Investigation of unsteady motion of a sphericalparticle falling in a Newtonian fluid utilizing PPM

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

Keywords:

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