Problem 5; 35 points) A stainless steel billet (k = 13 Btu/hr-ft-F, a = 0.24 ft-/hr), 4 inches in diameter, is passing through a 20 ft. long heat-treating furnace. The initial billet temperature is 200 F, and it must be raised to a minimum temperature of 1650F before working. The heat transfer coefficient between the furnace gases and the billet surface is 6 Btu/hr ft-F, and the furnace gases are at 2200F. At what maximum velocity (ft/min.) can the billet travel through the furnace and satisfy these conditions