Analyzing the heat and mass transfer behavior in a 2-D forchheimer porous medium on MHD Casson fluid flow over an inclined non-linear surface with viscous dissipation, chemical reaction, and Soret-Dufour parameters

The comprehensive analysis of Magnetohydrodynamic (MHD) Casson fluid (CF) flow in a Forchheimer porous medium (FPM) across an inclined non-linear surface, which includes the rarely coupled effects of viscous dissipation, chemical reaction, and Soret-Dufour parameters, is the distinctive feature of this study. In contrast to conventional research, which concentrates on linear drag forces or oversimplified porous media, this study provides a more precise representation of physical events by incorporating non-linear drag effects at elevated flow velocities. The Forchheimer porous medium is a sophisticated model in fluid mechanics that expands Darcy's law to include non-linear drag effects at elevated flow velocities. It is utilized in numerous practical issues, especially in the realms of heat and mass transmission and MHD within porous media, including geothermal energy, thermal insulation, and food processing, as well as in MHD fluid dynamics for nuclear reactor cooling, MHD generators, and astrophysical simulations. These applications are essential for enhancing energy, environmental, and industrial systems. A set of suitable similarity components is used to convert the governing equations into Ordinary differential equations (ODEs) that are not linear. Numerical solutions for nonlinear ODEs in MATHEMATICA are obtained by combining the R-K-Fehlberg (RKF45) approach with the shooting methodology. Numerical outcomes at several intervals of the physical variables including temperature, concentration, and velocity profiles were presented using graphs and tables. This research further includes the investigation of the skin friction coefficient, Nusselt number, and local Sherwood number. The research found that Velocity rises with higher Permeability, Grashof number, and Solutal Grashof number values, whereas Magnetic M,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(M\right),$$\end{document} Casson (beta)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta )$$\end{document} and Forchheimer (Fs)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Fs)$$\end{document} parameters show an opposite pattern. The heat transfer coefficient goes from a low to a high as the Prandtl and Dufour numbers go up. To verify the accuracy of our data, we performed a comprehensive comparison with existing studies and found a significant degree of agreement.