The theoretical approaches for mathematical modelling of the convective flows with mass transfer through the liquid–gas interface are discussed. The special attention is payed to modelling with use of the classical Boussinesq approximation of the Navier–Stokes equations. The diffusion equation and the effects of thermodiffusion and thermal diffusivity (the Soret and Dufour effects) are taken into account additionally to describe vapor and heat transfer processes in the gas-vapor phase. The use of the Oberbeck–Boussinesq equations allows one to apply the group-analytical methods in the theory of the evaporative convection and to construct the exact solutions of special type of the governing equations. Joint flows of the evaporating liquid and gas-vapor mixture are studied with the help of a partially invariant solution for the convection equations. The 2D and 3D solutions are demonstrated to simulate two-phase flows in the infinite channels with interface being under action of a longitudinal temperature gradient and perpendicularly directed gravity field. In the present paper the fluid flows with diffusive evaporation/condensation in the terrestrial and microgravity conditions are studied in the steady case. The new results obtained for combined thermal regime on the external rigid boundaries are presented.

中文翻译：

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基于精确解的扩散式蒸发两层对流流动特性分析

讨论了通过液-气界面传质的对流流动数学建模的理论方法。要特别注意使用Navier–Stokes方程的经典Boussinesq逼近进行建模。此外，还考虑了扩散方程以及热扩散和热扩散效应（Soret和Dufour效应）来描述气相中的蒸汽和传热过程。Oberbeck-Boussinesq方程的使用使人们可以将组分析方法应用于蒸发对流理论，并构造特殊类型的控制方程的精确解。借助于对流方程的部分不变解，研究了蒸发的液体和气体-蒸汽混合物的联合流动。演示了2D和3D解决方案，以模拟无限通道中的两相流，其中界面在纵向温度梯度和垂直方向的重力场的作用下进行。在本文中，研究了稳定情况下在地面和微重力条件下扩散扩散蒸发/凝结的流体流动。给出了在外部刚性边界上组合热工况获得的新结果。