Stainless steel (AISI 304) ball bearings, which have uniformly been heated to 850^o C, are hardened by quenching them in an oil bath that is maintained at 40^o C. The ball diameter is 20 mm, and the convection coefficient associated with the oil bath is 1000W/m²*K.   

(a) If quenching is to occur until the surface temperature of the balls reaches 100^o C, how long must the balls be kept in the oil? What is the center temperature at the conclusion of the cooling period?

(b) If 10,000 balls are to be quenched per hour, what is the rate at which energy must be removed by the oil bath cooling system in order to maintain its temperature at 40^o C?