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g
v
elo
city
.
A
k
ey
s
tr
en
g
th
o
f
t
h
is
s
tu
d
y
is
its
an
aly
tical
ap
p
r
o
ac
h
u
s
in
g
th
e
L
ap
lace
p
r
o
ce
d
u
r
e,
wh
ic
h
p
r
o
v
id
es
clo
s
ed
-
f
o
r
m
s
o
lu
ti
o
n
s
,
o
f
f
e
r
in
g
p
r
ec
is
e
in
s
ig
h
ts
in
to
th
e
ef
f
ec
ts
o
f
g
o
v
er
n
in
g
p
ar
a
m
eter
s
.
Fu
r
th
er
m
o
r
e,
it
ca
p
tu
r
es
th
e
tr
an
s
ien
t
b
eh
a
v
io
r
o
f
tem
p
e
r
atu
r
e
an
d
co
n
ce
n
tr
atio
n
f
ield
s
,
ad
d
in
g
d
ep
th
to
co
n
v
en
tio
n
al
s
tead
y
-
s
tate
an
al
y
s
es.
Ho
wev
er
,
a
n
o
tab
le
lim
itatio
n
is
th
e
ass
u
m
p
tio
n
o
f
an
in
f
in
ite
v
e
r
tical
p
late
,
w
h
ich
m
ay
n
o
t
f
u
lly
r
e
p
r
esen
t
p
r
ac
tical
s
ce
n
ar
io
s
with
f
in
ite
b
o
u
n
d
ar
ies.
Ad
d
itio
n
ally
,
th
e
s
tu
d
y
d
o
es
n
o
t
ac
co
u
n
t
f
o
r
tu
r
b
u
len
ce
o
r
th
r
ee
-
d
im
en
s
io
n
al
ef
f
ec
ts
,
w
h
ich
co
u
ld
f
u
r
t
h
er
r
ef
in
e
th
e
u
n
d
er
s
tan
d
in
g
o
f
f
l
o
w
d
y
n
am
ics
in
r
ea
l
-
wo
r
ld
a
p
p
licatio
n
s
.
Desp
ite
th
ese
lim
itatio
n
s
,
th
e
s
tu
d
y
co
n
tr
ib
u
tes v
alu
a
b
le
an
aly
tical
an
d
n
u
m
er
ical
in
s
ig
h
ts
in
to
c
o
n
v
ec
tiv
e
h
ea
t a
n
d
m
ass
tr
an
s
f
er
p
r
o
ce
s
s
es.
Flu
id
s
,
with
th
eir
f
lo
w
an
d
u
n
iq
u
e
p
r
o
p
er
ties
lik
e
v
is
co
s
ity
,
ar
e
s
tu
d
ied
in
f
lu
id
d
y
n
am
ics.
Un
s
tead
y
f
lu
id
m
o
tio
n
,
in
f
lu
e
n
ce
d
b
y
ch
an
g
in
g
p
r
o
p
er
ties
,
af
f
ec
ts
h
ea
t
tr
an
s
f
er
,
o
f
te
n
v
ia
co
n
v
ec
tio
n
,
wh
er
e
f
lu
id
s
p
ee
d
en
h
an
ce
s
h
ea
t
m
o
v
em
en
t
(
e.
g
.
,
ca
r
r
ad
iato
r
s
,
s
tirr
in
g
)
.
T
h
e
tr
an
s
f
er
o
f
m
ass
is
a
f
u
n
ctio
n
o
f
co
n
ce
n
tr
atio
n
g
r
ad
ien
ts
,
in
v
o
lv
es p
ar
ticle
m
o
v
em
en
t to
war
d
s
eq
u
ili
b
r
iu
m
in
m
ix
tu
r
es.
T
h
e
m
o
v
em
e
n
t
o
f
m
ass
,
r
esu
ltin
g
f
r
o
m
c
o
n
ce
n
tr
atio
n
d
if
f
e
r
en
ce
s
,
is
in
cr
ea
s
in
g
ly
v
ital
in
ch
em
ical
p
r
o
ce
s
s
in
g
,
en
v
ir
o
n
m
en
tal,
a
n
d
b
io
m
ed
ical
f
ield
s
,
an
d
i
m
p
ac
tin
g
ap
p
licatio
n
s
lik
e
air
p
u
r
if
icatio
n
,
d
r
u
g
d
eliv
er
y
,
an
d
ch
e
m
ical
r
ea
ctio
n
s
.
Similar
to
h
ea
t
tr
an
s
f
er
v
ia
tem
p
er
atu
r
e
g
r
a
d
ien
ts
,
it
s
ee
k
s
eq
u
ilib
r
iu
m
.
Ma
s
s
tr
an
s
f
er
f
lu
x
es
ar
e
cr
u
cial
in
clim
ato
lo
g
y
,
astro
p
h
y
s
ics,
an
d
g
e
o
p
h
y
s
ics,
ex
em
p
lifie
d
b
y
ev
e
r
y
d
a
y
p
h
en
o
m
en
a
lik
e
s
m
o
k
e
d
is
p
er
s
io
n
an
d
ev
ap
o
r
atio
n
.
C
o
m
b
in
ed
h
ea
t
an
d
m
ass
ex
ch
an
g
e
is
ess
en
tial
in
en
g
in
ee
r
in
g
,
p
ar
ticu
lar
ly
in
d
ev
ices
lik
e
h
u
m
id
if
ier
s
,
d
eh
u
m
id
if
ier
s
,
co
o
lin
g
to
wer
s
,
an
d
ev
ap
o
r
ativ
e
co
n
d
en
s
er
s
,
wh
er
e
h
ea
t a
n
d
m
o
is
tu
r
e
m
o
v
e
s
im
u
ltan
e
o
u
s
ly
.
T
h
e
p
r
im
a
r
y
o
b
jectiv
e
o
f
th
is
s
tu
d
y
was
to
p
r
o
v
id
e
a
d
etailed
u
n
d
e
r
s
tan
d
in
g
o
f
t
h
e
in
tr
icate
r
elatio
n
s
h
ip
s
b
etwe
en
m
o
m
en
tu
m
,
h
ea
t,
a
n
d
m
ass
tr
an
s
f
er
i
n
th
e
b
o
u
n
d
ar
y
lay
e
r
r
e
g
io
n
o
f
an
in
f
i
n
ite
v
er
tical
p
late.
