Frontiers of Mechanical Engineering >
On the MHD squeeze flow between two parallel disks with suction or injection via HAM and HPM
Received date: 18 Mar 2014
Accepted date: 11 May 2014
Published date: 10 Oct 2014
Copyright
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.
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
|
| 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
|
| 11 |
He J H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals, 2005, 26(3): 695-700
|
| 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
|
| 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
|
| 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
|
| 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
|
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