Natural convection in an inclined fluid layer with a transverse magnetic field. Analogy with a porous medium

Journal Article · Wed Feb 01 00:00:00 EST 1995 · Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States)

DOI:https://doi.org/10.1115/1.2822290· OSTI ID:6765218

Vasseur, P; Hasnaoui, M; Bilgen, E; Robillard, L ^[1]

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1. Ecole Polytechnique de Montreal (Canada)

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. 23 refs., 8 figs.

• OSTI ID: 6765218
• Journal Information: Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States), Vol. 117:1; ISSN 0022-1481
• Country of Publication: United States
• Language: English

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MAGNETIC FIELDS
MATHEMATICAL MODELS
NATURAL CONVECTION
NAVIER-STOKES EQUATIONS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
TEMPERATURE DISTRIBUTION
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