Mathematical Study on MHD Squeeze Flow between Two Parallel Disks with Suction or Injection via HAM and HPM and Its Applications

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2017 by IJETT Journal
Volume-45 Number-1
Year of Publication : 2017
Authors : Anil Kumar, S P Agrawal
DOI :  10.14445/22315381/IJETT-V45P207

Citation 

Anil Kumar, S P Agrawal " Mathematical Study on MHD Squeeze Flow between Two Parallel Disks with Suction or Injection via HAM and HPM and Its Applications", International Journal of Engineering Trends and Technology (IJETT), V45(1),27-32 March 2017. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group

Abstract
In this paper, we are considering the problem of magneto-hydrodynamic MHD squeeze flow of an electrically conducting fluid between two infinite, parallel disks are investigated. The analytical method called Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) are used to compute an approximation for the solution of nonlinear differential equations governing on the problem. The results of the mentioned methods are compared with a type of numerical analysis as Boundary Value Problem method.

 References

1] Hughes, W. F., Elco, R. A., Magnetohydrodynamic lubrication flow between parallel rotating disks, Journal of Fluid Mechanics, 13 (1962), 1, pp. 21–32.
[2] kuzma, D. C., Maki, E. R., Donnelly, R. J., The magneto hydrodynamic squeeze film,” Journal of Fluid Mechanics, 19(1964), 3, pp. 395–400.
[3] Krieger, R. J., Day, H. J., Hughes, W. F., The MHD hydrostatics thrust bearings—theory and experiments, ASME Journal of Lubrication Technology, 89(1967), pp. 307–313.
[4] Nayfeh, A.H., Perturbation Methods, Wiley, New York, USA, 2000.
[5] Ganji, D.D., Hashemi Kachapi, Seyed H., Analytical and numerical method in Engineering and applied Science, progress in nonlinear science, 3(2011), pp.1-579.
[6] Ganji, D.D., Hashemi Kachapi, Seyed H., Analysis of nonlinear Equations in fluids, progress in nonlinear science, 3 (2011), pp.1-294.
[7] He, J.H., Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul, 6(2005), pp. 207-208.
[8] He, J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26(2005),pp. 695-700.
[9] He, J. H., Homotopy perturbation technique, Comp. Meth. App. Mech. Eng., 178 (1999), pp. 257-262.
[10] Rostamiyan, Y., Ganji, D. D., Rahimi Petroudi, I., KhazayiNejad, M., analytical investigation of nonlinear model arising in heat transfer through the porous film , THERMAL SCIENCE,(in press).
[11] Ganji, D.D., Sadighi, A., Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J. Comput. Appl. Math,207 (2007),1,pp. 24-34.
[12] He, J.H., Variational iteration method – some recent results and new interpretations, Journal of Computational and Applied Mathematics, 207 (2007), 1, pp. 3–17.
[13] Momani,S ., Abuasad ,S., Application of He’s variational iteration method to Helmholtz equation, Chaos Solitons & Fractals, 27 (2006),5,pp. 1119–1123.
[14] 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, 368(2007),pp. 450–457.
[15] Liao SJ. Boundary element method for general nonlinear differential operators, Eng Anal Bound Elem, 202(1997), pp. 91–9.
[16] Liao SJ., Cheung KF. Homotopy analysis of nonlinear progressive waves in deep water. J Eng Math,45(2003), 2, pp. 103–16.
[17] Liao SJ., On the homotopy analysis method for nonlinear problems. Appl Math Comput, 47(2004), 2, pp. 499–513.
[18] S J Liao. Homotopy Analysis Method in Nonlinear Differential Equation, Berlin & Beijing: Springer & Higher Education Press, 2012.
[19] Esmaeilpour M, Ganji D.D.,solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method, computers and mathematics with applications, 59 (2010), pp.3405-3411.
[20] Herisanu 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, 45 (2010), pp. 847–855.
[21] Marinca, V., Herisanu, N, Nonlinear dynamic analysis of an electrical machine rotor-bearing system by the optimal homotopy perturbation method, computers and mathematics with applications, 61 (2011), pp. 2019-2024.
[22] G. Domairry and A. Aziz, Approximate Analysis of MHD Squeeze Flow between Two Parallel Disks with Suction or Injection by Homotopy Perturbation Method, journal of Mathematical Problems in Engineering, doi:10.1155/2009/603916.
[23] Anil Kumar, R. K. Saket, C L Varshney and Sajjan Lal : Finite difference technique for reliable MHD steady flow through channels permeable boundaries, International Journal of Biomedical Engineering and Technology (IJBET) UK, Vol. 4(2) pp 101-110, 2010.
[24] Anil Kumar, CL Varshney and Sajjan Lal: MHD free convective fluctuating flow through a porous effect with variable permeability Parameter, International Journal of Engineering, Iran, Volume 23 - 3&4 - Transactions A: Basics, ISSN 1025-2495 November 2010, pp. 313-322 2010.
[25] Anil Kumar and S P Agrawal (2015): Mathematical Analysis of MHD on Laminar Mixed Convection of Newtonian Fluid Between Vertical Parallel Plates Channel, , 09th INDIACom; 2015 2nd International Conference on Computing for Sustainable Global Development, 11-13 March 2015 , IEEE Bharti Vidyapeeth New Delhi, ISSN 0973-7529; ISBN 978-93-80544-15-1 pp 360-364.
[26] Anil Kumar, CL Varshney and Sajjan Lal : Crank-Nicholson Scheme to Transient MHD Free Convective Flow through Semi-Infinite Vertical Porous Plate with Constant Suction and Temperature Dependent Heat Source, Proceedings International Conference on Advances in Computing and Artificial Intelligence (ACAI 2011) pp 86-92, 2011,USA.

Keywords
Magneto-hydrodynamic Homotopy Perturbation Method, Squeeze flow, Temprature , nonlinear differential equations, incompressible flow