Mathematics & Physics 2016, 9(3), 279–287 УДК 517.532 On One Two-dimensional Binary Mixture’s Motion in a Flat Layer Nemat Darabi∗ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Hamid Malah† Institute of Applied Mathematics and Mechanics Peter the Great St. Petersburg Polytechnic University Polytechnicheskaya, 29, St.Petersburg, 195251 Russia Received 10.04.2016, received in revised form 10.05.2016, accepted 20.06.2016 In this paper is estimated a special solution for solving thermal diffusion equations, that describe motion of binary mixture in a flat layer. <...> When Reynolds number (Re → 0) is small, it is possible to simplify these equations to some easier problems. <...> In solving process to find pressure it is necessary to solve an inverse problem. <...> Answers for non-stationary regime are presented in trigonometric Fourier series. <...> Introduction Exact and approximate solutions of hydrodynamics equations are widely used for mathematical modeling of many processes in the chemical and petrochemical technology [1], including convection of mass processes and heat transfer, and various natural phenomena [2]. <...> This paper deals with the unsteady motions of a binary mixture in a flat layer with solid fixed walls. <...> Solution of the thermodiffusion convection equations is sought in a special form: one velocity component is a linear function along the length of channel, and the temperature and concentration are quadratic functions along this coordinate. <...> First time such solutions for the stationary Navier-Stokes equations are considered by Hiemenz [3]. <...> A review for similar type of exact solutions is available in [4]. <...> The solution was used to describe the flow of a viscous fluid on a plane taking into account the adherence on it [5]. <...> If in Himenz solution, pressure depends only on one spatial variable, then for the corresponding systems of equations it is necessary to solve direct problem [9]. <...> All rights reserved c – 279 – Nemat Darabi, Hamid Malah On One Two-dimensional Binary Mixture’s Motion . this case, the problem is reduced to a series of one-dimensional inverse problems for parabolic equations (thermal conductivity). <...> For creeping motions (Reynolds number Re ≪ 1) is found exact solution of non-stationary problems <...>