CBE 30356 - Lecture Notes - February 2, 2023
Announcements
Class notes
Read through pages 62-75 of the notes and view the online narration below. Don't forget to complete the quiz in Canvas!
The main points of the lecture were
- Sturm-Liouville Boundary Value Problems
- Solution Approach to Separation of Variables Problems
- Start-up of a Heated Slab
Goals:
After this class you should be able to:
- Know how to render a linear transport problem homogeneous.
- Calculate asymptotic solutions, lead eigenvalues, eigenfunctions and coefficients.
Reading
- The class notes.
- BS&L, 12.1
- Boyce & DiPrima, ch 10 & 11
Problem of the Day
Usually the asymptotic solution at long times to a transient problem is steady - but not always! In this problem we look at how you solve a problem where the asymptotic solution is still a function of time. The notes for this problem are provided here and the short matlab program to plot up the series solution is pod06plot.m.
Demonstration:
In this demonstration we look at the natural convection pattern produced by a quenched sphere (OK, a spheroidal jade weight) in a fluid. By suspending the cooling object at the midplane of a stratified fluid (lower fluid is dyed) the boundary layer around the object and convective plume can be directly observed.
David.T.Leighton.1@nd.edu