Mathematics & Physics 2016, 9(3), 296–306 УДК 536.25 Numerical Investigation of a Dependence of the Dynamic Contact Angle on the Contact Point Velocity in a Problem of the Convective Fluid Flow Olga N.Goncharova∗ Altai State University Lenina, 61, Barnaul, 656049 Russian Alla V. Zakurdaeva Institute of Thermophysics SB RAS Lavrentyev, 1, Novosibirsk, 630090 Russian Received 07.12.2015, received in revised form 09.02.2016, accepted 20.06.2016 A two-dimensional problem of the fluid flows with a dynamic contact angle is studied in the case of an uniformly moving contact point. <...> Mathematical modeling of the flows is carried out with the help of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. <...> On the thermocapillary free boundary the kinematic, dynamic conditions and the heat exchange condition of third order are fulfilled. <...> The slip conditions (conditions of proportionality of the tangential stresses to the difference of the tangential velocities of liquid and wall) are prescribed on the solid boundaries of the channel supporting by constant temperature. <...> The results demonstrate the contact angle behavior and the different flow characteristics with respect to the various values of the contact point velocity, friction coefficients, gravity acceleration and an intensity of the thermal boundary regimes. <...> Keywords: convective flow, free boundary, dynamic contact angle, moving contact point, mathematical model, computational algorithm. <...> Introduction The problems of flows of a viscous incompressible fluid in the domains with interfaces are very important for investigations. <...> Such interest is explained by need of study some phenomena in the flow structure, which arise due to the effects related with the gas phase and solid wall properties. <...> One of the most important questions of mathematical modeling of the convective fluid flows in a domain with an interface is a correct formulation of the boundary conditions. <...> The problem of dynamic contact angle occurs due to the incompatibility of the conditions on the free surface of the liquid and the conditions of adhesion on a solid surface ∗gon@math.asu.ru ⃝ Siberian Federal University. <...> All rights reserved c – 296 – Olga N.Goncharova, Alla V. Zakurdaeva Numerical Investigation of a Dependence of the Dynamic . . . in vicinity of the moving three-phase contact line. <...> There are various methods of statement of the problems with contact angles, describing a motion of a viscous incompressible liquid in the presence of a moving contact line (or contact point in the two-dimensional case <...>