Математическое моделирование течений с испарением в двухслойной системе с теплоизолированной верхней границей

Abstract

The problem of two-layer flow in an infinite horizontal channel with solid impermeable walls is studied. The upper boundary of the system is considered to be thermally insulated, and the longitudinal gradient of the temperature on the lower boundary is given. The lower layer is filled with a liquid that evaporates through the thermocapillary interface; the upper layer is a gas–vapor mixture. Stationary flows induced by action of gas flow in the upper layer and longitudinal temperature gradient are studied. The thermodiffusion and diffusive thermal conductivity effects are taken into account in the gas–vapor mixture. The mathematical model is based on the Boussinesq approximation of the Navier–Stokes equations, and the diffusion equation also holds for the upper layer. The exact solutions of a special type are constructed, where only the longitudinal velocity differs from zero and depends on the transverse coordinate, and the temperature and the vapor concentration are linearly dependent on the longitudinal coordinate. Evaporation of the liquid is taken into consideration using the mass balance and heat transfer conditions. Velocity and temperature profiles for liquid-gas systems such as ethanol-airand HFE7100-nitrogenare presented. The phenomenon of return flows near the interface is investigated. DOI 10.14258/izvasu(2017)4-16