Predictor-corrector FDM analysis of MHD Darcy-Forchheimer flow of a micropolar fluid with viscous dissipation and heterogeneous-homogeneous

Abstract

This research delves into an intricate exploration of fluid dynamics within heat transfer systems, with a specific focus on enhancing our understanding and improving system efficiency. Employing a sophisticated mathematical model, the study incorporates micropolar fluid dynamics, micro rotational effects, laminar flow characterized by the Darcy-Forchheimer model, inertia effects, and chemical reactions within a heat transfer system featuring boundary layer complexities. The mathematical framework consists of partial differential equations (PDEs), and the study utilizes advanced numerical techniques, including the (PC4-FDM) Predictor-Corrector Finite Difference Method and the shooting method, to solve these governing equations. The inclusion of quantized mesh points and analysis of convergence using 4th order finite difference methods enhances the precision of the obtained solutions. Various parameters are scrutinized to draw meaningful insights. The heterogeneous parameter reveals an increasing trend in fluid concentration, while the homogeneous parameter indicates a collision effect leading to a decrease in fluid concentration. The Eckert number, associated with viscous dissipation, exhibits a correlation with decreased fluid temperature and increased fluid velocity. Micro rotation parameters suggest a parallel increase in fluid velocity and a marginal decrease in fluid temperature. Notably, the Darcy-Forchheimer parameter, reflective of inertial effects, showcases an increase in fluid temperature and decrease in velocity in the convection system. Highlighting the industrial implications, the study underscores the significance of convection heat transfer systems in the context of industrialization. The findings offer valuable insights for optimizing heating and cooling processes in diverse industrial applications, ranging from power plants to waste heat recovery units and pharmaceutical industries.