Boundary-layer flows over deforming surfaces

In this paper a formulation of the incompressible Navier-Stokes equations is introduced which allows one to model boundary-layer flows induced by the motion of a deforming surface. Such a formulation may be used to model flows relevant in a wide variety of industries from polymer processing to glass manufacturing. We show that for particular sheet geometries and velocities, similarity solutions may be obtained that account for sheet thinning (or thickening) and roughness patterns observed in extrusion-type processes.