The experimental studies dealing with natural convection of nanofluids in differentially heated enclosures demonstrate that the addition of nanoparticles to a pure base liquid is substantially detrimental, which can be ascribed to the formation of two stagnant fluid layers near the top and bottom adiabatic walls. Thus, if the horizontal walls are differentially heated instead of being perfectly insulated, the consequent development of a pair of concentration boundary layers near them may possibly imply a heat transfer enhancement. In this connection, a two-phase mixture model is employed to perform a numerical study of laminar natural convection in a square cavity containing water suspensions of alumina nanoparticles with a diameter of 33nm and an average volume fraction in the range 0.001-0.04, assuming that Brownian diffusion and thermophoresis are the primary slip mechanisms between solid and liquid phases. The cavity is differentially heated at sides, whereas the horizontal walls are assumed to be either adiabatic or one heated and the other cooled, with a Rayleigh number in the range 4 x 10(5)-3 x 10(6). It is found that the heating-from-below configuration is featured by periodic heat transfer, with a rate remarkably higher than that typical of the pure base liquid.