This example uses a slab of some homogeneous material 10 cm by 10 cm by 1 cm, completely insulated on the top and bottom surfaces, but with the edges exposed. Initially, the slab is at one uniform temperature throughout. Then heat sources are applied to the four uninsulated edges that hold them at constant temperatures, specifically 100 degrees and 0 degrees on the two ends and 50 degrees on both of the two sides.
The goal of this chapter is to write a program that will answer this question: What is the temperature distribution in the slab when it becomes stable?
This can be treated as a two dimensional problem, as shown in Figure 3-1:
