A sheet of steel 5.0-mm thick has nitrogen atmospheres on both sides at 900 degr

Question

A sheet of steel 5.0-mm thick has nitrogen atmospheres on both sides at 900 degree C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 1.85 times 10^-10 m^2 /s, and the diffusion flux is found to be 1.0 times 10^-7 kg/m^2 middot s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 2 Kg/m^3. How far into the sheet from this high-pressure side will the concentration be 0.5 Kg/m^3? Assume a linear concentration profile.

Explanation / Answer

Given that

thickness of the steel = 5mm

temperature on both sides of sheet = 9000C

diffusion coefficient of nitrogen in steel [D]= 1.85x10-10 m2/s,

Diffusion flux [J] = 1.0x10-7 kg/m2s

Let's take CA be the point at which the concentration of nitrogen is  2 kg/m3 and xA becomes 0

and Let's take CB be the point at which the concentration of nitrogen is  0.5 kg/m3 and xB is to be calculated.

We know that, by fick's law,

J = -D dC/dx

J = -D (CA - CB) / (xA - xB)

substituting the values, we get

1.0x10-7 = - 1.85x10-10 (2-5) / (0 - xB)

xB= 5.55x10-3 m = 5.55mm

5.55 mm far from the sheet, the concentration will be 0.5 kg/m3

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