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ac
cu
r
ate
d
esi
g
n
m
et
h
o
d
s
n
e
ce
s
s
ar
y
f
o
r
en
er
g
y
co
n
v
er
s
io
n
d
ev
ice
s
,
t
h
e
u
s
e
o
f
n
e
w
m
ater
ial
s
,
h
y
p
er
s
o
n
ic
f
lo
w
a
n
al
y
s
i
s
,
a
n
d
o
th
er
s
.
Saj
id
a
n
d
Ha
y
at
[
1
3
]
h
av
e
in
v
e
s
ti
g
ated
t
h
e
i
n
f
lu
e
n
ce
o
f
t
h
er
m
al
r
ad
iatio
n
o
n
t
h
e
b
o
u
n
d
ar
y
la
y
er
f
lo
w
d
u
e
to
an
e
x
p
o
n
en
t
iall
y
s
tr
etc
h
i
n
g
s
h
ee
t.
B
h
attac
h
ar
y
y
a
an
d
L
a
y
ek
[
1
4
]
h
av
e
s
tu
d
ied
th
e
ef
f
e
cts
o
f
s
u
c
tio
n
/b
lo
w
i
n
g
o
n
s
te
ad
y
b
o
u
n
d
ar
y
la
y
er
s
tag
n
atio
n
-
p
o
in
t
f
lo
w
a
n
d
h
ea
t
tr
an
s
f
er
to
w
ar
d
s
a
s
h
r
in
k
i
n
g
s
h
ee
t
w
i
th
th
er
m
al
r
ad
iatio
n
.
P
r
am
a
n
ik
[
1
5
]
h
a
s
ex
p
lain
ed
ca
s
s
o
n
f
lu
id
f
lo
w
an
d
h
ea
t
tr
an
s
f
er
p
ast
a
n
ex
p
o
n
en
tial
l
y
p
o
r
o
u
s
s
tr
etc
h
i
n
g
s
u
r
f
ac
e
i
n
p
r
esen
ce
o
f
th
er
m
al
r
ad
iatio
n
.
E
f
f
ect
s
o
f
n
o
n
lin
ea
r
t
h
er
m
al
r
ad
iatio
n
o
n
MH
D
ch
e
m
icall
y
r
ea
ctin
g
Ma
x
w
ell
f
l
u
id
f
lo
w
p
ast
a
lin
ea
r
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tr
etch
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n
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h
ee
t
in
v
es
tig
a
ted
b
y
Mo
h
an
R
a
m
i
R
ed
d
y
et
al.
[
1
6
]
.
Ya
o
-
m
at
h
e
m
atica
l
an
d
n
u
m
er
ical
a
n
al
y
s
i
s
o
f
r
ad
iativ
e
h
ea
t tr
an
s
f
er
i
n
s
e
m
i
-
tr
an
s
p
ar
en
t
m
ed
ia
g
i
v
e
n
b
y
C
h
u
a
n
g
Han
et
al.
[
1
7
]
.
R
ate
o
f
ch
an
g
e
in
te
m
p
er
at
u
r
e
o
v
er
tim
e
is
ca
lled
r
a
m
p
ed
tem
p
er
atu
r
e.
I
n
f
e
w
i
n
v
esti
g
a
tio
n
s
r
esear
ch
er
s
co
n
s
id
er
ed
r
am
p
e
d
te
m
p
er
atu
r
e
p
r
o
f
iles
,
t
h
e
in
t
er
v
al
f
o
r
r
a
m
p
ed
w
it
h
r
esp
ec
t
to
ti
m
e
i
n
th
e
p
late
te
m
p
er
atu
r
e
i
s
as
s
u
m
ed
f
i
x
ed
i
.
e.
0
<
t
'
≤
t
0
(
t'
an
d
t
0
ar
e
ti
m
e
an
d
ch
ar
ac
ter
is
tic
t
i
m
e
r
esp
ec
tiv
el
y
)
w
h
ich
r
ed
u
ce
s
to
0<
t
≤
1
(
t
b
ein
g
th
e
d
i
m
e
n
s
i
o
n
less
ti
m
e)
in
n
o
n
-
d
i
m
e
n
s
io
n
al
f
o
r
m
.
I
t
is
to
b
e
n
o
ted
th
at
in
ter
v
al
f
o
r
r
am
p
ed
p
r
o
f
ile
v
a
r
ies
f
r
o
m
m
ater
ial
t
o
m
ater
ial
d
ep
en
d
i
n
g
u
p
o
n
t
h
e
s
p
ec
if
ic
h
ea
t
ca
p
ac
it
y
o
f
th
e
m
ater
ial.
