Natural convection, in a shallow horizontal cavity filled with a nanofluid, is studied. The flow is driven by Lid driven convection (LDC). External applied constant heat fluxes on the bottom wall of the cavity is applied, whereas the vertical walls are subjected to variable heat fluxes. The nanofluid concentration is treated as heterogeneous mixtures with a weak solutal diffusivity. A modified formulation taking into account the physical properties (thermal conductivity, viscosity) versus on nanofluids type and concentration and the spatial heterogeneous concentration induced by the Soret effect is presented. The induced nanofluid heterogeneity can affect the heat transfer. The heat transfer increases with increase of the boundary motion. The analytical solution, based on parallel flow approximation, is found to be in good agreement with numerical solution. The existence of both natural and anti-natural flows is demonstrated. Indeed, the subcritical Rayleigh number for the onset of instability tends to disappear when the supercritical threshold is largely affected. (C) 2017 Elsevier Ltd. All rights reserved.