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Advances and Unsolved Issues in Pulsating Heat PipesYuwen Zhang a; Amir Faghri ba Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia,
Missouri, USA b Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut, USA
Online Publication Date: 01 January 2008
To cite this Article Zhang, Yuwen and Faghri, Amir(2008)'Advances and Unsolved Issues in Pulsating Heat Pipes',Heat TransferEngineering,29:1,20 44To link to this Article: DOI: 10.1080/01457630701677114URL: http://dx.doi.org/10.1080/01457630701677114
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Heat Transfer Engineering, 29(1):2044, 2008Copyright C Taylor and Francis Group, LLCISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457630701677114
Advances and Unsolved Issuesin Pulsating Heat Pipes
YUWEN ZHANGDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, Missouri, USA
AMIR FAGHRIDepartment of Mechanical Engineering, University of Connecticut, Storrs, Connecticut, USA
Pulsating (or oscillating) heat pipes (PHP or OHP) are new two-phase heat transfer devices that rely on the oscillatoryflow of liquid slug and vapor plug in a long miniature tube bent into many turns. The unique feature of PHPs, comparedwith conventional heat pipes, is that there is no wick structure to return the condensate to the heating section; thus, thereis no countercurrent flow between the liquid and vapor. Significant experimental and theoretical efforts have been maderelated to PHPs in the last decade. While experimental studies have focused on either visualizing the flow pattern in PHPsor characterizing the heat transfer capability of PHPs, theoretical examinations attempt to analytically and numericallymodel the fluid dynamics and/or heat transfer associated with the oscillating two-phase flow. The existing experimentaland theoretical research, including important features and parameters, is summarized in tabular form. Progresses in flowvisualization, heat transfer characteristics, and theoretical modeling are thoroughly reviewed. Finally, unresolved issues onthe mechanism of PHP operation, modeling, and application are discussed.
INTRODUCTION
Evolution in the design of the heat pipea type of passivetwo-phase thermal control devicehas accelerated in the pastdecade due to continuous demands for faster and smaller mi-croelectronic systems. As modern computer chips and powerelectronics become smaller and more densely packed, the needfor more efficient cooling systems increases. The new design ofa computer chip at Intel, for instance, will produce localized heatflux over 100 W/cm2, with the total power exceeding 300 W. Inaddition to the limitations on maximum chip temperature, furtherconstraints may be imposed on the level of temperature unifor-mity in electronic components. Heat pipes are a very promisingtechnology for achieving high local heat-removal rates and uni-form temperatures on computer chips.
True development of conventional heat pipes (CHP) began inthe 1960s; since then, various geometries, working fluids, andwick structures have been proposed [1]. In the last 20 years, newtypes of heat pipessuch as capillary pumped loops and loopheat pipeswere introduced, seeking to separate the liquid and
Address correspondence to Professor Amir Faghri, Department of Mechan-ical Engineering, University of Connecticut, Storrs, CT 06269, USA. E-mail:[email protected]
vapor flows to overcome certain limitations inherent in conven-tional heat pipes. In the 1990s, Akachi et al. [2] invented a newtype of heat pipe known as the pulsating or oscillating heat pipe(PHP or OHP). The most popular applications of PHP are foundin electronics cooling because it may be capable of dissipat-ing the high heat fluxes required by next generation electronics.Other proposed applications include using PHPs to preheat airor pump water. This review article will describe the operation ofpulsating heat pipes, summarize the research and developmentover the past decade, and discuss the issues surrounding themthat have yet to be resolved.
Pulsating heat pipes, like conventional heat pipes, are closed,two-phase systems capable of transporting heat without any ad-ditional power input, but they differ from conventional heatpipes in several major ways. A typical PHP is a small mean-dering tube that is partially filled with a working fluid, as seenin Figure 1 [3]. The tube is bent back and forth parallel to itself,and the ends of the tube may be connected to one another ina closed loop, or pinched off and welded shut in an open loop(see Figure 1a and 1b). It is generally agreed by researchers thatthe closed-loop PHP has better heat transfer performance [4, 5].For this reason, most experimental work is done with closed-loop PHPs. In addition to the oscillatory flow, the working fluidcan also be circulated in the closed-loop PHP, resulting in heat
20
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Y. ZHANG and A. FAGHRI 21
Figure 1 Different PHPs: (a) closed-end, (b) closed-loop, (c) closed-loopwith check valve, and (d) PHP with open ends.
transfer enhancement. Although an addition of a check valve (seeFigure 1c) could improve the heat transfer performance of thePHPs by making the working fluid move in a specific direction,it is difficult and expensive to install these valves. Consequently,the closed-loop PHP without a check valve becomes the mostfavorable choice for the PHP structures. Recently, PHPs with asintered metal wick have been prototyped by Zuo et al. [6, 7]and analyzed by Holley and Faghri [8]. The wick should aid inheat transfer and liquid distribution. There has also been someexploration into pulsating heat pipes in which one or both endsare left open without being sealed (see Figure 1d) [911].
