UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 3
Due: Monday, September 26
1. Consider the nuclear fuel rod problem solved in class. The differential equation for the

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 5
Due: Wednesday, October 9
1. A CSTR is used to carry out the first order decomposition of a compound (A) with reactio

Homework 3 - Solution
Problem 1
The ODE to solve is
d 2
dx
2
2h
E
x
m cos
kR
k
2L
(1)
with BCs:
0 0 , x=L/2
(2)
d
0 , x=0
dx
(3)
p h
(4)
We use
We propose as a particular solution
x
p cos
2L
(5)
Substituting this solution into equation (1) le

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 5
Due: Monday, October 19
1. A CSTR is used to carry out the first order decomposition of a compound (A) with reaction

Problem Set 5 Solutions
Problem 1
We start with the mole balance on A,
dc A
1
(c Ai c A ) kc A
dt
tR
Let
1
k
tR
Then
cp
dc A
c
c A Ai sin(t )
dt
tR tR
Taking the Laplace transform of this equation using
L sin(t )
s 2
2
yields
(s ) cA c 0
t R s 2
cp
2

Problem Set 4 Solution
Original problem:
d dT
T
T 0
dx dx
T = 1 at x = 0
dT
0 at x = 1
dx
The ODE can be expressed as
2
d 2T
dT
T 2
T 0
dx
dx
d 2T
dx 2
2
1 dT
1
T dx
A system of two ODEs is formulated as follows. Let
dT
u
dx
then
du
u2
1
dxu
T

Problem Set 1 Solutions
Problem 1
ODE
x2
y4
2
d y
2
dx
d2y
y x3
d 3y
Linear? (yes/no)
yes
Homogeneous? (yes/no)
no
Order
2
no
no
3
no
yes
2
no
yes
1
yes
yes
2
1 0
dx 2 dx 3
d 2 y dy
3y 0
dx 2 dx
2
dy
y
dx
d2y
dy
sin( x ) y
2
dx
dx
Problem 2
The O

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 3
Due: Friday, September 25
1. Consider the nuclear fuel rod problem solved in class. The differential equation for the

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 2
Due: Friday, September 18
The growth of a cell colony in a batch reactor can be simulated by the rate equation
dN
Nc

Problem Set 1 Solution
(a) We start by separating and integrating the equation for the substrate:
cs
cs0
t
dcs
k dt
cs
0
This leads to
cs cs0e kt
The growth equation can now be written as
dN
Ncs 0e kt N
dt
Separating and integrating yields
N
N0
ln(
dN t

Problem Set 3 Solutions
Problem 1
The ODE to solve is
d 2
dx
2
2h
E
x
m cos
kR
k
2L
(1)
with BCs:
0 0 , x = L/2
(2)
d
0, x = 0
dx
(3)
p h
(4)
We use
We propose as a particular solution
x
p cos
2L
(5)
Substituting this solution into equation (

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 4
Due: Friday, October 9
An energy balance in a one-dimensional heat conduction process with variable thermal
conductiv

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 1
Due: Friday, September 4
1. Fill in the following table showing ODEs for y(x) (Appendix A of the class notes contains

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 7
Due: Wednesday, November 18
1. A long cylinder of radius R is being heated by an internal source at a rate that depen

Problem Set 6 - Solutions
Problem 1
Since there are two homogeneous BCs in x, we can solve this problem by separation of variables.
We start by postulating:
u F( t )G ( x )
(1)
Substituting in the PDE and separating leads to
1 dF 1 d 2G
2
2
F dt G dx
(2)

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Sets 8 and 9
Due: Wednesday, December 9
1. An example of a linear ODE with variable coefficients is Bessels equation of ord

Problem Sets 8 and 9 Solution
Problem 1
(a) The solution of the ODE (Bessels order 1) is
y AJ1 ( x ) BY1 ( x )
Since Y1(0) = and J1(0) = 0, the first boundary condition implies B = 0. The second boundary
condition leads to
1 AJ1 (1)
and the analytical sol

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2015
Problem Set 6
Due: Wednesday, November 4
1. The evolution of the dimensionless temperature, u(t,x), in a bar is described by the
fo

Problem Set 4 - Solution
The ODE and boundary conditions are:
d 2T
dx
2
2f 4
T
kR
(1)
T = T0, x = 0
(2)
T = T0, x = L
(3)
We reformulate the problem by defining
dT
z
dx
(4)
dz 2f 4
T
dx kR
(5)
so that
To solve the problem using IVP solvers in Matlab, we a

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 2
Due: Monday, September 16
Batch distillation will be used to separate a mixture of benzene (light component) and
cycl

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 1
Due: Monday, September 9
1. A radioactive waste consisting of an aqueous solution of 92Sr (strontium 92) at a concent

Problem Set 5 Solutions
Problem 1
We start with the mole balance on A,
dc A
1
(c Ai c A ) kc A
dt
tR
Let
1
k
tR
Then
cp
dc A
c
c A Ai sin(t )
dt
tR tR
Taking the Laplace transform of this equation using
L sin(t )
s 2
2
yields
(s ) cA c 0
t R s 2
cp
2

Problem Set 1 Solution
Problem 1
(a) This is a direct application of equation (1.23) with
cAi=16 mM, cA0=0
k=0.257 hr1=4.283103 min1
tR
V
400 L
266.7 min
Q 1.5 L/min
Substitution into equation (1.23) yields
3
c A 7.47(1 e 8.0310
t
) , t in min, cA in mM

Problem Set 2 - Solution
A Matlab code was developed to integrate equation (1.97). The initial temperature was obtained
by solving equation (1.104) with xW0=0.7. The result obtained was T0=91.44C.
To calculate xS, the following mole balance was used:
M ol

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 6
Due: Friday, October 18
1. We would like to simulate the heat transfer process in a thick concrete wall of a
furnace

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 10
Due: Wednesday December 11
Consider the following problem involving a parabolic PDE:
u 2u
t x 2
0 x 1, t 0
u sin(x),

Problem Set 6 Solutions
Problem 1
(a) Using the change of variables =TT0, the problem can be written as follows
2
t
y 2
(1)
=0, t=0
(2)
=0, y
(3)
k
q , y=0
y
(4)
We start by taking the Laplace transform of equation (1) using the initial condition (2),
d

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 7
Due: Monday, November 4
1. The evolution of the dimensionless temperature, u(t,x), in a bar is described by the
follo

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 4
Due: Wednesday, October 2
Thermal energy liberated in the International Space Station due mostly to use of electrical

UNIVERSITY OF ARIZONA
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
CHEE 402 Chemical Engineering Modeling
FALL 2013
Problem Set 8
Due: Monday, November 18
1. Certain problems in transport phenomena formulated in rectangular coordinates lead to
Poi