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: 2.52). 01/1998; 41(2):383-392. 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.

  • Source
    [Show abstract] [Hide abstract]
    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 · 2.56 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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 · 2.08 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a combined experimental and numerical study on natural convection in open-celled metal foams. The effective thermal conductivities of steel alloy (FeCrAlY) samples with different relative densities and cell sizes are measured with the guarded-hot-plate method. To examine the natural convection effect, the measurements are conducted under both vacuum and ambient conditions for a range of temperatures. The experimental results show that natural convection is very significant, accounting for up to 50% of the effective foam conductivity obtained at ambient pressure. This has been attributed to the high porosity (ε>0.9) and inter-connected open cells of the metal foams studied.Morphological parameters characterizing open-celled FeCrAlY foams are subsequently identified and their cross-relationships are built. The non-equilibrium two-equation energy transfer model is employed, and selected calculations show that the non-equilibrium effect between the solid foam skeleton and air is significant. The study indicates that the combined parameter, i.e., the porous medium Rayleigh number, is no longer appropriate to correlate natural convection by itself when the Darcy number is sufficiently large as in the case of natural convection in open-celled metal foams. Good agreement between model predictions and experimental measurements is obtained.
    International Journal of Heat and Mass Transfer 06/2005; 48(12):2452-2463. DOI:10.1016/j.ijheatmasstransfer.2005.01.002 · 2.52 Impact Factor