In this dissertation, we numerically studied the unsteady natural convective nanofluid flows within a two-dimensional right-trapezoidal cavity and a three-dimensional right-trapezoidal cuboid. The enclosures are filled with various porous mediums such as aluminum foam (AF), glass ball or glass bead (GB), and sandstone (ST). Different nanofluids considering various nanoparticles and base-fluids are used for simulation purposes. The fundamentals of nanofluids and their applications in numerous fields of science and engineering, the preparation process of nanofluids, and basic nanofluid flow mechanics in porous media are discussed in detail at the beginning of the study. To identify the regulating model parameters, a group of transformations of variables is utilized to make the governing nonlinear and coupled partial differential equations dimensionless. These equations are then numerically solved using the COMSOL Multiphysics software, which employs the Galerkin weighted residual scheme of finite element method. We investigated four different physical models in depth. The first three are considered within a two-dimensional right-angle trapezoidal enclosure, while the fourth one a three-dimensional right trapezoidal cuboid. In our investigation, we treated the nanofluid as a homogeneous mixture and flows through the porous medium following the non-Darcy model. For energy transport, two and three energy equations we considered for the model construction. The porosity and permeability of the porous medium are considered uniform as well as variable. The impacts of the controlling model parameters on the flow and thermal fields: Rayleigh number, the volume fraction of the nanoparticles, the Darcy number, the porosity of the porous medium, the Nield numbers, bead size creating the porous medium, different aspect ratios of the cavity, have been investigated. The local thermal non-equilibrium conditions between the nanofluid and the solid matrix are analyzed. The simulated results have been presented in terms of streamlines, isotherms, temperature profiles, and the average Nusselt number to determine the best heat transfer nanofluid in a porous medium. The results show that Nield and Darcy's numbers substantially influence the heat exchange between the nanofluid and the porous matrix. The critical Rayleigh number for the onset of the local thermal non-equilibrium (LTNE) state between the nanofluid and the solid matrix having variable porosity and permeability increases as the Nield number increases. It decreases as the diameter of the beads forming the porous medium and the porosity parameter increase, whereas the nanoparticle volume fraction does not affect the critical Rayleigh number. The heat transfer rate in a nanofluid-filled porous media with variable porosity is higher when compared to the uniform porosity of the media. Using Glass balls as a porous matrix raises the average Nusselt numbers of the nanofluid and solid matrix compared to the other porous matrixes tested. The copper-water nanofluid exhibits the highest average Nusselt numbers for base fluid, nanoparticles, and porous matrix compared to the other two examined types of nanofluids. Increased Rayleigh number and the diameter of the balls constructing the porous medium enhanced the average Nusselt numbers of the nanofluid and porous matrix. The average Nusselt numbers of base fluid and nanoparticles increase with the increase of the porosity parameter. The Nield numbers significantly affect the heat transfer in the base fluid, solid nanoparticles, and the porous matrix. The aspect ratios of the cavity played a vital role in heat transfer in all mediums. The trapezoidal cuboid exhibits the highest rate of heat transfer in the base fluid, nanoparticles, and solid matrix compared with the cube and the rectangular cuboid.