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I
SS
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2252
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8792
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I
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N
:
2252
-
8792
I
n
t J
A
p
p
l P
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w
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g
,
Vo
l.
9
,
No
.
1
,
A
p
r
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0
2
0
:
6
7
–
77
68
Di
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I
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p
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k
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as
b
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l,
m
icr
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n
n
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l a
n
d
an
n
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lu
s
[
1
-
7
]
.
Un
s
tead
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r
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v
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f
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tical
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[
1
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.
T
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[
2
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ex
a
m
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id
in
an
an
n
u
l
u
s
s
atu
r
ated
w
ith
p
o
r
o
u
s
m
ater
ial
w
h
er
e
th
e
in
n
er
c
y
lin
d
er
is
h
ea
ted
co
n
s
ta
n
tl
y
w
h
ile
th
e
o
u
ter
c
y
li
n
d
er
is
m
ai
n
tai
n
ed
at
co
n
s
tan
t
te
m
p
er
atu
r
e.
T
h
e
y
r
ep
o
r
ted
th
at
in
ad
d
itio
n
to
th
e
r
es
u
lts
o
b
tain
ed
f
r
o
m
th
eir
p
r
ev
io
u
s
w
o
r
k
[
1
]
,
th
e
h
ea
t
g
en
er
ati
n
g
f
l
u
id
is
d
esira
b
l
e
f
o
r
o
p
tim
u
m
m
a
s
s
f
l
u
x
i
n
t
h
e
an
n
u
lar
g
ap
m
o
s
t
i
m
p
o
r
tan
tl
y
w
h
e
n
t
h
e
co
n
v
ec
t
io
n
cu
r
r
en
t
is
e
n
h
a
n
ce
d
b
y
co
n
s
ta
n
t
h
ea
t
f
l
u
x
.
T
h
e
an
al
y
tic
al
ex
a
m
i
n
atio
n
f
o
r
la
m
i
n
ar
f
u
ll
y
d
ev
elo
p
ed
f
lo
w
o
f
v
is
co
u
s
i
n
co
m
p
r
ess
ib
le
an
d
elec
tr
icall
y
co
n
d
u
cti
n
g
f
l
u
id
in
an
an
n
u
lu
s
i
n
w
h
ic
h
th
e
w
all
o
f
t
h
e
in
n
er
cy
li
n
d
er
is
h
ea
ted
o
r
co
o
led
eit
h
er
is
o
th
er
m
all
y
o
r
at
a
co
n
s
tan
t
h
ea
t
f
lu
x
w
h
ile
th
e
o
u
ter
c
y
lin
d
er
is
m
ai
n
tai
n
e
d
at
am
b
ie
n
t te
m
p
er
at
u
r
e
w
as
co
n
s
id
er
ed
b
y
[
3
]
.
C
lo
s
ed
f
o
r
m
s
s
o
lu
tio
n
s
f
o
r
tr
an
s
ie
n
t
f
u
ll
y
d
e
v
elo
p
ed
f
r
ee
co
n
v
ec
tio
n
co
r
r
esp
o
n
d
in
g
to
f
o
u
r
f
u
n
d
a
m
en
ta
l
th
er
m
al
b
o
u
n
d
ar
y
co
n
d
itio
n
s
i
n
v
er
tical
co
n
c
en
tr
ic
an
n
u
lu
s
w
as
p
r
ese
n
ted
b
y
[
4
-
5
]
r
ep
o
r
ted
th
e
an
al
y
tica
l
s
o
lu
t
io
n
o
f
a
la
m
i
n
ar
f
u
ll
y
d
e
v
elo
p
ed
f
r
ee
co
n
v
ec
tio
n
in
b
et
w
ee
n
co
ax
ial
cy
lin
d
er
s
p
ar
tiall
y
f
illed
w
it
h
p
o
r
o
u
s
m
ater
ial.
C
o
n
s
id
er
ab
le
r
esear
ch
w
o
r
k
h
as
b
ee
n
d
ed
icate
d
to
ex
a
m
i
n
e
th
e
r
o
le
o
f
h
ea
t
s
o
u
r
ce
/s
i
n
k
o
n
v
is
co
u
s
f
lo
w
f
o
r
d
if
f
er
en
t
p
h
y
s
ical
p
h
en
o
m
en
o
n
.
