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

Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6
International Journal of Heat and Mass Transfer (Impact Factor: 2.38). 01/1998; 41(2):383-392. DOI: 10.1016/S0017-9310(97)00127-0


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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    • "Also, a great number of published studies are related with the analysis of natural convection in square/rectangular enclosures, particularly , with differentially heated vertical walls via isothermal heaters and adiabatic horizontal walls. Some important numerical results can be found in the studies by Walker and Homsy [6], Bejan [7], Prasad and Kulacki [8], Beckermann et al. [9], Gross et al. [10], Lai and Kulacki [11], Goyeau et al. [12], Manole and Lage [13], Choi et al. [14], Mamou et al. [15] and Saeid and Pop [16]. Some studies have also been performed to investigate the effect of inclination on natural convection in inclined square/rectangular enclosures filled with porous media or viscous (non-porous) fluids [17] [18] [19] [20] [21] [22] [23] [24] [25]. "
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    ABSTRACT: A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure ϕ, which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θs and the aspect ratio A. The side wall inclination parameter θs is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A=0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle ϕ is more influential on heat transfer and flow strength than that of the side wall inclination angle θs. It is also found that a Bénard regime occurs around ϕ=90°, which depends on the inclination of the side wall, Rayleigh number and aspect ratio.
    International Journal of Thermal Sciences 10/2008; 47(10):1316-1331. DOI:10.1016/j.ijthermalsci.2007.10.018 · 2.63 Impact Factor
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    • "They employed the Galerkin finite-element technique to solve the coupled time-dependent heat transfer and fluid flow differential equations to predict the evolving behavior of flow and temperature distribution . Natural convection in porous media, generated and sustained by a uniform heat source was investigated by Choi et al. [15]. Singular solutions were constructed using algorithms from bifurcation theory. "
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    ABSTRACT: Natural convection heat transfer in metal foam strips, with internal heat generation, was investigated experimentally for two porosities. An estimate of the non-equilibrium temperature distribution was done by image processing of the thermal maps on both the surface and the inner region of the metal foam specimen. It was shown that heat transfer at natural convection in the strip of metal foam was increased drastically (up to 18-20 times for metal foam of 20 ppi) relative to the flat plate of the same overall dimensions. The heat transfer from ligaments of metal foam was estimated. (author)
    Experimental Thermal and Fluid Science 09/2008; 32(8):1740-1747. DOI:10.1016/J.EXPTHERMFLUSCI.2008.06.011 · 1.99 Impact Factor
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    International Journal of Heat and Mass Transfer 01/2000; 44(2):253-366. DOI:10.1016/S0017-9310(00)00117-4 · 2.38 Impact Factor
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