### Conduction in Multi-layered Walls of Rectangular and Cylindrical Objects

#### Learning Outcomes

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

- use the thermal resistance concept to determine rate of heat transfer in a multi-layered rectangular wall
- determine the rate of heat transfer in a multi-layered cylindrical wall
- calculate temperature distribution inside rectangular or cylindrical walls

In this module, we will consider heat conduction in multi-layered walls commonly found in food processing plants. For example, storage tanks are covered with insulation to minimize heat loss. Similarly, the walls of a cold room will have a layer of insulation. An insulation layer on a steel wall presents us with a slightly more complex problem than we observed in the last module. In the following video, we will learn how to determine the rate of heat transfer through a three-layered wall. We will again use Fourierâ€™s law and use the thermal resistance concept for our analysis.

In the next video, we will obtain an expression for the rate of heat transfer through a multi-layered wall in cylindrical coordinates (e.g., representing insulation on a metal pipe). We will again use the thermal resistance concept for mathematical analysis.

Recap

In this module, we derived expressions for the rate of heat transfer in multi-layered walls in rectangular and cylindrical coordinates. We used the thermal resistance concept for our calculations. With an understanding of these principles, you should be able to handle problems involving any number of layers that may be present in a system. An important item to note is that so far, we have considered only conductive heat transfer. Therefore, in these problems, we determined heat transfer only from one surface to another (such as from the inside pipe surface to the outside surface of the insulation layer). In the next modules, we will learn how to incorporate the convection mode of heat transfer in our analysis so that we may extend heat transfer into fluids that surround the solid objects.