Var
iab
le
r
a
m
p
ed
tem
p
er
atu
r
e
p
r
o
f
iles
ap
p
ea
r
in
r
ea
l
w
o
r
ld
s
itu
atio
n
in
b
u
ild
in
g
air
co
n
d
itio
n
i
n
g
s
y
s
te
m
s
,
f
ab
r
icatio
n
o
f
th
i
n
-
f
i
l
m
p
h
o
to
v
o
ltaic
d
ev
i
ce
s
,
p
h
ase
tr
an
s
i
tio
n
i
n
p
r
o
ce
s
s
in
g
o
f
m
ater
ials
,
t
u
r
b
in
e
b
lad
e
h
ea
t
tr
an
s
f
er
,
h
ea
t
ex
ch
a
n
g
er
s
etc.
Siv
a
R
ed
d
y
Sh
er
i
et
al.
[
1
8
]
h
av
e
an
al
y
ze
d
h
ea
t
an
d
m
a
s
s
tr
an
s
f
er
ef
f
ec
t
s
o
n
MH
D
n
atu
r
al
co
n
v
ec
tio
n
f
lo
w
p
ast
an
i
m
p
u
ls
i
v
el
y
m
o
v
in
g
v
er
tical
p
lat
e
w
it
h
r
a
m
p
ed
tem
p
er
atu
r
e.
S
iv
a
R
ed
d
y
S
h
er
i
an
d
An
j
an
Ku
m
ar
[
1
9
]
h
av
e
d
is
cu
s
s
ed
f
i
n
ite
ele
m
en
t
a
n
al
y
s
is
o
f
h
ea
t
an
d
m
as
s
tr
an
s
f
er
p
ast
an
i
m
p
u
ls
i
v
el
y
m
o
v
i
n
g
v
er
tical
p
late
w
i
th
r
a
m
p
ed
te
m
p
er
at
u
r
e.
Si
v
a
R
ed
d
y
S
h
er
i
et
al.
[
2
0
]
h
av
e
i
n
v
esti
g
ated
h
ea
t
an
d
m
as
s
tr
an
s
f
er
ef
f
ec
ts
o
n
MH
D
n
at
u
r
al
co
n
v
ec
tio
n
f
lo
w
p
ast
an
in
f
i
n
ite
i
n
cli
n
ed
p
late
w
it
h
r
a
m
p
ed
te
m
p
er
atu
r
e.
Nan
d
k
eo
l
y
ar
et
al.
[
2
1
]
h
av
e
g
iv
e
n
ex
ac
t
s
o
lu
tio
n
s
o
f
u
n
s
tead
y
MH
D
f
r
ee
co
n
v
ec
tio
n
i
n
a
h
ea
t
ab
s
o
r
b
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N:
2252
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N
u
merica
l a
n
a
lysi
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f MHD
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a
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flu
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w
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…
(
C
h
.
V
ija
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B
h
a
s
ka
r
)
91
f
l
u
id
f
lo
w
p
ast
a
f
la
t
p
late
w
it
h
r
a
m
p
ed
w
al
l
te
m
p
er
atu
r
e.
Seth
et
al.
[
2
2
]
h
av
e
clar
i
f
ied
h
y
d
r
o
m
a
g
n
etic
n
atu
r
al
co
n
v
ec
tio
n
f
lo
w
w
it
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ea
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an
d
m
as
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m
icall
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r
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ctin
g
a
n
d
h
ea
t
a
b
s
o
r
b
in
g
f
lu
id
p
ast
an
ac
ce
ler
ated
m
o
v
i
n
g
v
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tic
al
p
late
w
it
h
r
a
m
p
ed
te
m
p
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e
an
d
r
a
m
p
ed
s
u
r
f
ac
e
co
n
ce
n
tr
at
io
n
t
h
r
o
u
g
h
a
p
o
r
o
u
s
m
ed
i
u
m
.
MH
D
Nat
u
r
al
co
n
v
ec
tio
n
s
f
lo
w
p
ast
a
m
o
v
i
n
g
v
er
tical
p
late
w
i
th
r
a
m
p
ed
te
m
p
er
atu
r
e
s
tu
d
ied
b
y
Vij
a
y
a
B
h
as
k
ar
et
a
l.
[
2
3
]
.
