A bifurcation study of natural convection in porous media with internal heat sources: the non-Darcy effects

Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4; Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6
International Journal of Heat and Mass Transfer (Impact Factor: 2.52). 01/1998; DOI: 10.1016/S0017-9310(97)00127-0

ABSTRACT Multiplicity features of natural convection flow in porous media, generated and sustained by a uniform internal heat source are investigated. The flow, in a two-dimensional enclosure, is described by the Brinkman's extension of the Darcy equation. No-slip boundary conditions are used. The focus is on the role of the Brinkman viscous term in influencing the location of singular points. The behavior of the system is regulated by two control parameters, the Rayleigh number (the dynamic parameter) and the Darcy number. The singular solutions are constructed using algorithms from bifurcation theory. Multiple solutions consisting of symmetric and nonsymmetric solution branches, are revealed as the control parameters change. The range of the Rayleigh number for which a unique solution exists is enlarged when the Darcy number is increased.

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