Effect of Magnetic field on Herschel-Bulkley fluid through multiple stenoses

K. Maruthi Prasad; R. Bhuvanavijaya; C. Uma Devi

doi:10.26637/mjm303/013

Abstract

A mathematical model for electrically conducting flow of Herschel-Bulkley fluid through a uniform tube of multiple stenoses has been studied. Analytical solutions of resistance to the flow and wall shear stress have been calculated. It is found that the resistance to the flow increases with the heights of the stenoses, power law index, volumetric flow rate, radius of the plug core-region and yield stress, but decreases with induced magnetic field and shear stress. It is also observed that the wall shear stress is increasing with the heights of
the stenoses and radius of the plug core-region.

Keywords:

Multiple stenoses, Herschel-Bulkley fluid, Magnetic field

Mathematics Subject Classification:

92C10, 92C30, 76S05

Authors Imprint References Funding Related Articles Downloads

K. Maruthi Prasad Department of Mathematics,GITAM University, Hyderabad Campus, Telangana, India
R. Bhuvanavijaya Department of Mathematics,JNTU College of Engineering, Anantapur, A.P, India.
C. Uma Devi Department of Mathematics, TKR College of Engineering, Hyderabad, Telangana, India.

Pages: 335-345
Date Published: 01-07-2015
Vol. 3 No. 03 (2015): Malaya Journal of Matematik (MJM)

D.F. Young, Effects of a time-dependent stenosis on flow through a tube, J. Engrg. Ind., Trans ASME, 90, $248-254,1968$. DOI: https://doi.org/10.1115/1.3604621

J.S. Lee, Y.C. Fung, Flow in Locally- constricted Tubes and Low Renolds Numbers, J. Appl. Mech., Trans ASME. 37, 9-16, 1970 DOI: https://doi.org/10.1115/1.3408496

Padmanabhan, Mathematical model of arterial stenosis. Med. Biol. Eng. Comput., 18, 281-286, 1980. DOI: https://doi.org/10.1007/BF02443380

J.R. Buchanan, C. Kleinstreuer, and J.K. Corner, Rheological effects on pulsatile hemodynamics in a stenosed tube. Computers and Fluids, 29, 695-724, 2000. DOI: https://doi.org/10.1016/S0045-7930(99)00019-5

P.K. Mandal, An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis . International journal of Non Linear Mechanics, 40, 151-164, 2005. DOI: https://doi.org/10.1016/j.ijnonlinmec.2004.07.007

Z. Ismail, I. Abdullah, N. Mustapha and N. Amin, A power-law model of blood flow through a tapered overlapping stenosed artery. Applied Mathematics and Computation, 195, 669-680, 2007. DOI: https://doi.org/10.1016/j.amc.2007.05.014

K. Maruthi prasad, G. Radhakrishnamacharya, Effect of multiple stenoses on Herschel-Bulkley fluid through a tube with non-uniform cross-section, International e-journal of engineering mathematics: Theory and Application, 1, 69-76, 2007.

P. Chaturani, R. Ponnalagar samy, A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases, Biorheol., 22, 521-531, 1985. DOI: https://doi.org/10.3233/BIR-1985-22606

E.E. Tzritzilakis, A mathematical model for blood flow in magnetic field. Physics of Fluids, 17: 077103, $1-15,2005$. DOI: https://doi.org/10.1063/1.1978807

K. Das and G.C. Saha, Arterial MHD pulsatile flow of blood under periodic body acceleration. Bulletin of Mathematical society, $16,68-81,2009$

I.I.H. Chen, Analysis of an intensive magnetic field on blood flow: part 2, Electromagnetic biology and Medicine, Vol 4, No1, 55-61, 1985.

A.T. Ogulu and T.M. Abbey, Simulation of Heat Transfer on an Oscillatory Blood Flow in an Indented Porous artery, International Communication in Heat and Mass Transfer, Vol. 32, No. 7, 983-989, 2005. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2004.08.028

S.Shaw, P.V.S. N Murthy, S.C. Pradhan, The effect of body acceleration on two dimensional flow of casson fluid through an artery with Asymmetric stenosis, The Open Transport Phenomena Journal, 2 55-68,2010. DOI: https://doi.org/10.2174/1877729501002010055

Rekha Bali and Usha Awasthi, A casson fluid model for multiple stenosed arteries in the presence of magnetic field. Applied Mathematics, 3, 436-441, 2012. DOI: https://doi.org/10.4236/am.2012.35066

D.S, Sankar, U. Lee, FDM Analysis for MHD flow of a non-Newtonian fluid in stenosed arteries, Journal of Mechanical Science and Technology, 25, 2573-2581, 2011. DOI: https://doi.org/10.1007/s12206-011-0728-x

Lokendra Parmar, S.B. Kulshreshthaand D.P. Singh, The role of magnetic field intensity in blood flow through overlapping stenosed artery: A Herschel-Bulkley fluid model. Advances in Applied Science Research, 4 (6), 318-328, 2013.

R. Bhargava, S. Rawat, H.S. Takhar, O.A.Beg, Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel, Meccanica, 42,247-262,2007 DOI: https://doi.org/10.1007/s11012-007-9052-z