T
o
ac
h
iev
e
th
is
,
th
e
r
esear
ch
an
aly
ze
d
th
e
e
f
f
ec
t
s
o
f
r
ad
iatio
n
tem
p
er
at
u
r
e,
ch
em
ical
r
ea
ctio
n
co
ef
f
icien
ts
,
Sch
m
id
t
n
u
m
b
er
,
Gr
ash
o
f
n
u
m
b
er
s
,
Pra
n
d
tl
n
u
m
b
er
,
an
d
tim
e
o
n
f
lu
id
v
elo
c
ity
,
co
n
ce
n
tr
ati
o
n
,
an
d
tem
p
e
r
atu
r
e
p
r
o
f
iles
.
T
h
e
L
ap
lace
tr
a
n
s
f
o
r
m
m
eth
o
d
was
u
s
ed
to
o
b
tain
an
aly
ti
ca
l
s
o
lu
tio
n
s
,
an
d
n
u
m
er
ical
co
m
p
u
tatio
n
s
wer
e
p
er
f
o
r
m
ed
to
v
is
u
alize
an
d
in
t
er
p
r
et
th
e
im
p
ac
t
o
f
th
ese
d
i
v
er
s
e
p
ar
am
eter
s
o
n
th
e
f
lo
w
an
d
tr
an
s
p
o
r
t
ch
ar
ac
t
er
is
tics
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
J
h
a
an
d
Pra
s
ad
[
1
]
ex
p
lo
r
ed
th
e
f
lo
w
d
ev
o
id
o
f
r
esis
tan
ce
a
n
d
m
ass
tr
a
n
s
f
er
in
th
e
s
ce
n
ar
io
o
f
f
lo
w
b
eh
in
d
an
ac
ce
ler
atin
g
v
er
tica
l
p
late
.
T
h
is
s
tu
d
y
lik
ely
ex
a
m
in
ed
h
o
w
m
ass
tr
an
s
f
er
o
cc
u
r
s
wh
en
th
e
f
lo
w
is
in
f
lu
en
ce
d
b
y
th
e
ac
ce
ler
atio
n
o
f
a
p
late,
a
s
itu
atio
n
co
m
m
o
n
in
ap
p
licatio
n
s
lik
e
ae
r
o
d
y
n
am
ics
an
d
f
lu
id
m
ec
h
an
ics.
C
h
am
b
r
é
an
d
Yo
u
n
g
[
2
]
co
n
ce
n
tr
ated
o
n
th
e
t
r
an
s
p
o
r
t
o
f
ch
em
ical
r
ea
ctio
n
s
u
b
s
tan
ce
w
ith
in
a
lam
in
ar
b
o
u
n
d
ar
y
lay
er
f
lo
w.
T
h
e
r
esear
ch
ex
p
l
o
r
ed
h
o
w
a
ch
em
ically
r
ea
ctiv
e
s
u
b
s
tan
ce
d
if
f
u
s
es
with
in
th
is
lay
er
,
wh
ich
is
im
p
o
r
tan
t
in
p
r
o
ce
s
s
es
lik
e
ch
em
ical
en
g
i
n
ee
r
in
g
a
n
d
en
v
ir
o
n
m
en
tal
s
cien
ce
s
.
C
u
s
s
ler
[
3
]
an
aly
ze
d
m
ass
tr
an
s
f
er
v
ia
d
if
f
u
s
io
n
in
f
lu
id
s
y
s
tem
s
.
T
h
is
is
a
cla
s
s
ic
s
tu
d
y
in
m
ass
tr
an
s
f
er
,
f
o
cu
s
in
g
o
n
h
o
w
p
ar
ticles
(
lik
e
ch
em
icals o
r
s
o
lu
tes)
m
o
v
e
th
r
o
u
g
h
a
f
lu
id
m
ed
iu
m
d
u
e
to
d
if
f
u
s
io
n
,
a
n
im
p
o
r
ta
n
t
p
r
o
ce
s
s
in
v
ar
io
u
s
in
d
u
s
tr
ies
s
u
ch
as
p
h
ar
m
ac
eu
tical,
c
h
em
ical
p
r
o
ce
s
s
in
g
,
an
d
e
n
v
ir
o
n
m
en
tal
e
n
g
i
n
ee
r
in
g
.
Das
et
a
l
.
[
4
]
ex
am
i
n
ed
Ma
s
s
tr
an
s
f
er
af
f
ec
ts
f
lo
w
d
y
n
am
ics
o
v
e
r
a
s
u
d
d
en
ly
s
tar
ted
in
f
in
ite
p
late
with
s
tead
y
th
er
m
o
d
y
n
am
ic
ch
em
ical
r
ea
ctio
n
s
.
T
h
e
s
tu
d
y
ex
p
lo
r
ed
h
o
w
th
e
o
n
s
et
o
f
m
ass
tr
a
n
s
f
er
af
f
ec
ts
f
lo
w
ch
ar
ac
ter
is
tics
wh
en
a
p
late
s
u
d
d
en
ly
s
tar
ts
m
o
v
in
g
,
a
s
itu
atio
n
en
co
u
n
ter
ed
in
m
an
y
f
lu
i
d
-
s
tr
u
ctu
r
e
in
ter
ac
tio
n
ap
p
licatio
n
s
.
An
ab
r
u
p
tly
s
tar
ted
in
f
in
ite
v
er
ti
ca
l
p
late,
u
n
d
er
g
o
in
g
ch
em
i
ca
l
r
ea
ctio
n
s
,
was
s
tu
d
ied
b
y
Das
et
a
l.
[
5
]
to
d
eter
m
in
e
th
e
im
p
ac
t
o
f
m
ass
tr
an
s
f
er
o
n
th
e
r
esu
ltin
g
f
lo
w.
Gu
p
ta
et
a
l.
