#### Transient Conduction into a Semi-infinite Solid: Summary

The answers to the ConcepTests are given below and will open in a separate window.

##### Key points from this module:

- When considering the transient heat transfer into a very thick part, especially if you are only interested in the temperature near the surface, consider modeling it as a semi-infinite solid.
- The solid starts at some initial temperature, \(T_i\). Over time the temperature near the surface changes. However, deep into the solid the temperature remains at \(T_i\).
- There are a number of different ways to characterize the temperature in a semi-infinite solid. Common approaches include assuming:
- the temperature at the surface is a constant;
- the heat flux near the surface is constant (This can be unrealistic for long times, as it suggests the temperature goes to infinity.);
- convective heat transfer at the surface is from a fluid at \(T_∞\); and
- heat transfer results from a second semi-infinite surface in contact with the first.

##### From studying this module, you should now be able to:

- Explain how thick solids heat up or cool down over time.
- Sketch qualitatively-accurate graphs of the temperature of the solid at various points in time, demonstrating that the temperature of the solid deep beneath the surface does not change as rapidly.
- Calculate the amount of time it takes for the temperature at a given depth to reach a particular value.
- At a given point in time, calculate the temperature at a particular depth.

*Prepared by Jeffrey Knutsen, Department of Mechanical Engineering, University of Colorado Boulder*