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 Galerldn 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 <= epsilon <= 0.9), nanopartides volume fraction (0 <= phi <= 0.02), interface convective heat transfer coefficient (1 <= H <= 1000), and the thermal conductivity ratio of two porous phases (1 <= gamma <= 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, Q(hnf) would be 1.33 and 5.85 times, respectively, at phi = 2%. (C) 2020 Elsevier B.V. All rights reserved.