Modeling of Thin Liquid Layer Flow on an Inclined Substrate Based on the Navier — Stokes Equations in the Case of Large Reynolds Numbers

The paper deals with the mathematical model constructed to study the flow of a thin liquid layer on an inclined, unevenly heated solid substrate. The system of Navier — Stokes and heat transfer equations representing the generalized kinematic, dynamic, and energy conditions at the boundary, including mass transfer, are selected as the governing equations. The paper considers a two-dimensional formulation of the problem at large Reynolds numbers. The long-wave approximation allows one to obtain analytical solutions for the main terms of the expansion in powers of the small parameter of the problem. The conducted parametric analysis helps identify the factors that influence the nature of the flow the most. Then, the evolution equation to determine the position of the liquid-gas interface is obtained. The presented developed algorithm is capable to solve numerically the problem of periodic liquid flow down an inclined solid substrate. The solution is obtained using the sweeping and parameter sweeping methods. The influence of solid substrate inclination angle on the liquid layer flow is investigated.