Suppose that a solid sphere of unit radius is immersed in a fluid in which the temperature 5.16. Continuous Heating of a Sphere increases steadily over time. The dimensionless temperature of the sphere is (r,t). The initial temperatures of the sphere and fluid are zero. For t>0, the fluid is heated in such a way that (1,t)=Ct, where C is a positive constant. (a) Use the FFT method to determine (r,t). (b) Show that the solution for large t is of the form (r,t)=f(r)+Ct where C is the constant heating rate defined above. Determine f(r) and use that result to improve the solution from part (a)