Natural convection of power law fluids in inclined cavities (original) (raw)

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 ¼ 10 4 and 10 5 , a Prandtl number of Pr ¼ 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 ¼ 10 4 and 10 5 and three Prandtl numbers of Pr ¼ 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 ɸ 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.