Question

9. (4 Marks) A sheet of steel 3 mm thick has nitrogen atmospheres on both sides at 900°C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 1.85 x 10-10 m2/s, and the diffusion flux is found to be 1.0 x 10-7 kg/m2.s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 2 kg/m3. How far into the sheet from this high pressure side will the concentration be 0.5 kg/m3? You may assume a linear concentration profile.

Answer 1

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Solution Tin Ginen conditions: Steady state diffusion condition Thickness of Metal sheet = 3mm Diffudion coefficient = 1.85x10-ma is Difusion Hua = 1.0x10* kg/ms concentration of Nitrogen = 2 kg 1m3 Concertmanion of CB=0.5kglm's Nit soorte dz. Asomption given is linear concentration Profile The Probelm Can be solved rearranging ficks low of difusion JAZ-Dars dco (flux in steady state flow) rearranging in the form of change in con SCA-CB J - DAB L GLA=23] Change in distance If we take CA to be the point at which the concentration of Nitrogen is 4 Kg 1m] then it becomes steressway to solve for ag as Necessary Concentration difference AB??At DAB Diffusion htlun Diffusion coeffcient i Assume da is zero at the surface X8=0 + 1,85x60cm199 244/m) — 0.5kg/m3)7 L 1.0x187 (Kg 1mis) | B = 1.85x10 cmeis) I ISCKS Imm 11.0x18-a (kg 125) 18 z 1.85*10****) X1.5X107) The concentration of 2kg 1m3 win = nB = 2.775 x 10 m = 2.795 mm be at 2.775x10m

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