The Unsteady Flow of a Carreau Fluid Through Inclined Catheterized Arteries Having a Balloon with Time-Variant Overlapping Stenosis
Keywords:
Carreau fluid, catheterized arterie, overlappings stenosis, unsteady flow, blood flowAbstract
This paper is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon (angioplasty) with time-variant overlapping stenosis. The nature of blood in small arteries are analyzed mathematically by considering it as a Carreau fluid. The analysis is carried out for an artery with a mild stenosis. The problem is formulated using a perturbation expansion in terms of a variant of the Weissenberg number to obtain explicit forms for the axial velocity, the stream function, the pressure gradient, the resistance impedance and the wall shear stress distribution. The results were studied for various values of the physical parameters, such as the Weissenberg number Wi, the power index n, the taper angle f, the maximum height of stenosis d*, the angle of inclination a, the maximum height of the balloon s*, the axial displacement of the balloon, the flow rate F and the Froud number Fr. The results show that the transmission of axial velocity curves through a Newtonian fluid (Wi = 0, n = 1) is substantially lower than that through a Carreau fluid near the wall of the balloon, while the inverse occurs in the region between the balloon and stenosis. The stream lines have a clearly distinguished shifting towards the stenotic region and this shifting appears near the wall of the balloon, while they have almost disappeared near the stenotic wall. Furthermore the size of trapping bolus in the case of the Newtonian fluid (Wi = 0, n = 1) is smaller than that through the Carreau fluid.doi:10.14456/WJST.2015.49
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Kh Mekheimer and MA Elkot. The micropolar fluid model for blood flow through stenotic arteries. Int. J. Pure Appl. Math. 2007; 4, 393-405.
Kh Mekheimer and MA Elkot. Influence of magnetic field and Hall currents on blood flow through stenotic artery. Appl. Math. Mech. Eng. Ed. 2008; 29, 1093-104.
Kh Mekheimer and MA Elkot. The micropolar fluid model for blood flow through a tapered arteries with a stenosis. Acta Mech. Sin. 2008; 24, 637-44.
Kh Mekheimer and MA Elkot. Suspension model for blood flow through arterial catheterization. Chem. Eng. Comm. 2010; 197, 1-20.
Kh Mekheimer, MH Haroun and MA Elkot. Effects of magnetic field, porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics. Appl. Math. Mech. Eng. Ed. 2011; 32, 1047-64.
S Chakravarty and PK Mandal. A nonlinear two-dimensional model of blood flow in an overlapping arterial stenosis subjected to body acceleration. Math. Comput. Model. 1996; 24, 43-58.
S Chakravarty and PK Mandal. Two-dimensional blood flow through tapered arteries under stenotic conditions. Int. J. Nonlinear Mech. 2000; 35, 779-93.
Z Ismail, I Abdullah, N Mustapha and N Amin. Power-law model of blood flow through a tapered overlapping stenosed artery. Appl. Math. Comput. 2008; 195, 669-80.
GC Layek, S Mukhopadhyay and RSD Gorla. Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction. Int. J. Eng. Sci. 2009; 47, 649-59.
VP Srivastava and R Rastogi. Blood flow through stenosed catheterized artery: Effects of hematocrit and stenosis shape. Comput. Math. Appl. 2010; 59, 1377-785.
G Varshney, VK Katiyar and S Kumar. Effect of magnetic field on the blood flow in artery having multiple stenosis: A numerical study. Int. J. Eng. Sci. Tech. 2010; 2, 67-82.
Kh Mekheimer, MH Haroun and MA Elkot. Induced magnetic field influences on blood flow through an anisotropically tapered elastic arteries with overlapping stenosis in an annulus. Can. J. Phys. 2011; 89, 201-12.
T Hayat, S Najma, Y Abdelmaboud and S Asghar. Peristaltic flow of a second-order fluid in the presence of an induced magnetic field. Int. J. Numer. Meth. Fluid. 2011; 67, 537-58.
K Vajravelu, S Sreenadh and VR Babu. Peristaltic transport of a herschel-bulkley fluid in an inclined tube. Int. J. Nonlinear Mech. 2005; 40, 83-90.
KM Prasad and G Radhakrishnamacharya. Flow of herschel-bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenoses. Arch. Mech. 2008; 60, 161-72.
S Nadeem and NS Akbar. Influence of heat transfer on a peristaltic transport of Herschel-Bulkley fluid in a non-uniform inclined tube. Comm. Nonlinear Sci. Numer Simulat. 2009; 14, 4100-13.
S Nadeem and NS Akbar. Peristaltic flow of Walter’s B fluid in a uniform inclined tube. J. Biorheol. 2010; 24, 22-8.
KM Prasad, G Radhakrishnamacharya and JV Murthy. Peristaltic pumping of a micropolar fluid in an inclined tube. Int. J. Appl. Math. Mech. 2010; 6, 26-40.
US Chakraborty. Devajyoti biswas and Moumita Paul, suspension model blood flow through an inclined tube with an axially non-symmetrical stenosis. Korea Aust. Rheol. J. 2011; 23, 25-32.
M Khan, Q Abbas and K Duru. Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study. Int. J. Numer. Meth. Fluid. 2010; 62, 1169-80.
R Ellahi, R Arshad, S Nadeem and M Ali. Peristalic flow of Carreau fluid in a rectangular duct through a porous medium. Math. Probl. Eng. 2012; 2012, Article ID 329639.
AE Naby, AE Hakeem and AEM Misiery. Effects of an endoscope and generalized Newtonian fluid on peristaltic motion. Appl. Math. Comput. 2002; 128, 19-35.
G Jayaraman and A Sarkar. Nonlinear analysis of arterial blood flow-steady streaming effect. Nonlinear Anal. 2005; 63, 880-90.
PK Mandal. Unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis. Int. J. Nonlinear Mech. 2005; 40, 151-64.
RB Bird, RC Armstrong and O Hassager. Dynamics of Polymeric Liquids: Fluid Mechanics. Vol I. John Wiley & Sons, New York, 1977, p. 1-672.
RI Tanner. Engineering Rheology. Oxford University Press, New York, 1985.
DF Young. Effect of a time dependent stenosis of flow through a tube. J. Eng. Ind. 1968; 90, 248-54.
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