Flow instabilities and heat transfer in buoyancy driven flows of inelastic non-Newtonian fluids in inclined rectangular cavities

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° and 90°and two cavity height based Rayleigh numbers, Ra=10⁴ and 10⁵, a Prandtl number of Pr = 10² and two cavity aspect ratios of 1, 4. For the vertical inclination of 90°, computations were performed for two Rayleigh numbers Ra=10⁴ and 10⁵and three Prandtl numbers of Pr = 10², 10³ and 10⁴. 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 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 φ 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. Despite significant differences in the heat transfer rate and flow configurations both Newtonian and non-Newtonian fluids of the power law type exhibit qualitatively similar behavior.