Condensation Heat Transfer and Pressure Drop in Horizontal

Rectangular Multiport Minichannels and Small Diameter

Microfin Tubes

By

Md. Mostaqur Rahman

A dissertation submitted in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy (Ph.D) in

Mechanical Engineering

Department of Science and Advanced Technology

Graduate School of Science and Engineering

Saga University

Japan

March 2018

i

ACKNOWLEDGEMENTS

First of all, Alhamdulillah, I should be grateful to Almighty, Gracious and Merciful

Allah. The words are not enough to praise Him for his comfort, strength and courage.

His presence is the main source of my inspiration, without His help; I would not

achieve this goal.

I would like to express my deep appreciation to my research advisor Professor Dr. Akio

Miyara who accepted me as his Ph.D student without any hesitation. It was my

privilege to work with him, who completely showed me what a wonderful advisor

should be like. Without his expert supervision, sincere and tireless supports,

appreciation, continuous inspiration, and trust, it would be impossible for me to achieve

this milestone. My special thanks are due to Dr. Keishi Kariya for making a number of

helpful suggestions. Without their valuable input, this thesis would not have been this

current quality.

I also would like to extend my sincere thanks to the members of my dissertation

committee, Professor Dr. Shigeru Matsuo and Professor Dr. Yuichi Mitsutake for their

time, comments and valuable ideas. I am grateful for their generous and suggestions

that helped improve this work significantly.

I would like to thank to my home university, Dhaka University of Engineering and

Technology, Gazipur-Bangladesh, for allowing me the opportunity to continue my

studies at the doctoral level. I would also like to express special thanks to the MEXT

(Ministry of Education, Culture, Sports, Science and Technology), Japan to grant me as

a Japanese Government sponsored student. Without their grant and support, this would

not have been possible.

I wish to thank to my beloved parents, my father, Md. Helalur Rahman Tarafder, is the

person who put the fundament my learning character, showing me the joy of intellectual

pursuit ever since I was a child; and my mother, Mrs. Morium Begum, is the one who

sincerely raised me with her caring and gently love. Their prayers, encouragement, and

advice have been and will always be a fortune for my life. I be obliged them everything

and wish I could show them just how much I love and appreciate them. I would like to

convey my heartfelt thanks to my beloved wife, Niger Sultana, whose love, support,

patience, encouragement and sacrifice allowed me to finish this journey. Without love

and sacrifice from her, I would not be able to complete my study today. I also want to

ii

be thankful to my only daughter, Musthasfia Mostaq, for her love, patience and

sacrifice.

Thanks are due to all the personnel at the Thermal Energy Engineering Miyara Lab.

They were a constant source of help when I was working with this work group. Thanks

to Kyosuke Nakaiso and Yasuhiro Kudo for helping me to collect experimental data in

the early stage of this study. Finally, I would like to thank all of my lab mates for their

supports. I would also like to express my gratitude to all Bangladeshi friends, Saga

Moslem Society and international students in Saga for making my Japan life more

comfortable and enjoyable. I also would like to thank everybody who was important to

the successful realization of my study, as well as expressing my apology that I could not

mention personally one by one.

iii

Abstract

Multiport minichannels and microfin tubes are increasingly being used for the

fabrication of compact and high performance heat exchangers in air-conditioning,

refrigeration, automotive, heat pump systems and some other industrial applications for

a wide variety of applications. The main target of using compact heat exchanger is to

improve the performance of the system and reduce the charge amount of refrigerant.

The charge reduction is very important in recent air-conditioning, refrigeration and heat

pumping systems because of the great impact of HCFC and HFC refrigerants on the

direct greenhouse effects. However, the pressure drop and heat transfer characteristics

in multiport minichannels and small diameter microfin tubes are questionably to be

different from the conventional tubes of diameter greater than 3.0 mm. The behavior of

the most important parameters such as pressure drop and heat transfer characteristics in

reduced geometry is not clarified sufficiently yet for the design of compact and high

performance heat exchangers. Although, several researchers extensively investigated

the pressure drop and heat transfer in multiport minichannels and small diameter

microfin tubes, but the design engineer still facing problem for accurate predictive tools

for pressure drop and heat transfer prediction in two-phase flow.

