Consider a homogeneous spherical piece of radioactive material of radius r ^O = 0.04 m that is generating heat at a constant rate of egen = 5 x 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 the sphere by solving the differential equation, and

(c) Determine the temperature at the center of the sphere.

FIGURE P2-96 -110C