HERSCHEL-BULKLEY FLUID: STUDY OF RHEOLOGICAL PROPERTIES FOR BLOOD FLOW OF PULSES IN ω-PROTOTYPE IN ARTERIES’ STENOSIS

Authors

  • Pawan Kumar IET, Dr. Shakuntala Misra National Rehabilitation University, Lucknow-226017

DOI:

https://doi.org/10.59436/d0nkz785

Keywords:

Non-Newtoian fluid, Herschel-Bulkley fluid model, Rheological Properties

Abstract

In this article, we examined the blood flow that was being pressed as part of the war. The Herschel-Bulkley fluid model is applied for representing non-Newtonian blood features in the small arteries. The current governing equation is guided by the fact that the flow has shape and is linear. The standard method of cleanup is used to get first-order expressions for different flow variables. The temporal distributions of axial velocity and wall shear stress, flow meter flow rate and flow resistance are shown in bold. Also discussed are the parameters involved in the contact of various fields of impact plug-flow. A comparison of blood flow and stimulus signals in the same area also causes the blood vessels to recover. All content is an article licensed underneath of a Creative Commons Attribution (CC BY) licence, if not in writing.

References

Dwivedi, P., Pal, T.S. and Rakesh, L. (1982). Micropolar fluid model for blood flow through a small tapered tube, Indian J. Technology 20: 295–299.

Chaturani, P. and Pralhad, R.N. (1985). Blood flow in tapered tubes with biorheological applications, Biorheology 22(4): 303–314. DOI: https://doi.org/10.3233/BIR-1985-22403

Tu, Deville et al. (1992). Finite element simulation of pulsatile flow through arterial stenosis, J. Biomechanics 25(10): 1141–1152. DOI: https://doi.org/10.1016/0021-9290(92)90070-H

Lee, J. and Fung, Y. (1970). Flow in locally constricted tube at low Reynolds number, J. Appl. Mech., 379–16. DOI: https://doi.org/10.1115/1.3408496

Azuma, T. and Fukushima, T. (1976). Flow patterns in stenotic blood vessel models, Biorheology. 13: 337–355. DOI: https://doi.org/10.3233/BIR-1976-13602

Morgan, E. and Young, D.F. (1974). An integral method for the analysis of flow in Arterial stenosis, Bull Math. Biol. 36: 39–53. DOI: https://doi.org/10.1016/S0092-8240(74)80005-4

Cheng, L.C., Robertson, J.M. and Clark, M.E. (1973). Numerical calculations of plane oscillatory non-uniform flow—II. Parametric study of pressure gradient and frequency with square wall obstacles, J. Biomechanics 6: 521–538. DOI: https://doi.org/10.1016/0021-9290(73)90010-9

Padmanabhan, N. (1980). Mathematical model of arterial stenosis, Med. Biol. Engng Comput. 18: 281–286. DOI: https://doi.org/10.1007/BF02443380

Kawaguti, M. and Hamano, A. (1983). Numerical study on post-stenotic dilatation, Biorheology 20: 507–518. DOI: https://doi.org/10.3233/BIR-1983-20508

O’Brien, V. and Ehrlich, L.W. (1985). Simple pulsatile flow in an artery with a constriction, J. Biomechanics, 18: 117–127. DOI: https://doi.org/10.1016/0021-9290(85)90004-1

Nadeem, S., Akbar, N.S., Hendi, A.A. and Hayat, T. (2011). Power law fluid model for blood flow through a tapered artery with a stenosis, Appl. Math. Comput. 217: 7108–7116. DOI: https://doi.org/10.1016/j.amc.2011.01.026

Chaturani, P. and Ponnalagar Samy, R. (1986). Pulsatile flow of a Casson fluid through stenosed arteries with application to blood flow, Biorheology, 23: 499–511. DOI: https://doi.org/10.3233/BIR-1986-23506

Mirza, A., Abdul Hameed, M. and Shafie, S. (2017). Magnetohydrodynamic approach of non-Newtonian blood flow with magnetic particles in stenosed artery, Applied Mathematics and Mechanics (English Edition), 38: 379–392. DOI: https://doi.org/10.1007/s10483-017-2172-7

Shukla, J.B., Parihar, R.S. and Rao, B.R.P. (1980). Effects of stenosis on non-Newtonian flow through an artery with mild stenosis, Bull. Math. Biol., 42: 283–294. DOI: https://doi.org/10.1016/S0092-8240(80)80051-6

Zaman, A. and Ali, N. (2016). Effects of peripheral layer thickness on pulsatile flow of Herschel–Bulkley fluid through a stenotic artery, Can. J. Phys., 94(9): 920-928. DOI: https://doi.org/10.1139/cjp-2014-0584

