Example $2.$ Unsteady$-$State Diffusion in

Semiinfinite Slab

A very thick slab has a uniform concentration of solute $A$ of $c_0=1\mathrm{.}0{10}^{-2}kg$

mol$\frac{A}{m^3}.$ Suddenly, the front face of the slab is exposed to a flowing fluid

having a concentration $C_1=0\mathrm{.}10$kgmol$\frac{A}{m^3}$ and a convective coefficient $k_C$

$=2{10}^{-7}\frac{m}{s}.$ The equilibrium distribution coefficient $K=\frac{C_{Li}}{C_i}=2\mathrm{.}0.$

Assuming that the slab is a semiinfinite solid, calculate the concentration in

the solid at the surface $(x=0)$ and $x=0\mathrm{.}01m$ from the surface after $t=3{10}^4$

$s.$ The diffusivity in the solid is $D_{AB}=4{10}^{-9}\frac{m^2}{s}.$