Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium
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Date
2012-01-25T07:56:38Z
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Abstract
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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Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium, I. S. Shivakumara, S. P. Suma, R. Indira, Y. H. Gangadharaiah, National Journal