Page 444 - Modelling in Transport Phenomena A Conceptual Approach

424 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

9.17 Using the solution given by Johnstone and Pigford (1942), the Sherwood
number is calculated as 3.41 for long contact times in Section 9.5.4.2. Obtain the
same result by using an alternative approach as follows:
a) In terms of the following dimensionless quantities

DABZ
q=-
vmaxs2
show that Eqs. (9.588)-(9.5-91) reduce to

b) Use the method of separation of variables by proposing a solution in the form

and show that the solution is given by

a0

n=l
where

and Gn(5) are the eigenfunctions of the equation

d2G, + (1 - t2) G, = 0
e2
c) Show that the Sherwood number is given by

kd - (aWt),=o
Sh=--
DAB 'b