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Stability of Marangoni Convection in a Composite Porous-Fluid with a Boundary Slab of Finite Conductivity

Norihan M. Arifin1, Ioan Pop2
Department of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia,43400 UPM Serdang, Selangor, Malaysia
Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

Fluid Dynamics & Materials Processing 2009, 5(2), 149-160. https://doi.org/10.3970/fdmp.2009.005.149

Abstract

A linear stability analysis is used to investigate the onset of Marangoni convection in a three-layer system comprising an incompressible fluid saturated porous layer over which lies a layer of the same fluid and below which lies a solid layer. The lower boundary is subjected to a fixed heat flux, while the upper free surface of the fluid is non-deformable. At the interface between the fluid and the porous layer, the Beavers-Joseph slip condition is used and the Darcy law is employed to describe the flow in the porous medium. The asymptotic analysis of the long-wavelength is performed and the results are compared with those for the case of porous-fluid layer system. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability are studied. It is found that the solid plate with a higher relative thermal conductivity or higher thickness ratio tends to stabilize the system.

Keywords

Linear stability, Marangoni convection, Porous medium, Regular Perturbation Method.

Cite This Article

Arifin, N. M., Pop, I. (2009). Stability of Marangoni Convection in a Composite Porous-Fluid with a Boundary Slab of Finite Conductivity. FDMP-Fluid Dynamics & Materials Processing, 5(2), 149–160.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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