[
6
]
e
x
am
in
ed
h
o
w
f
r
ee
co
n
v
ec
tio
n
af
f
ec
ts
f
lo
w
p
ast
a
v
er
tically
ac
ce
ler
atin
g
p
late
in
an
in
c
o
m
p
r
ess
ib
le,
en
er
g
y
-
co
n
s
er
v
in
g
f
l
u
id
.
T
h
e
s
tu
d
y
co
m
b
in
ed
co
n
v
ec
tio
n
(
h
ea
t
tr
an
s
f
er
d
u
e
to
f
lu
id
m
o
tio
n
)
with
a
cc
eler
atio
n
,
wh
ich
is
u
s
ef
u
l
f
o
r
u
n
d
er
s
tan
d
in
g
n
a
tu
r
al
co
n
v
ec
tio
n
in
v
ar
io
u
s
e
n
g
in
ee
r
in
g
ap
p
licatio
n
s
lik
e
co
o
lin
g
s
y
s
tem
s
an
d
n
atu
r
al
v
e
n
tilatio
n
.
T
o
d
eter
m
in
e
th
e
e
f
f
ec
ts
o
f
m
ass
tr
an
s
f
er
a
n
d
f
r
ee
co
n
v
ec
tio
n
,
Kaf
o
u
s
ias
an
d
R
ap
tis
[
7
]
an
aly
ze
d
th
e
f
lo
w
o
f
a
v
er
tical
ly
ac
ce
ler
atin
g
in
f
i
n
ite
p
late
with
v
ar
iab
le
s
u
ctio
n
o
r
in
jectio
n
.
T
h
e
in
clu
s
io
n
o
f
s
u
ctio
n
o
r
in
jectio
n
ad
d
s
co
m
p
lex
ity
,
as
it
in
v
o
lv
es
co
n
tr
o
llin
g
th
e
f
lo
w
b
y
r
em
o
v
in
g
o
r
a
d
d
in
g
f
lu
id
f
r
o
m
th
e
s
u
r
f
ac
e
,
wh
ich
is
cr
i
tical
in
h
ea
t
ex
ch
an
g
er
s
an
d
f
iltra
tio
n
s
y
s
tem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
imu
la
tio
n
o
f rea
ctive
flo
w
o
v
er a
p
a
r
a
b
o
lic
ve
r
tica
l p
la
te
u
s
in
g
MATLAB
(
S
iva
ku
ma
r
P
u
s
h
p
a
r
a
j
)
1675
Ma
zu
m
d
ar
a
n
d
Dek
a
[
8
]
a
n
al
y
ze
d
m
a
g
n
eto
h
y
d
r
o
d
y
n
am
ic
(
MH
D
)
f
lo
w
in
ter
ac
tin
g
with
an
in
f
in
ite
v
er
tical
s
u
r
f
ac
e
im
p
u
ls
iv
ely
b
eg
u
n
b
y
th
er
m
al
r
ad
iatio
n
.
T
h
e
L
ap
la
ce
-
tr
an
s
f
o
r
m
at
io
n
ap
p
r
o
ac
h
w
as
attu
n
ed
to
s
o
lv
e
d
im
en
s
io
n
less
g
o
v
er
n
i
n
g
eq
u
atio
n
s
.
Selv
ar
aj
an
d
J
o
th
i
[
9
]
aim
ed
to
d
eter
m
i
n
e
h
o
w
h
ea
t
s
o
u
r
ce
s
in
f
lu
en
ce
MH
D
f
lo
w
ac
r
o
s
s
an
ac
ce
ler
a
ted
p
late,
tak
in
g
in
to
ac
co
u
n
t
v
ar
iab
le
tem
p
e
r
atu
r
e
a
n
d
m
a
s
s
d
if
f
u
s
io
n
.
MH
D
f
lo
w
in
v
o
lv
es
t
h
e
in
ter
ac
tio
n
o
f
a
c
o
n
d
u
ctin
g
f
lu
id
(
e.
g
.
,
p
lasma
o
r
m
o
lten
m
etal)
wit
h
a
m
ag
n
etic
f
ield
,
wh
ich
is
im
p
o
r
tan
t
in
ad
v
a
n
ce
d
en
g
in
ee
r
in
g
ap
p
licatio
n
s
lik
e
n
u
clea
r
r
ea
cto
r
s
an
d
s
p
ac
e
tech
n
o
l
o
g
y
.
R
ap
tis
et
a
l
.
[
1
0
]
s
tu
d
ied
s
u
ctio
n
an
d
h
ea
t
f
lu
x
ef
f
ec
ts
in
h
y
d
r
o
m
ag
n
etic
co
n
v
ec
tio
n
f
lo
w
p
ast
an
ac
ce
ler
atin
g
in
f
in
ite
v
er
tical
p
late
.
T
h
is
wo
r
k
c
o
m
b
in
e
d
MH
D
a
n
d
h
ea
t
tr
an
s
f
er
,
in
v
esti
g
atin
g
h
o
w
s
u
ctio
n
(
r
em
o
v
al
o
f
f
lu
id
)
an
d
h
ea
t
f
lu
x
af
f
ec
t
f
lu
i
d
f
lo
w
in
m
ag
n
etic
f
ield
s
.
T
h
i
s
is
cr
it
ical
f
o
r
p
r
o
ce
s
s
es
lik
e
co
o
li
n
g
in
n
u
clea
r
r
ea
cto
r
s
o
r
elec
tr
o
m
a
g
n
etic
p
u
m
p
s
.
R
ap
tis
an
d
Sin
g
h
[
1
1
]
an
aly
ze
d
t
h
e
f
r
ee
c
o
n
v
ec
tio
n
s
tirr
in
g
o
f
a
v
er
tical
p
late
in
th
e
MH
D
d
o
m
ai
n
.
T
h
is
r
esear
ch
in
v
esti
g
ated
f
r
ee
co
n
v
ec
tio
n
d
y
n
am
ics
in
a
m
ag
n
etic
f
ield
f
o
r
a
n
elec
tr
ically
co
n
d
u
ctiv
e
f
lu
id
f
lo
win
g
p
ast
a
m
o
v
in
g
p
late,
with
ap
p
licatio
n
s
in
d
esig
n
in
g
s
p
ac
e
tech
n
o
lo
g
y
d
ev
ices
lik
e
elec
tr
o
m
ag
n
etic
p
u
m
p
s
a
n
d
h
ea
t
e
x
ch
a
n
g
er
s
.
