Numerical examination of the Darcy–Forchheimer Casson model with instigation energy and second-order momentum slip: Thermal features

Abstract

In this study, the Darcy–Forchheimer model is examined in relation to magnetohydrodynamic (MHD) Casson fluid flow over a stretchable exponential surface. The investigation incorporates several factors not previously considered, including Arrhenius activation/instigation energy, second-order slip, Joule heating, thermal radiation, viscous dissipation, and chemical reactions. The Darcy–Forchheimer model is employed to characterize flows within permeable materials under the influence of instigation energy. Additionally, we analyze the electrically conducting flows induced by an exponentially stretched and dissipated sheet. To transform the partial differential equations (PDEs) into ordinary differential equations (ODEs), appropriate similarity transformations are applied. Numerical and graphical results are presented using the Lobatto IIIA technique across various system scenarios, demonstrating the effectiveness of this approach as a reliable, accurate, and viable solver. Through the utilization of the BVP4C technique in MATLAB, a numerical representation of the formulation is achieved. Graphs are generated, illustrating the variations in ongoing parameters such as concentration velocity. This velocity increases with higher values of E and Γ , but decreases with σ . The fluid temperature rises with larger values of R , and it responds positively to first-order slip while decreasing with second-order slip.