Transient Diffusion in a Film with a First$-$Order Reaction

Consider transient diffusion in a liquid or solid film with a first$-$order, irreversible reaction. As shown ni Fig. P$5-7,$ assume that there si no reactant present initially and that for t $>0$ the reactant concentration at x$=0$ si constant. The surface at x$=1$is impermeable and unreactive. The Damk$$h$-$ ler number $($Da$)$ is not necessarily large or small.

$($a$)$ Determine Ox$,$t$)$ using the FFT method.

$($b$)$ Use the solution from part $($a$)$ to find the dimensional time required to reach a steady state $($ts$),$ for both small and large Da$.$ Compare the results from the FFT solution with ones obtained from order$-$of$-$magnitude considerations.