Hematocrit Effects on Blood Flow through an Overlapping Stenosed Artery with Permeable Wall

Document Type : Full Lenght Research Article

Authors

Department of Mathematics, University of Ilorin, Ilorin Nigeria.

Abstract

This present study discusses the contributions of the presence of hematocrit level on wall shear stress and flow resistance in a tapered and overlapping stenosed artery with permeable wall. It enables the prediction of the main property of the physiological flows which plays an important role in biomedical investigations. The equation governing the flow in a tapered overlapping stenosed artery was simplified and solved analytically for resistance to flow and wall shear stress. The results highlight that the resistance to flow increases with an increase in either stenosis height or artery shapes while It decreases slightly with a rise in hematocrit level within normal range. Darcy number rises as the resistance to flow decreases for non-tapering, diverging tapering and converging tapering artery shapes. There is a significant hike in wall shear stress as slip parameter or Darcy number increases for diverging tapering, non-tapering and converging tapering. Also, the wall shear stress is increasing with an increase in stenosis height and a decrease in artery shapes.

Keywords

Main Subjects

References

[1] Michael F. Oliver, 1979. Circulatory system anatomy. Editor of coronary Heart Disease in Young Women and others. University of Edinburgh.
[2] Ali Haghighi Asl, 2019. Two dimensional Simulation of mass transfer and nano-particle Deposition of cigarette smoke in a Human Airway. JHMTR, 5(1), pg. 79-85.
[3] Taylor., 1959. The influence of the anomalous viscosity of blood upon its oscillatory flow. Physics in Medicine and Biology. 3(3): 273 - 290.
[4] Leondes Cornelius., 2000 Knowledge Based Systems, Four-Volume Set, Computer Science Inter. Journal. Vol. 4.
[5] Ellahi R., Rahman S.U and Mudassar M., 2014. Mathematical model of non-Newtonian fluid micro-polar fluid in arterial blood flow through composite stenosis. Applied Mathematical and Information Sciences, 8(4): 1567 - 1573.
[6] Nerem, R., 1992. Vascular fluid mechanics the arterial wall and atherosclerosis, Biology Journal, 114:274-282.
[7] Lee, B. K., 2002. Hemodynamic effects on atherosclerosis-prone coronary artery: wall shear stress rate distribution and impedance phase angle in coronary and aortic circulation, Yonsei medical journal, Vol.42:375-383.
[8] Pralhad, R.N., Schultz, D.H., 2004. Modeling of arterial stenosis and its applications to blood diseases, Mathematical Biosciences. 190, 203-220.
[9] Srivastav, R. K., 2014. Mathematical Model of Blood Flow through a Composite Stenosis in Catheterized Artery with Permeable Wall, Application and applied: Intern. J., 9(1).
[10] Mishra S., Siddiqui, S.U., and Medhavi, A., 2011. Blood Flow through a Composite Stenosis in an Artery with Permeable Wall, Application and applied: Intern. J., 6(11).
[11] Chakravarty. S. and Mandal P. K.,1994. The Mathematical modelling of blood flow through an overlapping Arterial stenosis. Mathematical and Computer Modelling.19(1), page 59-70.
[12] Walker HK. Hall WD and Hurst JW., 1990. Clinical Methods: The History, Physical and Laboratory Examinations. Butterworth Publishers, a division of reed publishing, Bookshelf ID: NBK259 PMID: 2:125-0102.
[13] Srivastava, V.P., Rastogi R., 2010. Blood flow through a stenosed catheterized artery: Effects of hematocrit and stenosis shape. Computers and Mathematics with Application, 59(4), 1377-1387.
[14] Singh D.P, Lokendra P. and Singh, 2013. The role of magnetic field intensity in blood flow through overlapping stenosed artery: A Herschel-Bulkley fluid model, Pelagia Research 20 Library. ISSN: 0976 - 8610.
[15] Abubakar J.U. and Adeoye A.D, 2019. Effects of radiative heat and magnetic field on blood flow in an inclined tapered stenosed porous artery. 14( 1), 77 - 86.
[16] Malek A., Haque A., Mohiuddin MD., 2015. Effects of Hematocrit level on the blood flow through stenosed Artery. Engineering International, 3(2): 2409-3629.
[17] Mekheimer Kh.S. and El Kot M.A., 2012. Mathematical modelling of unsteady flow of a Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis. Applied Mathematical Modelling. 36, 5393-5407.
[18] Malek A. and Haque A., 2017. Hematocrit level on blood flow through a stenosed artery with permeable wall. AAM: An international journal. ISSN: 1932-9466.
[19] Walburn, F. J., and Schneck, D. J., 1976. A constitutive equation for whole human blood, Biorheology. 13, 201.
[20] Young, D. F., 1968. Effect of a time dependent stenosis on flow through a tube, J. Engg. Ind., Trans. Am. Soc. Mech. Engg. 90, 248-254.
[21] Beavers, G. S. and Joseph, D.D., 1967. Boundary conditions at a naturally permeable wall. Journal of Fluid Mechanics, 30(01), pp 197- 207.
A.J. Babatunde / JHMTR 8 (2021) 39- 47 47
[22] Shailesh M., Siddiqui S.U. and Amit M., 2011. Blood flow through a composite stenosis in an Artery with permeable wall. AAM: An International Journal. 6(11), 1798 - 1813.
[23] Somchai Sriyab., 2014. Mathematical Analysis of Non-Newtonian Blood Flow in Stenosis Narrow Arteries, Comput Math Methods Med. 4:79-152.
[24] Masuda H., Zhuang Y. J., Singh, T. M., Kawamura, K., Murakami M., Zarins, C. K., and Glagov, S., 1999. Adaptive remodeling of internal elastic lamina
and endothelial lining during flow-induced arterial enlargement, Arterioscler Thromb Vasc Biol, Oct; 19(10):2, 298-307.
[25] World Health Organization (WHO), 2017. Cardiovascular diseases. (health-topics) https://www.who.int.

Files

Cited by

History

  • Receive Date: 06 July 2020
  • Revise Date: 30 March 2021
  • Accept Date: 31 March 2021

Share

How to cite

Statistics