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首页> 外文期刊>Transport in Porous Media >Influence of Chemical Reaction on Stability of Thermo-Solutal Convection of Couple-Stress Fluid in a Horizontal Porous Layer
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Influence of Chemical Reaction on Stability of Thermo-Solutal Convection of Couple-Stress Fluid in a Horizontal Porous Layer

机译：化学反应对水平多孔层中耦合应力流体热对流稳定性的影响

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We consider the onset of thermo-solutal convection in a couple-stress fluid-saturated anisotropic porous medium, where the chemical equilibrium on the bounding surfaces and the solubility of the dissolved components depend on temperature. The entire study has been spilt into two parts: (ⅰ) linear stability analysis (ⅱ) weakly non-linear stability analysis. Stationary case of linear stability analysis is discussed for two modes of bounding surfaces (a) realistic bounding surfaces i.e. Rigid-Rigid and Rigid-Free (R/R and R/F), (b) non-realistic bounding surfaces i.e. Free-Free (F/F). Howsoever, investigation of oscillatory state and weakly non-linear stability are restricted to F/F case. Galerkin method is used to solve the eigenvalue problem for R/R and R/F cases, whereas, exact solutions are obtained for F/F case. A comparative study among flow stability for above different cases is made as function of ratio of viscosities (i.e., couple-stress viscosity to fluid viscosity which is defined as couple-stress parameter, (C)) and effective chemical reaction (i.e. chemical reaction parameter, (x)). It has been found that increasing viscosity of the couple-stress fluid, in terms of increasing C, increases flow stability in all three cases, but among all cases its stabilization effect for R/R is maximum. However, in the absence of couple-stress parameter the maximum stability of flow is observed for F/F. Apart from this, the chemical reaction stabilizes the flow for all the three cases. Furthermore, stability analysis for F/F case indicates that couple-stress parameter stabilizes the system in all modes (stationary, oscillatory and finite amplitude) of convection.Damkoehler number (x) is found to delay the stationary convection, however, it speeds up the onset of oscillatory convection. The non-linear theory based on truncated representation of Fourier series method predicts the occurrence of sub-critical instability in the form of finite amplitude motion. The effect of C and x on heat and mass transfer is also examined.
机译：我们考虑了在偶应力流体饱和各向异性多孔介质中热固对流的开始，其中边界面上的化学平衡和溶解组分的溶解度取决于温度。整个研究分为两个部分：（ⅰ）线性稳定性分析（ⅱ）弱非线性稳定性分析。讨论了两种边界表面模式的线性稳定性分析的平稳情况（a）实际边界表面，即刚性-刚性和自由刚性（R / R和R / F），（b）非现实边界表面，即自由-自由（F / F）。但是，对振动状态和弱非线性稳定性的研究仅限于F / F情况。 Galerkin方法用于解决R / R和R / F情况的特征值问题，而对于F / F情况则获得了精确的解。对上述不同情况下的流动稳定性进行了比较研究，该粘度与粘度比（即耦合应力粘度与流体粘度，定义为耦合应力参数（C））和有效化学反应（即化学反应参数）的函数有关， （X））。已经发现，在三种情况下，就增加C而言，增加偶合应力流体的粘度都会增加流动稳定性，但是在所有情况下，其对R / R的稳定作用都是最大的。但是，在没有耦合应力参数的情况下，对于F / F可以观察到最大的流动稳定性。除此之外，这三种情况下的化学反应都能稳定流量。此外，对F / F情况的稳定性分析表明，耦合应力参数可在所有对流模式（平稳，振荡和有限振幅）下使系统稳定，但发现Damkoehler数（x）会延迟固定对流，但会加快速度振荡对流的开始。基于傅立叶级数方法截断表示的非线性理论以有限振幅运动的形式预测了亚临界不稳定的发生。还检查了C和x对传热和传质的影响。

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