I
n
m
a
n
y
o
f
s
u
ch
p
r
o
b
le
m
s
,
th
er
e
m
a
y
b
e
p
lau
s
ib
le
te
m
p
er
at
u
r
e
d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
s
u
r
f
ac
e
an
d
th
e
s
u
r
r
o
u
n
d
i
n
g
f
l
u
i
d
.
T
h
is
d
e
m
a
n
d
s
th
e
co
n
s
id
er
atio
n
o
f
te
m
p
er
a
tu
r
e
d
ep
en
d
en
t
h
ea
t
s
o
u
r
ce
/s
in
k
w
h
ich
m
a
y
e
x
er
t
s
tr
o
n
g
ef
f
ec
t
o
n
t
h
e
h
ea
t
tr
a
n
s
f
er
ch
ar
ac
ter
is
t
ics.
A
n
a
n
al
y
tical
s
o
lu
tio
n
f
o
r
th
e
co
m
b
in
ed
ef
f
ec
t
o
f
h
ea
t
s
o
u
r
ce
,
p
o
r
o
s
it
y
an
d
t
h
er
m
a
l
r
ad
iatio
n
o
n
m
i
x
ed
co
n
v
ec
tio
n
f
lo
w
i
n
a
v
er
tical
a
n
n
u
l
u
s
w
a
s
p
r
esen
ted
b
y
[
6
]
.
His
f
in
d
in
g
s
ill
u
s
tr
ated
t
h
at
in
cr
ea
s
e
i
n
th
e
r
ad
iatio
n
p
ar
am
eter
an
d
h
ea
t
s
o
u
r
ce
p
ar
a
m
eter
ca
u
s
es
a
n
in
cr
ea
s
e
i
n
t
h
e
f
lu
id
te
m
p
er
atu
r
e
an
d
r
ate
o
f
h
ea
t
tr
an
s
f
er
.
R
ec
en
tl
y
,
r
e
f
er
en
ce
[
7
]
an
al
y
ze
d
th
e
u
n
s
tead
y
f
lo
w
o
f
a
v
i
s
co
u
s
,
in
co
m
p
r
ess
ib
le,
elec
tr
icall
y
a
n
d
th
er
m
all
y
co
n
d
u
ctin
g
f
lu
id
b
et
w
ee
n
t
w
o
in
f
i
n
ite
p
ar
allel
p
o
r
o
u
s
w
alls
p
lac
ed
at
y
=0
an
d
y
=
a
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
R
o
le
o
f h
ea
t so
u
r
ce
/s
in
k
o
n
ti
me
d
ep
en
d
e
n
t fr
ee
co
n
ve
ctive
flo
w
in
a
co
a
xia
l…
(
Ta
iw
o
S
.
Yu
s
u
f
)
69
I
t
is
as
s
u
m
ed
t
h
at
t
h
e
elec
tr
icall
y
co
n
d
u
cti
n
g
f
lu
id
i
s
d
r
iv
en
b
y
m
u
tu
al
ac
tio
n
o
f
t
h
e
i
m
p
o
s
ed
p
r
ess
u
r
e
g
r
ad
ien
t,
t
h
er
m
al
b
u
o
y
an
c
y
a
n
d
h
ea
t so
u
r
ce
o
r
s
in
k
,
o
th
er
r
elate
d
p
r
o
b
lem
s
ca
n
b
e
f
o
u
n
d
i
n
[8
-
1
3
]
.
T
h
e
e
f
f
e
c
t
o
f
b
u
o
y
a
n
t
f
o
r
c
e
s
o
n
m
a
g
n
e
t
o
h
y
d
r
o
d
y
n
a
m
i
c
(
M
H
D
)
f
r
e
e
c
o
n
v
e
c
t
i
v
e
f
l
o
w
o
f
a
n
e
l
e
c
t
r
i
c
a
l
l
y
co
n
d
u
cti
n
g
f
lu
id
in
th
e
p
r
esen
ce
o
f
h
ea
t
s
o
u
r
ce
/s
i
n
k
w
a
s
n
u
m
er
icall
y
s
t
u
d
ied
b
y
[
1
4
-
1
5
]
e
x
a
m
in
ed
th
e
e
f
f
ec
ts
o
f
h
ea
t
s
o
u
r
ce
/s
i
n
k
o
n
MH
D
f
lo
w
a
n
d
h
ea
t
tr
an
s
f
er
o
v
er
a
s
h
r
in
k
i
n
g
s
h
ee
t
w
it
h
m
a
s
s
s
u
cti
o
n
.
