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.

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


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

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