Analysis of the exact solution for the evaporative convection problem and properties of the characteristic perturbations

Abstract

The exact solution for the Boussinesq approximation of the Navier – Stokes equations is analytically constructed to describe the joint flow of an evaporating viscous heat-conducting liquid and gas-vapor mixture in an infinite horizontal channel. The effects of thermodiffusion and diffusive heat conductivity in the gas-vapor phase are additionally taken into account in the governing equations and interface conditions. Possible flow types are classified with respect to the types of the boundary conditions for the vapor concentration on the upper solid wall of the channel. The importance of a solution of special type is that it gives a possibility to specify on the qualitative level the physical factors defining the basic flow mechanisms. The constructed solution has the group nature and allows one to describe the real flow regimes and a formation of patterns observed in the experiments. It describes three classes of flows: pure thermocapillary, mixed and Poiseuille flows according to the dominant force or interaction of effects. The stability of the two-layer flows of the liquid and gas-vapor phase is investigated for the equal values of the longitudinal temperature gradients on the channel walls. In this case the perturbations of the basic flow can lead to the formation of the vortex and thermocapillary structures. The influence of the thermal load intensity and gas flow rate on the type of the arising instability is studied. The evolution of the perturbations is investigated numerically.