The Impact of Geometric Parameters on Three-Layer Flow Patterns in a Horizontal Channel: A Comprehensive Study

Abstract

This paper focuses on studying stationary flows in horizontal layers, taking into consideration the effects of heat and mass transfer. A mathematical model is presented for a three-layer flow in an infinite channel with solid, impermeable walls. The gas-vapor mixture flows over one-component immiscible liquids in the lower and middle layers. The paper considers the processes of heat and mass transfer at the "liquid-gas" and "liquid-liquid" thermocapillary boundaries, respectively. The Dufour and Soret effects are also considered in the upper layer of the system. Mathematical modeling is based on exact solutions of a special form of the Navier-Stokes equations in the Boussinesq approximation. The procedure for determining unknown parameters is explained. The paper derives dependencies of the longitudinal temperature gradients at the system boundaries from each other. The influence of the flow region's geometry on the nature of the process is studied using the "silicone oil-water-air" system as an example. The paper presents longitudinal velocity profiles and temperature distribution for different values of the liquid layer heights while other parameters of the system remain fixed. The paper concludes that, in this case, the thickness of the lower layer is more influential than the thickness of the middle layer.