Chapter 2, Problem 146P

Consider a short cylinder of radius r₀ and height H in which heat is generated at a constant rate of $e_{gen}$. Heat is lost from the cylindrical surface at $r=r_0$ by convection to the surrounding medium at temperature $T_{\infty }$ with a heat transfer coefficient of h. The bottom surface of the cylinder at $z=0$ is insulated, while the top surface at $z=H$ is subjected to uniform heat flux $q_H$. Assuming constant thermal conductivity and steady two-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of this heat conduction problem. Do not solve.