Sin
g
h
an
d
Sin
g
h
[
1
2
]
e
x
p
lo
r
e
d
th
e
ef
f
ec
t
o
f
m
ass
tr
an
s
f
er
o
n
f
lo
w
p
ast
a
v
er
tically
ac
ce
ler
atin
g
p
late
u
n
d
e
r
co
n
s
tan
t
h
ea
t
f
lu
x
.
T
h
e
s
tu
d
y
is
r
elev
an
t
to
ap
p
licatio
n
s
wh
er
e
h
ea
t
an
d
m
ass
n
ee
d
to
b
e
tr
an
s
f
er
r
ed
s
im
u
ltan
eo
u
s
ly
,
s
u
ch
as
in
h
ea
t
e
x
ch
an
g
er
s
,
ch
em
ical
r
ea
cto
r
s
,
an
d
en
v
ir
o
n
m
e
n
tal
s
y
s
tem
s
.
So
u
n
d
alg
e
k
ar
[
1
3
]
e
x
am
in
ed
h
o
w
m
ass
tr
an
s
f
er
a
f
f
ec
ts
a
co
n
s
tan
tly
m
o
v
in
g
v
er
ti
ca
l
p
late,
a
s
ce
n
ar
io
ap
p
licab
le
to
m
ater
ial
p
r
o
ce
s
s
in
g
an
d
co
o
lin
g
.
I
n
co
n
tr
ast,
th
e
s
tu
d
y
b
y
Uwa
n
ta
an
d
Sar
k
i
[
1
4
]
e
v
alu
a
ted
th
e
co
n
s
eq
u
en
ce
s
o
f
s
ig
n
i
f
ican
t
m
ass
d
if
f
u
s
io
n
an
d
tem
p
er
atu
r
e
v
ar
iatio
n
s
o
n
th
e
m
ec
h
a
n
is
m
s
o
f
h
ea
t
a
n
d
m
ass
tr
an
s
f
er
.
T
h
is
r
esea
r
ch
lik
ely
d
ea
lt
with
ca
s
es
wh
er
e
m
ass
d
if
f
u
s
io
n
f
o
llo
ws
an
ex
p
o
n
en
tial
p
atte
r
n
,
wh
ich
o
cc
u
r
s
in
m
an
y
d
if
f
u
s
io
n
-
d
r
iv
en
p
r
o
ce
s
s
es,
an
d
h
o
w
tem
p
er
atu
r
e
in
f
lu
en
ce
s
th
ese
p
r
o
ce
s
s
es in
ap
p
licatio
n
s
s
u
ch
as d
r
y
in
g
o
r
c
h
em
ical
r
ea
ctio
n
s
.
R
ajp
u
t
an
d
Ku
m
ar
[
1
5
]
a
n
a
ly
ze
d
th
e
d
y
n
am
ic
b
e
h
av
io
r
o
f
u
n
s
tead
y
MH
D
f
lo
w
o
v
er
an
im
p
u
ls
iv
ely
in
clin
ed
p
late,
with
p
ar
ticu
lar
atten
tio
n
to
th
e
co
u
p
led
ef
f
e
cts
o
f
v
ar
iab
le
tem
p
er
atu
r
e,
m
ass
d
if
f
u
s
io
n
,
an
d
h
all
cu
r
r
en
t.
MH
D
b
o
u
n
d
ar
y
lay
er
f
lo
w
o
v
er
v
e
r
tical
p
lates
u
n
d
er
r
a
m
p
in
g
tem
p
e
r
atu
r
e
cir
cu
m
s
tan
ce
s
is
s
tu
d
ied
.
I
n
th
eir
wo
r
k
,
Sar
m
a
an
d
Ah
m
ed
[
1
6
]
e
x
am
in
ed
h
o
w
h
ea
t
s
o
u
r
ce
s
im
p
ac
t
M
HD
f
lo
w
ar
o
u
n
d
a
n
ac
ce
ler
ated
p
late,
wh
ile
also
ac
co
u
n
tin
g
f
o
r
tem
p
er
atu
r
e
an
d
m
ass
d
if
f
u
s
io
n
v
ar
iatio
n
s
.
R
esear
ch
s
tu
d
ies
Kr
is
h
n
a
an
d
C
h
am
k
h
a
[
1
7
]
e
x
am
i
n
e
m
a
n
y
p
h
en
o
m
en
a,
in
clu
d
in
g
h
all
an
d
io
n
s
lip
,
ela
s
tico
-
v
is
co
u
s
f
lu
id
b
eh
av
io
r
,
an
d
n
a
n
o
f
l
u
id
d
y
n
a
m
ics,
in
d
is
tin
ct
MH
D
s
ettin
g
s
.
T
h
ese
in
v
esti
g
atio
n
s
elu
cid
ate
th
e
in
f
l
u
en
ce
o
f
p
o
r
o
u
s
m
ed
ia
a
n
d
th
e
r
m
al
co
n
d
itio
n
s
o
n
f
lo
w
c
h
ar
ac
ter
is
tics
an
d
h
ea
t
t
r
an
s
f
er
.
T
h
e
in
v
e
s
tig
atio
n
co
n
d
u
cted
b
y
R
ed
d
y
et
a
l.
[
1
8
]
f
o
cu
s
ed
o
n
u
n
s
tead
y
MH
D
f
lo
w
o
v
er
ac
ce
ler
atin
g
v
er
tical
p
lates,
co
n
s
id
er
in
g
a
co
n
s
tan
t
h
ea
t
f
lu
x
an
d
r
am
p
in
g
p
late
t
em
p
er
atu
r
e.
Ah
m
ed
et
a
l.
[
1
9
]
th
en
in
v
esti
g
ated
h
all
c
u
r
r
e
n
t
ef
f
ec
ts
in
MH
D
f
lo
w
o
v
er
an
a
cc
eler
atin
g
p
late.
