The Impact of Geometrical Parameters on Two-Layer Flow Patterns with Evaporation in an Inclined Channel

Abstract

The paper focuses on studying two-layer stationary convective flows of liquid and the accompanying flows of gas and vapor in inclined layers, taking into consideration the effects of heat and mass transfer. The thermocapillary boundary condition is assumed to be non-deformable. Mathematical modeling of two-layer flows in an infinite channel with solid impermeable walls is based on the exact solutions of a special form of differential convective equations. The effects of thermal diffusion and diffusive thermal conductivity are considered in the upper layer of the system. The vapor in the gas is assumed to be an admixture that does not affect the properties of the gas. The flow is studied when the vapor concentration function meets the condition of zero flux on the upper wall of the channel. The influence of the layer thicknesses on the flow topology is studied using the exemplary “benzine — air” system. The author’s programming code helps produce the data set for plotting the profiles of longitudinal velocity and concentration distributions of temperature and vapor for layers with different thicknesses. At the same time, all the other parameters of the system remain fixed. The results presented in the paper are obtained for the case when the closure condition for liquid flow is fulfilled, and at a given value of the gas flow rate. It is shown that a change in the thickness of the layer leads to both quantitative and qualitative changes in the characteristics of the flow process.