Thermocapillary deformation of a locally heated liquid film moving under the action of a gas flow

We propose a two-dimensional model of a steady laminar flow of a liquid film in a channel in the presence of a cocurrent gas flow. An analytical solution for the problem of temperature distribution is obtained for a linear flow velocity profile. The linearized problem of thermocapillary deformation of the film surface caused by local heating at a constant heat flux is solved. It is established that a thermocapillary bump is formed in the region where a thermal boundary layer emerges on the film surface. Additional perturbations, decaying in the upstream direction, can be present on the free surface in front of the bump. A criterion determining this effect is found.