International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2014, 2(4), 79-85
DOI: 10.12691/ijpdea-2-4-4
Open AccessArticle

Analytical investigation of the Laminar Viscous Flow in a Semi-Porous Channel in the Presence of a Uniform Magnetic Field

A. Majidian1, M. Fakour1, and A. Vahabzadeh1

1Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

Pub. Date: October 24, 2014

Cite this paper:
A. Majidian, M. Fakour and A. Vahabzadeh. Analytical investigation of the Laminar Viscous Flow in a Semi-Porous Channel in the Presence of a Uniform Magnetic Field. International Journal of Partial Differential Equations and Applications. 2014; 2(4):79-85. doi: 10.12691/ijpdea-2-4-4

Abstract

In this paper, the laminar fluid flow in a semi-porous channel in the presence of transverse magnetic field is investigated. The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. It has been attempted to exhibit the reliability and performance of the homotopy perturbation method (HPM) in comparison with the numerical method (Richardson extrapolation) in solving this problem. The influence of the two dimensionless numbers: the Hartmann number and Reynolds number on non-dimensional velocity profile are considered. The results indicate that velocity boundary layer thickness decrease with increase of Reynolds number and it increases as Hartmann number increases.

Keywords:
homotopy perturbation method (HPM) laminar viscous flow Semi-porous channel uniform magnetic field

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References:

[1]  V. Wernert, O. Schäf, H. Ghobarkar and R. Denoyel, Adsorption properties of zeolites for artificial kidney applications, Microporous and Mesoporous Materials, 83 1-3 (2005), 101-113.
 
[2]  A. Jafari, P. Zamankhan, S.M. Mousavi and P. Kolari, Numerical investigation of blood flow Part II: In capillaries, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 1396-1402.
 
[3]  A.R. Goerke, J. Leung and S. R. Wickramasinghe, Mass and momentum transfer in blood oxygenators, Chemical Engineering Science, 57 (2002), 2035-2046.
 
[4]  S.S. Mneina and G.O. Martens, Linear phase matched filter design with causal real symmetric impulse response, AEU-International Journal of Electronics and Communications, 63 (2009), 83-91.
 
[5]  Y. H. Andoh and B. Lips, Prediction of porous walls thermal protection by effusion or transpiration cooling: An analytical approach, Applied Thermal Engineering, 23 (2003), 1947-1958.
 
[6]  A. Runstedtler, On the modified Stefan–Maxwell equation for isothermal multicomponent gaseous diffusion, Chemical Engineering Science, 61 (2006), 5021-5029.
 
[7]  A.S. Berman, Journal of Applied Physics, 24 (1953), 1232.
 
[8]  J.F. Osterle and F.J. Young, Journal of Fluid Mechanics, 1 (1961), 512.
 
[9]  J.C. Umavathi, International Journal of Non-Linear Mechanics, 31 (1996), 371.
 
[10]  R. Askovic, P. Florent, C. Tournier and R. Roum, Science Technology, 35 (1990), 295.
 
[11]  R. Askovic, International Conference on Fluid and Thermodynamics- Indonesia, volume 1 (1994), 263.
 
[12]  P. Chandran, N.C. Sacheti and A.K. Singh, Internationa Communications of Heat and Mass Transfer, 23 (1996), 889.
 
[13]  A.J. Chamkha, International Communications of Heat and Mass Transfer, 23 (1996), 875.
 
[14]  A.J. Chamkha, International Communications of Heat and Mass Transfer, 25, (1998), 269.
 
[15]  A. Desseaux, Influence of a magnetic field over a laminar viscous flow in a semi-porous channel, International journal of Engineering Science, 37 (1999), 94.
 
[16]  M. Fakour, A. Vahabzadeh, D.D. Ganji,Scrutiny of mixed convection flow of a nanofluid in a vertical channel, International journal of Case Studies in Thermal Engineering, 4 (2014), 15-23.
 
[17]  M. Fakour, A. Vahabzadeh, D.D. Ganji, I.Rahimi Petroudi, “Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces,” Cent. Eur. J. Eng., vol. 4, pp. 341-355, 2014.
 
[18]  Ganji, D.D. and Sadighi, A. ‘‘Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations’’, Journal of Computational and Applied Mathematics, 207, pp. 24-34 (2007).
 
[19]  M. Fakour, D.D. Ganji, A. Vahabzadeh, S.H.H. Kachapi, Accuracy of VIM, HPM and ADM in Solving Nonlinear Equations for the Steady Three-Dimensional Flow of a Walter’s B Fluid in Vertical Channel, Walailak Journal of Science and Technology, 11 (2014), 7, 593-609.
 
[20]  M. M. Rashidi and S. M. Sadri,Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 15, 711-720.