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Browsing Paper Publication by Author "Gangadharaiah, Y. H."

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    Bernard-Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Layer with Deformable Free Surface
    (2013-08-06T06:52:23Z) Gangadharaiah, Y. H.; Suma, S.P
    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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    Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium
    (2012-01-25T07:56:38Z) Shivakumara, I. S.; Suma, S. P.; Indira, R.; Gangadharaiah, Y. H.
    Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers–Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value ofmechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.
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    Throughflow Effects on Penetrative Convection in Superposed Fluid and Porous Layers
    (2012-07-03T08:17:14Z) Suma, S. P.; Gangadharaiah, Y. H.; Indira, R.; Shivakumara, I. S.
    The effect of vertical throughflow on the onset of penetrative convection simulated via internal heating in a two-layer system in which a layer of fluid overlies and saturates a layer of porous medium is studied. Flow in the porous medium is governed by Forchheimer-extended Darcy equation, and Beavers–Joseph slip condition is applied at the interface between the fluid and the porous layers. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The eigenvalue problem is solved using a regular perturbation technique with wave number as a perturbation parameter. The ratio of fluid layer thickness to porous layer thickness, ζ , the direction of throughflow, and the presence of volumetric internal heat source in fluid and/or porous layer play a decisive role on the stability characteristics of the system. In addition, the influence of Prandtl number arising due to throughflow is also emphasized on the stability of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and vertical throughflow so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible.