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Accurate solution for acceleration motion of a vertically falling spherical particle in incompressible newtonian media
Author(s) -
Torabi Mohsen,
Yaghoobi Hessameddin
Publication year - 2013
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.21641
Subject(s) - acceleration , compressibility , newtonian fluid , mathematical analysis , mathematics , runge–kutta methods , perturbation (astronomy) , algebraic equation , classical mechanics , physics , differential equation , mechanics , nonlinear system , quantum mechanics
In this paper, the acceleration motion of a vertically falling spherical particle in incompressible Newtonian media was investigated. The instantaneous velocity and acceleration were carried out using analytical solution technique i.e. the differential transformation method (DTM). Using the DTM, the non‐linear constrained governing equations were reduced to recurrence relations and related initial conditions were transformed into a set of algebraic equations. The solutions were subsequently solved by a process of inverse transformation. The results were also compared with those derived from the homotopy perturbation method (HPM), closed‐form solution, the established fourth order Runge–Kutta method and experimental data in order to verify the accuracy of the proposed method. It was found that this method can achieve more accurate results compared with the HPM. © 2012 Canadian Society for Chemical Engineering