  Many technological processes include preparing some special materials
adhering to a product surface. For example, this problem is important for the
magnetic tape producing, wire adhering, etc. For a surface withdrawn from the
molten metal or the other liquid material there is a problem to determine a
profile of a film surface. It is subject of this paper. We developed the
mathematical model for the simulation of the adhering process of viscous liquid
film to a slowly moving plate, which is vertically withdrawn from the molten
metal or the other fluid capacity. The Navier-Stokes equations for a film flow
on a surface of the withdrawn plate are considered with the corresponding
boundary conditions, and the polynomial approximation is used for the film flow
profile. The equations after integration across the layer of a film flow result
in the system of partial differential equations for the wavy surface of a film
flow, of flow rate and of flow energy.The derived equations are used for
analysis of the nonlinear film flow that determines the quality of a fluid
adhering on a surface of the withdrawn plate.
