Advances and Unsolved Issues in Pulsating Heat Pipes

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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

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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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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.

Downlo

aded

By:

[Un

iver

sity

of

Miss

ouri

Col

umbi

a] A

t: 2

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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

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age)

Downlo

aded

By:

[Un

iver

sity

of

Miss

ouri

Col

umbi

a] A

t: 2

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Apri

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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

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

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