Among various plastic hoses, silicone hose has the highest diffusion coefficient for diffusion of nitrogen gas, which is kept under pressure, through the walls. By using shell balance method, derive the concentration profile for diffusion process. Explain how the flux changes with respect to the plastic hose types that are given in the table below. $($Boundary conditions:@ r$=$Ri $,$ CA$=$ CAi and @ r$=$R$0,$ CA$=$ CA$0).$

Teflon $1\mathrm{.}25$

Nylon $60\mathrm{.}00224$

PVC $0\mathrm{.}014$

Silicone $400$