 = distance from plate to interface = latent heat of fusion =
X I 6
p
=
density
w
= P?
T. D. HAMILL
.Veu Yurk CniLersitj AYeu Y o r k . AV Y
PI
SCBSCRIPTS = original phase = nexvly generated phase
S. G. BANKOFF
.\\'brthuestern C n i w s i t l ELanston, Ill
1 2
literature Cited
(1) Boltzmann, L.. Ann. Physrk (.Y.F.) 53, 959 (1894). ( 2 ) Boyer. R. H . . J . .\lath. Phjs. 40, 41 (1961). (3) Carslaw, H. S.. Jaeger. J . C.. "Conduction of Heat in Solids." 2nd ed.. p. 285. Oxford Univ. Prrss, London. 1959. (4) Hamill. T. D.. Bankoff. S. G.. A.I.17h.E. J . 9, '741 (1963).
RECEIVED for review December 28, 1962 ~ X X P T E D January 6, 1964 Technical report G-14773. Work supported by a U. S. Atomic Energy Commission fellowship and a National Science Foundation grant.
COMM UNICATION
T R A N S I E N T MASS TRANSFER IN A FIXED BED Transient mass transfer from a flowing fluid to a fixed b e d of particles has been studied mathematically for the conditions where either external diffusion, intraparticle diffusion, or surface adsorption processes control the rate.
In adsorption, ion-exchange, or extraction, the last two processes particularly can offer significant
resistances. A mathematical solution i s presented which takes all three resistances into account. The result, based upon a first order reversible surface adsorption process, i s in the form of an infinite integral expressed in terms of four dimensionless parameters: +
R(Xp,/DJ'
*, (D,/kJ), lO/Q,), (Ox
