How do we go about this?

Problem $3.$ Unsteady state diffusion

G$-$L chart for slab.pdf darr

A polymer block with dimensions $)$ containing a chemical is submerged in a

large volume of water. The initial concentration in the block is uniform at $C_0=5\mathrm{.}0{10}^{-2}$kgmo$\frac{l}{m^3}$

and the concentration in water is negligible $(C_{}=0(kg)\frac{\text{m}\text{o}\text{l}}{m^3}).$ All surfaces of the block are

subjected to convection with the mass transfer coefficient equal to $k_c=1\mathrm{.}0{10}^{-7}c\frac{m}{s}.$ The diffusivity

of the chemical in the solid block is $D_{\text{e}\text{f}\text{f}}=2\mathrm{.}0{10}^{-7}c\frac{m^2}{s}.$ We are interested in finding the

concentration distribution inside the block and the amount of the chemical released from the block

to the surrounding water at a specified time. $[$You can assume that the distribution coefficient

between the concentration in the liquid adjacent to the external surface and the concentration in

the solid adjacent to the external surface is $K_{eq}=1\mathrm{.}0.]$

A$.$ Use the Gurney$-$Lurie chart $($attached via download$)$ for transient diffusion in a slab to find the

concentrations at the center of the block $($point $1),$ the corner of the block $($point $2),$ the center of

bottom surface $($point $3),$ and the average concentration in the block at $t=120$ days. $(20$ pts$)$

B$.$ If the bottom surface of the block is insulated from the surrounding water $($i$.$e$.,$ no mass transfer

from the bottom surface to surrounding water$),$ what is the average concentration in the block at

$t=120$ days. $(5$ pts$)$

C$.$ If the length of the block was increased to infinity $($with the cross section remaining at $2cm2$

$cm),$ what would be the average concentration in the block at $t=120$ days? $(5$ pts$)$

D$.$ Estimate the fraction $(\%)$ of the total amount of chemical released from the polymer block at $t=$

$120$ days for the three cases $($A$,$ B$,$ and C$).$ Briefly discuss why and how the released amount

differ in the three cases. $(5$ pts$)$

E$.$ To release $>99\%$ of the chemical from the polymer block, how long will it take for the cube $($A$)$

and the infinitely long square bar $($C$),$ respectively?