The effect on the entropy production and MHD convection of the hybrid nanofluid Al₂O₃–Cu/water (water with Cu and Al₂O₃ nanoparticles) in a porous square enclosure is studied numerically via Galerkin finite element method. The enclosure used for flow and natural convection analysis is subjected to sinusoidal varying temperatures at the boundaries. Calculations were performed for specific parameters of the Rayleigh number (Ra = 10³–10⁶), porosity ratio (ε = 0.1–0.9), Darcy number (Da = 10⁻⁵–10⁻²), Hartmann number (Ha = 0–100) and nanoparticles concentration (φ = 0–0.08). The numerical results are presented by velocity profiles, isotherms, streamlines, and Nusselt number. They indicate that the isotherms subject to estimation variations under Ha boost from 0 to 100 as Ra enhances. At high Ha, the conduction transfer mechanism is more obvious. Also, it is seen that the convective heat transfer becomes stronger with the enhancement of the Ra while it detracts with the rise in Ha. Due to the Ra increase, the flow cell becomes stronger. For Ra = 10⁶ and higher Hartmann numbers, the isotherms remain constant which is an indication of convection predominance.