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

Abstract

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.