You wish to increase the carbon content of a slab of steel by exposing it to a carburizing atmosphere at elevated temperature. The carbon concentration in the steel before carburization is 299.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 8655.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 20.5 x 10-2 cm is one half the value of the carbon concentration at the surface. The diffusion coefficient of carbon in steel is 3.091 x 10-7 cm2/s at the carburizing temperature. Express your answer in hours.

Question

DATA: Error Function Values
erf(ξ < 0.6), use the approximation erf ξ = ξ
erf(1.0) = 0.84
erf(2.0) = 0.998

Answer 1

Step 1:

ξ= (0.5 * carbon concentration at the surface of the steel - carbon concentration at the surface of the steel)/ (carbon concentration in the steel before carburization - carbon concentration at the surface of the steel)

(0.5* 8655.0 - 8655.0 )/ ( 299.0 - 8655.0 )= erf(ξ)

Step 2:
erf(ξ < 0.6), use the approximation erf ξ = ξ

Step 3:

t= d^2/4*D*ξ^2

d=20.5 x 10-2 cm
D=3.091 x 10-7 cm2/s

Step 4:
t in sec -> hours
Conversion seconds to hours is total/(60x60)

Answer 2

I'm getting:

d = 0.205

D = 0.0000003091

0.205 / 0.0000003091 = 663215.78777094791329666774506632

663215.78777094791329666774506632 / 60 / 60 = 184.22660771415219813796326251842

I'm putting 184 in but it's wrong...any ideas where my math is going wrong?

Answer 3

184 hours = 7.6 days ==> 1 week? The steel industry will collapse if this is the answer. LOL! Just by seeing the figure one can tell this does not make sense.

Answer 4

Someone please help!