As
p
er
au
t
h
o
r
s
k
n
o
w
led
g
e
n
o
w
o
r
k
h
a
s
ta
k
en
p
lace
to
in
v
e
s
tig
a
te
t
h
e
n
u
m
er
ical
a
n
al
y
s
i
s
o
n
MH
D
ca
s
s
o
n
f
lu
id
f
lo
w
o
v
er
an
ex
p
o
n
en
tial
l
y
ac
ce
ler
ated
v
er
tical
p
late
in
em
b
ed
d
ed
p
o
r
o
u
s
m
ed
iu
m
w
it
h
r
a
m
p
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w
all
te
m
p
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a
n
d
r
am
p
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d
s
u
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f
ac
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co
n
ce
n
tr
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n
.
I
n
t
h
e
cu
r
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en
t
n
u
m
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i
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v
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s
ti
g
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n
t
h
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in
f
l
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e
n
ce
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f
ca
s
s
o
n
p
ar
a
m
eter
an
d
t
h
er
m
al
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ad
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n
o
n
h
y
d
r
o
m
ag
n
etic,
i
n
co
m
p
r
es
s
ib
le,
v
is
co
u
s
elec
tr
icall
y
co
n
d
u
cti
n
g
,
h
ea
t a
b
s
o
r
b
in
g
f
l
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id
o
v
er
an
ex
p
o
n
e
n
tiall
y
ac
ce
l
er
ated
v
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tical
p
late
in
e
m
b
ed
d
ed
p
o
r
o
u
s
m
ed
iu
m
w
it
h
r
a
m
p
ed
te
m
p
er
at
u
r
e
an
d
r
am
p
ed
s
u
r
f
ac
e
co
n
ce
n
tr
atio
n
h
as
b
ee
n
s
t
u
d
ied
.
T
h
e
f
lo
w
g
o
v
er
n
i
n
g
p
ar
tial
d
if
f
er
e
n
tial
eq
u
atio
n
s
alo
n
g
w
it
h
i
n
itial
an
d
b
o
u
n
d
ar
y
c
o
n
d
itio
n
s
ar
e
tr
an
s
f
o
r
m
ed
in
to
n
o
n
-
d
i
m
en
s
io
n
a
l
f
o
r
m
t
h
en
s
o
l
v
ed
w
ith
t
h
e
aid
o
f
f
i
n
ite
ele
m
en
t
m
et
h
o
d
(
FEM
)
.
T
h
e
ef
f
ec
t
s
o
f
v
ar
io
u
s
p
er
tin
e
n
t
p
ar
a
m
eter
s
o
n
f
lo
w
p
atter
n
ar
e
d
is
p
la
y
ed
g
r
ap
h
icall
y
a
n
d
in
ter
p
r
eted
in
d
etail.
Ver
if
icatio
n
o
f
co
m
p
u
ta
tio
n
s
w
it
h
p
r
ev
io
u
s
s
tu
d
ie
s
in
t
h
e
liter
at
u
r
e
is
al
s
o
in
clu
d
ed
.
T
h
e
r
esu
lts
w
it
h
r
esp
ec
t
to
d
im
e
n
s
io
n
les
s
v
e
lo
cit
y
,
te
m
p
er
at
u
r
e
,
an
d
co
n
ce
n
tr
atio
n
ca
n
b
e
u
s
ed
as a
r
ef
er
en
ce
f
o
r
an
y
f
u
t
u
r
e
s
tu
d
y
.
2.
F
O
RM
U
L
AT
I
O
N
O
F
T
H
E
P
RO
B
L
E
M
I
n
Fi
g
u
r
e
1
th
e
f
lo
w
b
ein
g
co
n
f
in
ed
to
y'
>0
,
w
h
er
e
y'
t
h
e
c
o
o
r
d
in
ate
is
i
s
m
ea
s
u
r
ed
in
th
e
n
o
r
m
a
l
d
ir
ec
tio
n
to
th
e
p
late
an
d
x'
-
is
tak
e
n
alo
n
g
th
e
w
all
i
n
th
e
u
p
w
ar
d
d
ir
ec
tio
n
.
I
n
itiall
y
,
at
ti
m
e
t'
=0
,
b
o
th
th
e
f
lu
id
an
d
t
h
e
p
late
ar
e
u
n
i
f
o
r
m
te
m
p
er
atu
r
e
T
an
d
t
h
e
co
n
c
en
tr
atio
n
n
ea
r
t
h
e
p
late
is
a
s
s
u
m
ed
to
b
e
C
at
all
th
e
p
o
in
ts
r
e
s
p
ec
tiv
el
y
.
