Consider the same problem with now a Robin condition at the surface: [left(frac{d c_{mathrm{A}}}{d xi} ight)_{1}=B ileft[1-left(c_{mathrm{A}} ight)_{1} ight]] Derive an expression for the effectiveness

Consider the same problem with now a Robin condition at the surface:

\[\left(\frac{d c_{\mathrm{A}}}{d \xi}\right)_{1}=B i\left[1-\left(c_{\mathrm{A}}\right)_{1}\right]\]

Derive an expression for the effectiveness factor as a function of \(B i\) in addition to the \(\phi\) parameter. Do the analysis for all three geometries.