Two-dimensional and three-dimensional numerical simulations were carried out to simulate the natural convection in a cylindrical envelope with an internal concentric cylinder with slots. For the case of steady flow, the numerical solutions in 2D and 3D simulations are in good agreement with the experimental results. When the convection in experiment becomes unsteady convection at the larger slot degree, the oscillated solutions in 3D simulation differ essentially from steady solutions in 2D simulation. The critical Rayleigh numbers from steady to unsteady flow in the 3D simulations are lower than those in the 2D simulations. (C) 2013 Elsevier Ltd. All rights reserved.