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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v11.i3.70
pages 305-321

Vortex Instability of Mixed Convection Boundary Layer Flow Adjacent to a Nonisothermal Horizontal Surface in a Porous Medium with Variable Permeability

Ahmed M. Elaiw
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt
Fouad S. Ibrahim
Department of Mathematics, University College, Umm Al-Qura University, Makkah, Saudi Arabia; Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

ABSTRACT

A linear stability theory is used to analyze the vortex instability of mixed convection boundary layer flow in a saturated porous medium adjacent to a horizontal surface, where the wall temperature is a power function of the distance from the origin. The permeability of the medium is assumed to vary exponentially with distance from the wall. The entire mixed convection regime is divided into two regions. The first region covers the forced convection-dominated regime, which is characterized by the parameter ξf = Rax/Pex3/2 and the eigenvalue Peclet number. The second region covers the free convection-dominated regime, which is characterized by the parameter ξn = Pex/Rax2/3 and the eigenvalue Rayleigh number. The two solutions provide results that cover the entire mixed-convection regime from pure forced- to pure free-convection limit. Velocity and temperature profiles as well as local Nusselt number for the base flow are presented for the uniform permeability (UP) and variable permeability (VP) cases. The critical Peclet and Rayleigh numbers and the associated wave numbers for both the UP and VP cases are obtained. It is found that the VP effect tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance.


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