A bifurcation study of natural convection in porous media with internal heat sources: the non-Darcy effects
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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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 01/2008; 32(8):1740-1747. · 1.60 Impact Factor
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ABSTRACT: The objective of this study is the comparison between the model of Darcy-Brinkman and the Navier-Stokes equations modified, in the case of the natural convection. The study is made in a porous vertical square cavity saturated by a Newtonian fluid. A cylindrical heat source maintained at a uniform heat flux is introduced into porous medium. The equations which describe the thermal transfer and the hydrodynamic flow of the two models are solved numerically by means of the software package Femlab 3.2 based on the finite element method. The results obtained are in the form of average kinetic energy per unit mass, the local and the average Nusselt numbers, the pressure and the viscous force per unit area.Leonardo Journal of Sciences. 01/2008;
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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 - INT J THERM SCI. 01/2008; 47(10):1316-1331.