Consider a porous catalyst with a series reaction represented as [mathrm{A} ightarrow mathrm{B} ightarrow mathrm{C}]

Consider a porous catalyst with a series reaction represented as

\[\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C}\]

Write governing equations for A and B. Express them in dimensionless form. How many dimensionless groups are needed?

Solve the equations for a case where the dimensionless concentrations at the catalyst surface are one and zero for A and B, respectively. Note that both concentrations are normalized with the concentration of \(\mathrm{A}\) at the surface.

Calculate the dimensionless gradient for these two species at the surface. From these expressions calculate the yield parameter defined as

\[S=-\left(d c_{\mathrm{B}} / d \xi\right) /\left(d c_{\mathrm{A}} / d \xi\right) \text { at } \xi=1\]

What is the significance of this parameter? Plot it as a function of \(\phi\). For a high selectivity to B, would you operate with a low \(\phi\) or a high \(\phi\).