Question

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 390.5 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 8180.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 96.5 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.

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

I got the right answer :)

Answer 2

how did you do it? please help to find value of erf and how to use approximation for values of erf(1) and erf(2)??

Answer 3

Step 1:

(0.5*8180.0 - 8180.0)/ (390.5 - 8180.0)= erf(ξ)

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

Step 3:

t= d^2/4*D*ξ^2

d=96.5 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)