Stu
d
ies
b
y
C
h
am
k
h
a
[
2
0
]
a
n
d
E
lb
ash
b
esh
y
[
2
1
]
f
u
r
t
h
er
e
x
am
in
ed
MH
D
f
r
ee
co
n
v
ec
tio
n
an
d
h
ea
t/m
ass
tr
an
s
p
o
r
t,
r
esp
ec
tiv
ely
.
L
ater
w
o
r
k
b
y
Ab
o
eld
a
h
ab
a
n
d
E
lb
a
r
b
ar
y
[
2
2
]
ex
p
lo
r
ed
b
u
o
y
a
n
cy
e
f
f
ec
ts
,
Po
p
et
a
l.
[
2
3
]
a
n
aly
ze
d
f
o
r
ce
d
co
n
v
ec
tio
n
u
s
in
g
n
u
m
er
ical
m
eth
o
d
s
,
a
n
d
Kim
[
2
4
]
s
tu
d
ied
u
n
s
tead
y
f
lo
w.
T
h
is
b
o
d
y
o
f
wo
r
k
s
h
o
ws
th
e
p
r
o
g
r
ess
io
n
o
f
r
esear
ch
in
th
is
ar
ea
.
E
ar
ly
r
esear
ch
in
to
MH
D
an
d
f
r
ee
co
n
v
ec
tio
n
p
h
e
n
o
m
en
a,
s
u
ch
as
t
h
at
b
y
E
n
g
lan
d
an
d
E
m
er
y
[
2
5
]
o
n
th
e
r
m
al
r
ad
iatio
n
,
laid
th
e
g
r
o
u
n
d
wo
r
k
f
o
r
s
u
b
s
eq
u
e
n
t stu
d
ies.
3.
F
O
RM
UL
AT
I
O
N
AND
AP
P
RO
ACH
At
th
e
in
itial
co
n
d
itio
n
,
b
o
th
th
e
p
late
a
n
d
t
h
e
f
lu
id
a
r
e
at
th
e
s
am
e
tem
p
er
atu
r
e,
an
d
th
e
co
n
ce
n
tr
atio
n
o
f
s
p
ec
ies
in
th
e
f
lu
id
is
u
n
if
o
r
m
at
ac
r
o
s
s
all
p
o
in
ts
.
Un
d
er
th
ese
in
itial
co
n
d
itio
n
s
,
th
e
p
late
is
s
tatio
n
ar
y
.
At
a
tim
e
′
>
0
,
th
e
p
late
b
eg
in
s
wi
th
a
v
elo
city
=
0
.
′
2
with
in
its
o
wn
p
lan
e.
T
h
e
u
n
s
tead
y
,
b
u
o
y
a
n
cy
-
d
r
iv
en
f
lo
w
o
f
a
f
l
u
id
n
e
ar
a
v
e
r
tical
p
late,
ch
ar
ac
ter
ized
b
y
lin
ea
r
ly
i
n
cr
ea
s
in
g
tem
p
er
atu
r
e
an
d
s
p
ec
ies
co
n
ce
n
tr
atio
n
,
is
an
aly
ze
d
.
A
u
n
if
o
r
m
,
t
r
an
s
v
er
s
e
m
ag
n
etic
f
ield
(
B
0
)
is
a
p
p
lie
d
.
Un
d
er
t
h
e
B
o
u
s
s
in
esq
ap
p
r
o
x
im
atio
n
,
t
h
e
co
u
p
led
g
o
v
er
n
in
g
eq
u
ati
o
n
s
f
o
r
m
ass
,
m
o
m
en
t
u
m
,
e
n
er
g
y
,
an
d
s
p
ec
ies
tr
an
s
p
o
r
t,
in
clu
d
in
g
r
a
d
iatio
n
an
d
ch
e
m
ical
r
ea
ctio
n
te
r
m
s
,
ar
e
s
o
lv
ed
to
o
b
tain
th
e
f
lo
w,
v
elo
city
tem
p
er
atu
r
e,
a
n
d
c
o
n
ce
n
tr
atio
n
f
ield
s
.
(
,
′
)
′
=
(
(
,
′
)
−
∞
)
+
∗
(
′
(
,
′
)
−
′
∞
)
+
2
(
,
′
)
2
(
1
)
(
,
′
)
′
=
2
(
,
′
)
2
−
(
,
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(
2)
′
(
,
′
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′
=
2
′
(
,
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2
−
(
′
(
,
′
)
−
′
∞
)
(
3
)
T
h
ese
ar
e
th
e
co
n
d
itio
n
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
5
0
2
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4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
39
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
6
7
3
-
1
6
8
2
1676
Fo
r
all
y
,
≤
0
:
(
,
0
)
=
0
,
(
,
0
)
=
∞
,
′
(
,
0
)
=
∞
′
=
0
:
(
0
,
′
)
=
0
.
′
2
,
(
0
,
′
)
=
∞
+
(
−
∞
)
′
′
,
′
(
0
,
′
)
=
′
(
4
)
→
∞
:
(
∞
,
′
)
=
∞
(
∞
,
′
)
=
0
,
′
(
∞
,
′
)
=
∞
′
W
e
ca
n
m
ak
e
eq
u
atio
n
s
(
1
)
,
(
2
)
,
an
d
(
3
)
d
im
en
s
io
n
less
b
y
u
s
i
n
g
th
ese
p
ar
a
m
eter
s
:
=
(
0
2
)
1
3
,
=
(
0
2
)
1
3
⁄
′
,
=
′
(
2
)
1
3
,
=
(
0
2
)
1
3
,
=
′
−
∞
′
′
−
∞
′
=
−
∞
−
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,
=
=
,
=
(
−
∞
)
(
.
0
)
1
3
,
=
(
′
−
′
∞
)
(
.
0
)
1
3
,
=
16
∗
.
