The transfer processes in a plane layer of viscous incompressible fluid with free boundaries are studied under conditions of action of the additional tangential stresses on these boundaries. Modeling of the fluid flows is carried out on the basis of the exact solutions of the Navier-Stokes equations with use of the numerical algorithms to find the velocity field and position of the free boundaries. The problem of finding of temperature distribution of fluid in the infinite layer leads to numerical solution of the heat transfer equation in a rectilinear domain with movable boundaries. The different types of the "smooth" boundary conditions on the "lateral walls" are investigated.

Key words: deformation of plane layer, thermocapillary forces, free boundaries, tangential stresses, heat transfer, numerical algorithms.