An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen

Question

An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1400 K (1127 Degree C). Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0 wt% C. (This process of carbon depletion is termed decarburization.) At a distance of 1.26 mm from the surface the carbon concentration is 0.15 wt% after a 10- h treatment. At what position will the carbon concentration be 0.15 wt% after a 20-h treatment?

Explanation / Answer

C(x,t) = Co * erfc(x/2sqrt(D*t))

0.85 = 1 * erfc(0.00126/(2*sqrt(D*10))

from erfc(x) tables we get erfc^-1(0.85) = 0.13

sqrt(D*10) = 0.00484615

D = 2.34852 mm^2/hour (a)

(b)   0.13   = x/(2*sqrt(2.34852*20)

       x = 1.782 mm from top surface

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