Home / Current Issue / Paper 1702429
Mathematical model for behavior of Blood Flow in Artery Through Stenosis
Subject area: Science,Engineering and Technology · Area of research: Mathematics
Abstract
The aim of this paper is to develop a mathematical model for studying the non-Newtonian flow of blood through a stenosed arterial segment. Power law fluid represents the non-Newtonian character of blood. The hemodynamic behavior of the blood flow is influenced by the presence of the arterial stenosis. The problem is solved by using analytical techniques with help of boundary conditions and results are displayed graphically for different flow characteristics like pressure drop, shear stress, velocity profile. For the validation of numerical model, the computation results are compared with the results from published literature.
Keywords
Herschel-Bulkley fluid, power law fluid model, pressure drop, stenosis height, shear stress
References
[1] D.Biswas and U.S.Chakraborty, (2010): Two-layered pulsatile blood flow in a stenosed artery with body acceleration and slip at wall, Applications and Applied Mathematics: An International Journal (AAM), 05(10), 1400 – 1417.
[2] F.R. Eirich, RheologyTheory and Applications, vol. 3, Academic press Inc. Publishers, New York, S.F., London, 1960.
[3] J.C. Misra and G.C.Shit ,(2006): Blood flow through arteries in a pathological state: A theoretical study,International Journal of Engineering Science, 44, 662-671.
[4] J.N. Kapur, (1985): Mathematical models in biology and medicine,New Delhi: East-West Press.
[5] Kumar, S. and Diwakar, C.S., 2013: A Mathematical Model of Power Law Fluid With an Apllication of Blood Flow through an Artery with Stenosis, Advances in Applied Mathematical Biosciences Vol. 4, No. 1 (2013), pp. 25-36.
[6] N. Casson, in: C.C. Mill (Ed.), Rheology of Disperse Systems, Pergamon Press, London, 1959, pp. 84–102.
[7] P.Mathur and S.Jain,(2011): Pulsatile flow of blood through a stenosed tube:effect of periodic body acceleration and a magnetic field, J Biorheol , doi: 10.1007/ s12573-011-0040-5.
[8] R. Ali, R. Kaur, V. K. Katiyar and M. P. Singh,(2009): Mathematical modeling of blood flow through vertebral artery with stenoses,Indian Journal of Biomechanics,special issue NCBM.
[9] R. Bali and U. Awasthi, (2007): Effect of a magnetic field on the resistance to blood flow through stenotic artery,Applied Mathematics and Computation,188, 1635–1641
[10] S. R Shah. and S. U.Siddiqui,(2011): Two-phase model for the study of blood flow through stenosed artery,International Journal of Pharmacy and Biological Sciences, 1,246-254. 12 Pankaj Mathur and Surekha Jain
[11] Shit, G.C. and Roy, M., 2012: “Hydromagnetic pulsating flow of blood in a constricted porous channel: A theoretical study”, Proceedings of the world congress on Engeering, London, U.K, vol. 1, pp 83-88.
[12] Shukla, J.B., Parihar, R.S. and Rao, B.R.P., 1980, “Effects of stenosis on non-Newtonian flow of the blood in an artery,” Bulletin of Mathematical Biology,vol. 42, pp. 283-294.
[13] Sinha, A., Misra, J.C. and Shit, G.C., 2011: “Mathematical modeling of blood flow in a porous vessel having double stenoses in the presence of an external magnetic field,” Inter. Journal of Biomath, vol. 4(2), pp. 207-225.
[14] V.K.Verma, M.P.Singh and Dr. V.K.Katiyar, (2004): Analytical study of blood flow through an artery with mild stenosis, Acta Ciencia IndicaVol. XXX M. (2), 281.
[15] W.W.Nichols and M.F.O. Rourke ,(1990): McDonald’s blood flow in arteries: theoretic, experimental and clinical principles, Third Edition, Edward Arnold A division of Hodder &Stoughton, London, Melbourne, Auckland.
[16] Y.C.Fung,(1981): Biomechanics,SpringerVerlag,NewYork,Heidelberg,Berlin Biology, 42, 283-294.
[17] Yadav A.K., Kumar S. et al. (2020): “Behavior of synovial fluid in a circular rigid artery” International Journal of Trend in Scientific Research and Development, Vol.4 issu 4, p 652-655
[18] Young, D.F., 1979, “Fluid mechanics of arterial stenosis”, J. Biomech. Eng. ASME, vol. 101, pp 157-175.
How to cite this paper
@article{1702429,
author = {Dr. Sushil Kumar, Karm Veer Singh, Dr. A. K. Yadav, Dr. S. S. Yadav},
title = {Mathematical model for behavior of Blood Flow in Artery Through Stenosis},
journal = {Iconic Research And Engineering Journals},
year = {2020},
volume = {4},
number = {1},
pages = {94-98},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1702429.pdf},
abstract = {The aim of this paper is to develop a mathematical model for studying the non-Newtonian flow of blood through a stenosed arterial segment. Power law fluid represents the non-Newtonian character of blood. The hemodynamic behavior of the blood flow is influenced by the presence of the arterial stenosis. The problem is solved by using analytical techniques with help of boundary conditions and results are displayed graphically for different flow characteristics like pressure drop, shear stress, velocity profile. For the validation of numerical model, the computation results are compared with the results from published literature.},
keywords = {Herschel-Bulkley fluid, power law fluid model, pressure drop, stenosis height, shear stress},
month = {July},
}