Consider a homogeneous spherical piece of radioactive material of radius r0 = 0.04 m that...

Consider a homogeneous spherical piece of radioactive material of radius r0 = 0.04 m that is generating heat at a constant rate of ėgen = 5 × 107 W/m3. The heat generated is dissipated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 110°C and  the thermal conductivity of the sphere is k= 15 W/mK.Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in thesphere by solving the differential equation, and (c) determine thetemperature at the center of the sphere.