Mathematics & Physics 2015, 8(3), 260–272 УДК 517.532 Two-dimensional Motion of Binary Mixture such as Hiemenz in a Flat Layer Nemat B.Darabi∗ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 10.04.2015, received in revised form 05.05.2015, accepted 08.06.2015 This paper considers solution of thermal diffusion equations in a special type, which describes twodimensional motion of binary mixture in a flat channel. <...> Substituting this solution to equations of motion and heat and mass transfer equations results initial-boundary problems for unknown functions as velocity, pressure, temperature and concentration. <...> If assume that Reynolds number is small (creeping motion),these problems become linear. <...> In addition, they are inverse since unsteady pressure gradient is also desired. <...> Solution of the problem is obtained by using trigonometric Fourier series, which are rapidly convergent for any time value. <...> Exact solution of the stationary and non-stationary problems is presented. <...> Such solutions 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. <...> This paper deals with unsteady and steady motions of a binary mixture in a flat channel with solid fixed walls. <...> First time such solutions for the stationary Navier-Stokes equations are considered by Hiemenz [2]. <...> In 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 stationary and non-stationary problems. ∗nematdarabi@gmail.com Siberian Federal University. <...> All rights reserved c – 260 – Nemat B.Darabi Two-dimensional Motion of Binary Mixture such as Hiemenz in a Flat Layer 1. <...> If C is concentration (mass fraction) of component 1, then concentration of component 2 is 1−C. We assume that the pressure gradient causes no significant molecular motion between mixture’s components relative to each other, and it is also assumed that deviations of temperature T, concentration C, and pressure p are small from the average values, and density is a function of T <...>