The Thermocapillary Convection in Locally Heated Laminar Liquid Film Flow Caused by a Co-Current Gas Flow in Narrow Channel

A two-dimensional model of a steady laminar flow of liquid film and co-current gas flow in a plane channel is considered. It is supposed that the height of a channel is much less than its width. There is a local heat source on the bottom wall of the channel. An analytical solution for the temperature distribution problem in locally heated liquid film is obtained, when the velocity profile is linear. An analytical solution of the linearized equation for thermocapillary film surface deformation is found. A liquid bump caused by the thermocapillary effect in the region where thermal boundary layer reaches the film surface is obtained. Damped oscillations of the free surface may exist before the bump. This is obtained according to the solution of the problem in an inclined channel. It depends on the forces balance in the film. The defining criterion is found for this effect. The oscillations of free surface do not exist for horizontally located channel.