A cylindrical tank needs to be designed which will hold 2 m3 of liquid. The tank is to be made of areinforced plastic material that is 1 cm thick and has a thermal conductivity of 0.8 W/m·K. The sides of the tank are further insulated with a foam of thickness 2 cm with thermal conductivity of 0.2 W/m·K. The top and bottom of the tank are not insulated. The tank rests on ground which is always at 20oC. The air around the tank is at 10oC and provides a convective heat transfer coefficient of 15 W/m2·K. The liquid in the tank must be kept at a temperature of 50oC by a heater. The liquid is stirred so it is all at the same temperature, and the resulting heat transfer coefficient on the inner surface of the tank is 200 W/m2·K. Radiation from the tank can be neglected.

a.)What inner diameter, D, and height, H, should be chosen for the tank to minimize the amount of power required for heating?
b.)What is the required heating power with these ideal dimensions?
c.)What is the temperature at the interface between the insulation and tank wall for this condition?