Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Deriving Shape Functions for a 20-Nodal Tri-quadratic Serendipity Element and Verified Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Bernstein Polynomial Collocation Method for Acceleration Motion of a Vertically Falling Non-spherical Particle

Authors : Sudhir Singh, K. Murugesan

Published in: Advances in Fluid Dynamics

Publisher: Springer Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This work deals with the falling of non-spherical particle in incompressible Newtonian media. The Bernstein polynomial collocation method (BPCM) is used to find out velocity and acceleration, and obtained results by BPCM are compared with variational iteration method (VIM), differential transform method (DTM), and the fourth-order Runge–Kutta method (RK-4). It is shown that this method gives a more accurate result when compared to the differential transform method, and the solution converges fast in comparison with VIM. Moreover, the use of BPCM is found to be simple, flexible, efficient, and computationally elegant.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter Performance and Emission Characteristics of Compressed Ignition Engine by Using Non-edible Coconut Biodiesel
next chapter Overlapping Multi-domain Bivariate Spectral Method for Systems of Nonlinear PDEs with Fluid Mechanics Applications
Literature
1.
Clift R, Grace J, Weber ME (1978) Bubbles, drops and particles. Academic, New York
2.
Chhabra RP (1993) Bubbles, drops and particles in non-Newtonian fluids. CRC Press, Boca Raton
3.
Tang P, Chan HK, Rapper JA (2004) Prediction of aerodynamic diameter of particles with rough surfaces. Powder Technol 147:64–78CrossRef
4.
Yow HN, Pitt MJ, Salman AD (2005) Drag correlation for particles of regular shape. Adv Powder Technol 363–372
5.
Hatami M, Ganji DD (2014) Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy multi-step differential transformation method. Powder Technol 258:94–98CrossRef
6.
Hatami M, Domairry G (2014) Transient vertically motion of a soluble particle in a Newtonian fluid media. Powder Technol 253:96–105
7.
Jalaal M et al (2011) Homotopy perturbation method for motion of a spherical solid particle in plane Couette fluid flow. Comput Math Appl 61:2267–2270MathSciNetCrossRef
8.
Jalaal M, Ganji DD, Ahmadi G (2012) An analytical study of settling of non-spherical particles. Asia Pac J Chem Eng 7:63–72CrossRef
9.
Jalaal M, Bararnia H, Domairry G (2011) A series exact solution for one-dimensional non-linear particle equation of motion. Powder Technol 207:461–464CrossRef
10.
Ferreira JM, Duarte Naia M, Chhabra RP (1998) An analytical study of the transient motion of a dense rigid sphere in an incompressible Newtonian fluid. Chem Eng Commun 1:168
11.
Ferreira JM, Chhabra RP (1998) Acceleration motion of a vertically falling sphere in incompressible Newtonian media: an analytical solution. J Powder Technol 97:6–15CrossRef
12.
Dogonchi AS, Hatami M Hosseinzadeh Kh, Domairry G (2015) Non-spherical particles sedimentation in an incompressible Newtonian medium by Pade’ approximation. Powder Technol 278:248–256
13.
Torabi M, Yaghoobi H (2013) Accurate solution for acceleration motion of a vertically falling spherical particle in incompressible Newtonian media. Powder Technol 91:376–381
14.
Malvandi A, Moshizi SA, Ganji DD (2014) An analytical study of unsteady motion of vertically falling spherical particles in quiescent power-law shear-thinning fluids. J Mol Liq 193:166–173CrossRef
15.
Yaghoobi H, Torabi M (2012) Novel solution for acceleration motion of a vertically falling non-spherical particle by VIM-Pade’ approximant. Powder Technol 215–216:206–209
16.
Torabi M, Yaghoobi H (2011) Novel solution for acceleration motion of a vertically falling spherical particle by HPM-Pade’ approximant. Adv Powder Technol 22:674–677
17.
Khan AR, Richardson JF (1987) The resistance to motion of a solid sphere in a fluid. Chem Eng Commun 62:135–150CrossRef
18.
Bagheri G, Bonadonna C (2016) On the drag of freely falling non-spherical particles. Powder Technol 301:526–544
19.
Krueger B, Wirtz S, Scherer V (2015) Measurement of drag coefficients of non-spherical particles with a camera-based method. Powder Technol 278:157–170CrossRef
20.
Chein SF (1994) Settling velocity of irregularly shaped particles. SPE Drill Complet 9:281–289CrossRef
21.
Song X, Xu Z, Li G (2017) A new model for predicting drag coefficient and settling velocity of spherical and non-spherical particles in Newtonian fluid. Powder Technol 321:242–250
22.
Hoshek J, Lasser D (1993) The fundamental of computer added geometric design. A. K. Peters, Wellesley
23.
Farouki RT (2012) The Bernstein polynomial basis: a centennial retrospective. Comput Aided Geom Des 29:379–419
24.
Basirat B, Shahdadi MA (2013) Numerical solution of nonlinear integro-differential equations with initial conditions by Bernstein operational matrix of derivatives. Int J Mod Nonlinear Theory Appl 2:141–149CrossRef
25.
Ordokhani Y, Far SD (2013) Application of the Bernstein polynomials for solving the nonlinear Fredholm integro-differential equations. J Appl Math Bionform 1(2):13–31MATH
26.
Tabrizidooz HR, Shabanpanah K (2018) Bernstein polynomial basis for numerical solution of boundary value problems. Numer Algorithms 77:211–228MathSciNetCrossRef
27.
Mittal RC, Rohila R (2017) A study of one-dimensional nonlinear diffusion equation by Bernstein polynomial based differential quadrature method. J Math Chem 55:673–695MathSciNetCrossRef
28.
Sahu PK, Saha Ray S (2016) Legendre spectral collocation method for the solution of the model describing biological species living together. J Comput Appl Math 296:47–55MathSciNetCrossRef
29.
Hosseini E, Loghmani GB, Heydari M, Rashidi MM (2017) Investigation of magneto-hemodynamic flow in a semi-porous channel using orthonormal Bernstein polynomials. Eur Phys J Plus 132:326
30.
Khataybeh SN, Hasim I, Alshbool M (2018) Solving directly third-order ODEs using operational matrices of Bernstein polynomials methods with application to fluid flow equations. J King Saud Univ-Sci
31.
Yousefi SA, Barikbin Z, Dehghan M (2012) Ritz-Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non-classic boundary conditions. Int J Numer Methods Heat Fluid Flow 22:39–48
32.
Yaghoobi H, Torabi M (2011) An application of differential transformation method to nonlinear equations arising in heat transfer. Int Commun Heat Mass Transf 38:815–820
33.
Moghimi SM, Ganji DD, Bararnia H, Hosseini M, Jalaal M (2011) Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem. Comput Math Appl 61:2213–2216MathSciNetCrossRef
34.
Noor MA, Mohyud-Din ST (2009) Variational iteration method for unsteady flow of gas through a porous medium using He’s polynomials and Pade approximants. Comput Math Appl 58:2182–2189MathSciNetCrossRef
Metadata
Title
Bernstein Polynomial Collocation Method for Acceleration Motion of a Vertically Falling Non-spherical Particle
Authors
Sudhir Singh
K. Murugesan
Copyright Year
2021
Publisher
Springer Singapore
Book
Advances in Fluid Dynamics

Print ISBN: 978-981-15-4307-4

Electronic ISBN: 978-981-15-4308-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-15-4308-1_53

Premium Partners

    Image Credits