Like a CHP, a PHP must be heated in at least one sectionand cooled in another. Often the evaporators and condensers arelocated at the bends of the capillary tube. The tube is evacuatedand then partially filled with a working fluid. The liquid andits vapor will become distributed throughout the pipe as liquidslugs and vapor bubbles. As the evaporator section of the PHP isheated, the vapor pressure of the bubbles located in that sectionwill increase. This forces the liquid slug toward the condensersection of the heat pipe. When the vapor bubbles reach the con-denser, it will begin to condense. As the vapor changes phase,the vapor pressure decreases, and the liquid flows back towardthe condenser end. In this way, a steady oscillating flow is setup in the PHP. Boiling the working fluid will also cause newvapor bubbles to form. The unique feature of PHPs, comparedwith conventional heat pipes, is that there is no wick structure toreturn the condensate to the heating section, and therefore thereis no countercurrent flow between the liquid and the vapor. Dueto the simplicity of the structure of a PHP, its weight is lowerthan that of conventional heat pipe, which makes PHP an idealcandidate for space application.
Research on PHPs can be categorized as either experimentalor theoretical. While experimental studies have focused on ei-ther visualizing the flow pattern in PHPs or characterizing theheat transfer capability of PHPs, theoretical examinations at-tempt to analytically and numerically model the fluid dynamicsand/or heat transfer associated with oscillating two-phase flow.The existing experimental and theoretical research and their pa-rameters are summarized in Table 1. The table lists the primaryinvestigators, reference number, and the year the study was pub-
lished, followed by the details of the modeling and/or experi-ment: theoretical approaches, major assumptions, the materialused to manufacture the PHP, the geometry and configurationof the flow channel, number of parallel channels, inclination an-gles, channel diameters, the working fluids tested, the chargeratios that they were tested at, range of heat transferred by thePHP, a summary of the conclusions drawn by the investiga-tor, and other significant comments. This article also presentsthe principles of operation, flow visualization, heat transfer, andmodeling, as well as a discussion of the unresolved issues in PHPresearch.
PRINCIPLES OF OPERATION
Although simple in their construction, PHPs become compli-cated devices when one tries to fully understand their operation:the thermodynamics driving PHP operation, the fluid dynam-ics governing the two-phase oscillating flow, heat transfer (bothsensible and latent), and the physical design parameters of thePHP must all be considered.
Thermodynamic Principles
Heat addition and rejection and the growth and extinction ofvapor bubbles drive the flow in a PHP. Even though the exactfeatures of the thermodynamic cycle are still unknown, Grolland Khandekar [12] described it in general terms using a pres-sure/enthalpy diagram as seen in Figure 2. The temperature andvapor quality in the evaporator and condenser are known, or canbe assumed, so the state at the outlets of the evaporator and con-denser are known. Starting at the evaporator inlet, point A onthe P-h diagram, the processes required to get to point B on thediagram can be simplified to heat input at a constant pressurecombined with isentropic pressure increase due to bubble ex-pansion. As one travels through the adiabatic section from theevaporator to the condenser, the pressure decreases isenthalpi-cally. The thermodynamic process between the condensers inletand outlet are complicated, but can be simplified to constant pres-sure condensation with negative isentropic work. An isenthalpicpressure drop in the adiabatic section completes the cycle. Be-cause of the numerous assumptions made in this description,thermodynamic analysis is insufficient to study PHPs.
Fluid Dynamic Principles
Fluid flow in a capillary tube consists of liquid slugs andvapor plugs moving in unison. The slugs and plugs initially dis-tribute themselves in the partially filled tube. The liquid slugsare able to completely bridge the tube because surface tensionforces overcome gravitational forces. There is a meniscus re-gion on either end of each slug caused by surface tension atthe solid/liquid/vapor interface. The slugs are separated by plugs
heat transfer engineering vol. 29 no. 1 2008
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Tabl
e1
Sum
mar
yo
fmo
delin
gan
dex
perim
ents
on
pulsa
ting
heat
pipe
s(PH
P) Open
/In
ves
tigat
orTh
eore
tical
clos
edFl
owpa
thPa
ralle
lIn
clin
atio
nD
Wo
rkin
gCh
arge
Conc
lusio
nsan
d(ye
ar)ap
proa
ches
Ass
umpt
ions
Mat
eria
lslo
opge
omet
rych
anne
lsan
gle
( )(m
m)flu
idra
tioq
(W)
com
men
ts
Aka
chie
tal.
[2](
1996
)N
one
N/A
Copp
erO
pen
Circ
ular
254,
1000
0.7,
1.2
R14
2b50
701
00,
450
Ther
mal
resis
tanc
eis
inde
pend
ento
fhea
tin
puta
nd
incl
inat
ion
angl
eif
the
nu
mbe
rof
turn
sis
grea
tert
han
80.
Mae
zaw
aet
al.
