Consider the sphere of radius R depicted below. Initially it is at a temperature T0 but we heat it uniformly at the surface with some value qr=q0 (negative so that the temperature is going up rather than down!). a. Write down the differential equation and boundary conditions that govern this problem and render them dimensionless. b. Solve for the asymptotic solution at long times (which will be an increasing function of time!). Determine the temperature at the surface. c. Calculate the average temperature of the sphere, and use that and the answer to b to determine the heat transfer coefficient for this