5.15 Carbon steel (AISI 1010) shafts of 0.1-m diameter are heat treated in a gas-fired furnace whose gases are at 1200 K and provide a convection coefficient of 100 W/m2 -K. If the shafts enter the furnace at 300 K, how long must they remain in the furnace to achieve a centerline temperature of 800 K?

The time required to reach the center line temperature of 800 K is t = 58 sec

Explanation:

Given data

D = 0.1 m

h = 100

Specific heat for carbon steel (C) = 502.4

Furnace temperature = 1200 K

Final temperature T = 800 K

Initial  temperature = 300 K

From lumped heat analysis

 ------- (1)

Now from equation (1)

㏑ 0.44 =  -(0.001415 ) t

-(0.001415 ) t = - 0.82

t = 58 sec

Thus the time required to reach the center line temperature of 800 K is

t = 58 sec

hope you got the answer