On Blood Flow Through an Overlapping Stenosed Artery
Conference paper
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Abstract
In the present study, an analysis of a mathematical model for blood flow through an overlapping stenosed artery is presented by treating the blood as a Newtonian fluid and taking the pressure gradient as a periodic function of time. Perturbation technique is applied to obtain the analytical expressions for velocity profile, volumetric flow rate and wall shear stress by assuming the Womersely parameter to be very small. Effects of overlapping stenosis and hematocrit of red cells on these flow variables are discussed graphically for better understanding of the model.
Keywords
Overlapping stenosis Womersely parameter Systolic and diastolic pressureReferences
- 1.Forrester, J.H., Young, D.F.: Flow through a converging diverging tube and its implications in occlusive vascular disease. J. Biomech. 3, 297–316 (1970)CrossRefGoogle Scholar
- 2.Haldar, K.: Effects of the shape of stenosis on the resistance to blood flow through an artery. Bull. Math. Biol. 47, 545–550 (1985)CrossRefGoogle Scholar
- 3.Misra, J.C., Chakravarty, S.: Flow in arteries in presence of stenosis. J. Biomech. 19, 907–918 (1986)CrossRefGoogle Scholar
- 4.Mandal, P.K.: An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis. Int. J. Non-Linear Mech. 40, 151–164 (2005)CrossRefMATHGoogle Scholar
- 5.Bali, R., Awasthi, U.: Effect of magnetic field on the resistance to blood flow through stenotic artery. Appl. Math. Comput. 188, 1635–1641 (2007)MathSciNetMATHGoogle Scholar
- 6.Philip, D., Chandra, P.: Flow of Eringen fluid (simple microfluid) through an artery with stenosis. Int. J. Eng. Sci. 34, 87–99 (1996)CrossRefMATHGoogle Scholar
- 7.Lee, J.S., Fung, Y.C.: Flow in locally constricted tube at low Reynolds number. J. Appl. Mech. 37, 9–16 (1970)CrossRefMATHGoogle Scholar
- 8.Ponalagusamy, R.: Blood flow through an artery with mild stenosis: a two-layered model, different shapes of stenoses and slip velocity at the wall. J. Appl. Sci. 7, 1071–1077 (2007)CrossRefGoogle Scholar
- 9.Chakravarty, S., Mandal, P.K.: Mathematical modeling of blood flow through an overlapping arterial stenosis. Math. Comput. Model. 19, 59–70 (1994)CrossRefMATHGoogle Scholar
- 10.Ismail, Z., Abdullah, I., Mustapha, N., Amin, N.: A power-law model of blood flow through a tapered overlapping stenosed artery. Appl. Math. Comput. 195, 669–680 (2007)MathSciNetMATHGoogle Scholar
- 11.Medhavi, A.: On macroscopic two-phase arterial blood flow through an overlapping stenosis. J. Sci. Technol. 5(6), 19–31 (2010)Google Scholar
- 12.Kumar, A., Awasthi, U.: A mathematical model for blood flow in a multiple stenosis artery. Int. J. Math. Anal. 4, 2465–2472 (2010)MathSciNetMATHGoogle Scholar
- 13.Varshney, G., Katiyar, V.K., Kumar, S.: Effect of magnetic field on the blood flow in artery having multiple stenosis: a numerical study. Int. J. Eng. Sci. Tech. 2, 67–82(2010)Google Scholar
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