Chapter 1, Problem 1.44P

Radioactive wastes are packed in a long, thin-walledcylindrical container. The wastes generate thermal energynonuniformly according to the relation $\stackrel{\dot{}}{q}={\stackrel{\dot{}}{q}}_0\left[1-{\left(r/r_0\right)}^2\right]$ , where $\stackrel{\dot{}}{q}$ the local rate of energy generation perunit volume, ${\stackrel{\dot{}}{q}}_0$ is a constant, and $r_o$ is the radius of thecontainer. Steady—state conditions are maintained by submerging the container in a liquid that is at $T_{\infty }$ and provides a uniform convection coefficient h.

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