Question

A sheet of steel 3.9 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 5.4 × 10^-11 m²/s, and the diffusion flux is found to be 2.2 × 10^-7 kg/m²-s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 5.3 kg/m³. How far into the sheet from this high-pressure side will the concentration be 1.5 kg/m³? Assume a linear concentration profile.

Answer 1

From the Ficks law of diffusion

diffusion coefficient D = 5.4 × 10-11 m2/s

concentration of nitrogen CA = 5.3 kg/m3

Final concentration CB = 1.5 kg/m3

diffusion flux J = 2.2 × 10-7 kg/m2-s

= 0 + (5.4 × 10-11) [ (5.3 - 1.5)/(2.2 × 10-7)]

= 0.000932 m x 1000mm/m

= 0.933 mm