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R
δ
s
ss
/(
−
1)
A
=
where
s
( )
s
−
0
0
The Navier-Stoke equation is
∂
p
1
∂
∂
B
−+
()
rz
+
μ
M
=
0
(2)
0
r
∂
z
∂
r
∂
z
For Casson fluid model, the relation between shear stress and shear rate is
given by Fung [18].
1/ 2
⎡
∂
u
r
⎤
⎛
⎞
ττ
≥
1/ 2
1/ 2
τ
=
τ
+
μ
−
if
⎜
⎟
⎢
⎥
H
H
∂
⎝
⎠
⎣
⎦
∂
u
r
ττ
≤
=
0
, if
(3)
H
∂
Therefore, the boundary conditions pertaining to the problem
rRz
=
()
at
(4)
u
=
0
r
=
0
is finite at
(5)
τ
rR
=
u
is the core
And in the core region of artery
and
, where
uu
=
c
c
velocity of blood.
Therefore, the nondimensional schemes are as follows:
r
z
R
p
u
τ
d
l
B
(6)
r
=
,
z
=
,
R
=
,
p
=
,
u
=
,
τ
=
,
d
=
,
l
=
0
,
B
=
2
2
0
R
l
R
ρ
u
u
ρ
u
l
l
B
0
0
0
0
0
0
B
is the external transverse uniform constant magnetic field; now, the
geometry is
{
}
R
(
z
)=
R
⎡
( )
s
−
s
⎤
;
1(
−
Al
)
(
zd
−
)
−
(
zd
−
)
dzdl
≤≤+
⎣
⎦
0
0
0
= 1, otherwise
(7)
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