Non-stationary fluid flows in a free layer are investigated analytically and numerically under conditions of weightlessness. A special class of solutions of the Navier-Stokes equations is used to model the flows and layer deformations caused by inhomogeneous temperature distributions and additional tangential stresses acting on the free boundaries. Two-dimensional solutions are characterized by a linear dependence of the longitudinal component of velocity on longitudinal coordinate. Numerical algorithms are constructed in order to find the velocity field, position of free boundaries and temperature distribution.

Key words: non-stationary flows, thermocapillary forces, free boundaries, tangential stresses, exact solution, numerical solution.