∞
3
(
2
0
)
2
3
,
=
(
0
2
)
1
3
(
5
)
I
n
(
5
)
is
em
p
lo
y
e
d
to
p
er
f
o
r
m
a
tr
an
s
f
o
r
m
atio
n
o
n
th
e
g
o
v
er
n
in
g
(
1
)
,
(
2
)
,
a
n
d
(
3
)
,
lead
i
n
g
t
o
,
(
,
)
=
(
,
)
+
(
,
)
+
2
(
,
)
2
(
6
)
(
,
)
=
2
(
,
)
2
−
(
,
)
(
7
)
(
,
)
=
1
2
(
,
)
2
−
(
,
)
(
8
)
T
h
e
f
o
r
m
o
f
th
e
co
n
d
itio
n
s
in
(
4
)
is
n
o
w
c
h
an
g
e
d
to
,
Fo
r
all
Y,
≤
0
:
(
,
0
)
=
0
,
(
,
0
)
=
0
,
(
,
0
)
=
0
=
0
:
(
0
,
)
=
2
,
(
0
,
)
=
00
,
(
0
,
)
=
1
→
∞
:
(
∞
,
)
=
0
,
(
∞
,
)
=
0
,
(
∞
,
)
=
0
(
9
)
4.
SO
L
U
T
I
O
N
D
E
T
E
R
M
I
NA
T
I
O
N
B
y
th
e
L
ap
lace
tech
n
iq
u
es
to
d
im
en
s
io
n
less
(
6
)
to
(
8
)
with
co
n
d
itio
n
s
(
9
)
,
th
e
f
o
llo
win
g
s
o
lu
tio
n
is
d
er
iv
ed
:
T
em
p
er
atu
r
e:
(
,
)
=
00
2
[
11
+
12
]
C
o
n
ce
n
tr
atio
n
:
(
,
)
=
1
2
[
3
+
4
]
Velo
city
:
(
,
)
=
2
(
2
6
[
(
3
+
12
2
+
4
4
)
1
−
√
(
10
+
4
2
)
2
]
)
+
(
01
2
[
9
+
10
]
−
01
2
[
15
+
16
]
)
+
(
(
1
−
02
2
[
7
+
8
]
−
1
2
[
3
+
4
]
+
02
2
[
13
+
14
]
)
+
(
00
2
[
11
+
12
]
−
00
2
[
5
+
6
]
)
W
h
er
e
=
(
1
−
)
,
=
(
1
−
)
(
−
)
,
=
(
1
−
)
(
−
)
,
=
.
,,
1
P
r
1
2
R
K
S
c
Y
cd
Sc
t
=
=
=
−−
00
=
(
)
)
,
01
=
(
)
)
,
02
=
(
)
)
1
=
(
)
,
2
=
(
−
2
)
,
03
=
2
√
(
)
(
)
3
=
(
03
)
(
04
)
,
04
=
√
+
√
,
4
=
(
05
)
(
06
)
,
05
=
−
2
√
,
06
=
√
−
√
,
5
=
(
07
)
(
08
)
,
07
=
2
√
,
08
=
+
√
,
09
=
−
2
√
6
=
(
09
)
(
10
)
,
10
=
−
√
,
16
=
(
11
)
(
12
)
,
11
=
−
2
√
,
12
=
−
√
,
15
=
(
29
)
(
30
)
29
=
2
√
,
30
=
+
√
,
7
=
(
13
)
(
14
)
,
13
2
L
d
t
=
,
14
=
+
√
,
15
=
−
2
√
,
16
=
−
√
,
9
=
(
17
)
(
18
)
,
17
=
2
√
(
+
)
,
18
=
√
√
(
+
)
,
10
=
(
19
)
(
20
)
,
19
=
−
2
√
(
+
)
,
20
=
√
√
(
+
)
,
11
=
(
21
)
(
22
)
,
21
=
2
√
(
)
(
+
)
,
22
=
√
√
(
+
)
,
12
=
(
23
)
(
24
)
,
13
=
(
25
)
(
26
)
,
23
=
−
2
√
(
)
(
+
)
,
24
=
√
√
(
+
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,
14
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(
27
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(
28
)
,
25
=
2
√
(
)
(
+
)
,
26
=
√
+
√
(
+
)
,
27
=
−
2
√
(
)
(
+
)
,
28
=
√
−
√
(
+
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
imu
la
tio
n
o
f rea
ctive
flo
w
o
v
er a
p
a
r
a
b
o
lic
ve
r
tica
l p
la
te
u
s
in
g
MATLAB
(
S
iva
ku
ma
r
P
u
s
h
p
a
r
a
j
)
1677
5.
P
RO
B
L
E
M
A
NAL
YSI
S
T
h
e
o
b
jectiv
e
o
f
th
is
co
m
p
r
e
h
en
s
iv
e
s
tu
d
y
,
wh
ich
p
r
o
v
id
e
s
ex
p
licit
m
ath
em
atica
l
s
o
lu
tio
n
s
,
is
to
ex
p
lo
r
e
t
h
e
im
p
ac
t
o
f
c
o
n
s
is
ten
t
m
ass
tr
an
s
f
er
f
r
o
m
a
n
id
e
alize
d
v
er
tical
p
late
o
f
in
f
i
n
ite
ex
ten
t.
Go
v
er
n
in
g
eq
u
atio
n
s
wer
e
s
o
lv
ed
;
r
esu
ltin
g
p
h
y
s
ical
co
n
s
eq
u
e
n
ce
s
ar
e
d
etailed
b
elo
w.
Ma
th
em
atica
l
s
im
u
latio
n
s
ar
e
co
n
d
u
cte
d
to
ex
p
lo
r
e
th
e
p
h
y
s
ical
co
n
s
eq
u
e
n
ce
s
o
f
th
e
p
r
o
b
lem
,
with
a
f
o
c
u
s
o
n
h
o
w
p
a
r
am
eter
s
s
u
ch
as
K
,
R
,
Sc
,
Gr
,
Gc
,
an
d
tt
in
f
lu
en
ce
th
e
f
lo
w
a
n
d
t
r
an
s
p
o
r
t
d
y
n
am
ics.
T
h
e
(
Sc
)
is
tak
en
as 0
.
6
,
r
e
p
r
e
s
en
tin
g
wate
r
v
ap
o
r
,
wh
ile
th
e
(
Pr
)
is
s
et
to
0
.
7
1
,
co
r
r
esp
o
n
d
in
g
to
air
.
