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Journal of Porous Media
Fator do impacto: 1.49 FI de cinco anos: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Imprimir: 1091-028X
ISSN On-line: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v15.i1.10
pages 1-10

THERMAL INSTABILITY IN SUPERPOSED POROUS AND FLUID LAYERS IN THE PRESENCE OF A MAGNETIC FIELD USING THE BRINKMAN MODEL

Hanadi Banjer
Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 6337, Makkah, Saudi Arabia
Abdullah A. Abdullah
Department of Mathematical Sciences, Umm Al-Qura University, Makkah 24382, Saudi Arabia

RESUMO

Thermal convection in a two-layer system consisting of a horizontal fluid layer overlying a layer of porous medium saturated with the same fluid, with uniform heating from below and in the presence of a vertical magnetic field, is investigated. The flow in the porous medium is assumed to be governed by the Brinkman model. The onset of convection is seen to have a bimodal nature in which convection may be dominated by the porous medium or by the fluid, depending on the depth of the relative layers and the strength of the magnetic field. Numerical results are obtained for different values of the parameter d (= depth of fluid layer/depth of porous layer) and for different values of the magnetic parameter Q. A comparison between the critical Rayleigh numbers in Brinkman and Darcy models reveals that in the absence of a magnetic field, the critical Ram for the Brinkman model is always greater than the corresponding one in the Darcy model; however, in the presence of a magnetic field when d ≥ 0.33, the critical Ram for the Darcy model is larger.