Question

A sheet of steel 2.5 mm thick has nitrogen atmosphere on both sides at 900 oC and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 1.2 x 10-10 m2/s, and the diffusion flux is found to be 1.0 x 10-7kg/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? Assume a linear concentration profile

Answer 1

1.8 mm

Step-by-step explanation:

given data

thick = 2.5 mm

flux = 1 ×
`10^(-7)` kg/m²

high pressure surface is 2 kg/m³

solution

we use fick first law for steady state diffusion

J = D ×
`(Ca - Cb)/(Xa - Xb)` ..........1

we take here Ca to point which concentration of nitrogen is 2 kg/m³

so we solve Xb

Xb = Xa + D ×
`(Ca - Cb)/(J)`

assume Xa = 0 at surface

Xb = 0 + ( 12 ×
`10^(-11)` ) ×
`(2 - 0.5)/(1*10^(-7))`

Xb = 1.8 ×
`10^(-3)`

Xb = 1.8 mm