Abstract

We consider a two-dimensional flow of a laminar film of a viscous liquid on a homogeneously or locally heated plate in the presence of a gas flow above the surface of the film. In the case of a localized heater, an analytical solution for the temperature distribution in the film is obtained. In the case of a small deformation of the film surface and weak heat transfer with gas, an analytical solution for the film thickness perturbation is obtained. In the case of an uniformly heated plate, the effect of the formation of a periodic structure on the film surface is considered. With a small deformation of the surface, a dependence of the structure period on the Marangoni number is determined. Periodic solutions appear only if the Marangoni number exceeds a threshold value.