[27]
(1996
)N
one
N/A
Copp
erO
pen
Circ
ular
8090
,0,
902
Wat
er,
R14
2b50
501
000
R14
2bpe
rform
sbet
ter
than
wat
er.B
otto
mhe
atm
ode
perfo
rmsb
ette
rth
anto
phe
atm
ode
.O
scill
atio
nha
sno
spec
ific
perio
dica
lfe
atur
e.M
iyaz
akia
nd
Aka
chi[
28]
(1996
)
Diff
eren
tial
rela
tions
hip
betw
een
prop
agat
ion
wav
eo
fp
and
Pres
sure
osc
illat
ion
and
osc
illat
ory
flow
reci
proc
ally
exci
teea
cho
ther
.
Copp
erCl
osed
Circ
ular
6090
,0,
901
R14
2b25
70
201
80O
ptim
ized
char
gera
tiofo
rbot
tom
and
top
heat
mo
desa
re70
%an
d35
%,r
espe
ctiv
ely.
Asy
mm
etric
alw
ave
iso
btai
ned
atpr
oper
char
gera
tio.
Miy
azak
ian
dA
kach
i[48
](19
98)
Wav
eeq
uatio
no
fpr
essu
rew
as
deriv
ed.
Aco
ntin
uous
distr
ibu
tion
of
vo
idfra
ctio
nw
asas
sum
ed.
N/A
Circ
ular
The
prog
ress
ive
wav
efo
ra
clos
ed-lo
opch
anne
lan
dth
est
andi
ngw
ave
fora
clos
ed-e
ndch
anne
lcan
beo
btai
ned
from
the
wav
e
equa
tion.
Miy
azak
ian
dA
rikaw
a
[49]
(1999
)
Non
eN
/ACo
pper
/po
lyca
rbon
ate
Rec
tang
ular
509
0R
-142
b42
Mea
sure
dw
ave
vel
ociti
esfa
irly
agre
edw
ithEq
.(14
).N
ishio
[29]
(1999
)N
one
N/A
Gla
ssCl
osed
Circ
ular
490
1.8,
2.4,
5.0
Wat
er,
soap
-su
ds,
etha
nol,
R14
1b
201
0070
PHP
perfo
rmed
best
with
char
gera
tioo
f35%
.PH
Pth
erm
alco
ndu
ctiv
ityis
500
times
high
erth
anco
pper
.H
eatt
rans
fer
rate
high
erth
anth
eco
nven
tiona
lhea
tpip
ew
ithth
esa
me
diam
eter
.
Gie
tal.
[4]
(1999
)N
one
N/A
Teflo
nO
pen/
clos
edCi
rcul
ar10
305
02
R14
2b20
50,
307
060
100
Flow
visu
aliz
atio
ns
(Con
tinue
do
nn
extp
age)
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iver
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Tabl
e1
(Con
tinue
d)
Ope
n/In
ves
tigat
orTh
eore
tical
clos
edFl
owpa
thPa
ralle
lIn
clin
atio
nD
Wo
rkin
gCh
arge
Conc
lusio
nsan
d(ye
ar)ap
proa
ches
Ass
umpt
ions
Mat
eria
lslo
opge
omet
rych
anne
lsan
gle
( )(m
m)flu
idra
tioq
(W)
com
men
ts
Hos
oda
etal
.[1
9](19
99)
Num
eric
also
lutio
no
f1-D
liqui
dan
dvap
orflo
w.
Thin
liqui
dfil
m,
pres
sure
loss
atbe
nds,
and
visc
ous
diss
ipat
ion
are
neg
lect
ed.
Gla
ssCl
osed
Circ
ular
2090
1.2
Wat
er30
90
802
20PH
Ppe
rform
edbe
stat
char
gera
tioo
f60%
.N
umer
ical
resu
ltsfo
rpr
essu
rear
ehi
gher
than
expe
rimen
tal
resu
ltsbu
tosc
illat
ion
issim
ulat
ed.
Lee
etal
.[15
](19
99)
Non
eN
/AB
rass
,acr
ylic
Clos
edR
ecta
ngul
ar8
309
01.
5
1.5
Etha
nol
208
0
Osc
illat
ion
cau
sed
byfo
rmat
ion
or
extin
ctio
no
fbu
bble
s.N
oflu
idci
rcul
atio
n.M
osta
ctiv
e
osc
illat
ion
iso
bser
ved
inbo
ttom
heat
ing
with
char
gera
tioo
f40
60%
.Zu
oet
al.[
6](19
99)
Osc
illat
ory
flow
mo
dele
dsim
ilar
tom
echa
nica
lv
ibra
tion
with
visc
ous
dam
ping
.
Vapo
risa
nid
eal
gas.
Lam
inar
liqui
dflo
w.
Hea
ttra
nsfe
ris
neg
lect
ed.
Sint
ered
and
plat
eco
pper
Clos
edTr
iang
ular
0,
90
Wat
er40
80
525
0Th
ew
ick
stru
ctur
edi
strib
ute
sliq
uid
even
ly,
and
redu
ces
loca
ltem
pera
ture
fluct
uatio
n.Th
erm
alre
sista
nce
isas
low
as
0.16
C/W
atan
opt
imum
char
gera
tioo
f70%
.Zu
oet
al.[
7](20
01)
Mas
s,m
om
entu
m,
and
ener
gyeq
uatio
nso
f1-
Dtr
ansie
nttw
o-p
hase
flow
are
solv
edu
sing
SIM
PLEC
sche
me.
