Abstract
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, \((\chi )\)). 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.Damkohler number \((\chi )\) 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 \(\chi \) on heat and mass transfer is also examined.
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