Unsteady time-dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method (HAM), homotopy perturbation method (HPM) and collocation method (CM)

Abstract

Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically. The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation. The powerful analytical methods called collocation method (CM), the homotopy perturbation method (HPM), and the homotopy analysis method (HAM) have been used to solve nonlinear differential equations. It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem. Also, velocity fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.