Liqu
idan
dvap
orph
ases
are
atlo
cal
equi
libriu
m.
Conv
ectio
ndo
min
ate
inax
iald
irect
ion.
Copp
erCl
osed
Rec
tang
ular
W
ater
408
010
250
Expe
rimen
tsho
ws
that
perfo
rman
ceo
fPH
Pis
sen
sitiv
eto
char
gera
tio.N
umer
ical
resu
ltsw
ere
no
trep
orte
din
the
pape
r.
Dob
son
and
Ham
s[9]
(1999
)
Expl
icit
finite
diffe
renc
esc
hem
eis
use
dto
solv
e
equa
tions
for
mo
tion
and
heat
tran
sfer
.
Vapo
risa
nid
eal
gas.
Inco
mpr
essib
leliq
uid.
No
heat
tran
sfer
inliq
uid.
Copp
erU
nloo
ped
with
ope
nen
d
Circ
ular
20
3.34
Wat
er
Th
rust
prod
uced
byPH
Pis
0.00
27N
.O
pen-
ende
dPH
Pm
ou
nte
do
na
float
inw
ater
.
Dob
son
[18]
(2004
)M
ass,
mo
men
tum
,an
den
ergy
equa
tions
are
solv
edu
sing
expl
icit
sche
me.
Vapo
risi
deal
gas.
Mom
entu
mo
fvap
orbu
bble
and
liqui
dfil
mar
en
egle
cted
.
Copp
erO
pen
Circ
ular
290
90
3.34
Wat
erTh
edo
min
ate
forc
esfo
rliq
uid
plug
mo
tion
are
vap
orpr
essu
redi
ffere
nce,
frict
ion
and
grav
ity.
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aded
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iver
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ouri
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l 2009
Dob
son
[11]
(2005
)
0
3.34
Wat
er
U
seo
fan
ope
nPH
Pto
pum
pw
ater
.M
assfl
owra
teo
fthe
pum
pis
0.2
mg/
sfor
100
mm
heig
ht.
Kise
evan
dZo
lkin
[43]
(1999
)
Non
eN
/ASt
ainl
esss
teel
Ope
nCi
rcul
ar46
01.
1A
ceto
ne60
153
00Ev
apor
ator
tem
pera
ture
isin
crea
sed
by30
%by
incr
easin
gac
cele
ratio
nfro
m6
gto
12g.
Wo
ng
etal
.[5
0](19
99)
Mas
san
dm
om
entu
mba
lanc
esin
a
Lagr
angi
anfra
me.
Adi
abat
ic,h
eat
inpu
twas
mo
dele
das
a
sudd
enpr
essu
reris
e.N
oliq
uid
film
.
N/A
Ope
nCi
rcul
ar4
0
50
Th
epr
essu
repu
lsein
duce
sosc
illat
ion
but
isda
mpe
do
utb
yfri
ctio
nbe
twee
nth
eliq
uid
and
pipe
wal
l.
Lin
etal
.[30
](20
00)
Non
eN
/ACo
pper
Ope
nCi
rcul
ar40
0,90
1.75
Ace
tone
255
014
020
40O
ptim
umch
arge
ratio
is38
%.O
pera
tion
isbe
tteri
nho
rizon
tal.
No
ope
ratio
nat
25%
char
ge.
Lin
etal
.[31
](20
01)
Non
eN
/ACo
pper
Ope
nCi
rcul
ar40
0,90
1.75
FC-7
2,FC
-75
305
014
020
40O
ptim
umch
arge
ratio
is50
%.F
C-72
perfo
rmed
bette
rtha
nFC
-75.
Ope
ratio
nis
bette
rin
horiz
onta
l.N
oo
pera
tion
at25
%ch
arge
.Per
form
ance
isin
depe
nden
tof
orie
ntat
ion.
Ton
get
al.
[20]
(2001
)N
one
N/A
Pyre
xgl
ass
Clos
edCi
rcul
ar14
0,90
1.8
Met
hano
l60
50Ci
rcul
atio
nw
aso
bser
ved,
and
circ
ulat
ion
vel
ocity
incr
ease
swith
incr
easin
ghe
atin
put.
Circ
ulat
ion
can
beei
ther
cloc
kwise
or
cou
nte
r-cl
ockw
ise.
Shafi
ieta
l.[1
3](20
01)
Mas
s,m
om
entu
m,
and
ener
gyeq
uatio
nsfo
rea
chliq
uid
slug
and
vap
orpl
ugar
eso
lved
.
Vapo
risa
nid
eal
gas.
Inco
mpr
essib
leliq
uid.
No
pres
sure
loss
inbe
nds.
N/A
Ope
n/cl
osed
Circ
ular
49
01.
5,3.
0W
ater
61.4
,89
.47
080
Majo
rity(95
%)o
fhea
tis
tran
sfer
red
byse
nsib
lehe
at.L
aten
thea
tser
ves
on
lyto
driv
eo
scill
atin
gflo
w.