A
t
ti
m
e
t'
>0
,
th
e
p
late
i
s
g
i
v
en
a
n
e
x
p
o
n
e
n
tiall
y
ac
ce
ler
ated
in
t
h
e
v
er
tica
l
d
ir
ec
tio
n
ag
ai
n
s
t
g
r
av
itat
io
n
al
f
ield
w
it
h
v
elo
cit
y
t
a
e
U
0
an
d
co
n
s
t
an
t
h
ea
t
f
l
u
x
0
t
t
T
w
T
T
,
w
h
en
t'≤
t
0
an
d
T
w
'
w
h
e
n
t'
>
t
0
r
esp
ec
tiv
el
y
w
h
ic
h
is
th
er
e
af
ter
m
ai
n
tai
n
ed
co
n
s
tan
t
T
w
'
an
d
th
e
le
v
el
o
f
m
a
s
s
tr
an
s
f
er
at
th
e
s
u
r
f
ac
e
o
f
th
e
p
late
i
s
r
ai
s
ed
o
r
lo
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93
3.
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2
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d
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ed
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2
5
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.
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co
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ce
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ical
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s
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id
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ical
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ical
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s
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T
h
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f
in
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m
e
n
t
m
eth
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d
(
F
E
M)
co
n
s
is
t
s
o
f
f
o
llo
w
i
n
g
s
te
p
s
:
Step
1
: D
is
cr
etiza
tio
n
o
f
t
h
e
d
o
m
a
in
T
h
e
f
u
n
d
a
m
e
n
tal
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ce
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t
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f
t
h
e
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to
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id
e
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e
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eg
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o
n
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e
p
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b
le
m
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n
to
s
m
all
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n
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te
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p
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s
,
ca
lled
f
i
n
ite
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en
t
s
.
T
h
e
g
r
o
u
p
o
f
ele
m
e
n
ts
is
ca
l
l
ed
th
e
f
in
ite
ele
m
e
n
t
m
es
h
.
T
h
ese
f
i
n
ite
e
le
m
e
n
t
s
ar
e
ass
o
ciate
d
in
a
n
o
n
-
o
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er
la
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p
in
g
m
a
n
n
er
,
s
u
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h
t
h
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th
e
y
c
o
m
p
lete
l
y
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v
er
t
h
e
en
t
ir
e
s
p
ac
e
o
f
th
e
p
r
o
b
lem
.
Step
2
: I
n
v
en
tio
n
o
f
t
h
e
ele
m
e
n
t e
q
u
atio
n
A
r
ep
r
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tati
v
e
ele
m
en
t
is
s
elec
ted
f
r
o
m
t
h
e
m
e
s
h
an
d
t
h
e
v
ar
iatio
n
a
l
f
o
r
m
u
latio
n
o
f
th
e
g
iv
e
n
p
r
o
b
lem
is
cr
ea
ted
o
v
er
th
e
ty
p
ica
l
ele
m
e
n
t.
O
v
er
an
elem
en
t,
an
ap
p
r
o
x
i
m
ate
s
o
l
u
tio
n
o
f
th
e
v
ar
iati
o
n
a
l
p
r
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lem
is
in
v
e
n
ted
,
an
d
b
y
s
u
r
r
o
g
atin
g
th
i
s
in
th
e
s
y
s
te
m
,
th
e
ele
m
e
n
t
eq
u
atio
n
s
ar
e
g
en
er
ated
.
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h
e
elem
en
t
m
atr
i
x
,
w
h
ic
h
is
al
s
o
k
n
o
w
n
a
s
s
ti
f
f
n
e
s
s
m
atr
ix
,
i
s
er
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ted
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y
u
s
in
g
t
h
e
ele
m
en
t i
n
ter
p
o
lati
o
n
f
u
n
ct
io
n
s
.
Step
3
: A
s
s
e
m
b
l
y
o
f
t
h
e
ele
m
e
n
t e
q
u
a
tio
n
s
T
h
e
alg
eb
r
aic
eq
u
atio
n
s
s
o
ac
h
iev
ed
ar
e
a
s
s
e
m
b
led
b
y
i
m
p
o
s
i
n
g
th
e
in
ter
ele
m
en
t
co
n
tin
u
it
y
co
n
d
itio
n
s
.
