UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 502 - ADVANCED CHEMICAL ENGINEERING ANALYSIS
FALL 2008
Problem Set 4
Due: Thursday, October 2
1. The problem of diffusion and first-order reaction in a long cylindrical catalyst pellet at steady
state is formulated by the ODE
kc)
r
dc
r(
dr
d
r
D=
∂
where c is the concentration of reactant, D is its effective diffusivity and k is the first-order
reaction rate constant. The reactant concentration at the surface of the pellet is specified,
c=c
0
, r=R
(a) Make the problem dimensionless by using the following definitions
x=r/R u=c/c
0
D
k
R=φ
The last parameter is called Thiele modulus.
(b) Find u(x).
(c) The effectiveness factor (
η
) is defined as the ratio between the total moles of reactant
consumed in the pellet per unit time and the total moles per unit time that would be consumed if
the whole pellet were at concentration c=c
0
:
∫
∫
=η
R
0
0
R
0
drrkc
rkcdr
Find an expression for
η.
