The variable property solution for the natural convection in air-filled horizontal concentric annuli is obtained by using the variable property-based lattice Boltzmann flux solver. The effect of temperature difference ratio is discussed under the condition that the Ra and Pr numbers are 5 x 10(4) and 0.71, respectively. In the large-gap annulus, only one pair of counter-rotating eddies is formed, and the equivalent conductivity increases with temperature difference ratio. In the moderate-gap annulus, the flow patterns depend on temperature difference ratio, and the equivalent conductivity sometimes has a notable decrease as the eddy number changes. These demonstrate that temperature difference ratio should be considered as an important parameter in the study about flow instability behaviors and heat transfer characteristics under non-Boussinesq conditions. (C) 2017 Elsevier Ltd. All rights reserved.