Two-dimensional motion of binary mixture such as Hiemenz in a flat layer

This paper considers solution of thermal diffusion equations in a special type, which describes two-dimensional 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.