Steady-state, one-dimensional conduction occurs in a rod of constant thermal conductivity k and variable crosssectional area  where A o and a are constants. The lateral surface of the rod is well...

Steady-state, one-dimensional conduction occurs in a rod of constant thermal conductivity k and variable crosssectional area
 where A_o
and a are constants. The lateral surface of the rod is well insulated.

(a) Write an expression for the conduction heat rate, q_x(x). Use this expression to determine the temperature distribution T(x) and qualitatively sketch the distribution for T(0) > T(L).

(b) Now consider conditions for which thermal energy is generated in the rod at a volumetric rate
 is a constant. Obtain an expression for q_x(x) when the left face (x = 0) is well insulated.