T
h
is
y
ield
s
a
lar
g
e
n
u
m
b
er
o
f
m
at
h
e
m
atica
l
eq
u
atio
n
s
k
n
o
w
n
as
th
e
g
lo
b
al
f
in
ite
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e
n
t
m
o
d
el,
w
h
ic
h
g
o
v
er
n
s
t
h
e
w
h
o
le
d
o
m
ain
.
Step
4
: I
m
p
o
s
itio
n
o
f
t
h
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
O
n
t
h
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a
c
c
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m
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u
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t
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n
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h
e
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n
i
t
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l
a
n
d
b
o
u
n
d
a
r
y
c
o
n
d
i
t
i
o
n
s
(
1
0
)
a
r
e
i
m
p
o
s
e
d
.
Step
5
: So
lu
tio
n
o
f
a
s
s
e
m
b
led
eq
u
atio
n
s
T
h
e
a
s
s
e
m
b
l
e
d
e
q
u
a
t
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o
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s
s
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o
b
t
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e
d
c
a
n
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o
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b
y
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n
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f
t
h
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s
,
n
a
m
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l
y
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G
a
u
s
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l
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t
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c
h
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o
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b
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5
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4.
VALI
DAT
I
O
NS O
F
NUM
E
RICA
L
RE
SUL
T
S
I
n
o
r
d
er
to
v
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d
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f
y
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p
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ese
n
t
n
u
m
er
ical
m
et
h
o
d
u
s
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th
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s
tu
d
y
i
n
t
h
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s
p
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w
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a
v
ailab
le
r
esu
lts
o
f
R
aj
Nan
d
k
eo
l
y
ar
et
al.
[
2
1
]
an
d
Seth
et
al.
[
2
2
]
is
ex
h
ib
ited
in
T
ab
les
1
-
2.
T
h
ese
tab
les
d
is
p
l
a
y
th
e
co
m
p
ar
is
o
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it is
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r
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[
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P
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Pr
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l
.
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Kr
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5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
E
x
ten
s
i
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n
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ical
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tio
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n
d
f
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r
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lo
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e
lo
cit
y
,
te
m
p
er
at
u
r
e
an
d
co
n
ce
n
tr
atio
n
(
6
-
9
)
u
n
d
e
r
th
e
i
n
itial
a
n
d
b
o
u
n
d
ar
y
co
n
d
itio
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s
(
1
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)
,
b
y
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s
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n
g
f
i
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ite
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m
e
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m
et
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d
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Ob
tain
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co
m
p
u
tatio
n
al
r
esu
lts
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e
p
r
esen
ted
g
r
ap
h
ical
l
y
in
Fi
g
u
r
es
2
-
1
6
to
illu
s
tr
ate
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e
in
f
lu
e
n
c
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o
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er
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i
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g
p
ar
a
m
eter
s
v
iz.
C
ass
io
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p
ar
a
m
eter
,
Ma
g
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ic
p
ar
am
eter
,
p
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r
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y
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ar
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m
eter
,
th
er
m
al
Gr
ash
o
f
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m
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m
as
s
Gr
ash
o
f
n
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,
P
r
an
d
tl
n
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,
h
ea
t
ab
s
o
r
p
tio
n
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t
h
er
m
al
r
ad
iatio
n
,
Sch
m
id
t
n
u
m
b
er
an
d
ch
e
m
ical
r
ea
c
tio
n
p
ar
a
m
et
er
o
n
v
elo
cit
y
,
te
m
p
er
atu
r
e
an
d
co
n
ce
n
tr
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
A
p
p
l P
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I
SS
N:
2252
-
8792
N
u
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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N
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late
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.
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
.
2
,
A
u
g
u
s
t 2
0
2
0
:
8
9
–
99
98
b.
I
n
cr
ea
s
in
g
th
e
P
r
an
d
tl
n
u
m
b
er
ca
u
s
es
a
d
ec
eler
atio
n
in
th
e
te
m
p
er
atu
r
e
o
f
th
e
f
lo
w
.
W
h
ile
a
r
ev
er
s
e
ten
d
en
c
y
h
as
b
ee
n
id
e
n
ti
f
ied
a
g
ain
s
t
i
n
cr
ea
s
i
n
g
v
a
l
u
e
s
o
f
h
e
at
ab
s
o
r
p
tio
n
an
d
r
ad
iatio
n
p
ar
a
m
eter
f
o
r
b
o
th
r
a
m
p
ed
an
d
is
o
th
er
m
al
p
lates.
c.