Effe
cto
fgra
vity
isn
eglig
ible
.
(Con
tinue
do
nn
extp
age)
Downlo
aded
By:
[Un
iver
sity
of
Miss
ouri
Col
umbi
a] A
t: 2
0:49
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Apri
l 2009
Tabl
e1
(Con
tinue
d)
Ope
n/In
ves
tigat
orTh
eore
tical
clos
edFl
owpa
thPa
ralle
lIn
clin
atio
nD
Wo
rkin
gCh
arge
Conc
lusio
nsan
d(ye
ar)ap
proa
ches
Ass
umpt
ions
Mat
eria
lslo
opge
omet
rych
anne
lsan
gle
( )(m
m)flu
idra
tioq
(W)
com
men
ts
Shafi
ieta
l.[1
4](20
02)
Thin
film
evap
orat
ion
and
con
dens
atio
nw
ere
solv
edto
getl
aten
thea
ttr
ansf
erco
effic
ient
.
Rad
ialc
on
duct
ion
on
lyin
thin
film
.Neg
lect
ing
shea
rstr
ess
atliq
uid-
vapo
rin
terfa
ce.
N/A
Ope
n/cl
osed
Circ
ular
4
1.5,
3.0
Wat
er64
.21
89.5
011
9H
eatt
rans
feri
sdue
mai
nly
toth
eex
chan
geo
fsen
sible
heat
.Hig
her
surfa
cete
nsio
nre
sults
ina
sligh
tinc
reas
ein
tota
lhea
ttra
nsfe
r.N
o
ope
ratio
nfo
rhig
hch
arge
ratio
.Ca
ieta
l.[1
7](20
02)
Non
eN
/AQu
artz,
copp
erCl
osed
,o
pen
Circ
ular
12,5
045
,02.
4,2.
2Et
hano
l,w
ater
,
acet
one,
etha
nol,
amm
o-
nia
50,4
060
100
600
Prop
agat
ion
and
extin
ctio
no
fbu
bble
sar
eo
bser
ved.
Flui
dsw
ithlo
wla
tent
heat
sar
ere
com
men
ded
topr
omot
eo
scill
ator
ym
otio
n.K
hand
ekar
etal
.[16
](20
02)
Non
eN
/AA
lum
inum
/gla
ss,
copp
er/g
lass
Clos
edR
ecta
ngul
ar,
rect
angu
lar,
circ
ular
12,1
2,10
090
2.2
2,1.
51,
2.0
Wat
er,
etha
nol
107
025
70
The
met
alPH
Pdi
dn
ot
ope
rate
inho
rizon
tal
orie
ntat
ion
buto
pera
ted
ver
tical
lyas
ther
mos
ypho
n.Pe
rform
ance
depe
nds
on
orie
ntat
ion,
char
gera
tio,a
nd
cro
ss-s
ectio
nge
omet
ry.
Kha
ndek
aret
al.[
56]
(2002
)
Arti
ficia
lNeu
ral
Net
wo
rk(A
NN)i
suse
dto
pred
ictP
HP
perfo
rman
ce.
Hea
tinp
utan
dch
arge
ratio
from
52da
tase
tsar
ein
putte
dto
AN
N.
Copp
erCl
osed
Circ
ular
1090
2Et
hano
l0
100
A
NN
Iist
rain
edby
expe
rimen
ts.Ef
fect
sof
diam
eter
,n
um
bero
ftu
rns,
leng
th,
incl
inat
ion
angl
e,an
dflu
idpr
oper
tiesa
ren
ot
inth
em
ode
l.K
hand
ekar
etal
.[24
](20
02)
N/A
G
lass
/co
pper
Clos
edCi
rcul
ar10
0,45
,90
2W
ater
,
etha
nol
010
05
15Ef
fect
ofg
rav
ityis
neg
ligib
le.B
ubbl
efo
rmat
ion
and
colla
pse
are
disc
usse
d.
Downlo
aded
By:
[Un
iver
sity
of
Miss
ouri
Col
umbi
a] A
t: 2
0:49
21
Apri
l 2009
Ma
etal
.[32
](20
02)
Liqu
idslu
go
scill
atio
nis
desc
ribed
byth
eba
lanc
eo
fth
erm
ally
driv
en,
capi
llary
,
frict
iona
l,an
del
astic
rest
orin
gfo
rces
.
Hea
ttra
nsfe
rin
evap
orat
oris
mo
dele
das
conv
ectiv
e
boili
ngin
a
tube
.
Copp
erO
pen
Circ
ular
40
1.67
Ace
tone
5
20M
inim
umo
nse
tte
mpe
ratu
redi
ffere
nce
is15
C.R
ange
of
ope
ratio
nalt
empe
ratu
redi
ffere
nce
isst
udie
d.M
odel
un
derp
redi
cts
tem
pera
ture
drop
s.
Zhan
gan
dFa
ghri
[10]
(2002
)
Evap
orat
ion
and
con
dens
atio
no
nth
infil
mle
ftbe
hind
byliq
uid
slug
isso
lved
.
