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 what position will the carbon concentration be 0.15 wt% after a 10-h treatment? the value of D at 1400 K is 6.9 times 10^-11 m^2/s.

Explanation / Answer

At what position will the carbon concentration be 0.15 wt% after a 10-h treatment? The value of D at 1400 K is 6.9 × 10^-11 m2 /s

Cx - C0/ Cx -C0 = 0.15 - 0.35 / 0 - 0.35 = 0.5714 = 1 –erf(x /s sqrt Dt)

erf(x /2 sqrt Dt) =0.4286

z

erf (z)

0.40

0.4284

z

0.4286

0.45

0.4755

z - 0.40/ 0.45 - 0.40 = 0.4286 - 0.4284   / 0.4755 - 0.4284

z = 0.4002

(x /2 sqrt Dt) =0.4002

x = 2(0.4002) sqrt Dt = (0.8004) sqrt of ((6.9 * 10^-11 m^2/s)(3.6 * 10^4 s))

= 1.26 × 10^-3 m = 1.26 mm

z

erf (z)

0.40

0.4284

z

0.4286

0.45

0.4755

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