This study investigates the flow characteristics of a two-dimensional (2D), steady-state, magnetohydrodynamic (MHD) hyperbolic tangent nanofluid using a hybrid analytical and numerical (HAN) approach over a porous, permeable wedge. Its flexibility lies in leveraging various numerical methods, making it a robust tool compared to other semi-analytical techniques. In industrial applications, such non-Newtonian fluids, including hyperbolic tangent fluids, MHD models, and nanofluids, are frequently encountered, particularly in scenarios involving radiation and magnetic fields. The research emphasizes the equations of energy, concentration, momentum, and continuity, which are transformed into a set of nonlinear, third-order coupled ordinary differential equations (ODEs) through similarity transformations. These ODEs are characterized by 11 key dimensionless parameters: the Lewis number (0.1–1), Prandtl number (0.5–4), Brownian diffusion (1–9), thermophoresis parameter (1–9), Dufour number (0 –4), Soret number (−1 to −5), and thermal radiation parameter (2–10). The study’s primary objective – and its most notable novelty – is to explore the parameters that influence both temperature and concentration distributions. It further examines the effect of these parameters on the Sherwood number, Nusselt number, and skin friction coefficient. Results indicate that the Prandtl number significantly reduces velocity while increasing fluid temperature, whereas Dufour and Soret numbers minimally affect velocity but increase concentration levels. Factors such as thermophoresis, Brownian diffusion, and thermal radiation markedly elevate temperature and concentration averages, while parameters like the Weissenberg number, power law index, wedge angle, and medium permeability show negligible impact.
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