A cylindrical shell of inner and outer radii, ri and r0, respectively, is filled with a heat-generating material that provides a uniform volumetric generation rate (W/m3) of q. The inner surface is insulated, while the outer surface of the shell is exposed to a fluid at T8 and a convection coefficient h.
(a) Obtain an expression for the steady-state temperature distribution, T(r), in the shell, expressing your result in terms of ri, r0, q, h, T8, and the thermal conductivity k of the shell material.
(b) Determine an expression for the heat rate, q'(ro), at the outer radius of the shell in terms of q and shell dimensions.