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In this paper is estimated a special solution for solving thermal diffusion equations, that describe motion of binary mixture in a flat layer. If Reynolds number is small, these equations are reduced to some easier inverse boundary problems. For solving these problems are used Laplace transformations. Temperatures are setted on the walls and velocity field is found. Analytical solution for stationary mode and numerical results for non-stationary regime are presented and is found, when boundary conditions stabilize with increasing time, then all velocity components and temperature go to stationary ones.

Solution of Non-stationary Motion of Binary Mixture by Laplace Transformation