In this contribution, free convection attributes of a water-based nanofluid containing CuO nanoparticles within a perturbed cavity filled by porous medium are examined using the two-phase mixture model. The simulations are conducted at Rayleigh numbers of 103–106, Darcy numbers of 0–60, and nanoparticle concentrations of 0–3%. Based on the results, the Nusselt number enhances by increasing the concentration, and it is greater in the perturbed region compared with the other areas. At the low Rayleigh numbers, the isotherms are rather parallel to each other, while this pattern is disturbed with the Rayleigh number increment because of the buoyancy force augmentation. The maximum horizontal velocity in the enclosure increases from 0.00012 to 0.006 m/s with the increment of the Rayleigh number from 103 to 106. Moreover, the isotherms are closer to each other in the vicinity of the perturbed side. The Nusselt number significantly reduces with increase of the Darcy number from 0 to 20, while it slightly increases with increment of the Darcy number from 20 to 60. In addition, more rotational cores are formed in the vicinity of the perturbed side in the cases with the porous medium. According to the signal to noise analysis, the porosity has more significant effect on the Nusselt number compared to the effect of the Rayleigh number and nanoparticle fraction.