IJPAM: Volume 36, No. 4 (2007)


Kh.S. Mekheimer$^1$, M.A. El Kot$^2$
$^1$Department of Mathematics
Faculty of Science
Al-Azhar University
Nasr City, Cairo, 11884, EGYPT
e-mail: kh_mekheimer@yahoo.com
$^2$Department of Mathematics
Faculty of Education
Suez Canal University
e-mail: m_aaosman@yahoo.com

Abstract.A micropolar model for blood flow through a horizontally nonsymmetreic artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the ($x$-axis) shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). Flow parameters such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed for different shape parameter $n$, the coupling number $N$ and the micropolar parameter $m$. It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape $n$ also the resistance to flow increases with the coupling parameter $N$ and decreases with the micropolar parameter $m$. The magnitudes of the resistance to flow are higher in the case of a micropolar fluid model than in the case of a Newtonian fluid model. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse variation to the resistance to flow with respect to $N$ and $m$. Finally, the effect of the coupling stress parameters $N$ and $m$ on the horizontal velocity is discussed.

Received: January 27, 2007

AMS Subject Classification: 92C50, 92C45

Key Words and Phrases: micropolar model, blood flow, horizontally nonsymmetreic artery, stenosis

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 4