Solutions of special type describing the three dimensional thermocapillary flows with an interface |
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Authors: | Olga N Goncharova Oleg A Kabov Vladislav V Pukhnachov |
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Affiliation: | 1. Altai State University, Faculty of Mathematics, Department of Differential Equations, Prosp. Lenina 61, Barnaul 656049, Russia;2. Institute of Thermophysics, Russian Academy of Sciences, Lavrentyev Prosp. 1, Novosibirsk 630090, Russia;3. Heat Transfer International Research Institute of Universite Libre de Bruxelles and Institute of Thermophysics of Russian Academy of Sciences, Av. F.D. Roosevelt 50, B-1050 Bruxelles, Belgium;4. Universite Libre de Bruxelles, Chimie-Physique EP Microgravity Research Center, Av. F.D. Roosevelt 50, B-1050 Bruxelles, Belgium;5. Centre of Smart Interfaces, Technische Universitaet Darmstadt, Petersenstrasse 32, Darmstadt 64287, Germany;6. Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, Lavrentyev Prosp. 15, Novosibirsk 630090, Russia;7. Novosibirsk State University, Faculty of Mechanics and Mathematics, ul. Pirogova 2, Novosibirsk 630090, Russia |
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Abstract: | The convective fluid flows with an interface are modeled using the classical Oberbeck–Boussinesq model of convection. The three dimensional solutions for the infinite domains with fixed heat-insulated boundaries and with the interface under action of a longitudinal temperature gradient are studied. Construction of the solutions for the flows of two immiscible fluids in a channel with a rectangular cross-section is carried out using a complete problem statement. The kinematic and dynamic conditions are prescribed at the interface. The additional condition of continuity of the tangential velocities, the conditions of continuity of temperature and of the thermal fluxes are assumed to be fulfilled on the interface. In the present paper the fluid flows are studied in the stationary case under conditions of gravity and microgravity. To investigate this problem numerically an iteration algorithm is introduced. This algorithm is based on a finite difference scheme (the alternating direction method) and it allows to find all the components of velocity for both phases and temperature distributions. The examples of flows which can be characterized as a combination of the translational and progressively rotational types of motion are presented. |
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