Zaman, A., Ali, N., Anwar Beg, O. and Sajid, M. (2016). Heat and mass transfer to blood flow through a tapered overlapping stenosed artery, International Journal of Heat and Mass Transfer, 95: 1084–1095. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2015.12.073

Zaman, A., Ali, N., Sajid, M. and Hayat, T. (2015). Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery, AIP Advances, 5: 037129. DOI: https://doi.org/10.1063/1.4916043

Ali, N., Zaman, A. and Sajid, M. (2014). Unsteady blood flow through a tapered stenotic artery using Sisko model, Computers & Fluids, 101: 42–49. DOI: https://doi.org/10.1016/j.compfluid.2014.05.030

Ali, N., Zaman, A., Sajid, M., Nieto, J.J. and Torres, A. (2015). Unsteady non-Newtonian blood flow through a tapered overlapping stenosed catheterized vessel, Mathematical Biosciences 269: 94–103. DOI: https://doi.org/10.1016/j.mbs.2015.08.018

Zaman, A., Ali, N., Anwar Beg, O. and Sajid, M. (2016). Unsteady two-layered blood flow through aw-shaped stenosed artery using the generalized Oldroyd-B fluid model, ANZIAM Journal, 58: 96–118. DOI: https://doi.org/10.1017/S1446181116000134

Zaman, A., Ali, N. and Sajid, M. (2016). Slip effects on unsteady non-Newtonian blood flow through an inclined catheterized overlapping stenotic artery, AIP Advances, 6: 015118. DOI: https://doi.org/10.1063/1.4941358

Shah, S.R. (2013). An innovative study for non-Newtonian behaviour of blood flow in stenosed artery using Herschel-Bulkley fluid model, International Journal of Bio-Science and Bio-Technology, 5: 233–240. DOI: https://doi.org/10.14257/ijbsbt.2013.5.5.24

Nikolov, S., Stoytchev, S., Torre, A. and Nieto, J.J. (2003). Biomathematical modeling and analysis of blood flow in an intracranial aneurysm, Neurological Research, 25: 497–504. DOI: https://doi.org/10.1179/016164103101201724

Sankar, S. and Lee, U. (2009). Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries, Commun Nonlinear Sci Numer Simul, 14: 2971–2981. DOI: https://doi.org/10.1016/j.cnsns.2008.10.015

Siddiqui, S.U., Verma, N.K., Mishra, S. and Gupta, R.S. (2009). Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis, App Math Comp., 210: 1–10. DOI: https://doi.org/10.1016/j.amc.2007.05.070

Chakravarthy, S. and Mandal, P.K. (1994). Mathematical modelling of blood flow through an overlapping stenosis, Math. Comput. Model., 19: 59–73. DOI: https://doi.org/10.1016/0895-7177(94)90116-3

Srivastava, V.P. and Rastigi, R. (2010). Blood flow through stenosed catheterized artery: Effects of hematocrit and stenosis shape, Comput. Math. Applc., 59: 1377–1785. DOI: https://doi.org/10.1016/j.camwa.2009.12.007

Maruthi, K.P., Vijaya, B. and Umadevi, C. (2014). A mathematical model of Herschel-Bulkley fluid through an overlapping stenosis, IOSR Journal of Mathematics (IOSR-JM), 10(2): 41–46. DOI: https://doi.org/10.9790/5728-10224146

Srikanth, J.V., Ramana Reddy, S. Jain, and Kale, A. (2015). Unsteady polar fluid model of blood flow through tapered-shape stenosed artery: Effects of catheter and velocity slip, Ain Shams Engineering Journal, 6: 1093–1104. DOI: https://doi.org/10.1016/j.asej.2015.01.003

Sankar, D.S. and Hemalatha, K. (2006). Pulsatile flow of Herschel–Bulkley fluid through stenosed Arteries–A mathematical model, International Journal of Non-Linear Mechanics, 41: 979–990. DOI: https://doi.org/10.1016/j.ijnonlinmec.2006.02.007

Downloads

Published

2021-02-20

How to Cite

HERSCHEL-BULKLEY FLUID: STUDY OF RHEOLOGICAL PROPERTIES FOR BLOOD FLOW OF PULSES IN ω-PROTOTYPE IN ARTERIES’ STENOSIS. (2021). Journal of Science Innovations and Nature of Earth, 1(1), 08-16. https://doi.org/10.59436/d0nkz785

Similar Articles

You may also start an advanced similarity search for this article.