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

Journal Article · Tue Jan 31 23:00:00 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), Journal Name: Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States) Vol. 117:1; ISSN 0022-1481; ISSN JHTRAO
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420200* -- Engineering-- Facilities
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& Techniques
420400 -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CONVECTION
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
FILMS
FLUIDS
HEAT FLUX
HEAT TRANSFER
HEAT TRANSFER FLUIDS
MAGNETIC FIELDS
MASS TRANSFER
MATHEMATICAL MODELS
MATHEMATICS
NATURAL CONVECTION
NAVIER-STOKES EQUATIONS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
TEMPERATURE DISTRIBUTION
THIN FILMS