Vapo
riss
atur
ated
and
isoth
erm
al.
Neg
lect
ing
iner
tia,s
hear
stre
ss,a
nd
inte
rfaci
alth
erm
alre
sista
nce
effe
cts.
N/A
Ope
nCi
rcul
ar1
0
O
vera
llhe
attr
ansf
eris
dom
inat
edby
sen
sible
heat
tran
sfer
.
Freq
uenc
yan
dam
plitu
dear
en
ot
affe
cted
bysu
rface
tens
ion.
Zhan
get
al.
[52]
(2002
)Li
quid
vap
orpu
lsatin
gflo
w
ina
U-s
hape
dm
inia
ture
tube
isin
ves
tigat
ed.
Vapo
risa
nid
eal
gas.
N/A
Ope
nCi
rcul
ar2
90
The
ampl
itude
and
frequ
ency
ofo
scill
atio
nw
ere
corr
elat
edto
the
heat
tran
sfer
coef
ficie
ntsa
nd
tem
pera
ture
diffe
renc
e.Zh
ang
and
Fagh
ri[5
3](20
03)
Liqu
idv
apor
pulsa
ting
flow
inPH
Pw
ithar
bitra
ryn
um
bero
ftur
nsis
inves
tigat
ed.
Vapo
risa
nid
eal
gas.
N/A
Ope
nCi
rcul
arA
ny9
0
A
mpl
itude
and
circ
ular
frequ
ency
decr
ease
byde
crea
sing
the
leng
ths
oft
hehe
atin
gan
dco
olin
gse
ctio
ns.
Incr
easin
gth
ech
arge
ratio
resu
lted
ina
decr
ease
ofa
mpl
itude
san
dan
incr
ease
of
circ
ular
frequ
ency
.
Char
oens
awan
etal
.[34
](20
03)
Non
eN
/ACo
pper
Clos
edCi
rcul
ar10
46
0,90
1.0,
2.0
Wat
er,
etha
nol,
R-1
23
5020
011
00G
rav
ityha
sasig
nific
ant
effe
cto
nPH
Ppe
rform
ance
.M
inim
umn
um
bero
ftu
rns
isn
eede
dfo
raho
rizon
talP
HP
too
pera
te.P
erfo
rman
ceim
prov
esby
incr
easin
gth
edi
amet
eran
dth
en
um
bero
ftur
ns.
(Con
tinue
do
nn
extp
age)
Downlo
aded
By:
[Un
iver
sity
of
Miss
ouri
Col
umbi
a] A
t: 2
0:49
21
Apri
l 2009
Tabl
e1
(Con
tinue
d)
Ope
n/In
ves
tigat
orTh
eore
tical
clos
edFl
owpa
thPa
ralle
lIn
clin
atio
nD
Wo
rkin
gCh
arge
Conc
lusio
nsan
d(ye
ar)ap
proa
ches
Ass
umpt
ions
Mat
eria
lslo
opge
omet
rych
anne
lsan
gle
( )(m
m)flu
idra
tioq
(W)
com
men
ts
Kha
ndek
aret
al.[
23]
(2003
)
Non
eN
/APy
rex
,gl
ass
Clos
edCi
rcul
ar20
58
0,90
2R
-123
505,
000
70,0
00W
/m2
Flow
osc
illat
esw
ithlo
w
ampl
itude
/hig
hfre
quen
cyat
horiz
onta
lm
ode
.Cap
illar
yslu
gan
dse
mi-a
nnul
ar/
ann
ula
rflow
depe
ndo
n
heat
inpu
tan
din
clin
atio
nan
gle.
Expe
rimen
talr
esu
ltsar
eco
rrel
ated
usin
gem
piric
alm
ode
l.K
hand
ekar
etal
.[33
](20
03)
Non
eN
/ACo
pper
Clos
edCi
rcul
ar10
0,90
2W
ater
,
etha
nol,
R-1
23
010
05
65,
560
,5
25
Opt
imum
char
gera
tios
fort
hree
fluid
sare
30,
20,a
nd
35%
,re
spec
tivel
y.O
rient
atio
naf
fect
spe
rform
ance
.H
oriz
onta
lmo
dedi
dn
otw
ork
.K
hand
ekar
and
Gro
ll[2
1](20
04)
Non
eN
/AG
lass
/co
pper
Clos
edCi
rcul
ar2
0,90
2Et
hano
l0
100
14.8
74.
4PH
Pdi
dn
oto
pera
tein
horiz
onta
lmo
de.
Capi
llary
slug
flow
and
ann
ula
rflow
depe
nds
on
heat
inpu
t.R
ittid
ech
etal
.[3
](20
03)
Non
eN
/ACo
pper
Ope
nCi
rcul
ar38
84
00.
55,
1.05
,2.
03
Etha
nol,
Wat
er,
R12
3
502,
000
12,0
00W
/m2
For
R-1
23,h
eatfl
uxin
crea
sesw
ithin
crea
sing
diam
eter
,
butt
hetr
end
isth
eo
ppos
itefo
reth
anol
.Co
rrela
tion
forh
eat
tran
sfer
was
prop
osed
base
do
nex
perim
ents.
