Weakly nonlinear analysis of Rayleigh-Bénard convection in a non-Newtonian fluid between plates of finite conductivity: Influence of shear-thinning effects

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Mondher Bouteraa, C Nouar

Abstract

Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Ra_{c} and the critical wave number k_{c} decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value α_{c} of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that α_{c} increases with decreasing ξ. The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξ_{c}, below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M...Continue Reading

Citations

Oct 3, 2019·Physical Review. E·S TopayevS A Bahrani

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