A mild-steel cylindrical billet, 25-cm in diameter, is to be raised to a minimum temperature of 760?C

Question:

A mild-steel cylindrical billet, 25-cm in diameter, is to be raised to a minimum temperature of 760?C by passing it through a 6-m long strip type furnace. If the furnace gases are at 1538?C and the overall heat transfer coefficient on the outside of the billet is 68 W/(m2 K), determine the maximum speed at which a continuous billet entering at 204?C can travel through the furnace.GIVENA mild-steel cylindrical billet is passed through a furnaceDiameter of billet = 25 cm = 0.25 mBillet is to be raised to a minimum temperature of 760?CLength of furnace = 6 mTemperature of furnace gases (T??) = 1538?CThe overall heat transfer coefficient (hc ) = 68 W/(m2 K)Initial temperature of billet (To) = 204?CASSUMPTIONSThe heat transfer coefficient is constantBillet is 1% carbon steelRadial conduction only in the billet, neglect axialconduction