Chapter 13, Problem 18RE

To determine

The steady state temperature $u\left(r,z\right)$ such that $\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{{\partial }^{2}u}{\partial z^2}=0,u\left(3,z\right)=u_0,u\left(r,0\right)=0$ and $u\left(r,1\right)=0$.