Page 414 - Modelling in Transport Phenomena A Conceptual Approach

394 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

On the other hand, the bulk concentration in dimensionless form can be expressed
as

CAb - CAb =o=
eb = (9.553)
CAW - CAb l(l-C%dt
Substitution of Eq. (9.552) into Eq. (9.553) gives the Sherwood number as

(9.554)

Constant wall concentration

When the wall concentration is constant, Eq. (9.541) indicates that
& = ( CAW - CA ) -
dCAb
a2 CAW - cAb dz (9.555)

The variation of CA~ as a function of the axial position can be obtained from Eq.
(9.524) as

-,At,
Since the mass transfer coefficient is constant for a fully developed concentration
profile, Eq. (9.556) becomes

cAb)
~D~(cA~ 4h(cAw - cAb)
dCAb
-- - - - (9.557)
-
dz Q D(VZ>
The use of Eq. (9.557) in Eq. (9.555) yields
-
CA)
&A ~~C(CA~ (9.558)
-- -
az D(V%>
Substitution of Eq. (9.5-58) into Eq. (9.542) gives
(9.559)

In terms of the dimensionless variables defined by Eqs. (9.547) and (9.548), Eq.
(9.559) becomes
(9.560)