Geometrical Analysis to Blood Flow Across Tapered-Non Tapered Arteries by the Use of Various Advanced Flow Parameters
The study of Arterial blood flow is a fascinating topic as arterial disease is responsible of death in many nations. This paper investigated the conduct of blood flow across a tapered artery with stenosis. This study has been simply explained by the use of a mathematical model that is appropriate. The graphical representations were created to support the results of the study. For various values of tapering angle, it is discovered that wall shear stress enhance when a peak is reached, then decreases. We also found that the velocity of the blood flow reduces with radius and also for distinct values of tapering angle. It is also evidenced that the blood flow rate reduces as the radius and tapering angle increase.
H. Abe, K. Hayashi and M. Sato (eds.), Data Book on the Mechanical Properties of Living Cells, Tissues, and Organs, Springer, Tokyo (1996), https://www.springer.com/gp/book/9784431701750.
S. A. Ahmed, An experimental investigation of pulsatile flow through a smooth, Experimental Thermal and Fluid Science 17 (1998), 309 – 318, DOI: 10.1016/S0894-1777(98)00009-0.
L. Ai and K. Vafai, An investigation of Stokes’ second problem for non-Newtonian fluids, Numerical Heat Transfer, Part A: Applications 47(10) (2005), 955 – 980, DOI: 10.1080/10407780590926390.
N. S. Akbar, S. Nadeem and C. Lee, Biomechanical analysis of Eyring Prandtl fluid model for blood flow in stenosed arteries, International Journal of Nonlinear Sciences and Numerical Simulation 14 (2013), 345 – 353, DOI: 10.1515/ijnsns-2012-0062.
H. I. Andersson, R. Halden and T. Glomsaker, Effects of surface irregularities on flow resistance in differently shaped arterial stenoses, Journal of Biomechanics 33(10) (2000), 1257 – 1262, DOI: 10.1016/s0021-9290(00)00088-9.
I. Bakırtas and H. Demiray, Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube, Applied Mathematics and Computation 154 (2004), 747 – 767, DOI: 10.1016/S0096-3003(03)00748-3.
I. Bakırtas and N. Antar, Evolution equations for nonlinear waves in a tapered elastic tube filled with a viscous fluid, International Journal of Engineering Science 41(11) (2003), 1163 – 1176, DOI: 10.1016/S0020-7225(03)00005-3.
S. A. Berger and L.-D. Jou, Flows in stenotic vessels, Annual Review of Fluid Mechanics 32(1) (2000), 347 – 382, DOI: 10.1146/annurev.fluid.32.1.347.
J. Bernsdorf and D. Wang, Non-Newtonian blood flow simulation incerebralaneurysms, Computers & Mathematics with Applications 58(5) (2009), 1024 – 1029, DOI: 10.1016/j.camwa.2009.02.019.
C. Bertolotti and V. Deplano, Three-dimensional numerical simulations of flow through a stenosed coronary bypass, Journal of Biomechanics 33(8) (2000), 1011 – 1022, DOI: 10.1016/s0021-9290(00)00012-9.
N. Bessonov, A. Sequeira, S. Simakov, Yu. Vassilevskii and V. Volpert, Methods of bloodflow modelling, Mathematics Modelling of Natural Phenomena 11(1) (2016), 1 – 25, DOI: 10.1051/mmnp/201611101.
T. Canchi, S. D. Kumar, E. Y. Ng and S. Narayanan, A review of computational methods to predict the risk of rupture of abdominal aortic aneurysms, BioMed Research International 2015 (2015), Article ID 86162, DOI: 10.1155/2015/861627.
S. Chakravarthy, Sarifuddin and P. K. Mandal, Unsteady flow of a two-layer blood stream pasta tapered flexible artery under stenotic conditions, Computational Methods in Applied Mathematics 4 (2004), 391 – 409, DOI: 10.2478/cmam-2004-0022.
S. Chakravarty and A. K. R. Sannigrahi, A nonlinear mathematical model of blood flow in a constricted artery experiencing body acceleration, Mathematical and Computer Modelling 29 (1999), 9 – 25, https://www.sciencedirect.com/science/article/pii/S0895717799000679/pdf?md5=268370df8a8d774b5907db66d874611f&pid=1-s2.0-S0895717799000679-main.pdf.
A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd edition, Springer (1993), https://bd.b-ok.africa/book/449688/baaaaf.
V. Deplano and M. Siouffi, Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis, Journal of Biomechanics 32(10) (1999), 1081 – 1090, DOI: 10.1016/s0021-9290(99)00098-6.
