Fifth International Conference on Thermal Engineering: Theory and Applications May 10-14, 2010, Marrakesh, Morocco * Corresponding author. Tel.: +216 98 549 074 E-mail: jbelii_r@hotmail.fr 1 On the effects of Uniform Magnetic Field on Natural Convection in Fluid- Saturated Porous Media Enclosures R. Djebali a, *, M. El Ganaoui b , H. Sammouda a and B. Pateyron b a LETTM, Univ. Tunis El Manar, Tunisia b UMR 6638, SPCTS, Univ. Limoges, France Abstract We investigate the behaviour of fluid in porous media under moderate magnetic field strength using a LBGK model. It was found that, in the chosen ranges of parameters, the flow is stabilized with increasing the magnetic field strength monitored by the Hartmann number. The flow pattern is forced to take a conductive character, as well with increasing the Hartmann number as with decreasing the Darcy number. Further on it is shown that the medium porosity has no remarkable effect on dynamic and thermal structures in the presence of magnetic field;. Numerically, it was observed that a very essential dependence of heat transfer and fluid flow on magnetic field. Additionally, the BGK approach is found to be a serious tool for describing the fluid physics with both accuracy and simplicity, compared to classical solvers and methods used in CFD. Keywords: Natural convection flow, Uniform magnetic field, parametric study, flow stabilization. Nomenclature H Porous medium size, m T Temperature of the flow, K p Pressure, Pa ui Velocity components, m/s xi System axis coordinates, m Cp Specific heat at constant pressure, J/KgK ek Discrete lattice vector B Magnetic field strength, T g Gravity acceleration, m/s 2 Greek Symbols  Dynamic viscosity, Pa.s  Electrical conductivity of the fluid, S  Thermal expansion coefficient, K -1 Œ Thermal conductivity of the fluid, W/mK ı Kinetic viscosity, m 2 /s  Thermal diffusivity, m 2 /s Subscripts ∞ Reference value e effective value Exponents eq Equilibrium part Notations ∂ /∂t Partial time derivative 1. Introduction Transport phenomena in porous media is one of the most interesting fields in engineering research; starting from heat and mass transfer, it cover a vast variety of applications including thermal insulation, solar energy collectors, heat exchangers, petroleum reservoir operations, food processing and so on Several numerical works on convective heat transfer in porous media enclosures have been reported for different physical formulation and geometric models with various boundary conditions [1], [2] and [3]. Most of these studies are interested to the Darcian effects, some others study the effects of the Brinkman exetension or the Forchheimer formulation of the non-linear drag for high infiltration velocities in porous media under the only gravity effect. Moreover, very little efforts have been reported on natural convection in porous media under external magnetic force. However, including the effects of external magnetic fields exhibit s particularly different behaviors for the flow patterns and isotherms, and demonstrates new ways for stabilizing/destabilizing convective flows. The objective of the present study is to explore the flow behaviour, within an enclosure having differentially heated vertical walls, in presence of external uniform magnetic field with changing a several monitoring parameters in (physical and geometrical) in a wide ranges. The Rayleigh number, Ra, the Darcy number, Da, the medium porosity and the Hartman number Ha. The numerical solution is obtained with the help of the lattice Boltzmann method.