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fl uid mechanics. Then an appropriate fi nite difference technique will be
adopted to solve the unsteady non-Newtonian fl ow of blood with differ-
ent boundary conditions in a cylindrical coordinate system. A quantitative
analysis will be done based on numerical computations by taking the dif-
ferent values of material constants and other parameters. The variation of
skin-friction with axial distance in the region of the stenosis is presented
graphically with respect to externally applied magnetic fi eld on stenosed
arterial segment. The qualitative and quantitative changes in the skin-
friction, shear stress, and volumetric fl ow rate at different stages of the
growth of the stenosis have also been presented in presence of an applied
magnetic fi eld.
Nomenclature
τ
shear stress
z
axial coordinate
yield stress
u
Axial average velocity of flow
τ
H
skin-friction
radius of the artery
τ
R
R
M
Magnetization
R
(
z
)
radius of the artery at stenosed portion
stenosis height
L
length of the artery
δ
flow resistance
length of the stenosis
λ
L
B
Applied Magnetic Field
p
pressure
Q
volumetric flow rate
k
viscosity coefficient
r
radial coordinate
n
fluid index
2.2
THE PROBLEM AND ITS SOLUTION
Consider the motion of blood following Herschel-Bulkley equation
through an axially symmetric stenosed artery under the influence of an
external applied uniform transverse magnetic field are shown in Figure
2.1 and Figure 2.2.
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