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Many technological processes include preparing some special materialsadhering to a product surface. For example, this problem is important for themagnetic tape producing, wire adhering, etc. For a surface withdrawn from themolten metal or the other liquid material there is a problem to determine aprofile of a film surface. It is subject of this paper. We developed themathematical model for the simulation of the adhering process of viscous liquidfilm to a slowly moving plate, which is vertically withdrawn from the moltenmetal or the other fluid capacity. The Navier-Stokes equations for a film flowon a surface of the withdrawn plate are considered with the correspondingboundary conditions, and the polynomial approximation is used for the film flowprofile. The equations after integration across the layer of a film flow resultin the system of partial differential equations for the wavy surface of a filmflow, of flow rate and of flow energy.The derived equations are used foranalysis of the nonlinear film flow that determines the quality of a fluidadhering on a surface of the withdrawn plate.

Derivation of the nonlinear equations for surface of fluid adhering to a moving plate withdrawn from a liquid pool