CBE 30356 - Lecture Notes - January 31, 2023
Announcements
Class notes
Read through pages 50-61 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
- The Nusselt and Biot Numbers
- Heat Transfer from a Quenched Sphere
- The Lumped Capacitance Model
Goals:
After this class you should be able to:
- Determine the rate of cooling of any object at low Biot number.
- Calculate the temperature distribution in a sphere at large Bi via separation of variables.
Reading
- The class notes.
- BS&L, 12.1
- Boyce & DiPrima, ch 10 & 11
Problem of the Day
In this problem we investigate how the Sturm-Liouville solution for a sphere at large Biot number can be used to calculate an effective internal heat transfer coefficient. The notes for this calculation are given here.
Demonstration:
Today's demonstration is the Benard-Marangoni instability. This occurs when there is a thin layer of fluid with a free surface above which is heated from below, and relies on the temperature dependence of surface tension. Local upwelling leads to a higher surface temperature, local decrease in surface tension, and thus a net convection away from the upwelling region. The effect is to have self-sustaining circulation cells which are visualized by the organization of tracers distributed on the bottom plate (drawn towards the centers of the upwelling regions).
David.T.Leighton.1@nd.edu