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26 February, 06:36

A sheet of steel 1.5 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  10-11 m2/s, and the diffusion flux is found to be 1.2  10-7 kg/m2 - s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3? Assume a linear concentration profile.

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  1. 26 February, 06:47
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    The answer is 0.001 m

    Explanation:

    Solution

    Recall that,

    A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at = 1200°C

    The diffusion coefficient for nitrogen in steel at this temperature is = 6 * 10-11 m2/s

    The diffusion flux is = 1.2 * 10^-7 kg/m2s

    Concentration of nitrogen in the steel at the high-pressure surface is = 4 kg/m3.

    The high-pressure side will the concentration is estimated to be = 2.0 kg/m3

    Now,

    The flux = - D dC/dx

    1.2 x 10-7 kg/m2s = - 6 x 10-11 m2/s dC/dx

    ∫ˣ₀ dx = - 5x^10-4 ∫²₄ dC

    so,

    x = (2-4) kg/m3 (-5x10-4 m4/kg)

    where x =.001 m

    Therefore x = 0.001 m
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