Bernard-Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Layer with Deformable Free Surface
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2013-08-06T06:52:23Z
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Abstract
The linear stability of Bernard-Marangoni convection in a two-layer system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity is studied. The upper fluid surface, free to atmosphere is considered to be deformable. Flow in the porous medium is assumed to be governed by Darcy’s law; the Beavers-Joseph condition is applied at the interface between the two layers. The boundaries are considered to be rigid, however permeable, and insulated
to temperature perturbations. The eigen value problem is solved using a regular perturbation
technique with wave number a as perturbation parameter. It is found that the Crispation number,
Bond number, depth of the relative layers, mechanical and thermal anisotropy parameters have a profound effect on the stability of the system. Decreasing the Crispation number and mechanical anisotropy parameter and increasing the Bond number and thermal anisotropy parameter leads to
stabilization of the system. Also, the effect of the ratio of the fluid to porous layer thickness along with the other various physical parameters on the control of convection is analysed in detail.
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Bernard-Marangoni Convection, Gangadharaiah, Suma, Bernard-Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Layer with Deformable Free Surface