A $5$ cm diameter radioactive sphere at steady state generates a total of $40$ W of thermal energy. The sphere is

covered by a layer of insulation $27\mathrm{.}5$ cm thick so that the total outside diameter is $60$ cm The thermal

conductivity of the radioactive material is $4\mathrm{.}0\frac{W}{m*K}.$ The thermal conductivity of the insulation is $0\mathrm{.}5$

$\frac{W}{m*K}.$ The insulated sphere is surrounded by a gas at $25C$ with a convective heat transfer coefficient of

$20\frac{W}{m^2(K)}.$ Compute the temperatures at the following points:

$($a$)$ Outside insulation surface.

$($b$)$ Interface between radioactive material and insulation.

$($c$)$ Centre of radioactive sphere

The volume of a sphere is $V=\frac{4}{3}{r}^3$ and the surface area of a sphere is $A=4r^2.$ This is a thermal energy generation in a spherical domain please use the general heat transfer equation in the spherical coordinates and boundary condtions.