Chapter 12.2, Problem 5E

In Problems 1–6 a rod of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value problem for the temperature u(x, t).

5. The left end is at temperature sin(πt/L), the right end is held at zero, and there is heat transfer from the lateral surface of the rod into the surrounding medium held at temperature zero. The initial temperature is f(x) throughout.