Fluid Analysis of Double-Layered Blood Flow through a Tapered Overlapping Stenosed Artery with a Porous Wall

Document Type : Full Length Research Article

Authors

1 Department of Mathematics, University of Ilorin, Ilorin, Nigeria

2 School of Early Childhood Care and Primary Education, Federal College of Education (T) Potiskum, Yobe State, Nigeria

Abstract

In this present work, we examine the fluid of double-layered blood flow through a tapered overlapping stenosed artery with a porous wall. This two-layered blood flow problem comprises the peripheral layer as Newtonian fluid flows and the central core layer of suspension of the erythrocytes as another Newtonian fluid flows and was analytically solved which the numerical results are shown graphically and discussed. It was found that resistance to flow accelerates with rising slip parameter, blood viscosity, and artery length while a rise in Darcy number and radius of the centre core to the tube radius in the unobstructed region decreases the resistance to flow. Also, the resistance to flow rises with increasing stenosis height whereas it increases with a rise in values of artery shape. The wall shear stress drops as the Darcy number accelerates and rises with rising viscosity of the blood and slip parameter. Furthermore, fluctuation of wall shear stress at the neck of the stenosis drops as the Darcy number increases. Moreover, it is observed that the shear stress increases with rising viscosity of the blood and slip parameter. This work is able to forecast the major attribute of the physiological flows which have played an important role in biomedical researches.

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References

[1]    Mann F. C., Herrick J. F., Essex H. E., and Blades E. J., 1938. Effects on blood flow of decreasing the lumen of blood vessels, Surgery, 4, 249–252.
[2]    Asha K. N. and Neetu Srivastava, 2021. Geometry of Stenosis and Its Effects on the Blood Flow Through an artery-A Theoretical Study, AIP Conference Proceedings, 2375, Issue 1: 10.1063/5.0066510.
[3]    Srivastava V.P., Rastogi R. and Vishnoi R., 2010. A two-layered suspension blood flow through an overlapping stenosis, Computers and Mathematics with Applications, 60, 432–441.
[4]    Arun Kumar Maiti, 2016. Mathematical Modelling on Blood Flow Under-Atherosclerotic condition. Americal Journal of Applied Mathematics, Vol. 4, No.6, 324-329.
[5]    Padma Joshi, Ashutosh Pathak and Joshi B.K, 2009. Two-layered model of blood flow through composite stenosed artery. AAM, vol. 4(2), 343-354.
[6]    Medhavi A., 2011. On macroscopic two-phase arterial blood flow through an overlapping stenosis, e-Journal of Science and Technology, 6, 19–31.
[7]    Medhavi A., Srivastav R. K., Ahmad Q. S. and Srivastava V. P., 2012. Two-phase arterial blood flow through a composite stenosis, e-Journal of Science and Technology, 7(4), 83–94.
[8]    Medhavi A., 2013. A macroscopic two-phase blood flow through a stenosed artery with a permeable wall, Appl Bionics and Biomechanics, 10(1), 11–18.
[9]    Srivastava V.P., Tandon M. and Srivastav R. K., 2012. A macroscopic two-phase blood flow through a bell-shaped stenosis in an artery with a permeable wall, Appl. and Appl Math., 7(1), 37–51.
[10]  Babatunde A. J. and Dada M. S., 2021. Effects of Hematocrit level on Blood flow through a tapered and overlapping stenosed Artery with Porosity. JHMTR, (1-9), 2007-1293.
[11]  Ponalagusamy R and Manchi R., 2020. The two-layered (K.L-Newtonian) model of blood flow in an artery with six types of mild stenosis. Applied Mathematics and Computation, Elsevier, vol. 367.
[12]  Puskar R. Pokhrel, 2021, Analysis of Two-layered Blood Flow through Artery with Mild Stenosis, Humanities and Social Sciences Journal, 13(1), 145-154.
[13]  Eldesoky I. M., Kernel M. H. & Hussien R. M., Abumandour, 2013. Numerical study of unsteady MHD pulsatile flow through a porous medium in an artery using Generalized Differential Quadrature Method, Intern. Jour. of Materials, Mechanics and Manufacturing, 1(2).
[14]  Bugliarello G. and Sevilla, 1970. Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheol, 7, 85–107.
[15]  Titiloye E.O, Babatunde A.J. and Dada M.S., 2016. Mathematical modelling of two-layered blood flow through a tapered artery with an overlapping stenotic condition, faculty of physical sci., University of Ilorin. ISSN: 2408-4808. Vol.3, 208-223.
[16]  Chakravarty. S. and Mandal P. K., 1994. The Mathematical modelling of blood flow through an overlapping Arterial stenosis. Math. & Comp. Modelling, Vol.19, Issue 1, page 59-70.
[17]  Sapna Ratan Shah, Anuradha, and Anamika, 2017. Mathematical modelling of blood flow through three-layered stenosed artery”. International Journal for Research in Applied Science & Eng. Tech., Vol. 5 Issue VI, ISSN: 2321-9653.
[18]  Rupesh K. Srivastav and V.P. Srivastava, 2014. On two-fluid blood flow through the stenosed artery with a permeable wall. Applied Bionics and Biomechanics, 11. 39-45.
[19]  Sharan M. and Popel A. S., 2001. A two-phase model for the flow of blood in narrow tubes with increased viscosity near the wall, Birheol, 38, 415–428.
[20]  Beavers G. S. and Joseph D. D., 1967. Boundary conditions at a naturally permeable wall. Journal of Fluid Mech, 30(1), 197–207.
[21]  Malek A. and Haque A., 2017. Hematocrit level on blood flow through a stenosed artery with a permeable                 wall. AAM: An international journal, ISSN: 1932-9466.

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History

  • Receive Date: 04 October 2021
  • Revise Date: 02 February 2023
  • Accept Date: 03 February 2023

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