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Current investigation aims to analyze the conjugate free convection inside a porous square cavity occupied with Ag–MgO hybrid nanofluid using the local thermal non-equilibrium (LTNE) model. Hybrid nanofluids are a novel kind of enhanced working fluids, engineered with enhanced thermo-physical and chemical properties. Two solid walls located between the horizontal bounds in two sides of cavity play the role of a conductive interface between the hot and cold walls, and moreover, the top and bottom bounds have been insulated. The governing differential equations are obtained by Darcy model and then for better representation of the results, converted into a dimensionless form. The finite element method is utilized to solve the governing equations. To evaluate the correctness and accuracy of the results, comparisons have been performed between the outcomes of this work and the previously published results. The results indicate that using the hybrid nanoparticles decreases the flow strength and the heat transfer rate. The heat transfer rate augments when Rk rises and the flow strength augments when Ra grows. Enhancing the porosity increases strongly the size and strength of the vortex composed inside the porous medium. When Kr is low, the heat transfer rate is low and by increasing Kr, thermal fields become closer to each other. The effect of hybrid nanoparticles on thermal fields with the thinner solid walls is more than that the thicker ones. An increment in H eventuates the enhancement of heat transfer and hence, the thermal boundary layer thickness. By increasing the volume fraction of the hybrid nanoparticles, Nuhnf and Nus decrease in constant Ra. Besides, increase in Ra enhances the Nuhnf and Nus. For a certain d, the reduction of Nus due to using the hybrid nanoparticles is more than that for Nuhnf. The increment of d lessens Nuhnf for all values of Kr and has not specific trends for Nus. Utilizing hybrid nanoparticles decreases Nus (except d = 0.4), rises Nus when Kr 18, while it can increase Nus for Kr[42. In constant d, increment of H, respectively, decreases and boosts Nuhnf and Nus. For all values of d, increment of e declines Nuhnf. In low value of d, the increase in e reduces Nus, whereas at higher values, Nus has continuously enhancing trend. For different values of d, the increase in e scrimps Nuhnf. The increment of d and also e, and H are, respectively, decreases and increases the heat transfer rate.