Mathematical simulation of gravitational liquid film flow on a vertical surface with fins

The process of liquid film flow on a vertical surface with fins is simulated; we consider the case of two-dimensional laminar steady flow. A boundary value problem for the flow equation is solved numerically by Galerkin's method, which allows us to find the values that characterize the flow: the flow rate, the average flow velocity, the density of irrigation, and the Reynolds criterion. The formulas for the average thickness of the film are obtained.