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Couple stress effects on the stability of three-component convection-diffusion in a porous layer

机译:对多孔层中三分对流扩散的稳定性的夫妇应力影响

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In this study, the stability (linear and weak nonlinear) of triple-diffusive convection in a couple stress fluid-saturated porous layer has been studied. A normal mode analysis yields an exact dispersion equation of fourth degree, and the criterion for the onset of stationary and oscillatory convection is obtained accordingly. The numerical computations are carried out for diffusivity elements experimentally determined for an aqueous NaCl-KCl-Sucrose system. Contrary to the double-diffusive couple stress fluid system, it is found that (ⅰ) oscillatory convection occurs even if the diffusivity ratios are greater than unity and (ⅱ) a disconnected heart-shaped oscillatory neutral curve exists for certain choices of physical parameters, demonstrating the requirement of three critical values of Darcy-Rayleigh number to specify the linear instability criteria. The impact of a couple stress parameter on some of these unusual behaviors is emphasized. The cubic Landau equations are derived by performing a weak nonlinear stability analysis and the stability of stationary and oscillatory bifurcating solutions is discussed. The heat and mass transfer for stationary and oscillatory convection modes is presented, and the influence of the couple stress parameter on the same is analyzed.
机译:在本研究中,研究了在耦合应力流体饱和多孔层中的三重扩散对流的稳定性(线性和弱非线性)。正常模式分析产生了第四度的精确色散方程,并且相应地获得了静止和振荡对流开始的标准。对实验确定的NaCl-Kcl-蔗糖系统进行实验确定的扩散元素进行数值计算。与双扩散夫妇应激流体系统相反,发现(Ⅰ)即使扩散比率大于单位,也发生振荡对流,并且存在断开的心形振荡中性曲线,用于某些物理参数的选择,展示了达西瑞利号码三个临界值的要求,以指定线性不稳定标准。强调了几个压力参数对一些不寻常行为的影响。通过执行弱的非线性稳定性分析来推导立方Landau方程,并讨论了静止和振动分叉解决方案的稳定性。提出了用于静止和振荡对流模式的热量和质量传递,分析了相同的耦合应力参数的影响。

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