Matlab
Files used in Class Examples


Demo
that illustrates the solution of a single IVP with the use of
Matlab’s ode23 routine. These
files also show how to use fzero to
plot an analytical solution if it is given in implicit form. 

Dynamic
simulation involving mass flow within a twotank system. This
demo illustrates how to use ode23
to solve of system of ODEs  a general IVP. This system is
unforced. 

Dynamic
simulation involving mass flow within a twotank system. This
demo illustrates how to use ode23
to solve of system of ODEs  a general IVP. This system has
a forcing function  an exponentially decreasing concentration
of salt flowing into Tank 1. 

Simulation
involving heat transfer in a cylindrical fuel pin. The system
is linear since the thermal conductivity is constant. This example
shows how to solve 2point BVPs using the Shooting Method and
the Finite Difference Method. The bvp2sh.m
file is needed for the Shooting Method (see Matlab Demos). 

This
file simply compares the analytical solution for the variable
thermal conductivity case versus the constant kf case. The heat
conduction equations was solved in class for the two cases and
the resultant temperature profiles are simply plotted with these
Matlab files. 

Simulation
involving heat transfer in a cylindrical fuel pin. The system
is nonlinear since the thermal conductivity is a function of
temperature. This example shows how to solve nonlinear 2point
BVPs using the Shooting Method and the Finite Difference Method.
The bvp2sh.m file is needed for the
Shooting Method (see Matlab Demos). 

This
demo simply illustrates how to evaluate an infinite series expansion.
It also illustrates the importance of the radius of convergence
of a particular series. The series used here is ln(1+x) = x
 (1/2)x^2 + (1/3)x^3  ... 

This
demo evaluates the infinite series expansion that was obtained
using the Power Series Expansion technique for a particular
2nd order IVP. As a check, it also uses ode23
to solve the given IVP  which allows comparison of the analytical
(Power Series) and numerical solutions. 

This
goal of this file is to solve the given BVP in terms of Bessel
functions: y'' + 9xy = 0 with y(1) = 10 and y(2) = 0. As a
check, it also uses bvp2sh.m to solve
the given BVP  which allows comparison of the analytical (Bessel
Function) and numerical solutions. 

This
goal of this file is to solve the given BVP in terms of Bessel
functions: xy'' + 2y'  y = 0 with y(3) = 2 and y'(6) = 2.
As a check, it also uses bvp2sh.m
to solve the given BVP  which allows comparison of the analytical
(Bessel Function) and numerical solutions. 

Demo
using eigenfunctions of a SturmLiouville problem for a generalized
Fourier series representation for two different functions, f1(x)
and f2(x). Demonstrates several features of generalized Fourier
series. 

Analytical
solution using Separation of Variables (SOV) to a particular
1D transient heat transfer problem. This problem models a 1D
laterally insulated bar which is initially at a constant temperature
of 100 C. At time t = 0, the left end is placed in an ice bath
(0 C) and the right end is perfectly insulated (u' = 0). The
object of the simulation is to compute and visualize the spacetime
temperature profile within the bar. 

Analytical
solution using Separation of Variables (SOV) to a particular
1D transient heat transfer problem. This problem models a 1D
laterally insulated bar which is initially at a constant temperature
of 100 C. At time t = 0, the left end is placed in a cold liquid
bath at 10 C and the right end is exposed to a convective environment
characterized by h/k and uinf. The object of the simulation
is to compute and visualize the spacetime temperature profile
within the bar. 

Analytical
solution using Separation of Variables (SOV) to a 2D steady
state heat conduction problem. The situation here models an
IC chip that has internal energy generation and is exposed to
different heat transfer coefficients on the top and sides. The
bottom base is well insulated. Symmetry is included to reduce
problem size. The goal here is to plot the T(x,y) distribution
and to determine the peak temperature in the chip. 