Abstract
A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.
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This paper was recommended for publication in revised form by Associate Editor Do Hyung Lee
D. S. Sankar received his B. Sc degree in Mathematics from the University of Madras, India, in 1989. He then received his M. Sc., M. Phil. And Ph.D degrees from Anna University, India, in 1991, 1992 and 2004 respectively. Dr. D. S. Sankar is currently an Associate Professor in the School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia. His serves as a referee for several reputed ISI journals and his research interest includes fluid dynamics, hemodynamics, differential equations and numerical analysis.
Usik Lee received his B.S. degree in Mechanical Engineering from Yonsei University, Korea in 1979. He then received his M.S. and Ph.D degrees in Mechanical Engineering from Stanford University, USA in 1982 and 1985, respectively. Dr. Lee is currently a Professor at the Department of Mechanical Engineering at Inha University in Incheon, Korea. He has served as a referee for many reputed international journals. Dr. Lee’s research interests include structural dynamics, biomechanics, and computational mechanics.
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Sankar, D.S., Lee, U. FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries. J Mech Sci Technol 25, 2573–2581 (2011). https://doi.org/10.1007/s12206-011-0728-x
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DOI: https://doi.org/10.1007/s12206-011-0728-x