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.
Type de document :
Article dans une revue
Journal of Non-Newtonian Fluid Mechanics, Elsevier, 2015, 219, pp.19 - 34. 〈10.1016/j.jnnfm.2015.03.002〉
Liste complète des métadonnées

https://hal.univ-lorraine.fr/hal-01417334
Contributeur : Lemta Ul <>
Soumis le : jeudi 15 décembre 2016 - 15:18:00
Dernière modification le : vendredi 7 décembre 2018 - 01:30:23

Identifiants

Citation

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〉

Partager

Métriques

Consultations de la notice

92