As
s
h
o
wn
in
Fig
u
r
es
1
an
d
2
,
As
th
e
r
ad
iatio
n
tem
p
er
atu
r
e
co
m
p
o
n
en
t
in
cr
ea
s
es,
th
e
f
lu
id
ex
p
er
ien
ce
s
m
o
r
e
h
ea
t
tr
an
s
f
er
v
ia
r
ad
iatio
n
,
T
h
er
e
f
o
r
e,
th
e
f
lu
id
’
s
s
p
ee
d
is
d
im
in
is
h
ed
,
o
w
in
g
to
th
e
co
m
b
in
ed
e
f
f
ec
t
o
f
s
tr
o
n
g
er
b
u
o
y
an
c
y
f
o
r
ce
s
an
d
a
m
o
d
if
ie
d
f
lo
w
r
eg
im
e.
Similar
ly
,
an
a
u
g
m
en
tatio
n
o
f
th
e
ch
em
ical
r
ea
ctio
n
co
ef
f
icien
t
r
aises
th
e
r
ate
o
f
r
ea
ctio
n
s
,
wh
ich
also
ca
u
s
es
a
r
ed
u
ctio
n
in
v
elo
city
as
it
alter
s
th
e
co
n
ce
n
tr
atio
n
an
d
th
er
m
a
l
p
r
o
p
er
ties
o
f
th
e
f
lu
id
,
cr
ea
tin
g
f
u
r
th
e
r
r
esis
tan
ce
to
th
e
f
lo
w.
As
s
h
o
wn
in
Fig
u
r
es
3
an
d
4
,
as
b
o
th
ti
m
e
an
d
ac
ce
ler
atio
n
in
cr
ea
s
e,
th
e
v
elo
city
o
f
t
h
e
f
lu
id
in
cr
ea
s
es.
Hig
h
er
ac
ce
ler
atio
n
p
r
o
v
id
es
m
o
r
e
d
r
iv
in
g
f
o
r
ce
,
wh
ich
p
r
o
m
o
tes
f
aster
f
lu
id
m
o
tio
n
.
A
d
d
itio
n
ally
,
as
tim
e
p
r
o
g
r
ess
es,
th
e
s
y
s
tem
s
tab
iliz
es,
an
d
th
e
f
lu
id
’
s
v
el
o
city
r
ea
ch
es
a
h
ig
h
er
,
m
o
r
e
s
tead
y
v
a
lu
e.
T
h
er
ef
o
r
e,
th
e
co
m
b
in
ed
in
f
lu
en
ce
o
f
t
h
ese
f
ac
to
r
s
lead
s
to
a
g
r
a
d
u
al
in
cr
e
ase
in
f
lo
w
v
elo
city
.
Fig
u
r
e
1
.
I
m
p
ac
t o
f
ch
em
ical
r
ea
ctio
n
ef
f
ec
ts
o
n
v
elo
city
p
r
o
f
iles
Fig
u
r
e
2
.
I
m
p
ac
t o
f
th
er
m
al
r
a
d
iatio
n
ef
f
ec
ts
o
n
v
elo
city
p
r
o
f
iles
Fig
u
r
e
3
.
C
o
m
p
a
r
is
o
n
p
r
o
f
iles
o
f
th
e
f
lo
w
v
elo
city
f
o
r
v
ar
io
u
s
‘
t
’
v
alu
es
Fig
u
r
e
4
.
C
o
m
p
a
r
is
o
n
p
r
o
f
iles
o
f
th
e
f
lo
w
v
elo
city
f
o
r
v
ar
io
u
s
‘
a
’
v
alu
es
Fig
u
r
e
5
v
is
u
alize
th
e
(
Sc)
in
f
lu
en
ce
s
th
e
v
elo
city
f
ield
o
f
th
e
f
lu
id
.
As
th
ese
n
u
m
b
er
s
in
cr
ea
s
e,
th
e
(
Sc)
ca
u
s
es
th
e
v
elo
city
to
d
ec
r
ea
s
e
b
ec
au
s
e
it
s
ig
n
if
ies
th
at
m
ass
tr
an
s
f
er
is
s
lo
we
r
th
an
m
o
m
en
tu
m
tr
a
n
s
f
er
,
in
cr
ea
s
in
g
th
e
r
esis
tan
ce
to
f
lu
id
m
o
v
em
en
t.
Fig
u
r
es 6
an
d
7
d
is
p
lay
th
e
(
Gr
)
an
d
(
Gc)
in
cr
ea
s
e,
th
e
b
u
o
y
an
cy
f
o
r
ce
s
b
ec
o
m
e
m
o
r
e
p
r
o
n
o
u
n
ce
d
,
lead
in
g
to
a
h
i
g
h
er
v
el
o
c
ity
.
T
h
is
is
d
u
e
to
th
e
s
tr
o
n
g
e
r
co
n
v
ec
tiv
e
ef
f
ec
ts
ar
is
in
g
f
r
o
m
b
o
th
tem
p
e
r
atu
r
e
g
r
a
d
ien
ts
(
f
o
r
Gr
)
an
d
co
n
ce
n
tr
atio
n
g
r
ad
ie
n
ts
(
f
o
r
Gc)
,
w
h
ich
e
n
h
an
ce
f
lu
id
m
o
tio
n
n
ea
r
th
e
s
u
r
f
ac
e
an
d
in
cr
ea
s
e
t
h
e
b
o
u
n
d
ar
y
lay
e
r
v
elo
city
p
r
o
f
ile.
Fig
u
r
e
8
v
is
u
alize
th
e
(
Pr)
in
f
lu
en
ce
s
th
e
v
el
o
city
f
ield
o
f
th
e
f
l
u
id
in
o
p
p
o
s
ite
way
s
.
As
th
ese
n
u
m
b
er
s
in
cr
ea
s
e,
t
h
e
(
Sc)
ca
u
s
es
th
e
v
elo
city
to
d
ec
r
ea
s
e
b
ec
au
s
e
i
t
s
ig
n
if
ies
th
at
m
ass
tr
an
s
f
er
i
s
s
lo
wer
th
an
m
o
m
en
t
u
m
tr
a
n
s
f
er
,
in
cr
ea
s
in
g
th
e
r
esis
tan
ce
to
f
lu
id
m
o
v
em
en
t.
