CBE 30356 - Lecture Notes - February 1, 2022
Announcements
Class notes
Read through pages 76-100 of the notes and view the online narration below, divided into two parts. The solver is slsolve.m and the examples are slexample.m and slexample2.m. Don't forget to complete the quiz in Sakai!
The main points of the lecture were
- Matrix methods for solving Sturm-Liouville problems
- Validation and application to problems where there is no analytical solution
- Start-up of a heated slab with position dependent conductivity
Goals:
After this class you should be able to:
- Solve general SL problems for which no analytical solution exists.
Reading
- The class notes.
- BS&L, 12.1
- Boyce & DiPrima, ch 8, 10 & 11
Problem of the Day
In this problem we examine use of the numerical solution approach to solve quenching of a sphere at finite Biot number. The writeup is given here and the code is pod07spherebiotexample.m.
Demonstration:
In this demonstration we look at an application of heat transfer: the Stirling Engine. In this fundamental thermodynamic cycle a gas is alternately heated and cooled, compressed and expanded with the cycle converting a temperature differential into useful work. While it has some advantages over other cycles, in modern times it has only been used in a few specialized applications. Interestingly, NASA has been looking into using the Stirling engine as a power source for deep space (replacing the "TG" of the RTG we've been looking at) due to its far greater efficiency. The Wikipedia article on the Stirling engine is quite informative (our demo is in the "gamma" configuration), and the NASA technical report may be found here.
David.T.Leighton.1@nd.edu