Steady$-$state, one$-$dimensional conduction occurs in a rod of constant thermal conductivity k and variable cross$-$sectional area $A_x(x)=A_o{e}^{ax},$ 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, $q_x(x),$ by starting from the thermal energy balance equation. $($b$)$ Use this expression to determine the temperature distribution $T(x).$