A 6-m-internal-diameter spherical tank made of 1.5-cm-thick stainless steel (k = 15 W/m·K) is used to store iced water at 0°C in a room at 20°C. The walls of the room are also at 20°C. The outer surface of the tank is black (emissivity ε = 1), and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. Assuming the entire steel tank to be at 0°C and thus the thermal resistance of the tank to be negligible, determine

(a) The rate of heat transfer to the iced water in the tank and

(b) The amount of ice at 0°C that melts during a 24-h period. The heat of fusion of water is 333.7 kJ/kg.