MAGNETO HYDRODYNAMIC EFFECTS ON AN ATHEROSCLEROTIC ARTERY—A THEORETICAL STUDY - Theoretical and Computational Research in the 21st Century - page 69

⎧ ⎫

⎛ ⎞

⎪ ⎜ ⎟ ⎪

⎡

n + 1 n + 1

⎤

∂ 1 ⎧ ∂ p ∂ B ⎫ ⎧ ∂ p ∂ B ⎫

⎪ ⎛ ⎞ ⎛ ⎞ ⎪

⎜ ⎟

τμ = ⎢ − mr − 2 τ − − mR − 2 τ ⎥

⎨ ⎨ ⎬ ⎨ ⎬ ⎬

⎜ ⎟ ⎜ ⎟

∂ p ∂ B

1 H 1 H

∂ r ⎛ ⎞ ∂ z ∂ z ∂ z ∂ z

⎜ ⎝ ⎠ ⎝ ⎠ ⎟

⎢ ⎩ ⎭ ⎩ ⎭ ⎥

⎪ ⎪

n

⎣ ⎦

2 m − m

⎜ ⎟

⎜ ⎟

2 1

⎪ ∂ ∂ ⎪

z z

⎝ ⎝ ⎠ ⎠

⎩ ⎭

⎧

n

⎫

μ ⎧∂ p mR ∂ ⎫

⎪ ⎛ ⎞ ⎪

, since r = R (23)

τ = − − 2 τ

⎨ ⎨ ⎬ ⎬

⎜ ⎟

1 H

n

2 mz ∂ ∂ z

⎝ ⎠

⎩ ⎭

⎪ ⎪

⎩ ⎭

2

2.3 NUMERICAL RESULTS AND DISCUSSION

To have 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, where the constitutive
coefficient index “ n ” for blood flow problems are generally taken to lie
between 0.9 and 1.1 [20-21], and in this analysis, we have used the value
0.95 for n < 1 and stenosis height,

δ

= (0.1,0.2,0.3,0.4,0.5),velocity of

τ = 0.05 then k = 3, when τ = 0.10
then k = 4, because viscosity of blood at 37°C is (3 − 4) × 10 −3 Pa.S. [22]. It
is seen that the shear stress decreases as the velocity increases from 0.5 to
8.5 with respect to different increasing externally used magnetic intensity.
Here, we have considered that the magnetic intensity assumed the values B
= ( B 1 = 1.1 × 10 4 , B 2 = 2.1 × 10 4 , B 3 = 4.1 × 10 4 ) [23-24] and B 0 = 8 tesla.
Measurement has also been performed for the estimation of the magnetic
susceptibility of blood, which was found to be 3.5 × 10 −6 and −6.6 × 10 −7
for the venous and arterial blood, respectively, considering the value of M
= −6.6 × 10 −7 . [16] Due to velocity gradient, where independent predictor
of hypertension improvement (odds ratio: 1.39; 95% confidence interval:
1.05-1.65; p = 0.013) is taken and therefore the severity of the stenosis
significantly affects the shear stress characteristics [25]. Approximately
considering the density of blood in stenosed artery is

blood ( u ) = (0.5, 2.5, 4.5, 6.5, 8.5 ,), H

ρ

= 1 (1.060 approx).
It is also estimated in this study that the different increasing magnetic in-
tensity and radial distance affect the volumetric flow rate of the nonsym-
metric stenosed artery.