O. Eytan, A. J. Jaffa and D. Elad, Peristaltic flow in a tapered channel: application to embryo transport within the uterine cavity, Medical Engineering & Physics 23(7) (2001), 473 – 482, DOI: 10.1016/s1350-4533(01)00078-9.
E. A. Finol and C. H. Amon, Flow dynamics in anatomical models of abdominal aortic aneurysms: computational analysis of pulsatile flow, Acta Científica Venezolana 54 (2003), 43 – 49.
A. R. Haghighi and N. Pirhadi, A numerical study of heat transfer and flow characteristics of pulsatile blood flow in a tapered artery with a combination of stenosis and aneurysm, International Journal of Heat and Technology 37 (2019), 11 – 21, DOI: 10.18280/ijht.370102.
T. Hashimoto, H. Meng and W. L. Young, Intracranial aneurysms: Links amonginflammation, hemodynamics and vascular remodeling, Neurological Research 28(4) (2006), 372 – 380, DOI: 10.1179/016164106X14973.
T. Ishikawa, L. F. R. Guimaraes, S. Oshima and R. Yamane, Effect of non-Newtonian property of blood on flow through a stenosed tube, Fluid Dynamics Research 22(5) (1998), 251 – 264, DOI: 10.1016/S0169-5983(97)00041-5.
M. Kothandapani and J. Prakash, Effect of radiation and magnetic field on peristaltic transport of nanofluids through a porous space in a tapered asymmetric channel, Journal of Magnetism and Magnetic Materials 378 (2015), 152 – 163, DOI: 10.1016/j.jmmm.2014.11.031.
M. Kothandapani and J. Prakash, Influence of heat source, thermal radiation and inclined magnetic field on peristaltic flow of a Hyperbolic tangent nanofluid in a tapered asymmetric channel, IEEE Transactions on NanoBioscience 14 (2015), 385 – 392, DOI: 10.1109/TNB.2014.2363673.
M. Kothandapani and J. Prakash, The peristaltic transport of Carreau Nanofluids under effect of a magnetic field in a tapered asymmetric channel: application of the cancer therapy, Journal of Mechanics in Medicine and Biology 15(3) (2015), 1550030, DOI: 10.1142/S021951941550030X.
M. Kothandapani, J. Prakash and S. Srinivas, Peristaltic transport of a MHD Carreau fluid in a tapered asymmetric channel with permeable walls, International Journal of Biomathematics 8(4) (2015), 1550054, DOI: 10.1142/S1793524515500540.
M. Kothandapani, J. Prakash and V. Pushparaj, Analysis of heat and mass transfer on MHD peristaltic flow through a tapered asymmetric channel, Journal of Fluids 2015 (2015), Article ID 561263, DOI: 10.1155/2015/561263.
D. Krex, H. K. Schackert and G. Schackert, Genesis of cerebral aneurysms – anupdate, Acta Neurochirurgica 143(5) (2001), 429 – 449, DOI: 10.1007/s007010170072.
M. Kroon and G. A. Holzapfel, Modeling of saccular aneurysm growth in a humanmiddle cerebral artery, Journal of Biomechanical Engineering 130(5) (2008), 051012 (10 pages), DOI: 10.1115/1.2965597.
S. C. Ling and H. B. Atabek, A nonlinear analysis of pulsatile blood flow in arteries, Journal of Fluid Mechanics 55 (1972), 492 – 511.
G.-T. Liu, X.-J. Wang, B.-Q. Ai and L.-G. Liu, Numerical study of pulsating flow through a tapered artery with stenosis, Chinese Journal of Physics 42 (4-I), 401 – 409, https://www.ps-taiwan.org/cjp/download.php?type=paper&vol=42&num=4-I&page=401.
Q. Long, X. Y. Xu, K. V. Ramnarine and P. Hoskins, Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis, Journal of Biomechanics 34(10) (2001), 1229 – 1242, DOI: 10.1016/s0021-9290(01)00100-2.
J. J. V. McMurray and S. Stewart, The burden of heart failure, European Heart Journal Supplements 4(6) (2002), 50 – 58, DOI: 10.1016/S1520-765X(02)90160-4.
Kh. S. Mekheimer and M. A. El Kot, Influence of magnetic field and hall currents on blood flow through a stenotic artery, Applied Mathematics and Mechanics 29 (2008), 1093 – 1104, DOI: 10.1007/s10483-008-0813-x.
Kh. S. Mekheimer and M. A. El Kot, Mathematical modelling of unsteady flow of a Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis, Applied Mathematical Modelling 36 (2012), 5393 – 5407, DOI: 10.1016/j.apm.2011.12.051.