I
n
cr
ea
s
in
g
Sc
h
m
id
t
n
u
m
b
er
an
d
ch
e
m
ica
l
r
ea
ctio
n
p
ar
am
et
er
r
esu
lts
a
r
ed
u
ctio
n
in
co
n
ce
n
tr
atio
n
v
al
u
e
s
f
o
r
b
o
th
r
a
m
p
ed
an
d
is
o
th
er
m
al
p
lates.
RE
F
E
R
E
N
C
E
S
[1
]
S.
Na
d
e
e
m
,
R.
U.
Ha
q
a
n
d
C.
L
e
e
,
“
M
HD
f
lo
w
o
f
a
Ca
ss
o
n
f
lu
id
o
v
e
r
a
n
e
x
p
o
n
e
n
ti
a
ll
y
sh
rin
k
in
g
sh
e
e
t
,
”
S
c
ien
ti
a
Ira
n
ica
,
v
o
l.
1
9
,
n
o
.
6
,
p
p
.
1
5
5
0
-
1
5
5
3
,
2
0
1
2
.
[2
]
S.
A
.
S
h
e
h
z
a
d
,
T
.
Ha
y
a
t,
M
.
Qa
sim
a
n
d
S
.
A
sg
h
a
r,
“
Eff
e
c
ts
o
f
m
a
ss
tran
s
f
e
r
o
n
M
HD
f
lo
w
o
f
c
a
ss
o
n
f
lu
id
w
it
h
c
h
e
m
i
c
a
l
re
a
c
ti
o
n
a
n
d
s
u
c
ti
o
n
,
”
B
ra
zili
a
n
J
o
u
rn
a
l
o
f
Ch
e
mic
a
l
En
g
in
e
e
rin
g
,
v
o
l.
3
0
,
n
o
.
1
,
p
p
.
1
8
7
-
1
9
5
2
0
1
3
.
[3
]
G
.
M
a
k
a
n
d
a
,
S
.
S
h
a
w
a
n
d
P
.
S
ib
a
n
d
a
,
“
Ef
fe
c
ts
o
f
ra
d
iatio
n
o
n
M
HD
f
re
e
c
o
n
v
e
c
ti
o
n
o
f
a
Ca
ss
o
n
f
lu
id
f
ro
m
a
h
o
rizo
n
tal
c
ircu
lar
c
y
li
n
d
e
r
w
it
h
p
a
rti
a
l
slip
i
n
n
o
n
-
Da
rc
y
p
o
ro
u
s
m
e
d
iu
m
w
it
h
v
isc
o
u
s
d
issip
a
t
io
n
,
”
B
o
u
n
d
a
ry
Va
lu
e
Pr
o
b
lem
s,
v
o
l
.
2
0
1
5
,
n
o
.
1
,
p
p
.
1
-
1
4
,
2
0
1
5
.
[
4
]
J
.
B
e
n
a
z
i
r
,
A
S
i
v
a
r
a
j
a
n
d
O
.
D
M
a
k
i
n
d
e
,
“
U
n
s
t
e
a
d
y
m
a
g
n
e
t
o
h
y
d
r
o
d
y
n
a
m
i
c
C
a
s
s
o
n
f
l
u
i
d
f
l
o
w
o
v
e
r
a
v
e
r
t
i
c
a
l
c
o
n
e
a
n
d
f
l
a
t
p
l
a
t
e
w
i
t
h
non
-
u
n
i
f
o
r
m
h
e
a
t
s
o
u
r
c
e
/
s
i
n
k
,
”
I
n
t
.
J
.
o
f
E
n
g
i
n
e
e
r
i
n
g
R
e
s
e
a
r
c
h
i
n
A
f
r
i
c
a
,
v
o
l
.
2
1
,
p
p
.
6
9
-
8
3
,
2
0
1
6
.
[5
]
N
.
A
h
m
e
d
,
A
.
H
.
S
h
e
ik
h
a
n
d
D.
P
.
Ba
ru
a
,
“
Ef
f
e
c
t
o
f
f
lu
id
su
c
ti
o
n
o
n
a
n
o
sc
il
lato
ry
M
HD
c
h
a
n
n
e
l
f
lo
w
w
it
h
h
e
a
t
tran
sf
e
r
,
”
Ap
p
li
c
a
ti
o
n
s
a
n
d
A
p
p
li
e
d
M
a
th
e
ma
ti
c
s: A
n
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l,
v
o
l.
