Investigation of unsteady motion of a spherical particle falling in a Newtonian fluid utilizing PPM H.

In this paper, nonlinear differential equation due to unsteady motion of a spherical particle falling in a Newtonian fluid has been considered. The main purpose of this article is obtaining solution of the considered problem by utilizing a strong semi-analytical method called parameterized perturbation method (PPM), afterward, verify accuracy and efficiency of proposed method base on comparison with achieved solutions of other analytical techniques named homotopy analysis method (HAM) and homotopy perturbation method (HPM) and also an accurate numerical solution. As an important result, it is depicted that obtained results by PPM has more accuracy in comparison with those obtained by HPM and HAM. After this verification, the mentioned method was applied for real combination of solid–fluid to show the efficiency of PPM for this type of problems. It has shown that in most cases, PPM is very accurate

Acceleration motion, Drag coefficient, Homotopy analysis method(HAM), Homotopy perturbation method (HPM), Parameterized perturbation method (PPM), Spherical particle