Question

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?

Answer 1

0.000324 kg/m²h

Step-by-step explanation:

`c_h` = High concentration = 2 kg/m³

`c_l` = Low concentration = 0.2 kg/m³

`x_h` = One Length = 0

`x_l` = Other Length = 2 mm

D = Diffusion coefficient =
`1* 10^(-10)\ m^2/s`

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

`J_x=-D(\partial c)/(\partial x)\\\Rightarrow J_x=-D(c_h-c_l)/(x_h-x_l)\\\Rightarrow J_x=-1* 10^(-10)* 3600* (2-0.2)/(0-2* 10^(-3))\\\Rightarrow J_x=0.000324\ kg/m^2h`

The flow rate through the wall is 0.000324 kg/m²h