To investigate the effects of different parameters on the pressure drop and heat

transfer, a new experimental apparatus to obtain explicit pressure drop and local

condensation heat transfer coefficient measurements over a range of test conditions has

been fabricated. Multiple variables were recorded in order to calculate pressure drop

and local heat transfer coefficient in two-phase adiabatic and condensing flow within

multiport minichannels and microfin tube, respectively. The effects of mass flux,

iv

saturation temperature, vapor quality and channel geometry on adiabatic frictional

pressure drop and condensation heat transfer coefficient were investigated and clarified.

The experimental results discovered that the mass flux, saturation temperature, vapor

quality, and channel geometry play an important role in increasing or decreasing an

adiabatic frictional pressure drop and condensation heat transfer coefficient in both

multiport minichannels and microfin tubes. Some models over-predicted the

experimental frictional pressure drop and condensation heat transfer data, some are

under-predicted and few models captured the trend correctly within the limits of

experimental error. Due to the variety in operating condition consideration during the

models development and complex characteristics of two-phase flow, most of the

existing models were failed to capture the experimental data with a high degree of

accuracy.

In addition, a new two-phase frictional pressure drop correlation is developed for

multiport minichannels to predict the frictional pressure drop correctly. The correlation

has been developed using the experimental data by considering the effects of inertia,

viscous force, fluid properties, channel geometry and surface tension. A new

condensation heat transfer correlation was also proposed to improve the accuracy of the

condensation heat transfer coefficients prediction of two-phase flow in horizontal

rectangular multiport minichannels.

Furthermore, the newly proposed correlations for frictional pressure drop and

condensation heat transfer coefficients prediction has also been validated with the

available frictional pressure drop and heat transfer data collected from the open

literature. Both frictional pressure drop and condensation heat transfer coefficient

correlations showed good agreement with the collected data.

v

Table of Contents

Acknowledgements i

Abstract iii

Table of Contents v

List of figures ix

List of tables xii

Nomenclature xiii

1 Introduction 1

1.1 Background 2

1.1.1 Minichannels 2

1.1.2 Microfin tube 7

1.1.3 Two-phase flow regimes (Flow pattern) 11

1.1.4 Two-phase flow mapping 14

1.2 Literature review 15

1.2.1 Condensation heat transfer in minichannels 15

1.2.2 Two-phase pressure drop in minichannels 22

1.2.3 Condensation heat transfer and pressure drop in microfin tube 27

1.3 Objectives of the present research 33

1.4 Overview of the thesis 34

References 35

2 Experimental Methods 50

2.1 Experimental Facility 51

2.1.1 Experimental Apparatus 51

2.1.2 The test sections

2.1.1.1 Multiport minichannels with and without fins

2.1.1.2 Smooth and microfin tubes

52

52

54

2.1.3 Range of test conditions 56

2.2 Data Reduction 58

2.2.1 Two-phase frictional pressure drop 58

vi

2.2.2 Condensation heat transfer 61

2.3 Experimental measurement uncertainties analysis 65

References 67

3 Adiabatic Frictional Pressure Drop Analysis 68

3.1 Two-phase frictional pressure drop in rectangular multiport

minichannels with and without fins

68

3.1.1 Effect of the mass flux and vapor quality 68

3.1.2 Effect of saturation temperature 70

3.1.3 Effect of channel hydraulic diameter 73

3.2 Two-phase frictional pressure drop in circular microfins and smooth

tubes

74

3.2.1 Influence of mass flux and vapor quality 74

3.2.2 Influence of microfins 76

3.2.3 Influence of saturation temperature 76

3.3 Conclusions 78

References 79

4 Condensation heat transfer 80

4.1 Condensation heat transfer in rectangular multiport minichannels with

and without fins

80

4.1.1 Effect of mass velocity and vapor quality 82

4.1.2 Effect of saturation temperature 83

4.1.3 Effect of minichannels diameter 85

4.2 Condensation heat transfer in circular microfins and smooth tube 86

4.2.1 Effect of the mass flux and vapor quality 86

4.2.2 Effect of tube diameter 87

4.3 Conclusions 90

References 91

5 Comparison of two-phase frictional pressure drop 93

5.1 Models review and comparison of frictional pressure drop in multiport

minichannels with the well-known correlations

93

vii

5.1.1 Models review 94

5.1.1.1 Correlation developed for convensional channels 94

5.1.1.1.1 Homogeneous model (Thome, 2006) 94

5.1.1.1.2 Lockhart and Martinelli correlation (1949) 95

5.1.1.1.3 The Friedel Correlation (1979) 96

5.1.1.1.4 The Müller-Steinhagen and Heck

correlation (1986)

