For expanding industrial applications of a natural convection in a channel under a high temperature difference, a compressible fluid flow is taken into consideration in governing equations instead of renunciation of the Bossinesq assumption. Due to the slowness of the velocity of fluid in the natural convection, the Roe scheme matching methods of preconditioning and dual-time stepping are used to solve the governing equations. In order to resolve reflections induced by acoustic waves at the boundaries of the channel, non-reflection conditions at the boundaries of the channel are derived. The results show that a more reasonable pressure distribution in the channel is first validated and average Nusselt numbers are expressed in terms of Rayleigh number for a wide range temperature difference. (C) 2009 Elsevier Ltd. All rights reserved.