Numerical study of a thin film flow of fourth grade fluid

Abstract

Purpose – The purpose of this paper is to study the thin film flow of a fourth grade fluid subject to slip conditions in order to understand its velocity profile. Design/methodology/approach – An exact expression for flow velocity is derived in terms of hyperbolic sine functions. The practical usage of the exact flow velocity is restrictive as it involves very complicated integrals. Therefore, an approximate solution is also derived using a Galerkin finite element method and numerical error analysis is performed. Findings – The behavior of fluid velocity with respect to various flow parameters is discussed. The results are not restrictive to small values of flow parameters unlike those obtained earlier using homotopy analysis method and homotopy perturbation method. Originality/value – An approximate solution based on finite element technique is derived.