Abstract
The flow of a thin layer of a viscous incompressible liquid along an inclined non-uniformly heated substrate is investigated in the two-dimensional case. Evaporation is taken into account at the thermocapillary interface. The system of Oberbeck-Boussinesq equations is used as a mathematical model. The kinematic, dynamic and energy conditions generalized for the case of a nonzero mass flux are assumed to be fulfilled at the interface. The value of the local mass flux is determined using the Hertz-Knudsen equation. Solutions to problems for the main terms of power decomposition of a small parameter of the problem are obtained. The evolution equation to determine the position of the interface is obtained. A numerical algorithm for solving the problem is constructed. The problem of periodic runoff of an incompressible liquid layer is considered. The effect of additional terms in the energy condition on the dynamics of the thickness of the liquid layer is studied.
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