Question

A plate of iron is exposed to a carbon-rich (carburizing) atmosphere on one side and a carbon-deficient atmosphere on the other side at 1200K. If a condition of steady state is achieved, calculate the diffusion flux of carbon through the plate if the concentrations of carbon at positions of 5 and 10 mm beneath the carburizing surface are 1.2 and 0.8 kg/m3, respectively. Assume the diffusion coefficient is 3×10-10 m2/s at this temperature.

Answer 1

Explanation:

The given data is as follows.

Concentration difference = (1.2 - 0.8)

                                          = 0.4

Diffusion coefficient (D) = $3 \times 10^{-10} m^{2}/s$

Path length = $5 \times 10^{-3}$

Relation between flux and concentration difference is as follows.

          $Flux = D \times \frac{\text{concentration difference}}{\text{Path length}}$

Putting the given values into the above formula as follows.

       $Flux = D \times \frac{\text{concentration difference}}{\text{Path length}}$    

                = $3 \times 10^{-10} m^{2}/s \times \frac{{0.4}}{5 \times 10^{-3}}$

               = $\frac{1.2 \times 10^{-10}}{5 \times 10^{-3}}$

               = $2.4 \times 10^{-8} kg/m^{2}sec$

Thus, we can conclude that the diffusion flux of carbon through the given plate is $2.4 \times 10^{-8} kg/m^{2}sec$.