BGHiggins/UCDavis/Vietnam_September_2012
Step by Step Solution of Transient
Heat Conduction Problem
Background
We consider the following heat conduction problem
u
t
=k
2 u
x2
,
0 < x < l, t > 0
(1)
The initial condition (IC) and boundary conditions(BC) fo

Hanoi University of Mining and Geology
Chemical Engineering Program
ECH 140 Mathematical Methods
September 2013
Homework Assignment #2: Due Friday Sep 5
Problems From Chapter 1 Haberman
Problem_1.4.1 (f)
Problem_1.4.1 (g)
Problem_1.4.1 (h)
Problem_1.4.7 (

Undergraduate Lectures
ECH140: Mathema8cal Methods for Chemical Engineers
September 2-17, 2013
Chapter 6: Lecture 6b:
Boundary Conditions of Third Kind:!
Newtons Law of Cooling!
Brian G. Higgins
Department of Chemical Engineer

Hanoi University of Mining and Geology
Chemical Engineering Program
ECH 140 Mathematical Methods
September 2013
Homework Assignment #3: Due Monday Sep 9
Problems From Chapter 2 Haberman
Problem_2.3.1 (a)
Problem_2.3.1 (d)
Problem_2.3.2 (d)
Problem_2.3.7

Hanoi University of Mining and Geology
Chemical Engineering Program
ECH 140 Mathematical Methods
September 2013
Homework Assignment #4: Due Monday Sep 16
Problem 1
Consider the following PDE
T
t
2 T
=
r2
+
1 T
r r
, 0<r<1
IC : T Hr, 0L = T1
BC1
T
r
H1, tL

ECH140 Practice Final
September 2013
No solutions will be provided, as at least one of the problems below will be on the Final Exam!
Problem 1
You are required to analyze the temperature distribution in a spherical shell with a heat source. The
mathematic

Transient Heat Conduction in a Sphere
Copyright Brian G. Higgins (2012)
Introduction
This notebook deals with the transient heat conduction of a sphere. Mathematica is used in various
parts of the analysis, and in the last section of the notebook we illus

ECH140ClassNotes/BGHiggins/Hanoi/Dec2012
Application of Bessel Functions:
Transient Heat Conduction in a Cylindrical Annulus
Introduction
Bessel functions routinely occur in the solution of PDEs defined on a domain that can be described by
cylindrical coo

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September2-17, 2013
Lecture 5 b:
Transient Heat Conduction in a Finite Cylinder!
Brian G. Higgins
Department of Chemical Engineering and
Materials

Undergraduate Lectures
ECH140: Mathema8cal Methods for Chemical Engineers
November 27- December 11, 2012
Lecture 12:
Partial Fractions!
Brian G. Higgins
Department of Chemical Engineering and
Materials Science
Univer

Undergraduate Lectures
ECH140: Mathema8cal Methods for Chemical Engineers
November 27- December 11, 2012
Lecture 13:
Introduction to Laplace Transforms!
Brian G. Higgins
Department of Chemical Engineering and
Materials

Hanoi University of Mining and Geology
Chemical Engineering Program
ECH 140 Mathematical Methods
September 2013
Homework Assignment #1: Due Thursday Sep 4
Problem_1.3
Find the general solution of the following ODE
1
x
2
x
Ix2 yM + y = 0
Problem_1.5
Find t

Transient heat conduction in a finite length cylinder
Copyright Brian G. Higgins (2012)
Introduction
This notebook builds on the work presented in previous notebooks dealing with separation of variables.
Here we study transient heat conduction in a finite

Undergraduate Lectures
ECH140: Mathema8cal Methods for Chemical Engineers
September 2-17, 2013
Chapter 5: Lecture 6a:
Sturm-Liouville Eigenvalue Problem!
Brian G. Higgins
Department of Chemical Engineering and
Materials

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 2- 17, 2013
Chapter 1: Lecture 1:
Overview!
Brian G. Higgins
Department of Chemical Engineering and
Materials Science
University o

BGHiggins/UCDavis/Vietnam_September_2012
Transient Heat Conduction Problem
With Flux BCs
Background
We consider the following heat conduction problem
u
t
=
2 u
x2
,
0 < x < L, t > 0
(1)
The initial condition (IC) and boundary conditions(BC) for this probl

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 17- 22, 2012
Chapter 2: Lecture 3b:
Linear Operators!
Brian G. Higgins
Department of Chemical Engineering and
Materials Science
Uni

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 2- 17, 2013
Chapter 1: Lecture 2b:
Derivation of 1-D Heat Conduction Equation!
with Variable Cross-Section !
Brian G. Higgins
Department of

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September2-17, 2013
Chapter 1: Lecture 4C:
Steady State Conduction in a Sphere with Source!
Brian G. Higgins
Department of Chemical Engineering and

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 2- 22, 2013
Chapter 1: Lecture 2a:
Derivation of Heat Conduction Equation!
Brian G. Higgins
Department of Chemical Engineering and
Mat

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 2-17, 2013
Lecture 5a:
Introduction to Bessel Functions!
Brian G. Higgins
Department of Chemical Engineering and
Materials Science
Uni

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 2- 17, 2013
Chapter 2: Lecture 3a:
Method of Separation of Variables!
Brian G. Higgins
Department of Chemical Engineering and
Material

BGHiggins/UCDavis_September2013
Steady State Solution in Spherical
Coordinates
Steady State Problem
A composite spherical shell of inner radius R1 = 0.25 m is constructed of lead of outer radius
R2 = 0.30 m. The cavity is filled with radioactive waste tha

BGHiggins/UCDavis_September2013
Transient Heat Conduction with
Heat Source
Background
Consider the following transient heat conduction problem:
u
t
=k
2 u
x2
+ q HxL,
0<x<L
u Hx, 0L = f HxL
IC :
u
BC1 :
x
u
BC2 :
x
(1)
H0, tL = 0
HL, tL = 0
(i) If the sou

Undergraduate Lectures
ECH140: Mathema8cal Methods for Chemical Engineers
November 27- December 11, 2012
Chapter 3: Lecture 4d:
Fourier Series!
Brian G. Higgins
Department of Chemical Engineering and
Materials Science