(a) A hollow sphere is constructed of aluminum (k = 204 W/mK) with an inner diameter of 4 cm and an outer diameter of 8 cm. The temperature of the inside surface of the sphere is 100 °C and the outside surface temperature is 50 °C. Calculate the heat transfer rate in Watts. (b) The sphere is then coated with a 1 cm thick layer of insulation material (k = 0.05 W/mK) and the outside of the insulation is exposed to an environment with h = 20 W/m²K and air temperature of 10 °C. The inside surface of the sphere remains at a temperature of 100 °C. Sketch the thermal network and calculate the heat transfer rate under these conditions. (c) For the insulated sphere in part (b), if radiation heat transfer from the outside surface of the sphere to the surroundings at 10 °C is now taken into consideration, in addition to convection heat transfer (convective heat transfer coefficient h = 20 W/m²K, as before), sketch the thermal network and calculate the heat transfer rate if the temperature of the outside surface of the insulation is 25 °C? What will be the temperature on the inner surface of the aluminum sphere? The surface emissivity of the outside of the insulation is 0.8 and the Stefan-Boltzmann constant is 5.67 x 10 W/m²K4. You may need all, or part, of the following information: Volume of sphere of radius r is (4/3)πr³ and its surface area is 4πr.