CBE 30356 - Lecture Notes - February 23, 2023

Announcements

Class notes

• Solution of the asymptotic heat transfer coefficient for a heated tube wall
• Solution of the transient solution
• Solution of the thermal boundary layer development solution

Goals:

• Know where the Nusselt number for heat transfer in a tube comes from.
• Know why the local Nusselt number varies with distance down the tube.

Reading

• The class notes.
• BS&L, 12.2 & 14.2

Problem of the Day:

The constant wall heat flux problem is useful because it has a simple analytic solution far down the tube (e.g., Nu = 48/11). In many cases, however, it is more reasonable to look at the solution for the analogous case of a step change in temperature at the wall. In this case the asymptotic heat transfer coefficient is only obtainable from the Sturm-Liouville soluton (and yields a slightly lower Nu of 3.66). The code which describes this is given by nusseltconstantwall.m. The notes on the problem are found here.

Demonstration:

In class today we will demonstrate an enhanced separation process: the Boycott effect. Originally described by A. E. Boycott in a brief letter to Nature in 1920, he observed that erythrocytes would settle out faster in a test tube if the tube were simply tilted at an angle. This phenomenon, closely related to the natural convection problem we will study next week, is described in detail in the paper by Acrivos & Herbolzheimer. The phenomenon forms the basis of lamella plate clarifiers for wastewater: basically, you place an array of plates at an angle in a vessel you would like clarified and particles settle out at a greatly accelerated rate. In recent years it has been of concern in effects as diverse as proppant distribution in fracking and mineral segregation in magma chambers.