In contrast to carburization , decarburization occurs when C diffusses from inte

Question

In contrast to carburization , decarburization occurs when C diffusses from interior of steel to the external surface and enters the furnace atmosphere. Consider steel having initial carbon content of 1wt%. If the furnace is maintained at 1200 degrees C and it is free of carbon, how long will it take to achieve a carbon content of 0.83wt% at a distance of 2mm below surface at 1200 degrees C? How long will it take at 1100 degrees C? for diffusion of carbon in steel, activation energy Q = 142,000 j/mole and Do = 2*10^-5 m^2/s

Explanation / Answer

D = Do exp( - Q / RT)

D = 2 x 10^-5 m^2/s exp( - 142000 / 8.314*(1200+273) )

D = 2 x 10^-5 * 9.17 x 10^-6 = 18.34 x 10^-11 m^2/s

Now,

C(x,t) = 0.83% = erf( x / 2 * sqrt(Dt) ) where erf = error fuction , t = time , x = distance

( x / 2 * sqrt(Dt) ) = 0.734

x^2 / 4*D*t = (0.734)^2

t = x^2 / (4 * D * (0.734)^2)

t = (2 x 10^-3)^2 / (4 * 18.34 x 10^-11 * (0.734)^2 )

t = 0.101 x 10^5 s

t = 1.01 x 10^4 s

t = 1.01 x 10^4 s / 86400 days = 0.117 days

At 1100 degreeC

D = Do exp( - Q / RT)

D = 2 x 10^-5 m^2/s exp( - 142000 / 8.314*(1100+273) )

D = 2 x 10^-5 * 4.12 x 10^-6 = 8.24 x 10^-11 m^2/s

Now,

D1 * t1 = D2 * t2

t2 = D1 * t1 / D2 = 18.34 x 10^-11 * 1.01 x 10^4 s / 8.24 x 10^-11 = 2.25 x 10^4 s

t2 = 2.25 x 10^4 s = 0.260 days

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