Numerical simulations are carried out for fluid flow and natural convection heat transfer induced by a temperature difference between a hot inner cylinder with different geometries (i.e., circular; triangular; elliptic; rectangular; and rhombic) and a cold outer square enclosure filled with nanofluid superposed porous-nanofluid layers. The Darcy–Brinkman model is applied for the saturated porous layer with nanofluid. Moreover, the transport equations (mass, momentum, and energy) are solved numerically using the Galerkin weighted residual method by dividing the domain into two sets of equations for every layer with incorporating a nonuniform mesh size. The considered domains in this investigation are closely examined over a wide range of Rayleigh number (10^{3} ≤ Ra ≤ 10^{6}), Darcy number (10^{−5} ≤ Da ≤ 10^{−1}), the thickness of porous layer (0% ≤ X_{p} ≤ 100%), thermal conductivity ratio (1 ≤ R_{k} ≤ 20), and nanoparticle volume fraction (0 ≤ *φ* ≤ 0.1), respectively. The nanofluid is considered to be composed of Ag-nanoparticle and water as a base fluid. The results showed that the obtained total surfaces-averaged Nusselt numbers of the enclosure, in all cases, at the same operating conditions, the rate of heat transfer from the outer enclosure which the triangular cylinder is located inside is better. Also, as the thickness of the porous layer is increased from 20% to 80%, the free convection performance will decrease significantly (to about 50%) due to the hydrodynamic properties of the porous material.