Ritt
idec
het
al.
[35]
(2005
)N
one
N/A
Copp
erO
pen
Circ
ular
16pe
rPH
P,32
PHPs
2
Wat
er,
R-1
2350
1460
350
4(T
ota
l)PH
Psw
ere
use
das
anai
rpr
ehea
terf
oren
ergy
thrif
tin
adr
yer.
Perfo
rman
ceim
prov
es
with
incr
easin
gev
apor
ator
tem
pera
ture
.PH
Pw
ithR
-123
perfo
rmsb
ette
rtha
nPH
Pw
ithw
ater
.
Downlo
aded
By:
[Un
iver
sity
of
Miss
ouri
Col
umbi
a] A
t: 2
0:49
21
Apri
l 2009
Lian
gan
dM
a[5
4](20
04)
Vapo
rbu
bble
isco
nsid
ered
as
gass
prin
g.
Vapo
rbu
bble
sar
eu
nifo
rmly
distr
ibu
ted.
N/A
Ci
rcul
ar
01,
2,5
Wat
er
Is
entro
pic
bulk
mo
dulu
sge
nera
tess
tron
ger
osc
illat
ions
than
the
isoth
erm
albu
lkm
odu
lus.
Gu
etal
.[44
](20
04)
Non
eN
/AA
lum
inum
Clos
edR
ecta
ngul
ar96
1
1
R11
450
60
1.4
5.9
PHP
perfo
rmed
bette
rin
mic
rogr
avity
than
norm
alor
hype
rgr
avity
.N
eweq
uatio
no
fcrit
ical
diam
eter
inm
icro
grav
ityis
devel
oped
.R
iehl
[36]
(2004
)N
one
N/A
Copp
erO
pen
Circ
ular
130,
901.
5A
ceto
ne,
etha
nol,
iso-
prop
yl,
alco
hol,
met
hano
l,w
ater
5010
50
Perfo
rman
ceis
bette
rw
hen
ope
ratin
gin
a
horiz
onta
lorie
ntat
ion.
Bet
terp
erfo
rman
ces
wer
eo
btai
ned
whe
nac
eton
ew
asu
sed
inver
tical
orie
ntat
ion
and
met
hano
lwas
use
do
n
horiz
onta
lorie
ntat
ion.
Zhan
get
al.
[5](
2004
)N
one
N/A
Copp
erO
pen
and
clos
edCi
rcul
ar6
901.
18FC
-72,
etha
nol,
wat
er
609
05
60O
pen
loop
PHP
did
no
tw
ork
.Am
inim
umhe
atin
puti
snec
essa
ryto
initi
ate
pulsa
ting
flow
.
Clos
edlo
opPH
P.O
ptim
umch
arge
ratio
is70
%fo
rall
thre
eflu
ids.
Saku
lcha
n-gs
atjat
aiet
al.[
51]
(2004
)
Mas
s,m
om
entu
m,
and
ener
gyeq
uatio
nsfo
rea
chliq
uid
slug
and
vap
orpl
ugar
eso
lved
.
Vapo
risa
nid
eal
gas.
Inco
mpr
essib
leliq
uid.
No
pres
sure
loss
inbe
nds.
O
pen
and
clos
ed
9
0
M
odel
issa
me
asSh
afii
etal
.(200
1).Th
epr
edic
ted
heat
tran
sfer
rate
isco
mpa
red
toex
perim
enta
lres
ults
inlit
erat
ure.
Kat
prad
itet
al.
[37]
(2005
)N
one
N/A
Copp
erO
pen
Circ
ular
10,2
0,30
0,90
0.66
,1.
06,
2.03
R-1
23,
etha
nol,
wat
er
50
Hea
tflux
incr
ease
swith
decr
easin
gev
apor
ator
leng
th,a
nd
incr
easin
gla
tent
heat
and
nu
mbe
ro
ftur
ns.C
orre
latio
nto
pred
icth
eatt
rans
fer
char
acte
ristic
swas
prop
osed
.
(Con
tinue
do
nn
extp
age)
Downlo
aded
By:
[Un
iver
sity
of
Miss
ouri
Col
umbi
a] A
t: 2
0:49
21
Apri
l 2009
Tabl
e1
(Con
tinue
d)
Ope
n/In
ves
tigat
orTh
eore
tical
clos
edFl
owpa
thPa
ralle
lIn
clin
atio
nD
Wo
rkin
gCh
arge
Conc
lusio
nsan
d(ye
ar)ap
proa
ches
Ass
umpt
ions
Mat
eria
lslo
opge
omet
rych
anne
lsan
gle
( )(m
m)flu
idra
tioq
(W)
com
men
ts
Xu
etal
.[25
](20
05)
Non
eN
/AG
lass
/co
pper
Clos
edCi
rcul
ar8
902
Wat
er,
met
hano
l70
10,3
0Fl
owci
rcul
atio
nw
as
obs
erve
d.Fl
ows
inso
me
chan
nels
are
inth
eo
ppos
itedi
rect
ion
ofb
ulk
circ
ulat
ion
Xu
and
Zhan
g[4
1](20
05)
Non
eN
/ACo
pper
Clos
edCi
rcul
ar8
902
FC-7
270
102
5.6
Bot
hst
artu
pan
dst
eady
ther
mal
osc
illat
ions
wer
est
udie
d.O
scill
atio
nflo
wat
low
heat
ing
pow
erdi
spla
ysra
ndo
mbe
hav
iora
nd
beco
mes
quas
i-per
iodi
cat
high
heat
pow
er.
