CHE 527 Advanced Applied Mathematical Analysis in Chemical Engineering Fall 2006
Homework 7
Due in class on Thursday, October 26.
1. Consider the transient heating of a flat plate initially at uniform termperature T0, after the termpera-
ture along its edges is suddenly raised to temperature T1. Solve for T(x, y, t) inside the plate by two
different approaches (hint: you can just write down the answer from your notes for the first method),
and show that the results are the same. If the plate is aluminum with L=H=1 meter, estimate how long
it takes the center of the plate to reach 90% of its final temperature increase (i.e., T−T0= 0.9(T1−T0)).
∂T
∂t =α∂2T
∂x2+∂2T
∂y2
where T=T0at t= 0 and T=T1at x= 0, L and y= 0, H for t > 0. (N.B., use the physical
properties of Aluminum at 20oC).
2. Problem 5.13 in Pinchover and Rubinstein
3. A gas dissolves into a thin liquid film and then diffuses in the liquid while undergoing a first-order
irreversible reaction.
A. Discuss the meaning of each term in the governing PDE, initial condition, and boundary conditions:
∂c
∂t =D∂2c
∂x2
−k1c
c= 0 at t= 0
−D∂c
∂x =U(c0−c) at x= 0
∂c
∂x = 0 at x=L
B. Find the steady-state solution for the this system.
C. Find the nonsteady-state solution for this system (okay to leave constants in terms of definite
integrals).
x = 0
x=L
x
Gas
Liquid
1