# 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 flow## Abstract

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*W*, the power index

_{i}*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

*F*. The results show that the transmission of axial velocity curves through a Newtonian fluid (

_{r}*W*= 0,

_{i}*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 (

*W*= 0,

_{i}*n*= 1) is smaller than that through the Carreau fluid.

doi:10.14456/WJST.2015.49

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*Walailak Journal of Science and Technology (WJST)*,

*12*(10), 863–883. Retrieved from https://wjst.wu.ac.th/index.php/wjst/article/view/631

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