CBE 30356 - Lecture Notes - February 9, 2023
Announcements
Class notes
Read through pages 101-113 of the notes and view the online narration below. The finite difference example code is marchingexample.m. Don't forget to complete the quiz in Canvas!
The main points of the lecture were
- Finite Difference Solutions to Non-Linear PDEs
- Start-up of a Heated Slab with Temperature Dependent Conductivity
Goals:
After this class you should be able to:
- Know how to solve a parabolic PDE using the finite difference approach.
- Know where to find more sophisticated solvers for more complicated problems.
Reading
- The class notes.
- BS&L, 12.1
Problem of the Day
In this problem we demonstrate what happens when the Neumann stability criterion is violated in doing our explicit marching solution to the heat equation. We look at the problem of one-dimensional unsteady heat transfer with a uniform source: easily solved via separation of variables, of course, but comparison with the numerical marching solution is instructive. The notes for this problem are provided here and the marching solution is given in the program pod08plot.m.
Demonstration:
In class today we look at how you can turn an old Christmas light filament into a hot wire anemometer, provided you have a good constant current power source! The notes describing a "back of the envelope" analysis of the filament are found here.
David.T.Leighton.1@nd.edu