Steady two-dimensional natural convection in rectangular two-dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0 degrees and 90 degrees and two cavity height based Rayleigh numbers, Ra = 10(4) and 10(5), a Prandtl number of Pr = 10(2) and three cavity aspect ratios of 1, 4 and 8. For the vertical inclination of 90 degrees, computations were performed for two Rayleigh numbers Ra = 10(4) and 10(5) and three Prandtl numbers of Pr = 10(2), 10(3) and 10(4). In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number (Nu) over bar on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination phi is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. A correlation relating (Nu) over bar to the power law index n for vertically heated cavities for the range 10(4) <= Ra <= 10(5) and 10(2) <= Pr <= 10(4) and valid for aspect ratios 4 <= AR <= 8 is given. (C) 2011 Elsevier Masson SAS. All rights reserved.