Numerical simulation of convective flows in a thin liquid layer at large Reynolds numbers

A mathematical model is proposed that describes the flow of a thin layer of liquid along an inclined unevenly heated substrate. The governing equations are the Navier–Stokes equations for a viscous incompressible liquid and relations representing generalized kinematic, dynamic, and energy conditions on the interface for the case of evaporation. The formulation is given in the two-dimensional case for large Reynolds numbers. The problem is solved within the framework of the long-wave approximation. A parametric analysis of the problem is carried out, and an evolutionary equation is derived to find the thickness of the liquid layer. An algorithm for a numerical solution is proposed for the problem of periodic flow of liquid along an inclined substrate. The influence of gravitational effects and the nature of heating of the solid substrate on the flow of the liquid layer is studied.