A numerical study of the natural convection heat transfer of cold water, having a density inversion between two isothermal horizontal concentric cylinders is studied. The governing equations are solved by upwind finite difference method for different annulus radius ratios with Rayleigh number range 10(2)-10(5) and the inversion parameter gamma varies between -2 and 0. The results indicate that the flow patterns are greatly influenced by the inversion parameter, which determines the effect of the additional convection that arises from the inversion of density of water at 3.98-degrees-C within the annulus.