R
ef
er
e
n
ce
[
1
6
]
in
v
e
s
ti
g
ated
t
h
e
e
f
f
ec
t
s
o
f
in
d
u
ce
d
m
a
g
n
et
ic
f
ield
an
d
h
ea
t
s
o
u
r
ce
/s
in
k
o
n
f
u
ll
y
d
ev
e
lo
p
ed
lam
in
ar
n
at
u
r
al
co
n
v
ec
ti
v
e
f
lo
w
o
f
a
v
is
co
u
s
in
co
m
p
r
ess
ib
le
an
d
elec
tr
icall
y
co
n
d
u
cti
n
g
f
l
u
id
in
th
e
p
r
esen
ce
o
f
r
ad
ial
m
ag
n
etic
f
ield
b
y
co
n
s
id
er
in
g
in
d
u
ce
d
m
a
g
n
et
ic
f
ield
i
n
to
ac
co
u
n
t
an
d
r
ep
o
r
ted
s
o
m
e
i
n
te
r
esti
n
g
r
esu
lt,
th
e
y
o
b
tain
ed
th
at
i
n
cr
ea
s
in
g
v
al
u
e
o
f
t
h
e
h
ea
t
s
o
u
r
ce
/s
in
k
p
ar
a
m
eter
lead
s
to
i
n
cr
ea
s
e
i
n
v
elo
c
it
y
.
R
ef
er
e
n
ce
[
1
7
]
co
n
d
u
cted
a
s
tu
d
y
o
n
MH
D
n
atu
r
al
co
n
v
ec
t
iv
e
f
lo
w
o
f
h
ea
t
g
en
er
ati
n
g
/ab
s
o
r
b
in
g
f
l
u
id
w
i
th
s
lip
ef
f
ec
t
in
an
an
n
u
lar
p
o
r
o
u
s
m
ed
i
u
m
.
T
h
e
y
ad
o
p
ted
th
e
A
d
o
m
i
a
n
d
ec
o
m
p
o
s
itio
n
m
et
h
o
d
(
A
DM
)
,
a
n
u
m
er
ical
s
c
h
e
m
e
to
o
b
tain
th
e
s
o
lu
tio
n
o
f
t
h
e
g
o
v
er
n
i
n
g
eq
u
atio
n
.
I
n
th
e
r
e
s
u
lt
th
e
y
p
r
esen
ted
,
h
ea
t
g
e
n
er
atio
n
p
ar
a
m
eter
en
h
a
n
ce
d
th
e
te
m
p
er
at
u
r
e
an
d
v
elo
cit
y
o
f
th
e
f
l
u
id
in
th
e
an
n
u
lar
g
ap
.
Mo
r
eo
v
er
,
s
lip
ef
f
ec
t
p
ar
a
m
eter
in
cr
e
ases
t
h
e
v
elo
cit
y
o
f
th
e
f
l
u
id
.
E
m
p
l
o
y
i
n
g
a
n
u
m
e
r
i
c
a
l
s
h
o
o
t
i
n
g
t
e
c
h
n
i
q
u
e
w
i
t
h
a
f
o
u
r
t
h
–
f
i
f
t
h
o
r
d
e
r
R
u
n
g
e
-
K
u
t
t
a
s
c
h
e
m
e
,
r
e
f
e
r
e
n
c
e
[
1
8
]
ca
r
r
ied
o
u
t
an
i
n
v
e
s
ti
g
atio
n
t
o
s
tu
d
y
a
p
r
o
b
lem
o
f
t
h
e
c
h
e
m
ical
r
ea
ctio
n
an
d
h
ea
t
g
e
n
er
atio
n
o
r
ab
s
o
r
p
tio
n
ef
f
ec
ts
o
n
MH
D
m
i
x
ed
co
n
v
e
ctiv
e
b
o
u
n
d
ar
y
la
y
er
f
lo
w
o
f
a
n
an
o
f
lu
id
th
r
o
u
g
h
a
p
o
r
o
u
s
m
ed
iu
m
d
u
e
to
an
ex
p
o
n
en
t
iall
y
s
tr
etc
h
i
n
g
s
h
ee
t.
