Analytical Solutions for Unsteady Flow of a Fourth-Grade Fluid Arising in the Metallic Wire Coating Process Inside a Cylindrical Roll Die

Abstract

The unsteady flow of a non-Newtonian fluid in a metallic wire coating process inside a cylindrical roll die is considered. The constitutive equations of the fluid are modeled for a fourth-grade non-Newtonian fluid with non-homogenous boundary conditions. Analytical solutions for the axial velocity field have been obtained in explicit forms by modified homotopy perturbation transform method. These solutions are written as the sum between the permanent and the transient solutions. However, for large values of t, both of these solutions become identical. The obtained velocity field is compared with the existing exact solution of the same flow problem for a second grade fluid. Also, graphs representing the solutions are discussed and appropriate conclusions drawn.