Effect of motion of a local heat source on thermocapillary deformation of a thin liquid film flowing down under the action of gravity

The influence of a moving local heat source on the structure of flow in a thin liquid film flowing down on an inclined substrate under the action of gravity has been theoretically studied. Two-dimensional steady-state and conjugated hydrodynamic heat transfer problem has been solved in a long-wave approximation. The characteristics of flow are compared for various regimes: from the liquid film flowing down on a vertical surface with an immobile heat source to the behavior of a horizontal liquid layer under the action of a moving heat source. It is shown that changes in the flow velocity profile related to an increase in the velocity of the heat source motion and a decrease in the substrate slope under other equal conditions (constant flow rate, film thickness, and heat release) lead to a sharply increased thermocapillary deformation of the liquid film.