Two-Layer Fluid Flows with Evaporation at an Interface in the Presence of an Anomalous Thermocapillary Effect
Mathematical modeling of stationary convective flows with evaporation at an interface is carried out with the help of the exact solutions of the Boussinesq approximation of the Navier- Stokes equations for the two-dimensional case. The effects of thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. The gas flow rate in the upper layer of the system is considered as a given. At the fixed impermeable walls of the channel the no-slip conditions for the velocity vector are fulfilled. The lower rigid boundary is assumed to be a heat insulated boundary. The constant heat flux is defined at the upper boundary of the channel. On the straight interface, being a thermocapillary boundary, the kinematic and dynamic conditions, the condition of heat transfer and the mass balance equations are satisfied. The vapor concentration saturation is defined as a sequence of the Clapeyron- Clausius equation, and a condition of zero vapor flux is assumed to be fulfilled at the upper rigid boundary. The constructed exact solutions can be applied for modeling of flows in two-layer gasliquid system for the case when a liquid has a property of the anomalous thermocapillary effect.
Key words: mathematical model, interface, evaporation, exact solution, anomalous thermocapillary effect
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