### Conduction in Rectangular and Cylindrical Walls

#### Learning Outcomes

At the end of this module, you will be able to:

- determine the rate of heat transfer through the walls of a rectangular object
- determine the rate of heat transfer through the walls of cylindrical objects such as a metal tube
- describe the analogy between electrical and thermal resistance

In this module, we will learn how to determine the rate of heat transfer through the walls of rectangular or cylindrical objects. For this purpose, we will use Fourier’s Law in rectangular and radial coordinates. The derivations shown in the following videos are rather simple, yet they help us understand the differences in the final algebraic solutions for these different shapes. Let us first consider, in the following video, a rectangular wall and determine the rate of heat transfer through it.

Now that we have seen the use of Fourier’s Law for rectangular geometry, let us consider a cylindrical-shaped object such as a pipe used to convey air, water, steam, or liquid foods in a food processing plant. The following video is about heat transfer through the walls of a tube.

In these two videos, you learned the derivation of algebraic solutions of Fourier’s Law in rectangular and cylindrical coordinates. Before we work through a numerical example, there is another important concept that you should know -- an analogy between electrical and thermal resistance. From your class in Physics, you learned about an electrical circuit and the relationship between electrical resistance, voltage difference, and current. Using an analogy, we will derive an expression for thermal resistance that will help us later in solving more complex problems involving heat transfer through multi-layered walls.

Recap

In this module, you learned the derivation of Fourier’s Law in rectangular and cylindrical coordinates. You used the algebraic expression of Fourier’s law to determine the rate of heat transfer through a rectangular or a cylindrical wall. You also learned the concept of thermal resistance as an analogy of electrical resistance.