### Abstract

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.

Original language | English |
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Pages (from-to) | 8-17 |

Number of pages | 10 |

Journal | International Journal of Thermal Sciences |

Volume | 53 |

DOIs | |

Publication status | Published - Mar 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Engineering(all)

### Cite this

*International Journal of Thermal Sciences*,

*53*, 8-17. https://doi.org/10.1016/j.ijthermalsci.2011.10.020