Biomedical Engineering Reference
In-Depth Information
and
2
2
2(
π+
AQbu
)(
(,)
bt
−
au
( ,))
at
−π− ++
(
ba NAQD t
)(2
)
()
r
r
1
(2.80)
2
2
+π +
2(
AQbU
)(
(,)
bt
−
aU
( ,))
at
−π −
(
baRQDt
)(
+
)(
()
−Θ =−
)
Pt
( )
r
r
1
at any cross section
S.
In handling this problem, having nonhomogeneous boundary condi-
tions, Papathanasopoulou et al. employed the following approach. They
assumed that a function
w
=
w
(
r, t
) exists such that
ℵ
w
(
r
,
t
) = 0 ⇒
w
(
r
,
t
) =
A
1
(
t
)
r
+
A
2
(
t
)/
r
(2.81)
which satisfies the conditions
++
∂
w
r
AQ
w
r
(2
NAQ
)
∂
++ +
(
)
Dt
( )
1
(2.82)
pt
() at
ra
=
++
∂
w
r
w
r
=
(
QR
)
∂
++ +Θ
Dt
()
1
0at
rb
=
and
2
2
2
π
(
AQRbwbt wat
++ −
2
)((,)
(,))
+
π
(
b
−
aNA
)(
2
+
+
QQRDt
2
+
)()
1
(2.83)
2
2
+− +
π
(
baRQ
)(
)
Θ
=
Pt
()
or, equivalently,
2
N
a
++ +
2(
NA QRAt
2
)
()
−
At
() (
+++
AQRD t
2
)()
= −+Θ
pt
( )(
RQ
)
(2.84)
1
2
1
2
2
N
b
++ +
2(
NA QRAt
2
)
()
−
At
() (
+++
AQRD t
2
)()
=−+Θ
(
RQ
)
(2.85)
1
2
1
2
Pt
ba
()
++ ++++ =
π−
−+Θ
2(
AQRA t
2
)
() (2
NAQRD t
2
)
()
(
RQ
)
(2.86)
1
1
2
2
(
)
Then, the functions
urt
(,)
=
urt
( ,)
+
wrt
(,),
Urt
(,)
=
Urtwrt
( ,)
+
(,)
(2.87)
r
r
r
r
