Chapter 3, Problem 3.90P

A nuclear fuel element of thickness 21, is covered with a steel cladding of thickness b. Heat generated within the nuclear fuel at a rate $\stackrel{.}{q}$ is removed by a fluid at $T_{\infty },$ which adjoins one surface and is characterized by a convection coefficient h. The other surface is well insulated, and the fuel and steel have thermal conductivities of $k_f$ and $k_s,$ respectively.

1. Obtain an equation for the temperature distribution $T\left(x\right)$ in the nuclear fuel. Express your results in terms of $\stackrel{.}{q},k_f,L,b,k_s,h,$ and $T_{\infty }.$
2. Sketch the temperature distribution $T\left(x\right)$ for the entire system.