Page 413 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 393

Constant wall mass flux
As shown in Example 9.11, in the case of a constant wall mass flux, the concentra-
tion gradient in the axial direction is constant and expressed in the form

(9.543)

Since we are interested in the determination of the Sherwood number, it is ap
propriate to express &A/& in terms of the Sherwood number. Note that the
Sherwood number is given by

(9.544)

Therefore, Eq. (9.543) reduces to

bcA Sh (CAW - ‘Ab) DAB (9.545)
-- -
8% R2(VZ)
Substitution of Eq. (9.545) into Eq. (9.542) yields

(9.5-46)

In terms of the dimensionless variables

(9.547)

7-
[=- (9.548)
R
l3q. (9.5-46) takes the form

(9.549)

It is important to note that 8 depends only on [ (or, r).
The boundary conditions associated with Eq. (9.549) are

(9.550)

at <=1 8=1 (9.551)
Note that EQs.(9.549)-(9.551) are identical with Eqs. (9.3-46)-(9.3-48) with only
exception that Nu is replaced by Sh . Therefore, the solution is
Sh
8 = 1 - - (3 -4t2+S4) (9.552)
8