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Article
Accurate solution for acceleration motion of a vertically falling spherical particle in incompressible newtonian media
Article first published online: 19 JAN 2012
DOI: 10.1002/cjce.21641
Copyright © 2012 Canadian Society for Chemical Engineering
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How to Cite
Torabi, M. and Yaghoobi, H. (2013), Accurate solution for acceleration motion of a vertically falling spherical particle in incompressible newtonian media. Can. J. Chem. Eng., 91: 376–381. doi: 10.1002/cjce.21641
Publication History
- Issue published online: 28 DEC 2012
- Article first published online: 19 JAN 2012
- Manuscript Accepted: 24 NOV 2011
- Manuscript Revised: 22 OCT 2011
- Manuscript Received: 9 FEB 2011
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Keywords:
- solid spherical particle;
- acceleration motion;
- solid–liquid systems;
- sedimentation;
- non-linear differential equation;
- differential transformation method (DTM);
- experimental data
Abstract
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