Question

An iron-carbon alloy initially containing 0.219 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1190°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 0.0 wt% C. At what position will the carbon concentration be 0.164 wt% after a 8 h treatment? The value of D at 1190°C is 1.6 × 10^-10 m²/s.

Answer 1

Equation. : C (x,t)- C_o/C_s-C_o = 1-erf(x/2)

t = 8 hrs = 8 x 3600 secs = 28800 secs

Co = 0.219 wt%

Cx,t = 0.164 wt%

Cs = 0 %

Insert these values in the above equation ,

0.164 -0.219/0-0.219 = 1-erf (x/2Dt)

0.2511 = 1-erf (x/2Dt)

0.2511-1 = -erf (x/2Dt)

0.7488 = erf (x/2Dt)

Based on z value table and linear interpolation

Z. erf (z)

0.8 . 0.7421

Z. 0.7488

0.85. 0.7707

Z-0.8/0.85-0.8 = 0.7488-0.7421/0.7707-0.7421

Z-0.8/0.05 = 0.0067/0.0286

Z-0.8 = 0.0117

Z = 0.0117+0.8 = 0.8117

This shows that . X/2Dt = 0.8117

X = 0.8117 x 2 1.6 ×10^-10 m²/s×28800 s

X = 0.8117 x 2 x 214.66 x 10^-5 m

x = 348.48 x 10^-5 m = 3.48 mm

The x value = 3.48 mm