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problem, considering hemodynamic and cardiovascular disorders due to
non-Newtonian flow of blood in multistenosed arteries. The application of
magneto hydrodynamics principles in medicine and biology is of growing
interest in the literature of bio-mathematics [13-15]. Bali and Awasthi [16]
suggested that by Lenz's law, the Lorentz's force will oppose the motion
of conducting fluid. As blood is an electrically conducting fluid, the MHD
principles may be used to decelerate the flow of blood in a human arterial
system, and thereby, it is useful in the treatment of certain cardiovascu-
lar disorders and in the diseases that accelerate blood circulation, such
as hemorrhages, hypertension, etc. [17]. This provides us an opportunity
to consider the problem of blood flow through a stenosed segment of an
artery where the rheology of blood is described by Casson fluid model
under the influence of externally applied magnetic field. 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
shear stress and skin-friction with different radial distance in the region
of the stenosis is presented graphically with respect to externally applied
magnetic field on stenosed arterial segment. The qualitative and quantita-
tive changes in the skin-friction, shear stress, and volumetric flow rate at
different stages of the growth of the stenosis have also been presented in
the presence of
an applied magnetic field.
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
B
Applied magnetic field
length of the stenosis
L
Q
volumetric flow rate
p
pressure
R
radial coordinate
k
viscosity coefficient
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