I
t
w
a
s
f
o
u
n
d
th
at
Nu
s
s
elt
n
u
m
b
er
is
a
d
ec
r
ea
s
in
g
f
u
n
ctio
n
o
f
t
h
e
h
ea
t
g
en
er
atio
n
/ab
s
o
r
p
tio
n
p
ar
a
m
e
ter
an
d
th
e
ch
e
m
ical
r
ea
ctio
n
p
ar
am
e
ter
.
L
ater
o
n
,
R
e
f
er
e
n
ce
[
1
9
]
ex
a
m
in
ed
th
e
co
m
b
i
n
ed
e
f
f
ec
ts
o
f
m
ag
n
et
ic
f
ield
an
d
h
ea
t
g
e
n
er
atio
n
/ab
s
o
r
p
tio
n
o
n
u
n
s
tea
d
y
b
o
u
n
d
ar
y
-
la
y
er
co
n
v
ec
ti
v
e
h
ea
t
a
n
d
m
as
s
t
r
an
s
f
er
o
f
a
n
o
n
-
Ne
w
to
n
ian
n
an
o
f
lu
id
o
v
er
a
p
er
m
ea
b
le
s
tr
etch
i
n
g
w
al
l
an
d
co
n
cl
u
d
ed
th
at
t
h
e
t
h
e
r
m
al
a
n
d
co
n
ce
n
tr
atio
n
b
o
u
n
d
ar
y
-
la
y
er
th
ic
k
n
es
s
h
as
h
ig
h
er
v
al
u
es
w
it
h
th
e
in
cr
ea
s
in
g
o
f
m
a
g
n
etic
f
i
eld
an
d
h
ea
t
g
en
er
atio
n
i
n
th
e
ca
s
e
o
f
a
p
s
eu
d
o
p
last
ic
n
an
o
f
l
u
id
th
a
n
o
th
er
s
.
Oth
er
r
elate
d
ar
ticles
b
y
d
if
f
er
en
t
r
esear
ch
er
s
ad
d
r
ess
i
n
g
s
o
m
e
r
e
m
ar
k
ab
le
p
r
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b
lem
s
o
n
th
e
e
f
f
ec
t
o
f
h
ea
t
g
en
er
atio
n
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o
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er
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f
l
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in
[
2
0
-
2
5
]
.
T
h
e
p
r
esen
t
p
ap
er
in
v
e
s
tig
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en
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illed
w
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l.
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itio
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2.
M
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CAL F
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id
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ir
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1
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(
1
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.
Fig
u
r
e
1
.
Sch
e
m
atic
d
iag
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o
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p
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8792
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I
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R
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6
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ied
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lt is
4
.
7
.
2
.
2
.
Va
lid
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t
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f
t
he
m
et
ho
d
T
o
v
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ate
th
e
n
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m
er
ical
s
c
h
e
m
e
ad
o
p
ted
in
i
n
v
er
ti
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g
(
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5
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th
e
ti
m
e
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ai
n
,
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e
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et
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t
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tain
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tate
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,
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ie
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ed
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y
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m
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ield
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s
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in
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w
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h
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an
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ie
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t
s
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at
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h
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e
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y
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n
g
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m
e
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io
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ed
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d
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if
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en
tial
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atio
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g
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w
it
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h
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v
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itial a
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o
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ar
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(
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h
e
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a
r
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o
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n
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er
th
e
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o
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n
d
ar
y
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n
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itio
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to
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tain
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ield
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s
k
i
n
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ictio
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e
s
u
r
f
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e
o
f
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h
e
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y
li
n
d
er
s
,
Nu
s
s
elt
n
u
m
b
er
an
d
m
as
s
f
lo
w
r
ate.
T
h
e
s
o
lu
ti
o
n
s
ar
e
g
i
v
en
a
s
:
(
)
=
1
0
(
)
+
2
0
(
)
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
1
,
A
p
r
il 2
0
2
0
:
6
7
–
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72
(
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T
o
f
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th
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estab
lis
h
t
h
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cu
r
ac
y
o
f
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h
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R
ie
m
a
n
n
-
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u
m
ap
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x
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p
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th
e
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DE
P
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is
u
s
ed
to
s
o
lv
e
(
1
,
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)
w
it
h
(
4
,
5
)
as
th
e
in
it
ial
an
d
b
o
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n
d
ar
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n
d
it
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r
esp
ec
tiv
el
y
.
