1. A spherical shell of inner and outer radii ri and ro, respectively, is filled with a heat-generating material that provides for a uniform volumetric generation rate (W/m3) of q. The outer surface of the shell is exposed to a fluid having a temperature Too and a convection coeffi- cient h. Obtain an expression for the steady-state tem- perature distribution T(r) in the shell, expressing your result in terms of ri, ro, q, h, Too, and the thermal conduc- tivity k of the shell material.
2. A spherical tank of 3-m diameter contains a liquified- petroleum gas at -60°C. Insulation with a thermal con- ductivity of 0.06 W/m · K and thickness 250 mm is applied to the tank to reduce the heat gain.
(a) Determine the radial position in the insulation layer at which the temperature is 0°C when the ambient air temperature is 20°C and the convection coeffi- cient on the outer surface is 6 W/m2 · K.
(b) If the insulation is pervious to moisture from the atmospheric air, what conclusions can you reach about the formation of ice in the insulation? What effect will ice formation have on heat gain to the LP gas? How could this situation be avoided?