Heat is being generated uniformly throughout a solid sphere at volumetric rate q. The radius of the sphere is R and the sphere is made of a material having thermal

conductivity k. The temperature at the surface of the sphere is T. Assume one-dimensional steady conduction in the radial direction and do the following: a) Use the equation (2.14b) for VT in spherical coordinates and the heat diffusionequation to produce the differential equation that models the conduction in thesphere. \text { b) Find the general form of the solution for } \left.T(r) \text { answer: } T(r)=-\frac{a r^{2}}{6 k}-\frac{C_{1}}{r}+C_{2}\right) \text {. } c) Show that C, =0. \text { d) Find the temperature at the center of the sphere arsuer: } T_{0}=T_{5}+\frac{q R^{2}}{6 k} \text {. }