Stability and entropy generation analysis of MHD Homann stagnation-point flow of a ternary hybrid nanofluid

The present analysis explores the thermodynamic and stability analysis of three-dimensional MHD Homann stagnation-point flow of a ternary hybrid nanofluid through a Darcy–Forchheimer porous medium over a vertically moving stretching/shrinking surface. The proposed mathematical model uniquely integrates anisotropic velocity slip, nonlinear thermal radiation, viscous dissipation, homogeneous chemical reaction, and entropy generation within a dual-solution framework, providing a comprehensive thermodynamic and stability analysis. Non-similar transformations are employed to convert the governing nonlinear partial differential equations for momentum, thermal, and mass transport into a system of coupled ordinary differential equations, which are numerically solved using MATLAB’s adaptive bvp4c solver. A linear stability analysis is applied to determine the physical compatibility of the dual solutions, confirming that the upper branch is stable and physically acceptable, whereas the lower branch is unstable. Quantitative evaluations indicate that the heat and mass transfer rates are significantly enhanced when the Reynolds number (Re) increases from 0.1 to 0.5; specifically, the Nusselt number increases by approximately 110–120%, while the Sherwood number rises by 115–125%. Over the same range of Re, the first skin-friction coefficient (Cf1) increases by 25–30%, whereas the second skin-friction coefficient (Cf2) decreases by 50–55%. Furthermore, the physical mechanism of thermodynamic irreversibility reveals that the entropy generation rate increases by 15–55% with an increasing Brinkman number, by 65–75% with an increasing diffusion variable, and by 85–100% with an increasing radiation parameter. The insights gained from this analysis offer valuable guidelines for optimizing flow stability and heat and mass transfer, and minimizing the irreversibility of porous media systems utilizing ternary hybrid nanofluids.