Weakly nonlinear analysis of Rayleigh–Bénard convection in shear-thinning fluids: nature of the bifurcation and pattern selection
Weakly nonlinear analysis of Rayleigh–Bénard convection in shear-thinning fluids: nature of the bifurcation and pattern selection
复制标题
剪切稀化流体中瑞利-贝纳德对流的弱非线性分析：分岔的性质和模式选择
DOI：
10.1017/jfm.2015.64
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发表时间：
2015
影响因子：
3.7
通讯作者：
Aurélie Kalck
中科院分区：
文献类型：
--
作者：
Mondher Bouteraa;C. Nouar;E. Plaut;C. Métivier;Aurélie Kalck
摘要对从下加热的两个水平板之间的剪切变薄流体层中的对流进行了线性和弱非线性分析。目的是研究粘度随剪切速率的非线性变化对分岔性质的影响，以及辊子、正方形和六边形之间的平台选择问题，以及对传热系数的影响。在顶壁和底壁采用了纳维尔滑移边界条件。卡罗模型描述了流体的剪切变薄行为。通过考虑无穷小扰动，确定了与对流开始相对应的临界条件。在这个阶段，非牛顿效应不会起作用。随着滑移量的增大，临界瑞利数减小，临界波数增大。对于有限振幅的扰动，非线性效应进入动力学。对振幅方程中三次饱和系数的分析表明，分岔的性质取决于流体的流变特性，即流体特征时间和剪切减薄指数。对于弱剪切变薄流体，分叉是超临界的，传热系数比牛顿情况增大。当剪切减薄特性足够大时，分岔处于亚临界状态，这表明了流变规律引起的非线性的破坏作用。从起始点出发，在振幅展开中进行了五阶的弱非线性分析。对流动结构、黏度场的变化和努塞尔数进行了表征。研究了滚动、正方形和六边形之间的竞争。不像Albaalbaki和Khayat （J. Fluid）。动力机械。， vol. 668, 2011, pp. 500-550)，证明了在超临界状态下，只有轧辊是近起点稳定的。
Abstract A linear and weakly nonlinear analysis of convection in a layer of shear-thinning fluids between two horizontal plates heated from below is performed. The objective is to examine the effects of the nonlinear variation of the viscosity with the shear rate on the nature of the bifurcation, the planform selection problem between rolls, squares and hexagons, and the consequences on the heat transfer coefficient. Navier’s slip boundary conditions are used at the top and bottom walls. The shear-thinning behaviour of the fluid is described by the Carreau model. By considering an infinitesimal perturbation, the critical conditions, corresponding to the onset of convection, are determined. At this stage, non-Newtonian effects do not come into play. The critical Rayleigh number decreases and the critical wavenumber increases when the slip increases. For a finite-amplitude perturbation, nonlinear effects enter in the dynamic. Analysis of the saturation coefficients at cubic order in the amplitude equations shows that the nature of the bifurcation depends on the rheological properties, i.e. the fluid characteristic time and shear-thinning index. For weakly shear-thinning fluids, the bifurcation is supercritical and the heat transfer coefficient increases, as compared with the Newtonian case. When the shear-thinning character is large enough, the bifurcation is subcritical, pointing out the destabilizing effect of the nonlinearities arising from the rheological law. Departing from the onset, the weakly nonlinear analysis is carried out up to fifth order in the amplitude expansion. The flow structure, the modification of the viscosity field and the Nusselt number are characterized. The competition between rolls, squares and hexagons is investigated. Unlike Albaalbaki & Khayat (J. Fluid. Mech., vol. 668, 2011, pp. 500–550), it is shown that in the supercritical regime, only rolls are stable near onset.
宇宙放射性碳和太阳活动。
DOI：
--
发表时间：
2010
期刊：
J. Physical Society Japan, Suppl. 78
影响因子：
--
作者：
K. Masuda;K. Nagaya;H. Miyahara;Y. Muraki;T. Nakamura
通讯作者：
T. Nakamura
瑞利弱非线性理论的有效性范围
影响因子：
1.7
作者：
Gyoko Nagayama;Kosuke Yanai;Takaharu Tsuruta;S. C. Generalis and K. Fujimura
通讯作者：
S. C. Generalis and K. Fujimura