A spherical vessel, with 30.0-cm outside diameter, is used as a reactor for a slow endothermic reaction. The vessel is completely submerged in a large water-filled tank, held at a constant temperature of 30°C. The outside surface temperature of the vessel is 20°C. Calculate the rate of heat transfer in steady operation for the following cases:

(a) The water in the tank is still,

(b) The water in the tank is still (as in a part a), however, the buoyancy force caused by the difference in water density is assumed to be negligible,

(c) The water in the tank is circulated at an average velocity of 20 cm/s.