RESEARCH ARTICLE

On the MHD squeeze flow between two parallel disks with suction or injection via HAM and HPM

  • D. D. GANJI , 1 ,
  • M. ABBASI 2 ,
  • J. RAHIMI 3 ,
  • M. GHOLAMI 4 ,
  • I. RAHIMIPETROUDI , 2
Expand
  • 1. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
  • 2. Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
  • 3. Department of Electrical and Computer Engineering, Babol University of Technology, Babol, Iran
  • 4. Department of Mechanical Engineering, College of Mechanic, Tehran Science and Research Branch, Islamic Azad University, Damavand, Iran

Received date: 18 Mar 2014

Accepted date: 11 May 2014

Published date: 10 Oct 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

An analysis has been performed to study the problem of magneto-hydrodynamic (MHD) squeeze flow of an electrically conducting fluid between two infinite, parallel disks. The analytical methods called Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) have been used to solve nonlinear differential equations. It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as Boundary Value Problem (BVP) in solving this problem. Also, the velocity fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the velocity field. Furthermore, the results reveal that HAM and HPM are very effective and convenient.

Cite this article

D. D. GANJI , M. ABBASI , J. RAHIMI , M. GHOLAMI , I. RAHIMIPETROUDI . On the MHD squeeze flow between two parallel disks with suction or injection via HAM and HPM[J]. Frontiers of Mechanical Engineering, 2014 , 9(3) : 270 -280 . DOI: 10.1007/s11465-014-0303-0

1
Hughes W F, Elco R A. Magnetohydrodynamic lubrication flow between parallel rotating disks. Journal of Fluid Mechanics, 1962; 13(01): 21-32

2
Kuzma D C, Maki E R, Donnelly R J. The magnetohydrodynamic squeeze film. Journal of Fluid Mechanics, 1964, 19(03): 395-400

3
Krieger R J, Day H J, Hughes W F. The MHD hydrostatics thrust bearings—theory and experiments. Journal of Tribology, 1967, 89(3): 307-313

DOI

4
Sheikholeslami M, Ganji D D. Magnetohydrodynamic flow in a permeable channel filled with nanofluid. Scientia Iranica B, 2014, 21(1): 203-212

5
Sheikholeslami M, Hatami M, Ganji D D. Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. Journal of Molecular Liquids, 2014, 190: 112-120

6
Sheikholeslami M, Gorji-Bandpy M, Ganji D D, Soleimani S. Heat flux boundary condition for nanofluid filled enclosure in presence of magnetic field. Journal of Molecular Liquids, 2014, 193: 174-184

7
Nayfeh A H. Perturbation Methods. New York, USA: Wiley, 2000

8
Ganji D D, Hashemi Kachapi Seyed H. Analytical and numerical method in engineering and applied science. Progress in Nonlinear Science, 2011, 3: 1-579

9
Ganji D D, Hashemi Kachapi Seyed H. Analysis of nonlinear equations in fluids. Progress in Nonlinear Science, 2011, 3: 1-294

10
He J H. Homotopy perturbation method for bifurcation of nonlinear problems. International Journal of Nonlinear Sciences and Numerical Simulation, 2005, 6(2): 207-208

DOI

11
He J H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals, 2005, 26(3): 695-700

DOI

12
He J H. Homotopy perturbation method for solving boundary value problems. Physics Letters A, 2006, 350(1): 87-88

13
Abbasi M, Ganji D D, Rahimipetroudi I, Khaki M. Comparative analysis of MHD boundary-layer flow of viscoelastic fluid in permeable channel with slip boundaries by using HAM, VIM, HPM. Walailak Journal for Science and Technology, 2014, 11(7): 551-567

14
Ganji D D, Sadighi A. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. Journal of Computational and Applied Mathematics, 2007, 207(1): 24-34

15
He J H. Variational iteration method — some recent results and new interpretations. Journal of Computational and Applied Mathematics, 2007, 207(1): 3-17

16
Momani Sh, Abuasad S. Application of He’s variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals, 2006, 27(5): 1119-1123

17
Ganji D D, Afrouzi G A, Talarposhti R A. Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations. Physics Letters A, 2007, 368(6): 450-457

DOI

18
Liao S J. Boundary element method for general nonlinear differential operators. Engineering Analysis with Boundary Elements, 1997, 20(2): 91-99

19
Liao S J, Cheung K F. Homotopy analysis of nonlinear progressive waves in deep water. Journal of Engineering Mathematics, 2003, 45(2): 105-116

20
Liao S J. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 2004, 47(2): 499-513

21
Liao S J. Homotopy Analysis Method in Nonlinear Differential Equation. Berlin & Beijing: Springer & Higher Education Press, 2012

22
Esmaeilpour M, Ganji D D.Solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method, computers and mathematics with applications, 2010, 59(11): 3405-3411

23
Herişanu N, Marinca V. Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia. Meccanica, 2010, 45(6): 847-855

DOI

24
Marinca V, Herişanu N. Nonlinear dynamic analysis of an electrical machine rotor-bearing system by the optimal homotopy perturbation method. Computers and mathematics with applications, 2011, 61: 2019-2024

25
Aziz A. Heat conduction with Maple. Philadelphia (PA): R.T. Edwards, 2006

26
Domairry G, Aziz A. Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by Homotopy Perturbation Method. Journal of Mathematical Problems in Engineering, 2009: 603916

DOI

27
Wehgal A R. Ashraf M, MHD asymmetric flow between two porous disks. Punjab Universiy Journal of Mathematics, 2012, 44: 9-21

28
Shereliff J A. A text book of magneto-hydrodynamics. Oxford: Pergoman Press, 1965

29
Rossow V J. On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field. Tech Report 1358 NASA, 1958

Outlines

/