Drug $A$ in water $(C_{}=8\mathrm{.}0{10}^{-3}(kg)\frac{\text{m}\text{o}\text{l}}{m^3})$ is diffused into a long solid square bar

$m$ at a uniform initial concentration of $C_i=2\mathrm{.}0{10}^{-3}$kgmo$\frac{l}{m^3}.$ The effective diffusivity of the drug in

the solid bar is $D_{\text{e}\text{f}\text{f}}=4\mathrm{.}5{10}^{-3}c\frac{m^2}{s}$ and the convection mass transfer coefficient is $k_c=9{10}^{-5}c\frac{m}{s}.$

We are interested to find the concentration profiles $(C_1,C_2,$dots,$C_6)$ in the square bar $($see the

diagram$)$ at any time using the finite difference method. Note that the distance between $C_1$ and $C_2$ is

$x$ and $C_2$ and $C_4$ is $y,$ and $x=y=5cm.$

A$.$ Do mass balance to derive the finite difference equations for C$.$ Co$.....$ Cs in the square bar.

Note: vou must show vour work on mass balance for each of the six nodes leading to the finite

difference equations for C$1,$ C$2,...,$ C$6$

B$.$ For the arid size Ax $=^$v$=5$ cm$.$ what is the maximum time step Af vou can use in the finite

difference equations obtained in part A in order to find the concentrations at various times.