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h
e
n
u
m
er
ic
al
v
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s
o
b
tain
ed
f
r
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th
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R
ie
m
an
n
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u
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ap
p
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x
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m
atio
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,
s
tead
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tate
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d
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P
ar
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llip
tic
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tial
Dif
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en
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E
q
u
atio
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s
(
P
DE
PE)
ar
e
p
r
esen
ted
in
T
ab
le
1
.
T
ab
le
1
.
Nu
m
er
ical
v
al
u
es o
f
t
h
e
tr
an
s
ien
t
s
tate
v
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cit
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b
ta
in
ed
u
s
in
g
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e
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ie
m
a
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n
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s
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m
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et
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d
,
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an
d
th
at
o
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tain
ed
f
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m
t
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t
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Da
T
R
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n
n
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s
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a
p
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a
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t
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4
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6
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t
e
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e
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1
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5
3
0
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0
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(
=
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04
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71
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3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
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e,
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cit
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,
s
k
in
f
r
ictio
n
o
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th
e
w
al
ls
o
f
t
h
e
c
y
lin
d
er
,
N
u
s
s
elt
n
u
m
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as
s
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lo
w
r
ate
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lar
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,
a
M
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m
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w
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)
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d
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=
7
.
0
)
w
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r
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i
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r
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,
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S
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s
s
p
ec
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ied
in
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(
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Fig
u
r
e
2
s
h
o
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t
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r
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=
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in
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w
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g
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at
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Dar
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(
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l
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d
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to
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ican
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.
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s
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n
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f
l
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is
co
s
it
y
.
Var
iat
io
n
o
f
s
k
i
n
f
r
ictio
n
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
R
o
le
o
f h
ea
t so
u
r
ce
/s
in
k
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n
ti
me
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(
Ta
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o
S
.
Yu
s
u
f
)
73
alo
n
g
th
e
i
n
s
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lated
w
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F
ig
u
r
e
s
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w
ith
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f
o
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b
o
th
h
ea
t
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o
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ce
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s
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t
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d
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m
t
h
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g
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r
e
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at
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h
e
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k
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f
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ictio
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alo
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h
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w
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o
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th
e
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n
er
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n
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d
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as
Dar
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atio
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d
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r
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r
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u
r
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Dar
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n
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ter
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Fi
g
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ab
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2
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N
u
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elt
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m
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as
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w
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a)
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Fig
u
r
e
2
.
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em
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Fig
u
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3
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Velo
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t so
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t sin
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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R
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Fig
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Var
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9
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Var
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)
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I
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T
ab
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2
.
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m
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ical
v
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es o
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t
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e
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CO
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A
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ated
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s
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ied
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t.
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lu
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ai
n
f
in
d
i
n
g
s
o
f
t
h
i
s
w
o
r
k
ar
e:
a.
T
h
e
f
lu
id
te
m
p
er
atu
r
e
is
an
i
n
cr
ea
s
in
g
f
u
n
ct
io
n
o
f
ti
m
e,
alth
o
u
g
h
t
h
e
in
cr
ea
s
e
is
m
o
r
e
p
r
o
n
o
u
n
ce
d
w
h
e
n
h
ea
t so
u
r
ce
i
s
ap
p
lied
.
b.
Velo
cit
y
i
n
cr
ea
s
es
w
i
th
i
n
cr
ea
s
e
in
Dar
c
y
n
u
m
b
er
a
n
d
ti
m
e.
T
h
e
r
ev
er
s
e
tr
en
d
is
o
b
s
er
v
ed
w
it
h
i
n
cr
ea
s
e
i
n
th
e
v
i
s
co
s
it
y
r
atio
.
c.
Sk
i
n
f
r
ictio
n
s
o
n
b
o
th
w
all
s
o
f
th
e
c
y
li
n
d
er
ar
e
en
h
an
ce
d
with
in
cr
ea
s
e
in
Dar
c
y
n
u
m
b
er
as
ti
m
e
p
ass
e
s
an
d
d
r
o
p
s
as th
e
v
is
co
s
it
y
r
ati
o
is
in
cr
ea
s
ed
.
RE
F
E
R
E
NC
E
S
[1
]
B.
K.
Jh
a
a
n
d
T
.
S
.
