Solutions of special type describing the three dimensional thermocapillary flows with an interface

Abstract

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.