Chapter 13.2, Problem 4E

(a)

To determine

The steady state temperature $u\left(r,z\right)$ when $u\left(r,4\right)=f\left(r\right)\text{ , }0<r<2$ such that the lateral side of the cylinder is insulated.

(b)

To determine

To show: The steady state temperature obtained in sub-part $\left(\text{a}\right)$ is $u\left(r,z\right)=\frac{u_{0}z}{4}$ if $f\left(r\right)=u_0$.