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A differential nitrogen pressure exists across a 2 mm thick steel furnace wall. After some time, steady-state diffusion is established across the wall. The nitrogen concentrations are 2 kg/m3 on the high-pressure surface of the wall and 0.2 kg/m3 on the low pressure side of the wall. If the diffusion coefficient for the nitrogen in this steel is 1.0E-10 m2/s at the furnace operating temperature, what is the nitrogen flow through the wall in kg/m2*h?

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Answer:

0.000324 kg/m²h

Explanation:

[tex]c_h[/tex] = High concentration = 2 kg/m³

[tex]c_l[/tex] = Low concentration = 0.2 kg/m³

[tex]x_h[/tex] = One Length = 0

[tex]x_l[/tex] = Other Length = 2 mm

D = Diffusion coefficient = [tex]1\times 10^{-10}\ m^2/s[/tex]

The flow rate through a wall from Fick's Law is given by

[tex]J_x=-D\frac{\partial c}{\partial x}\\\Rightarrow J_x=-D\frac{c_h-c_l}{x_h-x_l}\\\Rightarrow J_x=-1\times 10^{-10}\times 3600\times \frac{2-0.2}{0-2\times 10^{-3}}\\\Rightarrow J_x=0.000324\ kg/m^2h[/tex]

The flow rate through the wall is 0.000324 kg/m²h

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