On Blood Flow Through an Overlapping Stenosed Artery

Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 11)

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 pressure 

References

  1. 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. 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. 3.
    Misra, J.C., Chakravarty, S.: Flow in arteries in presence of stenosis. J. Biomech. 19, 907–918 (1986)CrossRefGoogle Scholar
  4. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsKrishnath College BerhamporeMurshidabadIndia

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