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Abstract

This paper investigates the onset of thermal convection in a bounded system comprising a horizontal viscous fluid layer of infinite extent overlying an anisotropic horizontal permeable layer saturated with the same fluid. It is assumed that this system is heated from below and cooled from above in the presence of internal heat generation. It is also assumed that the material parameters, such as viscosity and thermal conductivity differ between the layers, and that the Brinkman model is used to describe the flow in the porous region. An extensive linear stability analysis has been performed with an aim to determine the key factors having a significant bearing on stabilizing the convection. For this, the governing non-dimensional momentum and thermal PDEs, after carrying out the usual stability manipulations, have been solved using the Galerkin method, subject to a host of matching conditions at the fluid-porous interface together with no-slip conditions at the bounding upper and lower rigid walls. A novelty of this paper worth mentioning has been the use of stress-jump condition at the interface separating the two layers. Besides the usual dominating Rayleigh number, due to the buoyancy forces, there arises another Rayleigh number based on heat generation. It has been shown that all-important critical Rayleigh number, the key determinant of the instability criteria, depends on a host of controlling parameters such as viscosity ratio, thermal conductivity ratio, anisotropy and stress-jump, besides a few others. The impact of these important parameters on this Rayleigh number has been illustrated extensively to bring out some salient stability features. It has been found that the effect of stress-jump parameter is to destabilize the system while, on the other hand, the thermal conductivity ratio parameter provides stability.

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