Radioactive wastes are packed in a long, thin$-$walled

cylindrical container. The wastes genera.e thermal

energy non$-$uniformly according to the relation $q^{}=$

$q_o^{}(1-\frac{r^2}{r_o^2}),$ where $q^{}$ is the local rate of energy gen$-$

eration per unit volume, $q_o^{}$ is a constant, and $r_o$ is

the radius of the container. Steady state conditions are

maintained by submerging the container in a liquid that

is at $T_{}$ and provides a uniform convection coefficient

h$.($a$)$ Obtain an expression for the total rate at which

energy is generated per unit length of the container

$($b$)$ Use this expression to obtain temperature $T_s$ of the

container wall.