$[$Shell Balance $]$ Radial conduction in a pipe wall. A high$-$pressure steam line loses heat to its surroundings. Consider the temperature distribution within the pipe wall.

a$.$ Apply the shell balance to the pipe wall to find the differential equation for heat flux.

b$.$ Select the boundary conditions. Assume that the steam is $2$ phase and at constant pressure throughout the pipe. Assume that the room temperature is constant, $T_a.$ The pipe has an inner radius of $R_1$ and an outer radius of $R_2.$