Magnetic Field and Hall Currents Influences on Blood Flow Through a Stenotic Artery

Kh. S. Mekheimer; M. A. El Kot

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(8): 991-1002

Kh. S. Mekheimer, M. A. El Kot. Magnetic Field and Hall Currents Influences on Blood Flow Through a Stenotic Artery[J]. Applied Mathematics and Mechanics, 2008, 29(8): 991-1002.

Citation:

Kh. S. Mekheimer, M. A. El Kot. Magnetic Field and Hall Currents Influences on Blood Flow Through a Stenotic Artery[J]. Applied Mathematics and Mechanics, 2008, 29(8): 991-1002.

Citation:

Kh. S. Mekheimer, M. A. El Kot. Magnetic Field and Hall Currents Influences on Blood Flow Through a Stenotic Artery[J]. Applied Mathematics and Mechanics, 2008, 29(8): 991-1002.

PDF( 806 KB)

Magnetic Field and Hall Currents Influences on Blood Flow Through a Stenotic Artery

Kh. S. Mekheimer¹,
M. A. El Kot²

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt;

Received Date: 2007-03-22
Rev Recd Date: 2008-06-06
Publish Date: 2008-08-15

Abstract

Abstract

A micrnpolar model for blood of mag}etol}ydrodynamic flow through a horizontally nonsymmetric arterial but vertically symmetric artery with a mild stenosis is presented.To estimate the effect of the stenosis shape,a suitable geometry was considered such that the horizontal shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter).Flow parameters such as velocity,the resistance to flow (the resistance impedance),the wall shear stress distribution in the stenotic region and its magnitude at the maavmum height of the stenosis (stenosis throat) were computed for different shape parameter,the Hartrnann number and Hall parameter.It is shown that the resistance to flow decreases with increasing values of the parameter deterrninirrg the stenosis shape and Hall parameter,while the resistance to flow increase with increasing the Hartrnann number.The wall shear stress and the shearing stress on the wall at the maavmum height of the stenosis possess an inverse character to the resistance to flow with respect to any given values of Hartmann number and Hall parameter.Finally,the effect of the Hartrnann number and the Hall paruneter on the horizontal velocity was examined.
- blood of magnetohydnodynamic flow,
- micropolar model,
- stenotic artery,
- Hall currents,
- Hartmann number

FullText(HTML)

References(24)

References

[1]	Craig I J D, Watson P G.Magnetic reconnection solutions based on a generalized Ohm's law[J].Solar Phys,2003,214(1):131-150. doi: 10.1023/A:1024075416016
[2]	Stud V K, Sephon G S, Mishra R K.Pumping action on blood flow by a magnetic field[J].Bull Math Biol,1997,39(3):385-390.
[3]	Agrawal H L,Anwaruddin B.Peristaltic flow of blood in a branch[J].Ranchi Univ Math J,1984,15:111-121.
[4]	Bharali A, Borkakati A K.The effect of Hall currents on MHD flow and heat transfer between two parallel porous plates[J].Appl Sci Res,1982,39(2):155-165. doi: 10.1007/BF00457017
[5]	Asghar S, Parveen S, Hanif S,et al.Hall effects on the unsteady hydromagnetic flows of an Oldroyd-B fluid[J].Internat J Engrg Sci,2003,41(6):609-619. doi: 10.1016/S0020-7225(02)00153-2
[6]	Megahed A A, Komy S R, Afify A A.Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate[J].Internat J Non-Linear Mech,2003,38(4):513-520. doi: 10.1016/S0020-7462(01)00077-4
[7]	Mohyuddin M R, Ashraf E E.Inverse solutions for a second-grade fluid for porous medium channel and Hall current effects[J].Proc Indian Acad Sci,Math Sci,2004,114(1):79-96. doi: 10.1007/BF02829673
[8]	Hayat T, Naz R, Asghar S. Hall effects on unsteady duct flow of a non-Newtonian fluid in a porous medium[J].Appl Math Comp,2004,157(1):103-114. doi: 10.1016/j.amc.2003.08.069
[9]	Hayat T, Wang Y, Hutter K. Hall effects on the unsteady hydromagnetic oscillatory flow of a second-grade fluid[J].Internat J Non-Linear Mech,2004,39(6):1027-1037. doi: 10.1016/S0020-7462(03)00094-5
[10]	Eringen A C. Theory of micropolar fluid[J].J Math Mech,1966,16(1):11-18.
[11]	Agarwal R S,Dhanapal C.Numerical solution to the flow of micropolar fluid between porous walls of different permeability[J].Internat J Engrg Sci，1987，25(33):325-336. doi: 10.1016/0020-7225(87)90039-5
[12]	Haldar K.Effects of the shape of stenosis on the resistance to blood flow through an artery[J].Bull Math Biol,1985,47(4):545-550.
[13]	Srivistava L M.Flow of couple stress fluid through stenotic blood vessels[J].J Biomech,1985,18(7):479-485. doi: 10.1016/0021-9290(85)90662-1
[14]	Srivastava V P.Arterial blood flow through a nonsymmetrical stenosis with applications[J].Jpn J Appl Phys,1995,34(12):6539-6545. doi: 10.1143/JJAP.34.6539
[15]	Ang K C, Mazumdar J N.Mathematical modeling of three dimensional flow through an asymmetric arterial stenosis[J].Math Comput Modelling,1997,25(1):19-29.
[16]	Srivastava V P,Saxena M.Suspension model for blood flow through stenotic arteries with a cell-free plasma layer[J].Math Biosci,1997,139(2):79-102. doi: 10.1016/S0025-5564(96)00130-7
[17]	Chakravarty S, Mandal P K.Two-dimensional blood flow through tapered arteries under stenotic conditions[J].Internat J Non-Linear Mech,2000,35(5):779-793. doi: 10.1016/S0020-7462(99)00059-1
[18]	Liu B, Tang D.A numerical simulation of viscous flows in collapsible tubes with stenosis[J].Appl Numer Math,2000,32(1):87-101. doi: 10.1016/S0168-9274(99)00015-X
[19]	El-Shahed M.Pulsatile flow of blood through a stenosed porous medium under periodic body acceleration[J].Appl Math Comput,2003,138(2/3):479-488. doi: 10.1016/S0096-3003(02)00164-9
[20]	Jung H, Choi J W,Park C G. Asymmetric flows of non-Newtonian fluids in symmetric stenosed artery[J].K-A Rheol J，2004,16(6):101-108.
[21]	Liu G T, Wang X J, Ai B Q,et al.Numerical study of pulsating flow through a tapered artery with stenosis[J].Chinese J Phys,2004,42(4):401-409.
[22]	Mandal P K.An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis[J].Internat J Non-Linear Mech,2005,40(1):151-164. doi: 10.1016/j.ijnonlinmec.2004.07.007
[23]	Pralhad R N, Schulz D H.Modeling of arterial stenosis and its applications to blood diseases[J].Math Biosci,2004,190(2):203-220. doi: 10.1016/j.mbs.2004.01.009
[24]	Young D F.Effect of a time dependent stenosis of flow through a tube[J].J Engrg Ind,Trans ASME,1968,90:248-254. doi: 10.1115/1.3604621