A semi-analytical solution of a nonlinear boundary value problem arises in porous catalysts

Abstract

In the heterogeneous catalysis, the interaction of transport effects significantly influences reaction rates. Heterogeneous catalysis is essential in several industrial processes and has various practical applications, such as protecting the environment, power generation, synthesis of chemicals, and the manufacturing of biodiesel. This intricate interaction includes external mass transfer resistance and intra-particle diffusion within the porous catalysts, which are often different from conventional chemical kinetics. The heterogeneous catalysts employed in many chemical applications are either porous materials or are created as microscopic particles with a few nanometers diameter coated on a porous substrate like silica or alumina. Mathematical modeling of such phenomena involves nonlinear boundary value problems, with necessitating approximate solutions due to their complexity. This article introduces the efficient Akbari-Ganji method (AGM), which is a semi-analytical approach for solving the nonlinear equations without requiring problem transformation or distinct nonlinear term treatment. We utilize the AGM to derive reliable analytical solutions for a nonlinear reaction-diffusion equation, specifically encompassing the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model. By comparing AGM results with numerical simulations implemented in the MATLAB, this study highlights the AGM's ability in addressing nonlinear boundary value problems. The AGM's significance resides in its potential to unravel complex catalyst-related challenges and engineering applications. This work underlines the power of analytical solutions, allowing explicit insights, broad generalizations, sensitivity analyses, and parametric studies, and hence enriching our understanding of transport phenomena in the heterogeneous catalysis.