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Therefore, the constitutive equation according to Herschel-Bulkley
fl uid model
∂
−= − =
u
1
(
n
ττ
)
f
( );
ττ τ
≥
H
H
k
∂
∂
−=− =
r
u
(3)
n
k
(
)
(
ττ
)
f
( );
ττ τ
≥
H
H
∂
∂
r
u
and
=≤
0;
ττ
H
∂
r
Therefore, the boundary conditions pertaining to the problem
u
=
0
rRz
=
()
at
(4)
τ
r
=
0
is finite at
(5)
uu
=
rR
=
u
is the
And in the core region of artery
and
,
where
c
c
core velocity of blood.
Therefore, the nondimensional schemes are as follows:
r
z
R
p
u
τ
d
r
=
z
=
R
=
p
=
u
=
τ
=
d
=
,
,
,
,
,
,
,
R
R
ρ
u
2
u
ρ
2
l
l
0
0
0
0
0
l
B
l
=
0
B
=
,
(6)
0
l
B
0
B
is the external transverse uniform constant magnetic fi eld; now the
geometry is
{
}
dzdl
≤≤+
R
⎡
( )
s
−
s
⎤
1(
−
Al
)
(
zd
−
)
−
(
zd
−
)
(
z
) =
;
⎣
⎦
0
0
0
= 1; otherwise
(7)
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