Chapter 1, Problem 1.44P

Radioactive wastes are packed in a long, thin-walled cylindrical container. The wastes generate thermal energy nonuniformly according to the relation where $\stackrel{.}{q}$ is the local rate of energy generation per unit volume, ${\stackrel{.}{q}}_o$ 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 and provides a uniform convection coefficient h.

Obtain an expression for the total rate at which energy is generated in a unit length of the container. Use this result to obtain an expression for the temperature $T_s$ of the container wall.