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 positive will the carbon concentration be 0.15 wt% after a 10-h treatment? The value of D at 1400 K is 6.9 times 106-12 m^/s. Error function values are given in the tables below.

Explanation / Answer

Based on the D and T relationship, the value of D at 1400 K will be 6.9 * 10^ -11 m2/s.

From Equation 5.5

(CxC0)/(CsC0) = (0.150.35)/ 00.35

= 0.5714 =1 – erf (x/(2*sqrt(Dt))

Thus,

erf (x/(2*sqrt(Dt)) = 0.4268

Using data in Table 5.1 and linear interpolation

z          erf (z)

           0.40        0.4284

z           0.4286

            0.45       0.4755

z0.40/0.450.40 = 0.42860.4284/0.47550.4284

And,

z = 0.4002

Which means that

x/2*sqrt(Dt) = 0.4002

And, finally

x = 2*(0.4002)Dt

=(0.8004)*sqrt((6.9*10^11 m2/s)(3.6*10^4 s))

= 1.26 * 10^-3 m = 1.26 mm

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