Hol
ley
and
Fagh
ri[8
](20
05)
Mas
s,m
om
entu
man
den
ergy
equa
tions
are
solv
edfo
rPH
Pw
ithsin
tere
dco
pper
wic
kan
dvar
ying
chan
nel
diam
eter
.
Liqu
idis
inco
mpr
essib
le.
Neg
lect
ing
loss
esat
bend
s.Sa
tura
ted
vap
orw
ithn
eglig
ible
flow
frict
ion.
90,
45,
90W
ater
206
0Va
ryin
gdi
amet
erbe
twee
npa
ralle
lcha
nnel
sin
duce
sflow
circ
ulat
ion
and
may
incr
ease
heat
tran
sfer
capa
city
.B
otto
mhe
atm
ode
perfo
rmed
bette
rth
anto
phe
atm
ode
.Se
nsiti
vity
togr
avity
decr
ease
swhe
nin
crea
sing
the
nu
mbe
ro
fcha
nnel
s.Ca
ieta
l.[4
0](20
06)
Non
eN
/ASt
ainl
esss
teel
,co
pper
Ci
rcul
ar24
01.
397,
1.56
8W
ater
40,5
5,70
100
400
Min
imal
tem
pera
ture
diffe
renc
ean
dflu
ctua
tion
appe
arat
ope
ratin
gte
mpe
ratu
rebe
twee
n12
0C
and
160
C.M
aet
al.[
45]
(2006
)N
one
N/A
Copp
erCl
osed
Circ
ular
2490
1.65
Nan
oflui
d(w
ater
with
diam
ond
nan
o-
parti
cles
)50
533
6A
t100
W,th
etem
pera
ture
diffe
renc
eca
nbe
redu
ced
from
42 C
to25
Cfo
rthe
nan
oflu
idO
HP
aso
ppos
edto
the
pure
wat
erO
HP.
Downlo
aded
By:
[Un
iver
sity
of
Miss
ouri
Col
umbi
a] A
t: 2
0:49
21
Apri
l 2009
Ma
etal
.[55
](20
06)
Lapl
ace
tran
sfor
mat
ion
was
use
dto
solv
eth
eO
DE
that
acco
un
tsfo
rthe
bala
nce
oft
herm
ally
driv
en,
frict
iona
l,an
del
astic
rest
orin
gfo
rces
.
Pres
sure
diffe
renc
ebe
twee
nev
apor
ator
and
con
dens
eris
rela
ted
tote
mpe
ratu
redi
ffere
nce
byCl
apey
ron-
Clau
siseq
uatio
n.
N/A
Ci
rcul
ar
01.
65W
ater
,
acet
one
50
Osc
illat
ing
mo
tion
depe
ndso
nch
arge
ratio
,tot
alch
arac
teris
ticle
ngth
,di
amet
er,
tem
pera
ture
diffe
renc
ebe
twee
nth
eev
apor
atio
nan
dco
nde
nser
sect
ions
,w
ork
ing
fluid
,an
do
pera
ting
tem
pera
ture
.
Char
oens
awan
and
Terd
toon
[38]
(2007
)
Non
dim
ensio
nal
empi
rical
corr
elat
ion
for
heat
tran
sfer
of
PHP
ispr
opos
ed.
Fou
r dim
ensio
nles
sn
um
bers
are
iden
tified
.
Copp
erCl
osed
Circ
ular
10,2
2,32
,52
01,
1.5,
2W
ater
,
etha
nol
30,5
0,80
Pran
dtln
um
bero
fliq
uid,
Kar
man
nu
mbe
r,m
odi
fied
Jaco
bn
um
ber,
bond
nu
mbe
r,K
uta
tela
dzen
um
bera
re
iden
tified
asin
fluen
tial
nu
mbe
rs,S
TDo
fthe
empi
rical
corr
elat
ion
is3
0%.
Quet
al.[
39]
(2007
)N
one
N/A
Copp
erCl
osed
Squa
re,
tria
n-gl
e16
90,
901,
1.5
Wat
er25
40
7.3
33.3
W/c
m2
PHP
with
tria
ngle
chan
nel
perfo
rmsb
ette
rtha
nth
atw
ithsq
uare
chan
nel.
PHP
with
1.5
mm
chan
nel
perfo
rmsb
ette
rtha
nth
atw
ith1
mm
chan
nel.
Chia
nget
al.
[47]
(2007
)N
one
N/A
Alu
min
umO
pen
Squa
re,
tria
ngle
26,3
690
,0Et
hano
l,ac
eton
e,n
ano
fluid
208
0