Numerical Analysis of Mixed Convection of Hybrid Ferrofluid in a Double Lid-driven Porous Hexagonal Cavity with a Square Heated Block

This study numerically explores magnetohydrodynamic (MHD) mixed convection (MC) of an Fe₃O₄–Al₂O₃/water hybrid ferrofluid (HFF) in a double lid-driven porous hexagonal cavity containing a centrally placed square heated block. The top and bottom walls move in opposite directions (U = 1 and U = −1) and are kept cold, the slanted walls are adiabatic, and a uniform horizontal magnetic field acts on the fluid under the influence of gravity. The Darcy–Brinkman–Forchheimer model describes the flow through the copper-foam porous medium, and the governing equations are solved with the Galerkin weighted residual finite element method (GWR-FEM). The unsteady flow and thermal fields are analyzed through streamlines, isotherms and the average Nusselt number (Nuav) on the surface of the heated block, for Richardson numbers Ri = 0.1, 1 and 10, Hartmann numbers Ha = 0, 20 and 40, Re = 100 and Da = 10⁻². The results show that at low Ri the flow is dominated by shear from the moving lids, while at high Ri buoyancy produces a strong circulation around the block, thinner thermal boundary layers and a higher Nuav. In contrast, increasing Ha damps the fluid motion through the Lorentz force, weakens the vortices, moves the thermal field toward conduction and lowers Nuav In all cases, Nuav is highest at the start of the simulation and then decreases toward a quasi-steady value. The findings are useful for the thermal management of electronic components, heat transfers (HT) and magnetically controlled cooling systems.