Kh. S. Mekheimer and M. A. El Kot, Suspension model for blood flow through arterial catheterization, Chemical Engineering Communications 197 (2010), 1195 – 1214, DOI: 10.1080/00986440903574883.
Kh. S. Mekheimer and M. A. El Kot, The micropolar fluid model for blood flow through a stenotic arteries, International Journal of Pure and Applied Mathematics 36 (2007), 393 – 405, https://ijpam.eu/contents/2007-36-4/5/5.pdf.
Kh. S. Mekheimer and M. A. El Kot, The micropolar fluid model for blood flow through a tapered artery with a stenosis, Acta Mechanica Sinica 24 (2008), 637 – 644, DOI: 10.1007/s10409-008-0185-7.
M. S. Moayeri and G. R. Zendehbudi, Effects of elastic property of the wall on flow characteristics through arterial stenoses, Journal of Biomechanics 36 (4) (2003), 525 – 535, DOI: 10.1016/S0021-9290(02)00421-9.
S. Mukhopadhyay and G. C. Layek, Analysis of blood flow through a modeled artery with ananeurysm, Applied Mathematics and Computation 217(16) (2011), 6792 – 6801, DOI: 10.1016/j.amc.2010.10.011.
L. J. Myers and W. L. Capper, Exponential taper in arteries: an exact solution of its effect on blood flow velocity wave forms and impedance, Medical Engineering & Physics 26 (2004), 147 – 155, DOI: 10.1016/S1350-4533(03)00117-6.
M. Nakamura and T. Sawada, Numerical study on the unsteady flow of non-Newtonian fluid, Journal of Biomechanical Engineering 112(1) (1990), 100 – 103, DOI: 10.1115/1.2891118.
E. V. Nikolova, On nonlinear waves in a blood-filled artery with ananeurysm, AIP Conference Proceedings 1978 (2018), 470050, DOI: 10.1063/1.5044120.
C. S. Peskin, Numerical analysis of blood flow in the heart, Journal of Computational Physics 25(3) (1977), 220 – 252, DOI: 10.1016/0021-9991(77)90100-0.
G. Pontrelli, Pulsatile blood flow in a pipe, Computers & Fluids 27(3) (1998), 367 – 380, DOI: 10.1016/S0045-7930(97)00041-8.
D. S. Sankar, A two-fluid model for pulsatile flow in catheterized blood vessels, International Journal of Non-Linear Mechanics 44 (2009), 337 – 351, DOI: 10.1016/j.ijnonlinmec.2008.12.008.
G. J. Sheard, Flow dynamics and wall shear stress variation in a fusiform aneurysm, Journal of Engineering Mathematics 64(4) (2009), 379 – 390, DOI: 10.1007/s10665-008-9261-z.
M. Siouffi, V. Deplano and R. Pelissier, Experimental analysis of unsteady flows through a stenosis, Journal of Biomechanics 31(1) (1998), 11 – 9, DOI: 10.1016/s0021-9290(97)00104-8.
J. S. Stroud, S. A. Berger and D. Saloner, Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture, Journal of Biomechanics 33(4) (2000), 443 – 455, DOI: 10.1016/s0021-9290(99)00207-9.
P. S. Swaye, L. D. Fisher, P. Litwin, P. A. Vignola, M. P. Judkins, H. G. Kemp, J. G. Mudd and A. J. Gosselin, Aneurysmal coronary artery disease, Circulation 67(1) (1983), 134 – 138, DOI: 10.1161/01.cir.67.1.134.
G. B. Thurston, Plasma release cell layering theory for blood flow, Biorheology 26(2) (1989), 199 – 214, DOI: 10.3233/BIR-1989-26208.
G. B. Thurston, Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood, Biorheology 16 (1979), 149 – 162, DOI: 10.3233/bir-1979-16303.
C. Tu and M. Deville, Pulsatile flow of non-Newtonian fluids through arterial stenoses, Journal of Biomechanics 29(7) (1996), 899 – 908, DOI: 10.1016/0021-9290(95)00151-4.
A. Valencia and M. Villanueva, Unsteady flow and mass transfer in models of stenotic arteries considering fluid-structure interaction, International Communications in Heat and Mass Transfer 33 (2006), 966 – 975, DOI: 10.1016/j.icheatmasstransfer.2006.05.006.
G. R. Zendehbudi and M. S. Moayeri, Comparison of physiological and simple pulsatile flows through stenosed arteries, Journal of Biomechanics 32(9) (1999), 959 – 965, DOI: 10.1016/s0021-9290(99)00053-6.
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