Natural convection of power law fluids in inclined cavities

Lyes Khezzar, Dennis Siginer, Igor Vinogradov

Research output: Contribution to journalArticle

48 Citations (Scopus)

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 languageEnglish
Pages (from-to)8-17
Number of pages10
JournalInternational Journal of Thermal Sciences
Volume53
DOIs
Publication statusPublished - Mar 1 2012

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Prandtl number
Natural convection
free convection
inclination
Aspect ratio
Rayleigh number
cavities
Fluids
fluids
aspect ratio
Finite volume method
Nusselt number
Conservation
Momentum
Heat transfer
conservation equations
finite volume method
configurations
heat transfer
momentum

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Engineering(all)

Cite this

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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.",
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Natural convection of power law fluids in inclined cavities. / Khezzar, Lyes; Siginer, Dennis; Vinogradov, Igor.

In: International Journal of Thermal Sciences, Vol. 53, 01.03.2012, p. 8-17.

Research output: Contribution to journalArticle

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