Étude de la stabilité des écoulements des métaux liquides

Abstract

Heat and mass transfer are frequented in nature and industry: metallurgy, drying process, thermal isolation, and solar energy storage. In this study, convection heat and mass transfer in fluid medium are numerically studied with finite volume method. The geometry considered is a square enclosure with insulated and impermeable horizontal walls. The active vertical walls are maintained at constant temperature and concentration. Steady, conjugate natural convection flow in a square enclosure is considered. The left vertical wall of the enclosure is thick with a finite thermal conductivity, while the other three walls are taken to be of zero thickness. The enclosure is subjected to horizontal temperature gradient. The physical problem depends on seven parameters: the Rayleigh number Ra, the Prandtl number Pr, the wall to fluid thermal conductivity ratio Kr, wall thickness D, the wall to fluid thermal diffusivity ratio α*, Hartmann number Ha and its inclination angle φ . In the case where the magnetic field is neglected, the main focus is on examining the effect Rayleigh number, conductivity ratio and wall thickness on conjugate natural convection. A comparison with the particular isothermal wall case is also studied. The obtained results show that natural convection can be strength by the increase of both Rayleigh number and conductivity ratio, because of the increase of the effective temperature difference driving the flow. For low Rayleigh number and poor conducting wall (Kr=0.1), where the solid part is an insulated material and the thermal resistance is more important the average Nusselt number is approximately constant and having low values comparing with equal (Kr=1) and high (Kr=10) conducting wall, indicating that most of heat transfer is by heat conduction. For Ra>104 and Kr >0.5, the wall-fluid interface temperature is found to be quite non- uniform. This non uniformity tends to make the flow pattern in the enclosure asymmetric. In the case where the magnetic field is present, the enclosure is filled with liquid gallium. The main focus in this case is on examining the effect of both inclination angle and Hartmann numbers on fluid flow and heat transfer. The results show that for a given Ra, as the value of Hartmann number increases, convection is suppressed progressively and the rate of heat transfer is reduced in the enclosure. Convection mechanism is also affected by the direction of the magnetic field. It is found that the rate of convection heat transfer is more reduced with the x-direction of the magnetic field (inclination angle φ =0°). Also the results show that for poor conducting wall (Kr=0.1) where the convection is dominated by heat conduction, that the presence of a magnetic field is not important and its effect in this case can be neglected. Steady, double diffusion natural convection flow in the presence of a magnetic field in a square enclosure with partially active vertical wall and subjected to horizontal temperature and concentration gradients are also considered. The flow is driven by cooperating or opposite thermal and solutal buoyancies. The active location takes three positions in the left wall: top (T), middle (M) and bottom (B). The physical problem depends on five parameters: thermal Rayleigh number, Prandtl number, Schmidt number and buoyancy forces ratio (N=1). In the first case the main focus is on examining the effect of both Rayleigh and Hartmann numbers on fluid flow and heat and mass transfer. In the absence of a magnetic field the obtained results show that the increase of Rayleigh number (Rat) leads to enhance heat and mass transfer rates. Furthermore it is found that for a given Rat, the presence of a magnetic field suppresses convection mechanism by reducing flow velocity and the rate of heat transfer. In the second case, the main focus of the study is on examining the effect of Rayleigh number on thermosolutal natural convection flow. The obtained results show that the increase of Rat leads to enhance heat and mass transfer rates. The flow is steady at: Rat<7.104 for (T)and Rat<6.105 for (M). The unsteady flow appears by the formation of regular (periodic)oscillations of particles in the flow when Rat=7.104 for top and Rat=6.105 for middle. While for case bottom, the flow is steady for high Rayleigh number (Rat=108). The fast Fourier transformation has been used to determine the dominant period of oscillations. Which is (1/20) for (T) and (1/7.43) for (M).