Reaction in the catalyst pellet with external transport resistances is another classic problem in chemical reaction engineering. This system needs to be modeled as a set of two second-order differential equations, one for concentration and the other for temperature, with the respective Robin boundary conditions, unlike the previous case shown in the text where the Dirichlet condition was used. The model equations, and the respective boundary conditions used, and the other details can be found in Aris and Hatfield (1969).

It was shown in the original paper that this system exhibits multiple steady states for certain ranges of transport parameters. Up to five steady states are observed for certain values of the Thiele modulus.

Your goal is to reproduce some of these results using arc-length continuation. You should also examine in a qualitative manner the controlling regimes for each of these steady states by comparing the center and surface concentrations as well as the temperature.