1
1
,
n
o
.
1
,
p
p
.
2
6
6
-
2
8
4
,
2
0
1
6
.
[6
]
M
.
A
z
iz,
El
.
A
b
d
a
n
d
A
.
A
.
Af
i
fy
,
“
Eff
e
c
t
o
f
Ha
ll
c
u
rre
n
t
o
n
M
H
D
slip
f
lo
w
o
f
Ca
s
so
n
n
a
n
o
f
lu
i
d
o
v
e
r
a
stre
tch
in
g
sh
e
e
t
w
it
h
z
e
ro
n
a
n
o
p
a
rti
c
le m
a
ss
f
lu
x
,
”
T
h
e
rm
o
p
h
y
sic
s a
n
d
Aer
o
me
c
h
a
n
ics
,
v
ol
.
26
,
n
o
.
3
,
p
p
4
2
9
-
4
4
3
,
2
0
1
9
.
[7
]
H.
R.
Ka
taria
a
n
d
R.
P.
.
Ha
rsh
a
d
,
“
S
o
re
t
a
n
d
h
e
a
t
g
e
n
e
ra
ti
o
n
e
f
f
e
c
t
s
o
n
M
HD
Ca
ss
o
n
f
lu
id
f
lo
w
p
a
st
a
n
o
sc
il
latin
g
v
e
r
t
i
c
a
l
p
l
a
t
e
e
m
b
e
d
d
e
d
t
h
r
o
u
g
h
p
o
r
o
u
s
m
e
d
i
u
m
,
”
A
l
e
x
a
n
d
r
i
a
E
n
g
i
n
e
e
r
i
n
g
J
o
u
r
n
a
l
,
v
o
l
.
5
5
,
n
o
.
3
,
p
p
.
2
1
2
5
-
2
1
3
7
,
2
0
1
6
.
[8
]
S
.
M
o
h
y
u
d
-
Din
a
n
d
I
.
K
h
a
n
,
“
N
o
n
li
n
e
a
r
ra
d
iati
o
n
e
f
f
e
c
ts
o
n
sq
u
e
e
z
in
g
f
lo
w
o
f
a
Ca
ss
o
n
f
lu
id
b
e
twe
e
n
p
a
ra
ll
e
l
d
isk
s
,
”
Aer
o
sp
a
c
e
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
4
8
,
p
p
.
1
8
6
-
1
9
2
,
2
0
1
6
.
[9
]
N.
S.
A
k
b
a
r,
“
In
f
lu
e
n
c
e
o
f
m
a
g
n
e
ti
c
f
ield
o
n
p
e
ristalti
c
f
lo
w
o
f
a
Ca
ss
o
n
f
lu
id
i
n
a
n
a
sy
m
m
e
tri
c
c
h
a
n
n
e
l
:
A
p
p
li
c
a
ti
o
n
i
n
c
ru
d
e
o
i
l
re
f
in
e
m
e
n
t
,
”
J
o
u
rn
a
l
o
f
M
a
g
n
e
ti
sm
a
n
d
M
a
g
n
e
t
ic M
a
ter
ia
ls,
v
o
l
.
3
7
8
,
p
p
.
4
6
3
-
4
6
8
,
2
0
1
5
.
[1
0
]
K
.
V
a
jrav
e
lu
,
S
.
S
re
e
n
a
d
h
,
R.
H
.
Re
d
d
y
a
n
d
K.
M
u
ru
g
e
sa
n
,
“
P
e
rist
a
lt
ic
tran
sp
o
rt
o
f
a
Ca
ss
o
n
f
lu
id
i
n
c
o
n
tac
t
w
it
h
a
Ne
w
to
n
ian
f
lu
id
i
n
a
c
ircu
lar
tu
b
e
w
it
h
p
e
r
m
e
a
b
le
w
a
ll
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
F
lu
i
d
M
e
c
h
a
n
ics
Res
e
a
rc
h
,
v
o
l.
3
6
,
no
.
3
,
p
p
.
2
4
4
-
2
5
4
,
2
0
0
9
.
[1
1
]
P
.
Na
g
a
ra
n
i,
G
.
S
a
ro
ja
m
m
a
a
n
d
G
.
J
a
y
a
r
a
m
a
n
,
“
Ex
a
c
t
a
n
a
l
y
sis
o
f
u
n
ste
a
d
y
c
o
n
v
e
c
ti
v
e
d
iff
u
sio
n
in
Ca
ss
o
n
f
lu
id
f
lo
w
in
a
n
a
n
n
u
l
u
s
-
A
p
p
li
c
a
ti
o
n
t
o
c
a
th
e
teriz
e
d
a
rter
y
,
”
Acta
M
e
c
h
a
n
ica
,
v
o
l.
