Theoretical research has been devoted to the study of binary metal melts behavior in a thin capillary. Earlier it has been found experimentally that unusually significant and quick redistribution of melts components takes place along capillary after the cooling. Numerical simulation of concentration-induced convection has been carried out to explain these experimental data. Two-component melt of both liquid metals filling vertical thin capillary with non-uniform temperature distribution on the boundaries is considered. It is assumed that the condition of absolute non-wetting is valid on the sidewalls. Because of this effect there is a free surface on vertical boundaries, where thermocapillary force is appeared due to the external longitudinal temperature gradient. It makes to move liquid elements at a big distance, compared with axial size of capillary. Effects of adsorption-desorption on the surface, thermal and concentration-capillary forces, convective motion in a volume and diffusion generate the large-scale circulation. This process includes the admixture carrying-out on the surface in the more hot higher part of the channel, its following transfer down along the boundary due to the thermocapillary force and its return in the volume over the desorption in the lower part of capillary. Intensity of motion and processes of adsorption-desorption on the free boundary have the decisive influence upon the formation of concentration fields and speed of components redistribution. Thus, one of the possible mechanisms of longitudinal division on components of liquid binary mixtures in thin channels has been demonstrated.