CBE 30356 - Lecture Notes - February 8, 2022
Announcements
Class notes
Read through pages 114-128 of the notes and view the online narration below. The finite difference example code is lecture09example.m and miss.m. Don't forget to complete the quiz in Sakai!
The main points of the lecture were
- Heat Transfer in a Semi-Infinite Medium
- Morgan's Theorem and Self-Similarity via Simple Affine Stretching
Goals:
After this class you should be able to:
- Know how to approach a boundary layer problem.
- Know how to use simple affine stretching to obtain a self-similar solution in boundary layers.
- Know what canonical form is and how to use it!
- Know how to solve boundary layer problems numerically as systems of first order equations.
Reading
- The class notes.
- BS&L, 12.1
Problem of the Day
In this problem we look at the constant heat flux analog to the step change in wall temperature problem discussed in the notes and solve it numerically to determine the temperature distribution as a function of time. The notes for this are found here which uses the function miss2.m and script pod09plot.m.
Demonstration:
In this demonstration we revisit our heated rod, this time well coated in wax. As the rod temperature reaches the melting point of the wax the wax should fall off to reveal the location of the melt zone. We shall see how well this corresponds to the calculations in the problem of the day! The program which calculates the dimensional expected melt region is given here: lecture09demo.m.
David.T.Leighton.1@nd.edu