Abstract This paper investigates the natural convection of Ag-MgO/water nanofluids within a porous enclosure using a Local Thermal Non-Equilibrium (LTNE) model. The Darcy model is applied to simulate the flow dynamics throughout the porous medium. Using non-dimensional parameters, the dimensionless form of the prevailing equations has been derived. Finally, the Galerkin finite element method is utilized to solve governing equations using a non-uniform structured grid, numerically. The key parameters of this study are Rayleigh number (10 ≤ Ra ≤ 1000), porosity (0.1 ≤ e ≤ 0.9), nanoparticles volume fraction (0 ≤ φ ≤ 0.02), interface convective heat transfer coefficient (1 ≤ H ≤ 1000), and the thermal conductivity ratio of two porous phases (1 ≤ γ ≤ 10). It is indicated that dispersing Ag–MgO hybrid nanoparticles in the water strongly decreases the transport of heat through two phases of the porous enclosure. For glass ball and aluminum foam, by increasing the H from 1 to 1000, Qhnf would be 1.33 and 5.85 times, respectively, at φ = 2%.