Heuristic computational approach for nonlinear reaction–diffusion kinetics in catalytic systems

The Lane-Emden equations are essential tools for modeling heat and mass transfer, chemical reactions, and various scientific fields. This study focuses on solutions to Lane-Emden equations in chemical engineering. It examines the impact on concentration profiles in both catalyst and biocatalyst systems with cylindrical and spherical geometries. The research proposes a hybrid approach combining a collocation method with genetic algorithms to solve Lane-Emden equations in diffusion-reaction systems. It also investigates how different parameters, such as Thiele modulus (ρ), dimensionless activation energy (µ), and dimensionless heat of reaction (α) affect these solutions. The methodology is effective across both low and high values of ρ, µ, and α. Overall, the results demonstrate the potential to address limitations of previous methods and highlight the strength of the GA-based approach.