Chapter 13.5, Problem 2P

1. Find the steady-state temperature distribution in a solid semi-infinite cylinder if the boundary temperatures are $u=0$ at $r=1$ and $u=y=r\sin \theta$ at $z=0$ Ilints: In (5.10) you want the solution containing $\sin \theta ;$ therefore you want the functions $J_1.$ You will need to integrate $r^2{J}_1$ follow the text method of integrating $r{J}_0$ just before (5.15).
2. Do part (a) if the cylinder radius is $r=a$.