A sheet of steel 2.4 mm thick has nitrogen atmospheres on both sides at 1200°C a

Question

A sheet of steel 2.4 mm thick has nitrogen atmospheres on both sides at 1200°C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 5.6 × 10-11 m2/s, and the diffusion flux is found to be 3.1 × 10-7 kg/m2·s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4.8 kg/m3. How far into the sheet from this high-pressure side will the concentration be 1.4 kg/m3? Assume a linear concentration profile.

Explanation / Answer

This problem is solved by using Equation

J=-D(CA-CB)/XA-XB

If we take CA to be the point at which the concentration of nitrogen is 4.8 kg/m3 , then it becomes necessary to solve for xB, as

XB=XA+D(CA-CB)/J

Assume xA is zero at the surface, in which case

XB =0+ 5.6 × 10-11(4.8-1.4)/3.1 × 10-7 =6.14 × 10-4 m = 0.614 mm

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