Optimal homotopy analysis method for the non-isothermal reaction–diffusion model equations in a spherical catalyst

Abstract

We consider the Lane–Emden boundary value problems which appear in chemical applications, biochemical applications, and scientific disciplines. The Lane–Emden problem is transformed into an equivalent integral equation. The optimal homotopy analysis method is used to solve two specific models. The first problem models reaction–diffusion equation in a spherical catalyst, while the second problem models the reaction–diffusion process in a spherical biocatalyst. We obtain reliable analytical solutions of the concentrations and the effectiveness factors. Numerical results and graphs show the reliability and efficiency applicability of the employed method.