2000 , Volume 5, № 2, p.14-25

The steady gravitational-thermocapillary convection in semicircular regions with free surfaces is considered. Cases when both mechanisms of the convection (gravity and thermocapillary) play an essential role are analyzed. Two models of the convection are used: the first one is the classical Oberbeck\,-\,Boussinesq model and the second model is the new model for description of the convection at low gravity forces, in small domains and fast changing temperature fields. The velocity field in the new model is not a solenoidal vector. This paper presents the results of calculations of convective flows in the domains with free boundaries at the microgravity forces typical of a space orbital laboratory. Numerical solutions are obtained for a range of Prandtl number and at different Marangoni and Grashof numbers. Velocity and temperature fields are presented. Analysis of conditions of applicability of both models is given.

*35R35 Free boundary problems for PDE

65N06 Finite difference methods

76R10 Free convection