Temperature Distributions in the Presence of Heat Sources

There are a number of situations in which there are sources of heat in the domain of interest. Examples are:

1) Electrical heaters where electrical energy is converted resistively into heat

2) Nuclear power supplies

3) Propellants where chemical energy is the source

These situations can be analyzed by looking at a model problem of a slab with heat sources α (W/m3 ) distributed throughout. We take the outside walls to be at temperature Tw. and we will determine the maximum internal temperature.

There is a change in heat flux with x due to the presence of the heat sources. The equation for the temperature is

This distribution is sketched in Figure 4.2. It is symmetric about the mid-plane at 2 L x = , with half the energy due to the sources exiting the slab on each side.