Semi-analytical method for solving the problem of heating of the liquid film moving under gravity and gas flow

A semi-analytical method is proposed to calculate heat transfer in the liquid film. Here, the temperature field in the liquid is presented as a series of basic functions, meeting the boundary conditions. The proposed method is demonstrated by the example of the problem of heating of the liquid film, moving under gravity and gas flow on the wall with a constant temperature. The impact of gas flow on the film is taken into account through the shear stress and the heat transfer coefficient on the liquid surface. The analytical solution considering shear stress on the interfacial surface has been obtained for the thermal entry region. Calculations using the proposed method are in good agreement with the numerical solution, obtained by a finite-difference method.