Now suppose that in the situation described in the previous problem, species A undergoes an

irreversible, first$-$order, homogenous reaction with a rate constant $k_1.$ The wall is unreactive.

$($a$)$ Show that the liquid$-$phase Sherwood number that is valid for $x$ is

$S{h}_A=\frac{tanh}{[1-\frac{3}{2cosh}\{\frac{sinh}{}(1-\frac{2}{{}^2})+\frac{2}{{}^2}\}]}$;$,{}^2=Da=\frac{k_1{H}^2}{D_A}$

Examine the limiting behavior of Sh for slow and fast reactions.

Note: It may be helpful to assume that $\underset{x}{lim}{C}_A(x,y)=f(y)$

$($b$)$ Show, using order of magnitude analysis, that Sh for $x0$ will be same with and without

reaction.