$1-$D Conduction Heat Transfer in Spherical Containers

Consider a homogenous spherical nuclear reactor of radius r$0=0\mathrm{.}04$ m$,$ which contains radioactive material and is generating heat at a constant rate g$=4$x$107$ W$/$m$3.$

The heat generated is dissipated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of $70\backslash$deg C and the thermal conductivity k of the material of the sphere is $15$ W$/$m $\backslash$deg C$.$

Assuming steady $1-$D heat transfer:

i$.$ Express the differential equation and the boundary conditions for the heat conduction

through the sphere,

ii$.$ Obtain a relation for the variation in temperature in the sphere by solving the

differential equation,

And

iii. Determine the temperature at the centre of the sphere