A 50cm iron rod is heated until it is at 100oC at every point. It is then placed between two blocks of ice so that the two ends are held at 0oC. How does the temperature change?
This problem is the Computing Project in Section 9.5 of Edwards & Penney (1996). The temperature function in the rod is
u(x,t) = [4 T0 / pi] sumn odd [exp (-n2 pi2 k t / L2) sin (n pi x / L)].The first 25 terms of the series were used to calculate the temperature profile for the animation.