This contribution gives a numerical investigation of buoyancy-driven flow of natural convection heat transfer and entropy generation of non-Newtonian hybrid nanofluid (Al₂O₃-Cu) within an enclosure square porous cavity. Hybrid nanofluids represent a novel type of enhanced active fluids. During the current theoretical investigation, an actual available empirical data for both thermal conductivity and dynamic viscosity of hybrid nanofluids are applied directly. Numerical simulation have been implemented for solid nanoparticles, the volumetric concentration of which varies from 0.0% (i.e., pure fluid) to 0.1% of hybrid nanofluids. Heat and sink sources are situated on a part of the left and right sides of the cavity with length B, while the upper and bottom horizontal sides are kept adiabatic. The stated partial differential equations describing the flow are mutated to a dimensionless formulas, then solved numerically via the help of an implicit finite difference approach. The acquired computations are given in terms of streamlines, isotherms, isomicrorotations, isoconcentraions, local Began number, total entropy, local and mean Nusselt numbers. The data illustrates that variations of ratio of the average Nusselt number to the average Nusselt of pure fluid Nu_m⁺ is a decreasing function of Ha and φ, while e⁺ is an increasing function of Ha and φ parameters of hybrid nanofluid.