Numerical nonlinear analysis of subcritical Rayleigh-Bénard convection in a horizontal confined enclosure filled with non-Newtonian fluids

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DOIResolve DOI: http://doi.org/10.1063/1.4890829
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TypeArticle
Journal titlePhysics of Fluids
ISSN1070-6631
1089-7666
Volume26
Issue7
Article number073101
SubjectThermal convection; Shear thinning; Viscosity; Shear rate dependent viscosity; Boundary value problems
AbstractNon-Newtonian subcritical convection in a Rayleigh-Bénard configuration was investigated numerically, using rigid boundary conditions. The flow configuration consisted of a finite aspect ratio enclosure subject to a vertical temperature gradient, which was established by heating and cooling the lower and the upper walls by either a constant heat flux or by applying constant temperatures. The non-Newtonian fluid viscosity was modeled using the Carreau-Yasuda model. The convective flow was governed by the conservation equations, which were solved numerically using a finite difference method with a time-accurate scheme. For a shallow enclosure, when the walls were subject to constant heat fluxes, an asymptotic solution was derived assuming a parallel flow behavior. A comparison between the numerical and asymptotic solutions was performed. The effects of the controlling parameters, namely, the Rayleigh and the Prandtl numbers, and the fluid rheological parameters on the onset of subcritical convective flow were investigated. The threshold for the onset of subcritical convection was found to be well below the threshold of stationary convection and decreased considerably (with the fluid rheological parameters variation) as the fluid became more and more shear thinning. Depending on the governing parameters, steady and unsteady-periodic flow solutions were possible. Within a square enclosure with slip or no-slip vertical walls, maintaining the active walls at a constant heat flux or at constant temperature, the rheological subcritical flow behavior remained qualitatively the same, but led to different subcritical convection thresholds.
Publication date
PublisherAIP Publishing
LanguageEnglish
AffiliationAerospace; National Research Council Canada
Peer reviewedYes
NPARC number23000093
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Record identifier0c45cfc1-df29-40f8-a801-852303e976c5
Record created2016-06-02
Record modified2016-06-02
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