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.

Question

GIVEN

• A mild-steel cylindrical billet is passed through a furnace

• Diameter of billet = 25 cm = 0.25 m

• Billet is to be raised to a minimum temperature of 760°C

• Length of furnace = 6 m

• Temperature of furnace gases (T?) = 1538°C

• The overall heat transfer coefficient h c= 68 W/(m2 K)

• Initial temperature of billet (To) = 204°C

FIND

• The maximum speed at which a continuous billet can travel through the furnace

ASSUMPTIONS

• The heat transfer coefficient is constant

• Billet is 1% carbon steel

• Radial conduction only in the billet, neglect axial conduction

SKETCH

Answer 1

The Biot number for the billet is



Therefore, internal resistance is significant and we cannot use the lumped parameter method, approximate

solution must be used.

The billet must obtain a centerline temperature of 760°C, therefore

for r=0 we have



For Bi=0.198 for Infinite cylinder, From we have



J (0)=1



Solving for the time



The maximum speed of the billet is