Y
u
su
f
,
“
T
ra
n
sie
n
t
f
re
e
c
o
n
v
e
c
ti
v
e
f
lo
w
w
it
h
h
e
a
t
g
e
n
e
ra
ti
o
n
/ab
so
r
p
ti
o
n
i
n
a
n
a
n
n
u
lar
p
o
r
o
u
s
m
e
d
iu
m
:
a
se
m
i
-
a
n
a
l
y
ti
c
a
l
a
p
p
ro
a
c
h
,”
J
.
Pro
c
e
ss
M
e
c
h
.
En
g
.
,
v
o
l
.
2
3
2
,
n
o
.
5
,
p
p
.
5
9
9
-
6
1
2
,
2
0
1
7
.
[2
]
T
.
S
.
Yu
su
f
a
n
d
B.
K
.
Jh
a
,
“
A
se
m
i
-
a
n
a
l
y
ti
c
a
l
so
lu
ti
o
n
f
o
r
ti
m
e
d
e
p
e
n
d
e
n
t
n
a
t
u
ra
l
c
o
n
v
e
c
ti
o
n
f
lo
w
w
it
h
h
e
a
t
g
e
n
e
ra
ti
o
n
/ab
so
r
p
ti
o
n
in
a
n
a
n
n
u
lu
s
p
a
rti
a
ll
y
f
il
led
w
it
h
p
o
ro
u
s
m
a
teria
l
,
”
M
u
l
ti
d
isc
ip
.
M
o
d
e
l.
M
a
ter
.
S
tru
c
t
.
,
v
o
l.
1
4
,
n
o
.
5
,
p
p
.
1
0
4
2
-
1
0
6
3
,
2
0
1
8
.
[3
]
T
.
S
.
Yu
su
f
,
“
Ex
a
c
t
so
lu
ti
o
n
o
f
a
n
M
HD
n
a
tu
ra
l
c
o
n
v
e
c
ti
o
n
f
lo
w
in
v
e
rti
c
a
l
c
o
n
c
e
n
tri
c
a
n
n
u
lu
s
w
it
h
h
e
a
t
a
b
so
rp
ti
o
n
,”
In
t.
J
.
Fl
u
id
M
e
c
h
.
T
h
e
rm
a
l
S
c
i
.
, v
o
l.
3
,
n
o
.
5
,
p
p
.
5
2
-
6
1
.
2
0
1
7
.
[4
]
M.
A
.
A
l
-
Ni
m
r
a
n
d
T
.
T
.
Da
ra
b
s
e
h
,
“
A
n
a
l
y
ti
c
a
l
so
lu
ti
o
n
f
o
r
tran
s
ien
t
lam
in
a
r
f
u
ll
y
d
e
v
e
lo
p
e
d
f
re
e
c
o
n
v
e
c
ti
o
n
in
o
p
e
n
-
e
n
d
e
d
v
e
rti
c
a
l
c
o
n
c
e
n
tri
c
p
o
ro
u
s a
n
n
u
l
i
,”
J
.
He
a
t
T
ra
n
sf
.
, v
o
l
.
1
17
,
n
o
.
3
,
p
p
.
7
6
2
-
7
6
4
,
1
9
9
5
.
[5
]
T
.
P
a
u
l
a
n
d
A
.
K.
S
i
n
g
h
,
“
Na
tu
ra
l
c
o
n
v
e
c
ti
o
n
b
e
tw
e
e
n
c
o
a
x
ial
v
e
rti
c
a
l
c
y
li
n
d
e
rs
p
a
rti
a
ll
y
f
il
led
w
it
h
a
p
o
r
o
u
s
m
a
teria
l,
”
Fo
rs
c
h
.
In
g
.
-
W
e
s
.
, v
o
l.
6
4
,
p
p
.
1
5
7
-
1
6
2
,
1
9
9
8
.
[6
]
M
.
O.
On
i
,
“
Co
m
b
in
e
d
e
f
fe
c
t
o
f
h
e
a
t
so
u
rc
e
,
p
o
r
o
sity
a
n
d
th
e
rm
a
l
ra
d
iatio
n
o
n
m
ix
e
d
c
o
n
v
e
c
ti
o
n
f
l
o
w
in
a
v
e
rti
c
a
l
a
n
n
u
l
u
s: A
n
e
x
a
c
t
so
lu
ti
o
n
,
”
E
n
g
.
S
c
i.
T
e
c
h
.
,
I
n
t.
J
.
,
v
o
l.
2
0
,
n
o
.
