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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

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

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v8.i2.100
pages 237-246

Effect of Variable Permeability and Viscous Dissipation on a Non-Darcy Natural-Convection Regime with Thermal Dispersion

I. A. Hassanien
Department of Mathematics, Faculty of Science, Assiut University, Assiut, 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
Gh. M. Omer
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

ABSTRACT

The effect of variable permeability on non-Darcy natural-convection flow along an isothermal vertical wall embedded in a saturated porous medium is initiated. The flow field is divided into a non-Darcy regime G 0, an intermediate regime G = 0(1), and a limit Darcy regime G → ∞ using the inertia buoyancy scales. Thermal dispersion effects are also taken into consideration. The effect of viscous dissipation increases as we move from a non-Darcy to a limit Darcy regime. The effect of viscous dissipation in non-Darcy, intermediate, and limit Darcy regimes is studied with and without thermal dispersion for uniform and variable permeability. The results show a significant decrease in the heat transfer rate with the inclusion of viscous effect. It is seen that as the value of the dispersion parameter increases, the effect of viscous dissipation increases in all three regimes and the percentage decrease in the value of Nu/Rax1/4 increases with the value of G.


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