Study of the gas flow rate effect on the parameters of evaporative convection regimes using an exact solution

The Oberbeck–Boussinesq equations and boundary conditions resulting from the conservation laws and thermodynamics principles provide the basis for mathematical modeling of evaporative convection in a bilayer liquid–gas–vapor system. The processes of fluid dynamics and heat and mass transfer in the volume phases and through the interface are successfully described with the help of a partially invariant solution of the constitutive equations. The solution is the efficient tool for studying regularities of physical phenomena as well as for describing heat-mass exchange processes with respect to the Ludwig–Soret mass transport and the diffusion thermoeffect appeared in the gas phase due to the presence of a volatile component. An exact solution of convection equations is derived under the assumption that evaporation/condensation is a process of the diffusive type and has an inhomogeneous character along the interface. Based on the comparison of the calculated and experimental values of the evaporation mass flow rate, the correct problem statement is specified that provides acceptable qualitative and quantitative agreement. The influence of the kinematic characteristics of the gas on the parameters of convective regimes arising in a horizontal mini-channel is investigated within the frame of the selected problem statement for the ethanol–air fluid system under the terrestrial gravity field. The topological structure of the bilayer flows, pattern of the temperature and vapor concentration fields, evaporation rate variations as well as the stability of the convective flows are analyzed with respect to different values of the gas flow rate. The destabilizing influence of the pumping gas on the threshold characteristics of the stability for the two-layer flow is ascertained. Three different wave modes of instability are predicted.