Question

A sheet of steel 1.7 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 6.8 x 10-11 m/s, and the diffusion flux is found to be 1.4 x 10 kg/m2-s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 5.5 kg/m. How far into the sheet from this high-pressure side will the concentration be 4.2 kg/m? Assume a linear concentration profile.

Answer 1

In the given problem, we need to calculate the distance far away into the sheet from high pressure side. The complete step by step procedure for solution is provided below.

solution ! viven data ! thickness of steel sheet, t=1.7mm Diffusion coefficient, D=6.8x10 m²/s Diffusion flun, J=1.4x10 kg/m²s Surface concentration, s=5.5kg/m3 concentration at depth x, Cx=4.2kg /m² from fick's law of diffusion, J=-D.de dx where, de = concentration gradient. - Four a linear concentration profile, the equation changes to J = - D. AC 1.4x107 kg =-[6.8x10" m/s]x m?s [ 5.5kg – 4.2 kg/m3 7 o-x

1.4x10 kg =- [6.8x10" m²/s] x [(5.5-4-2) K91m3] . - = - [6.8 xjö'm2/s 3x 5.5-4.2 kg/m3 104 x 107 kg Mia = 0.6314 x10 ml Answer the sheet is far away to high- pressure side by 0.6314 x 103 m.

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