High Accuracy Analysis for Acceleration Motion of Vertically Falling Spherical Particles in Incompressible Newtonian Fluid by Varinational Iterations Method

Abstract

In this paper, the acceleration motion of a vertically falling spherical particles made of Glass, Iron, Copper and Silver with diameter (D=1mm) in Newtonian fluid is discussed using Varinational Iteration Method (VIM) & Diagonal Pade’ approximant and compare the results with Runge-Kutta 4^th order method to verify the accuracy. It observed  that the VIM which was used to solve such  nonlinear differential equations is more accurate and simpler as compared to Diagonal pade’, Collocation Method (CM), Homotopy Perturbation Method (HPM), Akbari- Ganji’s Method (AGM)etc. The Conclusions clearly reveals that the time of reaching the particle at terminal velocity in a vertically falling procedure is significantly increased with increasing the density of a particles and the acceleration period for lighter particles is shorter than other. Further from these four particles, the glass’s particle has low velocity and reaches early at terminal velocity due to its lowest density as compared to other. To obtain the results for all different methods, the symbolic calculus software MATLAB was used.