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11.3
NUMERICAL RESULTS AND DISCUSSION
To obtain an estimate of the quantitative effects of the various parameters
involved in the analysis, it is necessary to evaluate the analytical results
obtained for dimensionless shear stress to flow,
τ
. It is based on area-axial
average velocity of flow on constant tube diameter, stenosis height consid-
ered as
δ
= (0.1, 0.2, 0.3, 0.4, 0.5),
u
= (0.5, 2.5, 4.5, 8.5),
H
τ
= 0.05, then
k
= 3, when
H
= 0.10 then
k
= 4, because the viscosity of blood at 37°C is
(3 − 4) × 10
−3
Pa.S [19]. It is seen that the shear stress increases as the axial
distance
z
increases from 0 to 0.5, and then it decreases as
z
increases from
0.5 to 1. This is due to large velocity gradient, and therefore, the severity
of the stenosis
significantly affects the shear stress characteristics [20].
Here, we have considered that the magnetic intensity assumed the values
as
B
= (1.1 × 10
4
, 2.1 × 10
4
, 4.1 × 10
4
) [21, 22] and
B
0
= 8 tesla. Measure-
ment has also been performed for the estimation of the magnetic suscep-
tibility of blood, which was found to be 3.5 × 10
−6
and −6.6 × 10
−7
for the
venous and arterial blood, respectively [20]. Approximately considering
the density of blood in stenosed artery is
τ
ρ
= 1 (1.060 approx).
To obtain an estimate of the quantitative effects of various parame-
ters involved in this analysis, the relevant computational work has been
performed for some specifi c cases using available experimental data. The
purpose of this numerical computation is to bring out the effects of mag-
netic fi eld intensity, slip velocity, stenotic height, shear stress, and radial
distance on the rheology of blood through stenosed artery taking the non-
Newtonian (Casson fl uid model) for blood.
FIGURE 11.3
Variation of velocity of flow with respect to different increasing magnetic
field intensity and radial distance.
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