1
8
7
,
n
o
.
1
,
p
p
.
1
8
9
-
2
0
2
,
2
0
0
6
.
[1
2
]
S
.
P
riy
a
d
h
a
rsh
in
i
a
n
d
R
.
P
o
n
a
la
g
u
sa
m
y
,
“
M
a
th
e
m
a
ti
c
a
l
m
o
d
e
ll
in
g
f
o
r
p
u
lsa
ti
le
f
lo
w
o
f
Ca
ss
o
n
f
l
u
id
a
l
o
n
g
w
it
h
m
a
g
n
e
ti
c
n
a
n
o
p
a
rti
c
les
i
n
a
st
e
n
o
se
d
a
rtery
u
n
d
e
r
e
x
tern
a
l
m
a
g
n
e
ti
c
f
i
e
ld
a
n
d
b
o
d
y
a
c
c
e
l
e
ra
ti
o
n
,
”
Ne
u
r
a
l
Co
mp
u
t
in
g
a
n
d
Ap
p
li
c
a
t
io
n
s
,
v
o
l
.
3
1
,
no
.
3
,
p
p
.
8
1
3
-
8
2
6
,
2
0
1
9
.
[1
3
]
M
.
S
a
ji
d
a
n
d
T
.
Ha
y
a
t,
“
In
f
lu
e
n
c
e
o
f
t
h
e
rm
a
l
ra
d
iatio
n
o
n
th
e
b
o
u
n
d
a
ry
lay
e
r
f
lo
w
d
u
e
to
a
n
e
x
p
o
n
e
n
ti
a
ll
y
stre
tch
in
g
sh
e
e
t
,
”
In
ter
n
a
ti
o
n
a
l
C
o
mm
u
n
ic
a
ti
o
n
s i
n
He
a
t
a
n
d
M
a
ss
T
ra
n
sfe
r,
v
o
l
.
3
5
,
n
o.
3
,
p
p
.
3
4
7
-
3
5
6
,
2
0
0
8
.
[1
4
]
K.
Bh
a
tt
a
c
h
a
ry
y
a
a
n
d
G
.
C.
L
a
y
e
k
,
“
E
ff
e
c
ts
o
f
su
c
ti
o
n
/b
l
o
w
in
g
o
n
ste
a
d
y
b
o
u
n
d
a
ry
la
y
e
r
sta
g
n
a
ti
o
n
-
p
o
i
n
t
f
lo
w
a
n
d
h
e
a
t
tran
sf
e
r
to
w
a
rd
s
a
sh
ri
n
k
in
g
sh
e
e
t
w
it
h
th
e
rm
a
l
r
a
d
iatio
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
He
a
t
a
n
d
M
a
ss
T
ra
n
sfe
r,
v
o
l.
5
4
,
n
o
.
1
-
3
,
p
p
.
3
0
2
-
3
0
7
,
2
0
1
1
.
[1
5
]
S.
P
ra
m
a
n
ik
,
“
Ca
ss
o
n
f
lu
id
f
lo
w
a
n
d
h
e
a
t
tran
sf
e
r
p
a
st
a
n
e
x
p
o
n
e
n
t
ially
p
o
ro
u
s
stre
tch
in
g
s
u
rf
a
c
e
in
p
re
se
n
c
e
o
f
th
e
rm
a
l
ra
d
iatio
n
,
”
Ai
n
S
h
a
ms
En
g
i
n
e
e
rin
g
J
o
u
rn
a
l,
v
o
l.
5
,
n
o
.
1
,
p
p
.
2
0
5
-
2
1
2
,
2
0
1
4
.
[1
6
]
A.
M.
Ra
m
iRed
d
y
,
J.
V
.
Re
d
d
y
,
N.
S
a
n
d
e
e
p
a
n
d
V.
S
u
g
u
n
a
m
m
a
,
“
Eff
e
c
t
o
f
n
o
n
li
n
e
a
r
th
e
rm
a
l
ra
d
iatio
n
o
n
M
HD
c
h
e
m
i
c
a
ll
y
r
e
a
c
ti
n
g
m
a
x
we
ll
f
lu
i
d
f
lo
w
p
a
st
a
li
n
e
a
rl
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