Analysis of Characteristics of Two-Layer Convective Flows with Diffusive Type Evaporation Based on Exact Solutions

Abstract

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.