Numerical study of two dimensional unsteady flow of an anomalous Maxwell fluid

Purpose - The purpose of this paper is to undertake an unsteady flow problem of an anomalous Maxwell fluid. The flow takes place between two side walls over a plate perpendicular to them and is driven by a sudden pressure force with constant gradient. Design/methodology/approach - A finite element method is invoked and is blended with a finite difference method for left Caputo fractional time derivatives in order to study the anomalous dynamics of the fluid. Findings - A numerical scheme for the constitutive equations of the prescribed flow in order to approximate the velocity field is designed. The graphical results to draw different physical conclusions on the flow problem are also presented. Originality/value - A rigorous mathematical exposition of the numerical scheme is provided and the results are valid for large values of the parameters.