Etude numérique de la convection thermocapillaire et thermogravitaire dans les milieux confines sous l'action d'un champ magnetique

Abstract

When a free surface is present in free convection liquid flow, variations of surface tension, due to the temperature gradient, can induce motion within the fluid. Such flow is known either as thermocapillary flow or Marangoni convection. Besides convective flows driven by both buoyancy and surface tension play an important role in the growth of crystals and materials processing, especially in small-scale and low gravity hydrodynamics. This work concerns a convective instabilities study, in the case of a horizontal Bridgman configuration filled with a low Prandtl number material. The problem is considered by combining the buoyancy and thermocapillary convection flow of an electrical conducting fluid in an enclosure under an externally imposed time-independent uniform magnetic field. Relative influence, of thermocapillary convection and buoyancy driven convection on this process and of an external magnetic field witch with independently varying the orientation and the magnitude of the applied magnetic field are respectively investigated and studied. The top horizontal surface of the rectangular cavity is assumed to be free and the bottom one insulated, whereas the left vertical wall is cold and the right is uniformly hot. The equations are non-dimensionalized and solved numerically by a finite volume methode together with a line by line technique. An appropriate ( for liquid metal and semi-conductor melts) small Prandtl number (Pr =0.054) is chosen. Effects of magnetic field with those of the buoyancy and thermocapillary convection are presented graphically in terms isotherms, streamline, velocity and temperature at the free surface plots. Physical parameters versus heat transfer rate, from the cold and heated surface of the enclosure, is also depicted for some values of the Marangoni, Rayleigh and Hartmann numbers, as respectively Ma =0.0 to 10000, Ra =0.0 to 100000 and Ha =0.0 to 130