Natural convection of power law fluids in inclined 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 = 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°, 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 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 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 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.