On Stability Analysis of Soret Convection Within a Horizontal Porous Layer
The Soret effect, which describes the diffusion of solute along a temperature gradient, within a horizontal layer heated from below has attracted considerable interest in pattern formation and hysteresis phenomena. In such convective configuration, negative Soret coefficient, which causes the heavier component to migrate towards the hot wall, induces a variety of pattern formation phenomena. Multiple steady/oscillatory states, subcritical flows, standing/travelling waves and Hopf bifurcations are some examples of these phenomena that have been observed experimentally and predicted numerically. A literature review showed that great interest is paid to porous or fluid binary infinite horizontal layer with stress-free boundaries. However, in practical situations, experiments are usually conducted within a finite aspect ratio layer, with non-slip boundaries. Since this type of problem remains intractable analytically and difficult to tackle with the classical analytical methods, it has received less attention. The motivation of the present study is driven by the fact that, in practical situations, the temperature is usually varying along the heated or cooled walls. Therefore, the constant flux boundary conditions are the best approach to study the convective phenomena related to industrial or natural problems. In a laboratory, it is easy to heat a wall with a constant heat flux. However, cooling with constant heat flux could be achieved when the wall materials are poorly heat conductive.
KeywordsRayleigh Number Hopf Bifurcation Linear Stability Analysis Critical Rayleigh Number Constant Heat Flux
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