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Numerical study of subcritical Rayleigh–Bénard convection rolls in strongly shear-thinning Carreau fluids

Abstract : Abstract The Rayleigh–Bénard thermoconvection of Newtonian fluids has been extensively studied. The transition from the conductive, static state to thermoconvection flows corresponds in this case to a supercritical bifurcation. In shear-thinning fluids, on the contrary, recent weakly nonlinear studies have shown that the transition may become subcritical. Using a custom numerical code developed with Freefem++ to compute bidimensional, fully nonlinear roll solutions in Carreau fluids, for a large range of rheological parameters, and more particularly for strongly shear-thinning fluids, approaching power-law fluids, we confirm this result. A simple expression of the value of the Rayleigh number at which subcritical convection rolls appear is proposed. This law suggests to reconsider the choice of the reference viscosity for shear-thinning fluids. Indeed, when the shear-thinning effects increase, the critical Rayleigh number increases or decreases depending on the choice of the reference viscosity. The ‘neutral’ or ‘effective’ viscosity, which gives a constant value of the Rayleigh number at the onset of subcritical convection rolls, is close to the bulk average viscosity. In addition, a correlation is proposed to estimate the Nusselt number of subcritical rolls.
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https://hal.univ-lorraine.fr/hal-01417334
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Submitted on : Thursday, December 15, 2016 - 3:18:00 PM
Last modification on : Friday, May 24, 2019 - 5:29:58 PM

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Mathieu Jenny, Emmanuel Plaut, Antoine Briard. Numerical study of subcritical Rayleigh–Bénard convection rolls in strongly shear-thinning Carreau fluids. Journal of Non-Newtonian Fluid Mechanics, Elsevier, 2015, 219, pp.19 - 34. ⟨10.1016/j.jnnfm.2015.03.002⟩. ⟨hal-01417334⟩

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