Page 319 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WITHOUT CONVECTION 299

'Pable 8.11 The physical significance and the order of magnitude of the terms
in a. (8.458).

Term Physical Significance Order of Magnitude

Rate of diffusion

2k"(cA) Rate of reaction 2 kSCAo
R R

Therefore, the ratio of the rate of reaction to the rate of diffusion is given by
Rate of reaction - 2 kScAo/R =- 2 ks L2
-
Rate of diffusion DABCA,/L~ RVAB (8.462)
In the literature, this ratio is often referred to as the Thiele modulus or the Damkoh-
ler numbe@ and expressed as

(8.463)

Before solving Eq. (8.458), it is convenient to express the governing equation
and the boundary conditions in dimensionless form. Introduction of the dimen-
sionless quantities

e=-.- (CA ) (8.4-64)
cAo
z
t=- (8.465)
L
reduces Eqs. (8.458)-(8.460) to
;:
-- - h2e (8.466)

at [=O B=1 (8.467)
(8.4-68)

Note that these equations are exactly equal to the equations developed for the fin
problem in Section 8.2.4. Therefore, the solution is given by EQ. (8.2-91), i.e.,

(8.469)

While the Thiele modulus is preferred in the analysis of mass transport in a porous medium,
the Damkohler number is used for packed bed analysis.