Question

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?

Answer 1

Answer:

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 $\frac{W}{m^{2}K }$

Specific heat for carbon steel (C) = 502.4 $\frac{J}{Kg K}$

Furnace temperature $T_ o$ = 1200 K

Final temperature T = 800 K

Initial  temperature $T_i$ = 300 K

From lumped heat analysis

$\frac{T - T_o}{T_i -T_o} = e^({- \frac{6h}{\rho C D} } } ) t$  ------- (1)

$\frac{6h}{\rho CD} = \frac{(6)(100)}{(7850)(540)(0.1)}$

$\frac{6h}{\rho CD} = 0.001415$

Now from equation (1)

$\frac{800-1200}{300-1200} = e^{-0.001415t}$

㏑ 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