Chapter 2, Problem 145P

A spherical vessel has an inner radius r₁ and an outer radius r₂. The inner surface $(r=r_1)$ of the vessel is subjected to a uniform heat flux q₁. The outer surface $(r=r_2)$ is exposed to convection and radiation heat transfer in a surrounding temperature of $T_{\infty }$. The emissivity and the convection heat transfer coefficient on the outer surface are $\epsilon$ and h, respectively. Express the boundary conditions and the differential equation of this heat conduction problem during steady operation.