Mathematics & Physics 2016, 9(1), 48-59 УДК 536.25 Modeling of Two-layer Fluid Flows with Evaporation at the Interface in the Presence of the Anomalous Thermocapillary Effect Olga N.Goncharova∗ Ekaterina V. Rezanova† Altai State University Lenina, 61, Barnaul, 656049 Russia Received 02.10.2015, received in revised form 16.12.2015, accepted 20.01.2016 Stationary convective flows of two immiscible viscous incompressible fluids (liquid and gas) under action of the transverse gravity field and longitudinal temperature gradient along the interface are studied analytically. <...> Mathematical model of the fluid flows with the effects of evaporation at the interface is based on exact solutions to the Navier-Stokes equations in the Oberbeck-Boussinesq approximation. <...> The effects of the thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. <...> The obtained solutions are used to model the flows in the two-layer gas-liquid system in the case when a liquid exhibits the anomalous thermocapillary effect. <...> Examples of the two-layer fluid flows are presented for various values of the gas flow rate, longitudinal temperature gradient at the interface and the gravity force acceleration. <...> Introduction Stationary two-layer fluid flows are studied on the basis of exact solutions to the NavierStokes equations in the Oberbeck-Boussinesq approximation in two-dimensional case [1–3]. <...> The solutions are obtained in the case when only the longitudinal velocity is not equal to zero and it depends on the transverse coordinate. <...> The longitudinal gradients of temperature and vapor concentration depend linearly on the transverse coordinate. <...> One of the first results devoted to construction of an exact solution in the infinite layer with evaporation at the "liquid-liquid" interface were obtained in [4]. <...> The solution of Birikh [5] has been constructed to describe the stationary convection in an infinite horizontal strip with solid boundaries or with a non-deformable free boundary under the action ∗gon@math.asu.ru †katerezanova@mail.ru ⃝ Siberian Federal University. <...> All rights reserved c – 48 – Olga N.Goncharova, Ekaterina V. Rezanova Modeling of Two-layer Fluid Flows with Evaporation . of the gravity field and constant longitudinal temperature gradient (see also [6–8]). <...> In the present paper the Soret and Dufour effects [10, 11] are taken into consideration in the gas-vapor layer (see [3]). <...> The exact solutions allow us to analyze the problem statements and peculiarities of modeling of flow effects including the effect of anomalous <...>