A 3-m-internal-diameter spherical tank made of 1-cm-thick stainless steel is used to store iced water at 0°C. The tank is located outdoors at 25°C. 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-hour period. The heat of fusion of water at atmospheric pressure is hif = 333.7 kJ/kg. The emissivity of the outer surface of the tank is 0.75, and the convection heat transfer coefficient on the outer surface can be taken to be 30 W/m2 · °C. Assume the average surrounding surface temperature for radiation exchange to be 15°C.