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where
ss
/(
−
1)
δ
s
A
=
s
Rl
00
( )
s
−
Now, Eqs. (2) and (3) reduce to
∂
p
1
∂
μ
MB
∂
B
−+
r
zrr
()(
τ
+
0
0
)
=
0
(8)
2
∂
∂
ρ
u
∂
z
0
∂
−=−
∂
u
And
reduces in its non-dimensional form as
)
n
k
(
)
(
ττ
H
r
∂
u
u
2
2
)
n
k
(
−
)(
0
)
=
(
τρ
u
−
τ
ρ
u
0
H
0
∂
rr
0
k u
uR r
∂
n
(
ττ
−
)
=
(
−
∂
)
(9)
H
n
21
n
−
ρ
0
0
k
μ
ρ
MB
m
=
Where considering
m
=
(
0
0
)
and
2
ρ
n
uR
21
n
−
1
2
u
0
0
0
Now, the boundary conditions becomes
u
=0 at
R
(
z
) =
r
and
τ
is fi nite at
r
= 0
Again, from Eqs. (7) and (8)
∂
p
1
∂
∂
B
−+
()
r
τ
+
m
=
0
(10)
1
∂
zrr
∂
∂
z
∂
u
n
(
ττ
−
)
=
m
(
−
∂
)
(11)
H
2
r
∂
∂
u
r
ττ
≤
=0;
H
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