A novel thermal immersed boundary-lattice Boltzmann method is developed to simulate the 2D natural convection in a concentric horizontal annulus with a constant flux wall. In the present work, we focus on the multiple steady solutions of this problem. And the case with a fixed aspect ratio Ar = 2 is considered. In addition to the dual steady solutions which was reported by the previous work (Yoo, 2003), a new steady solution consisting more of eddies is found in this paper when the Rayleigh number exceeds a certain critical value. (C) 2014 Elsevier Ltd. All rights reserved.