RESEARCH PAPERS: Natural and Mixed Convection

Natural Convection in an Inclined Fluid Layer With a Transverse Magnetic Field: Analogy With a Porous Medium

[+] Author and Article Information
P. Vasseur, M. Hasnaoui, E. Bilgen, L. Robillard

Ecole Polytechnique de Montréal, Mechanical Engineering Department, C.P. 6079, St. A, Montréal, P.Q. H3C 3A7 Canada

J. Heat Transfer 117(1), 121-129 (Feb 01, 1995) (9 pages) doi:10.1115/1.2822290 History: Received June 01, 1993; Revised September 01, 1993; Online December 05, 2007


In this paper the effect of a transverse magnetic field on buoyancy-driven convection in an inclined two-dimensional cavity is studied analytically and numerically. A constant heat flux is applied for heating and cooling the two opposing walls while the other two walls are insulated. The governing equations are solved analytically, in the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation. Solutions for the flow fields, temperature distributions, and Nusselt numbers are obtained explicitly in terms of the Rayleigh and Hartmann numbers and the angle of inclination of the cavity. In the high Hartmann number limit it is demonstrated that the resulting solution is equivalent to that obtained for a porous layer on the basis of Darcy’s model. In the low Hartmann number limit the solution for a fluid layer in the absence of a magnetic force is recovered. In the case of a horizontal layer heated from below the critical Rayleigh number for the onset of convection is derived in term of the Hartmann number. A good agreement is found between the analytical predictions and the numerical simulation of the full governing equations.

Copyright © 1995 by The American Society of Mechanical Engineers
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