T
h
e
(
Pr)
also
ca
u
s
es
a
v
elo
city
d
ec
r
ea
s
e
b
ec
au
s
e
it
in
d
icate
s
s
lo
we
r
th
er
m
al
d
if
f
u
s
iv
ity
co
m
p
a
r
ed
to
m
o
m
en
tu
m
d
if
f
u
s
iv
ity
,
lead
i
n
g
to
th
ick
er
th
er
m
al
b
o
u
n
d
a
r
y
lay
er
s
an
d
r
ed
u
ce
d
h
ea
t
tr
an
s
f
er
,
wh
ich
in
tu
r
n
af
f
ec
ts
th
e
f
lo
w
v
elo
city
.
I
t
is
th
u
s
ev
id
en
t
th
at
an
au
g
m
en
tatio
n
o
f
eith
er
th
e
Sch
m
id
t
o
r
th
e
Pra
n
d
tl
n
u
m
b
e
r
s
en
g
e
n
d
er
s
a
r
ed
u
ctio
n
in
f
lu
id
v
el
o
city
.
Sp
ec
if
ically
,
an
u
p
war
d
tr
en
d
in
th
e
Pra
n
d
tl
n
u
m
b
er
r
esu
lts
in
th
e
f
lu
id
’
s
m
o
m
en
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I
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5
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I
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J
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&
C
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Sci
,
Vo
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39
,
No
.
3
,
Sep
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20
25
:
1
6
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u
r
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o
m
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a
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o
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iles
o
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e
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o
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ates,
as
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e
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S
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e
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e
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ates
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ates
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atio
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o
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ates
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at
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ely
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ater
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2
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s
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ates
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n
ce
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e
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ely
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icatin
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3
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atio
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er
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ely
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elate
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ter
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ea
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ig
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r
f
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ce
n
t
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ile
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er
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o
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ce
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c
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ile
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r
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ef
lectin
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ty
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ical
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t a
cc
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m
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d
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.
T
ab
le
1
.
Pre
s
en
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th
e
ex
p
er
im
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tally
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er
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m
e
r
ical
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m
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ar
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v
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r
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iles
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im
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m
e
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ical
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m
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ar
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o
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iles
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r
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me
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2
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im
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m
e
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ical
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m
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ar
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o
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n
ce
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n
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atu
r
e
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r
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iles
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o
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7
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0
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1
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,
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1
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7
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20
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5
5
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5
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1
6
,
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3
,
0
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6
0
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1
6
0
.
1
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6
t
0
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4
0
.
2
,
0
.
4
,
0
.
6
,
0
.
8
0
.
6
0
.
2
,
0
.
4
,
0
.
6
,
0
.
8
a
0
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2
3
0
.
5
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
39
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
6
7
3
-
1
6
8
2
1680
6.
CO
NCLU
SI
O
NS A
ND
F
UT
URE P
E
R
SPE
CT
I
VE
S
T
h
e
p
r
o
ce
s
s
o
f
an
aly
s
is
is
im
p
lem
en
ted
to
d
eter
m
in
e
th
e
r
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le
o
f
ch
em
ical
r
ea
ctio
n
s
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eg
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d
in
g
th
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f
lo
w
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y
n
am
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o
f
a
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ar
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o
lic
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tical
p
late
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f
in
f
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ite
with
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n
en
tial
tem
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er
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r
e
g
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ad
ien
t
an
d
u
n
if
o
r
m
m
ass
tr
an
s
f
er
ap
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city
in
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ea
s
es
with
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i
s
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g
tim
e,
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ce
ler
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n
,
an
d
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o
th
(
Gr
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d
(
Gc)
,
wh
ile
it
d
ec
r
ea
s
es
with
h
ig
h
e
r
(
Sc)
,
(
Pr)
,
an
d
th
er
m
al
r
ad
iatio
n
v
alu
es.
T
em
p
er
atu
r
e
is
o
b
s
er
v
ed
t
o
r
is
e
wit
h
in
cr
ea
s
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g
tim
e,
b
u
t
it
d
ec
r
e
ases
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th
e
(
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in
cr
ea
s
es.
A
d
d
itio
n
ally
,
t
h
e
(
Sc)
in
cr
ea
s
e
s
as
co
n
ce
n
tr
atio
n
d
ec
r
ea
s
es,
wh
ile
co
n
ce
n
tr
atio
n
r
is
es
with
in
cr
ea
s
in
g
tim
e.
T
h
is
s
tu
d
y
in
v
esti
g
ates
th
e
im
p
ac
t
o
f
v
a
r
io
u
s
ch
em
ically
r
ea
ctiv
e
s
p
ec
ies.
T
h
e
f
in
d
i
n
g
s
o
f
th
is
r
esear
ch
h
av
e
p
r
ac
tical
ap
p
licatio
n
s
with
in
th
e
ch
em
ical
p
r
o
ce
s
s
in
g
in
d
u
s
tr
y
.
T
h
e
f
in
d
in
g
s
also
h
av
e
p
r
ac
tical
ap
p
li
ca
tio
n
s
f
o
r
th
e
ae
r
o
s
p
ac
e
in
d
u
s
tr
ies.
T
h
is
s
tu
d
y
m
ay
also
b
e
ex
p
a
n
d
ed
to
c
o
n
s
i
d
er
h
all
ef
f
ec
ts
.
Fu
r
th
er
m
o
r
e,
in
s
tead
o
f
u
s
in
g
a
New
to
n
ian
f
lu
id
,
a
n
an
o
f
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ay
b
e
em
p
lo
y
e
d
.
T
h
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c
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k
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rp
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m
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c
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m
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la
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J
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&
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39
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3
,
Sep
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20
25
:
1
6
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1682
Ra
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c
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c
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tac
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d
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m
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:
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m
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sh
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a
d
h
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c
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c
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m
M
a
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Ka
m
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ra
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Un
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,
M
.
P
h
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re
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m
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m
Ala
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d
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fr
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m
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M
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r
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h
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c
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a
c
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th
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