Numerical investigation of natural convective heat transfer and fluid flow in a differentially heated square cavity filled with a CuO-water nanofluid having variable properties is performed. Governing partial differential equations formulated in nondimensional stream function, vorticity, temperature, and nanoparticles volume fraction are solved by the second-order accurate finite difference method and taking into account the Brownian diffusion and thermophoresis. The effects of Rayleigh number (Ra = 10^{4}–10^{6}), initial nanoparticles volume fraction (C_{0} = 0–0.09), location of the heater (Δ = 0.0–0.9), and dimensionless time (*τ* = 0–300) on flow patterns, isotherms, and concentration fields as well as the local and average Nusselt numbers at the heater surface are studied. The isoconcentrations reveal that for most of the cavity domain the nanoparticle concentration is around the initial average concentration of nanoparticles except for a very limited variation in a region close to the cavity walls that experiences minor deviation from the initial concentration. It was found that the flow strength within the cavity (i.e., $\psi maxRa\u22c5Pr$) is inversely proportional to the heater location Δ and is directly proportional to the Rayleigh number. Also, it was found that the best location of the heater, from a heat transfer perspective, is placing it entirely at the left wall of the cavity where a maximum average Nusselt number is registered. This study revealed that for all heater locations there is always an adverse impact of nanoparticles on the heat transfer and the worst case is registered for the Δ = 0 and the least deterioration is noticed for Δ = 0.9.