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A thin layer of a viscous incompressible liquid flowing down an inclined, non-uniformly heated substrate under conditions of a concomitant gas flow is studied. The flow is accompanied by evaporation at the thermocapillary interface. Dynamic processes in a gas are not taken into account (one-side model). The mathematical model of a thin liquid layer flow is based on the Navier-Stokes equation and the heat transfer equation, as well as generalized kinematic, dynamic and energetic conditions at the thermocapillary boundary. The local mass flux at the interface is determined using the Hertz-Knudsen equation. Analytical solutions of the problem are constructed for the zeroth-order terms of the expansions of the desired functions in powers of a small parameter of the problem. Parametric analysis of the problem is performed. An evolutionary equation for determining the thickness of the liquid layer is obtained. An algorithm for numerical solution of the evolutionary equation is constructed. The results of numerical studies of flows of a thin layer of ethanol and HFE-7100 with evaporation at the interface are obtained.

Numerical modeling of the liquid film flow with evaporation on the basis of the generalized interface conditions