Page 421 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WIT73 CONVECTION 401

Carrying out the integrations yields

(9.598)

where the average mass transfer coefficient, (k,), is defined by
lL
(kc) = / kc dz (9.599)
0
The rate of moles of species A transferred to the liquid is
nA = [(cAb>~, - CA,] = e {(c> - CA,) - [c: - (CAb)~]) (9.5100)

Elimination of between Eqs. (9.598) and (9.5100) leads to
IC;
)
, qc?-;:$L]
nA = (wL)(kc) (c> - cA~ - - (cAb ) L 1 (9.5101)
+

(ACA)LM
When 7 > 0.1, all the terms in Eq. (9.5-92), excluding the first, become almost
zero, i.e.,
(9.5-102)

The use of Eq. (9.5102) in Q. (9.598) gives
e
(kc) = - (5.12137 + 0.241) (9 5-1 03)
WL
Since we restrict our analysis to long contact times, i.e., 7 is large, then Eq. (9.5
103) simplifies to e

(kc) = (5.12137) (9.5104)
Substitution of Eq. (9.593) into Eq. (9.5104) and the use of Q = (v,)Wb gives
DAB
(k,) = 3.41 - (9.5-105)
6
Therefore, the average value of the Sherwood number becomes

(9.5106)

It is also possible to arrive at this result using a different approach (see Problem
9.17). Equation (9.5106) is usually recommended when

(9.5-107)