Numerical analysis and regression-based performance prediction of MHD water-based ternary hybrid nanofluid flow and heat transfer in a finned cavity

This study numerically investigates forced convection heat transfer and entropy generation of a water-based ternary hybrid nanofluid (Fe 3 O 4 + CuO + MoS 2 ) inside a two-dimensional square cavity containing three circular hot fins, under the influence of a direction-dependent magnetic field ( \(γ\) = 0°–90°). The finite element method (COMSOL Multiphysics 6.2) is employed to solve the governing equations. Four key parameters are systematically examined: Reynolds number (100–1000), Hartmann number (1–100), nanoparticle volume fraction (1%–10%), and magnetic field angle. An oblique magnetic field angle of \(γ\) = 30° enhances the local Nusselt number by up to 78.6% compared to \(γ\) = 0° at Ha = 100, owing to reduced Lorentz damping and the generation of beneficial secondary flows. Moderate Ha ≈ 25 provides a 2.7% improvement in peak Nusselt number at Re = 700, while Ha ≥ 50 suppresses convection, reducing lower-cavity heat transfer by up to 95%. Detrimental effect of nanoparticles: Increasing \(φ\) from 1 to 10% reduces peak Nusselt number by 11.2% at Re = 1000 and Ha = 25 and increases local entropy generation by 27.6–43.4%, despite higher thermal conductivity attributed to viscosity-dominated boundary layer thickening. A strong transverse magnetic field ( \(γ\) = 90°) at Ha = 100 reduces peak total entropy generation by 89% compared to \(γ\) = 0°, producing a nearly uniform irreversibility distribution, optimal for thermodynamic efficiency. Predictive regression models: Novel multiple linear regression equations for average temperature and entropy generation are derived with high statistical significance (p-value < 10 –29 ) within the investigated parameter ranges, providing rapid design tools without further CFD. These findings establish that \(γ\) = 30° with Ha ≈ 25 and low \(φ\) offers the best heat transfer–entropy trade-off, while \(γ\) = 90° is recommended when minimizing irreversibility is the primary objective.