Thermocapillary flow in a jet of liquid film painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively higher temperat ure ejected from a vessel and painted on the moving solid boundary is analy zed. The thermocapillary flow is driven by the temperature gradient on the free surface of a liquid film, because of the heat transfer from the liquid with higher temperature to the environmental gas with relatively lower tem perature. The thermocapillary flow changes the height profile of the liquid film. The analysis is based on the approximations of lubrication theory an d perturbation theory, and the equation of liquid height and the process of thermal hydrodynamics in the liquid film are solved for a given temperatur e distribution on the solid boundary.