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

doi:10.1007/s11465-014-0303-0

Front. Mech. Eng.

2014, Vol. 9

Issue (3) : 270-280 https://doi.org/10.1007/s11465-014-0303-0

RESEARCH ARTICLE

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

D. D. GANJI^1,^*(

),M. ABBASI²,J. RAHIMI³,M. GHOLAMI⁴,I. RAHIMIPETROUDI^2,^*(

)

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

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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.

Keywords Homotopy Analysis Method Homotopy Perturbation Method incompressible flow magneto-hydrodynamic flow parallel disks

Corresponding Author(s): D. D. GANJI

Online First Date: 11 August 2014 Issue Date: 10 October 2014

Cite this article:

D. D. GANJI,M. ABBASI,J. RAHIMI, et al. On the MHD squeeze flow between two parallel disks with suction or injection via HAM and HPM[J]. Front. Mech. Eng., 2014, 9(3): 270-280.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0303-0
https://academic.hep.com.cn/fme/EN/Y2014/V9/I3/270

Fig.1 Physical model for hydro magnetic squeeze flow

Fig.2 The ?- validity for S=0.01,M=5 and different value of A

Fig.3 The ?- validity for S=0.3,A=-1 and different value of M

Fig.4 The comparison between the HAM, HPM [26] and numerical solutions for f(η),f′(η) when S=0.01,M=5,A=1

Fig.5 The comparison between the HAM, HPM [26] and numerical solutions for f(η),f′(η) when S=0.01,M=0,A=-1

Fig.6 The comparison between the HAM, HPM and numerical solutions for f(η),f′(η) when S=0.5,M=1,A=0

Fig.7 The comparison between the HAM, HPM and numerical solutions for f(η),f′(η) when S=1,M=3,A=1

Fig.8 Effects of Hartmann number on 6th-order approximation of the velocity profile at M=5,A=±1

Fig.9 Effects of squeeze number on 6th-order approximation of the velocity profile at M=5,A=-1

Fig.10 Effects of squeeze number on 6th-order approximation of the velocity profile at M=5,A=±1

Tab.1 Results of HAM, HPM and Numerical methods for f(η) when S=0.4,M=2,A=1

Tab.2 Results of HAM, HPM and Numerical methods for f′(η) when S=0.4,M=2,A=1

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 https://doi.org/10.1115/1.3616978
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 https://doi.org/10.1515/IJNSNS.2005.6.2.207
11	He J H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals, 2005, 26(3): 695-700 https://doi.org/10.1016/j.chaos.2005.03.006
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 https://doi.org/10.1016/j.physleta.2006.12.086
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	Heri?anu 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 https://doi.org/10.1007/s11012-010-9293-0
24	Marinca V, Heri?anu 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 https://doi.org/10.1155/2009/603916
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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