In the present study, turbulent flow of a Cu-water nanofluid through a porous cavity is investigated using a numerical method. Two rotating cylinders with different temperatures are placed inside the porous enclosure to generate turbulent structures. Forced and natural convective heat transfer mechanisms are compared for different Cu nanoparticle concentrations. The natural convection within the enclosure is resulted from buoyancy forces as an effect of temperature differences among hot and cold cylindrical turbulators. To investigate the effect of the cavity geometry on the natural convection heat, the simulations are done for various Rayleigh number values. Accordingly, Rayleigh number increment provides higher Nusselt number values. However, in turbulent flow regimes, forced convection may weaken the natural convection. It is proven that for lower Reynolds numbers, the Nusselt number reaches higher values because of buoyant-driven convective heat transfer deterioration. Moreover, the angular velocity directions of both cylinders slightly affect the Nusselt number. Besides, the impact of porosity on the heat transfer rate is studied for different Darcy numbers. It is concluded that, for lower Ra numbers, as Darcy number rises, the average Nusselt number through the cavity is slightly boosted. In addition, it is shown that for cases with high Ra and Re values, Cu nanoparticle addition adversely affects the heat transfer process. At Ra = 1011, as Cu nanoparticle increases from 0 to 0.02 and 0.04, the average Nu decreases up to 17.65% and 27.48%, respectively.