Accurate solution for motion of a spherical solid particle in plane Couette Newtonian fluid mechanical flow using HPM–Padé approximant and the Boubaker polynomials expansion scheme BPES

In this paper the analytical solutions for the motion of a spherical particle in a plane Couette Newtonian fluid flow are investigated, by using homotopy perturbation method (HPM) and Padé approximant and the Boubaker polynomials expansion scheme (BPES). The current results are then compared with those derived from HPM and the established fourth order Runge–Kutta method in order to verify the accuracy of the proposed method. It is found that this method can achieve more suitable results compare with HPM.