Here is a typical steady-state heat ow problem. Consider a thin steel plate to be a10 20 (cm)2 rectangle. If one side of the 10 cm edge is held at 1000C and the otherthree edges are held at 00C, wha

Here is a typical steady-state heat 

ow problem. Consider a thin steel plate to be a

10 20 (cm)2 rectangle. If one side of the 10 cm edge is held at 1000C and the other

three edges are held at 00C, what are the steady-state temperature at interior points?

We can state the problem mathematically in this way if we assume that heat 

ows

only in the x and y directions:

Find u(x; y) (temperature) such that