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1.
Boundary domain integral method for the study of double diffusive natural convection in porous media
Janja Kramer Stajnko, Renata Jecl, Leopold Škerget, 2007, original scientific article

Abstract: The main purpose of this paper is to present a boundary domain integral method(BDIM) for the solution of natural convection in porous media driven by combining thermal and solutal buoyancy forces. The Brinkman extension of the classical Darcy equation is used for the momentum conservation equation. The numerical scheme was tested on a natural convection problem within a square porous cavity, where different temperature and concentration values are applied on the vertical walls, while the horizontal walls are adiabatic and impermeable. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared withpublished work. There is a good agreement between those results obtained using the presented numerical scheme and reported studies using other numerical methods.
Keywords: double diffusive natural convection, porous medium, velocity-vorticity formulation, Brinkman extended Darcy formulation, boundary domain integrated method
Published: 31.05.2012; Views: 1119; Downloads: 57
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2.
Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavity
Renata Jecl, Leopold Škerget, 2003, original scientific article

Abstract: The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated.The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the non-Darcy viscous effects. The governing equations are transformed by the velocity-vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many non-Newtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtainedin terms of a modified Rayleigh number Ra*, Darcy number Da, and the non-Newtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium.
Keywords: natural convection, non-Newtonian fluid, porous medium, cavity flow, boundary element method, boundary domain integral method
Published: 01.06.2012; Views: 982; Downloads: 58
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