The effectiveness factors for a porous catalyst in the presence of significant temperature gradients can be larger than one. Explain why.

Your goal is to generate such a plot of \(\eta\) as a function of \(\phi\) for the following set of parameters: \(\beta=1 / 3, \gamma=27, B i_{\mathrm{m}}=300\), and \(B i_{\mathrm{h}}=100\).

Vary \(\phi\) as a parameter gradually and generate a plot of the effectiveness factor. Careful continuation of parameters based on a good starting solution is needed in order to track the profile. An alternative method is the arc-length continuation.