2
,
p
p
,
5
1
8
-
5
2
7
,
2
0
1
7
.
[7
]
O.
D.
M
a
k
in
d
e
,
Z.
H.
Kh
a
n
,
R.
A
h
m
a
d
,
Riz
w
a
n
Ul
Ha
q
,
a
n
d
W
.
A
.
Kh
a
n
,
“
Un
ste
a
d
y
M
HD
flo
w
in
a
p
o
ro
u
s
c
h
a
n
n
e
l
w
it
h
t
h
e
rm
a
l
ra
d
iatio
n
a
n
d
h
e
a
t
so
u
rc
e
/si
nk
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ap
p
li
e
d
a
n
d
Co
mp
u
ta
t
io
n
a
l
M
a
th
e
ma
ti
c
s
,
v
o
l.
5
,
n
o
.
5
9
,
p
p
.
1
-
2
1
,
2
0
1
9
.
[8
]
B.
K.
Jh
a
a
n
d
T
.
S
.
Y
u
su
f
,
“
In
v
e
stig
a
ti
o
n
o
f
h
e
a
t
g
e
n
e
ra
ti
o
n
/ab
s
o
rp
t
i
o
n
o
n
n
a
tu
ra
l
c
o
n
v
e
c
ti
o
n
f
l
o
w
in
a
v
e
rti
c
a
l
a
n
n
u
lar m
icro
-
c
h
a
n
n
e
l:
a
n
e
x
a
c
t
so
lu
ti
o
n
,”
M
u
lt
i
d
isc
ip
.
M
o
d
e
l.
M
a
t
e
r.
S
tru
c
t
.
,
v
o
l.
1
4
,
n
o
.
5
,
p
p
.
1
4
3
-
167
,
2
0
1
8
.
[9
]
B.
K.
J
h
a
,
M
.
O.
On
i
,
a
n
d
B
.
A
in
a
,
“
S
tea
d
y
f
u
ll
y
d
e
v
e
lo
p
e
d
m
ix
e
d
c
o
n
v
e
c
ti
o
n
f
lo
w
in
a
v
e
rti
c
a
l
m
icro
-
c
o
n
c
e
n
tri
c
a
n
n
u
l
u
s
w
i
t
h
h
e
a
t
g
e
n
e
r
a
t
i
n
g
/
a
b
s
o
r
b
i
n
g
f
l
u
i
d
:
a
n
e
x
a
c
t
s
o
l
u
t
i
o
n
,”
A
i
n
S
h
a
m
s
E
n
g
.
J
.
,
v
o
l
.
9
,
n
o
.
4
,
p
p
.
1
2
8
9
-
1
3
0
1
,
2
0
1
8
.
[1
0
]
Y
.
M
a
h
m
o
u
d
i
,
“
C
o
n
s
t
a
n
t
w
a
l
l
h
e
a
t
f
l
u
x
b
o
u
n
d
a
r
y
c
o
n
d
i
t
i
o
n
i
n
m
i
c
r
o
-
c
h
a
n
n
e
l
s
f
i
l
l
e
d
w
i
t
h
a
p
o
r
o
u
s
m
e
d
i
u
m
w
i
t
h
i
n
t
e
r
n
a
l
h
e
a
t
g
e
n
e
r
a
t
i
o
n
u
n
d
e
r
l
o
c
a
l
t
h
e
rm
a
l
n
o
n
-
e
q
u
i
l
i
b
r
i
u
m
c
o
n
d
i
t
i
o
n
,”
I
n
t
.
J
.
H
e
a
t
M
a
ss
T
r
a
n
s
f
.
, v
o
l
.
85
,
p
p
.
524
-
5
4
2
,
2
0
1
5
.
[1
1
]
S
.
Os
trac
h
,
“
Co
m
b
in
e
d
n
a
tu
ra
l
a
n
d
f
o
rc
e
d
-
c
o
n
v
e
c
ti
o
n
f
lo
w
a
n
d
h
e
a
t
tran
sf
e
r
o
f
f
lu
id
s
w
it
h
a
n
d
w
it
h
o
u
t
h
e
a
t
so
u
rc
e
s
in
c
h
a
n
n
e
ls w
it
h
li
n
e
a
rly
v
a
r
y
in
g
w
a
ll
te
m
p
e
ra
tu
re
s
,”
NACA
T
N
3
1
4
1
,
1
9
5
4
.
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