Page 247 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 227

where

(3)

c) Show that the integration of Eq. (2) leads to

+- &(u - 1) } (4)
ip2 tan-' (2p - 1 + u [(2/P) - 11

where
u3 = 1 - (1 + p3p (5)

7.11 Rework Example 7.3 if the rate of reaction is given by

a) For the filling period show that the governing differential equation is given by

Using the substitution
1 du
CA = -- (3)
ku dt
show that Eq. (1) reduces to

Solve Eq. (4) and obtain the solution as

Note that Eq. (2) indicates that CA = CA, at t = 0. Obtain the same result from
Eq- (5).
b) Show that the governing differential equation for the unsteady-state period is
given in the form
- +kC2, -I-- = -
CA,
CA
dCA
dt 7 7-