Ball bearings of plain carbon steel are to be hardened by quenching them in a water bath at a temperature of 37oC. You are asked to devise a continuous process in which the ball could roll from a soaking oven at a uniform temperature of 870oC into the water, where a rubber conveyor belt carries them away. The rubber conveyor belt, however, would not be satisfactory if the surface temperature of the balls leaving the water is above 90oC. If the convective coefficient is equal to 590 W/m2.K, (a) find the minimum allowable cooling time in the water for balls up to 1.0 cm in diameter, (b) calculate the total amount of heat to be removed from the water bath in order to maintain a uniform temperature if 100,000 balls are to be quenched per hour.