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

Abstract

A computational model for the dynamic stabilization of Rayleigh-Bénard convection in a cubic cavity

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

“…Benouared et al [12] found a subcritical Rayleigh number R sc ¼ 800, whereas our computations show that 780 < R sc < 782:5, which is only 2% smaller. Moreover, the value of Nusselt number at R ¼ 800 found by [12] is Nu ¼ 1:4798 to compare to our value, Nu ¼ 1:4751: the relative difference is smaller than 0:32%. A second point was compared at R ¼ 2000, and the relative difference of the Nusselt numbers is 0:38% (Nu ¼ 2:7759 for [12] and Nu ¼ 2:7655 for us).…”

“…To validate our numerical method when g 1 -0, we compare with [12] for P ¼ 10; n i ¼ 0:6; k ¼ 0:4; g 1 ¼ 0:01, and for an aspect ratio of the cell L x =d ¼ 1, which would not bring significantly different results than with our value L x =d ¼ 1:008. Benouared et al [12] found a subcritical Rayleigh number R sc ¼ 800, whereas our computations show that 780 < R sc < 782:5, which is only 2% smaller.…”

“…As already discussed, the strategy adopted by [9] is used, i.e., we compute only one roll in a row of rolls of critical wavenumber. During the course of this work, we become aware of the recent study [12]. In their section V.G, they study a system quite similar to the one addressed here, except for a slightly smaller aspect ratio.…”

“…þ1 : therefore, our results are for interest for Carreau fluids but also for power-law fluids. Nevertheless, a comparison with [12] will be shown in Section 7. A very good agreement is found.…”

“…However, the theoretical literature concerning Rayleigh-Bénard convection of power-law fluids in extended geometry is sparse. In fact, to our knowledge, as far as convection rolls in extended geometry are concerned, the relevant articles are [9][10][11][12]. Eq.…”