CBE 30356 - Lecture Notes - January 19, 2023

Announcements

Class notes

• Equation of change for heat conduction in solids
• One dimensional heat transfer through one or more layers

Goals:

• Know how to derive the equation governing heat transfer in solids.
• Apply the equation to simple one-dimensional heat transfer problems.

Reading

• The class notes.
• BS&L, 10.1, 10.6

Problem of the Day

• The Idaho National Lab waste treatment facility has a reactor which is prone to forming a sediment cake layer at the walls. It is necessary to determine when the cake layer is forming without any probe internal to the reactor. In this example we look at the possibility of an external temperature probe measuring the thickness of the internal cake layer. "Back of the envelope" calculations relating to this problem are given here. A narration of these notes can be found here.

Demonstration:

A classic phenomenon in mass transfer and fluid mechanics (OK, no heat in this one) is the "Legs of Wine". This results from a Marangoni flow (induced by gradients in surface tension arising from the vaporation of ethanol) in a very thin film of wine which draws fluid up along the inner surface of the glass. At some point the wine collects in a thin ring which then becomes unstable, and drips down, forming the legs. The process continues until all the ethanol has evaporated. While the basics of the phenomenon have been known for many years, the details of the phenomenon (surprisingly complex) have actually been the subject of recent investigations. Two useful papers describing the effect are the 1992 paper of Fournier and Cazabat and the more recent (2020) paper by Dukler, et al. showing that the ring at the top which leads to the legs is actually an undercompressive shock (somewhat analogous to a hydraulic jump). We can get a rough idea of the thickness of the layer (if you "swirl" the wine first to wet the glass) by doing a simple unidirectional flow balance. The notes describing this are given here.