# Question: consider a solid radioactive sphere with radius r1 and constant...

###### Question details

Consider a solid radioactive sphere with radius r_{1}
and constant thermal conductivity k. Heat is generated in the
sphere with a uniform heat generated g (W/m^{3}). The
sphere is cooled with a fluid such that the temperature at the
surface of the sphere is T_{s}. Assume steady state.
Determine the following:

(a) Mathematical Model (governing equation and boundary conditions.

(b) Determine the variation of temperature of the sphere and the heat flux at the surface of the sphere.

(c) Consider that r_{1}=0.1 m, k =50 W/m C and g =500000
W/m^{3}. Determine the temperature at the center of the
sphere and the heat flux q (W/m^{2}) at the surface
r_{1}=0.1m. The temperature at the surface of the sphere is
60°C.