Taylor series solutions to steady-state non-isothermal diffusion–reaction problems for porous catalyst pellets with arbitrary kinetics

In this study, we present Taylor series solutions for steady-state non-isothermal diffusion–reaction problems pertaining to porous catalyst pellets exhibiting arbitrary kinetics. Using the Damkohler relation, the system of two nonlinear differential equations is reduced to a single differential equation subject to the algebraic constraint. We derive the novel semi-analytical and closed-form explicit approximate solutions for the reactant concentration and temperature in catalyst pellets of planar, cylindrical, and spherical geometries. The derived semi-analytical and explicit approximations give insight into the effect of process parameters on concentration and temperature profiles. The proposed methods are verified numerically for isothermal and non-isothermal steady-state problems with power-law kinetics. They can serve as a practicable alternative to numerical schemes.