MAGNETO HYDRODYNAMIC EFFECTS ON AN ATHEROSCLEROTIC ARTERY—A THEORETICAL STUDY - Theoretical and Computational Research in the 21st Century - page 61

for both normal and stenotic arteries. In most of the investigations rel-
evant to the domain under discussion, the Newtonian behavior of blood
(single-phase homogeneous viscous fl uid) was accepted. This model of
blood is acceptable for high shear rate in case of a fl ow through narrow
arteries of diameter ≤1,000 μm; on the basis of the experimental observa-
tions, Bernett and Whitemore [1] suggested that blood behaves similar
to a non-Newtonian fl uid under certain conditions. H-B fl uid model and
Casson fl uid models are used in the theoretical investigation of blood fl ow
through narrow arteries. Investigations have mentioned that blood obeys
H-B equation at low shear rates when fl owing through a tube of diameter
of 0.095 mm or less and represents fairly closely occurring fl ow of blood
in arteries.
The laminar fl ow of blood in different arteries under certain conditions
behaves like a visco-elastic fl uid motion [2, 3]. Also, the blood fl ow affects
the thermal response of living tissues, which depends on the geometric
structure of artery (tapered artery) and fl ow variation of blood due to ste-
nosis. It has been established that once a mild stenosis develops, the re-
sulting fl ow disorder further infl uences the development of the disease and
arterial deformity, and changes the regional blood rheology [3, 4]. Steady
fl ow through an axi-symmetric stenosis has been investigated extensively
by Smith using an analytical approach indicating that the fl ow patterns
strongly depend on the geometry of the stenosis and the upstream Reyn-
olds number ( n ) [5]. In recent years, some studies [6-10] have reported on
the analysis of blood fl ow through single arteries in the presence of certain
conditions [6-10]. Misra and Chakraborty [11] developed a mathematical
model to study the unsteady fl ow of blood through arteries treating blood
as a Newtonian viscous incompressible fl uid paying due attention to the
orthotropic material behavior of the wall tissues. The analysis explored the
wall stress in the stenotic region and the shear stress at the stenotic throat.
The tapered blood vessel segment having a stenosis in its lumen is mod-
eled as a thin elastic tube with a circular cross-section containing a non-
Newtonian incompressible fl uid. Siddiqui et al. [12] presented a study of
pulsatile fl ow of blood through stenosed artery by modeling blood as Her-
schel-Bulkley fl uid with two parameters—the yield stress and the power
index n . The variation of velocity with radial distance in different mag-
netic intensity, taking n = 0.95, is exhibited graphically. Also, the variation
of wall shear stress and longitudinal impedance are shown taking differ-
ent values of the parameters. Misra et al. [13, 14] presented a theoretical