97

5.1.1.1.5 The Wang et al. correlation (1997) 97

5.1.1.2 Correlations developed for minichannels 98

5.1.1.2.1 The Mishima and Hibiki correlation (1996) 98

5.1.1.2.2 The Lee and Lee correlation (2001) 98

5.1.1.2.3 The Koyama et al. correlation (2003) 99

5.1.1.2.4 The Lee and Mudawar correlation (2005) 99

5.1.1.2.5 The Hwang and Kim correlation (2006) 100

5.1.1.2.6 The Sun and Mishima correlation (2009) 100

5.1.1.2.7 The Zhang et al. correlation (2010) 101

5.1.1.2.8 The Li and Wu correlation (2010) 101

5.1.1.2.9 The Kim and Mudawar correlation (2012) 102

5.1.1.2.10 The Jige et al. correlation (2016) 103

5.1.2 Comparison with existing correlations 104

5.2 Models review and comparison of frictional pressure drop in microfins

tube with the well-known correlations

113

5.2.1 Models review 113

5.2.1.1 The Miyara et al. correlation (2000) 113

5.2.1.2 The Koyama and Yonemoto correlation (2006) 114

5.2.1.3 The Müller-Steinhagen and Heck correlation (1986) 115

5.2.1.4 The Goto et al. correlation (2001) 115

5.2.1.5 The Haraguchi et al. correlation (1994) 116

5.2.1.6 The Olivier et al. correlation (2004) 116

5.2.1.7 The Kedzierski and Goncalves correlation (1999) 117

5.2.2 Comparison of experimental frictional pressure drop of

microfins tube with existing correlations

117

5.3 Conclusions 120

viii

References 121

6 Comparison of Condensation Heat Transfer 124

6.1 Models review and comparison of heat transfer coefficients in

minichannels with existing correlations

124

6.1.1 Models review 125

6.1.1.1 Correlations developed for convensional tube 125

6.1.1.1.1 The Shah correlation (1979) 125

6.1.1.1.2 The Haraguchi et al. correlation (1994) 125

6.1.1.1.3 The Dobson and Chato correlation (1998) 126

6.1.1.2 Correlations developed for mini and microchannels 126

6.1.1.2.1 The Wang et al. correlation (2002) 126

6.1.1.2.2 The Koyama et al. correlation (2003) 128

6.1.1.2.3 The Park et al. correlation (2011) 129

6.1.1.2.4 The Bohdal et al. correlation (2012) 129

6.1.1.2.5 The Kim and Mudawar correlation (2013) 129

6.1.1.2.6 The Shah correlation (2016) 130

6.1.1.2.7 The Jige et al. correlation (2016) 131

6.1.2 Comparison with existing correlations 133

6.2 Comparison of condensation heat transfer coefficients in microfin tube

with existing correlations

139

6.3 Conclusions 144

References 145

7 Development of New Correlations 147

7.1 Development of new pressure drop correlation for minichannels 147

7.2 Development of new heat transfer correlation for minichannels 153

7.3 Conclusions 157

References 158

8 Conclusions and recommendations 162

8.1 Conclusions 162

8.2 Future works 164

ix

List of Figures

1.1 Examples of minichannels 3

1.2 Cross-section of different geometry of minichannels 4

1.3

1.4

1.5

1.6

1.7

1.8

Examples of applications of minichannels cooling (Kim and Mudawar,

2014)

Microfin tube (Photo Ref. http://www.wieland-industrierohre.de/)

Characteristic geometrical parameters of inside microfin tube (Cavallini

et al., 2000)

Shabtay microfin tube (Shabtay et al., 2014)

Examples of different microfin tube (Cavallini et al., 2000, 2003)

Schematics of flow patterns and variation of heat transfer coefficient in

minichannels with uniform circumferential heat flux (Kim and Mudawar,

2014).

6

9

9

10

11

12

2.1 A photograph of the test sections. 50

2.2 Schematic diagram of the experimental apparatus 52

2.3 Test section (Multiport minichannels) 54

2.4 Photograph of the test tube 55

2.5 Test section (Circular tube) 56

2.6

2.7

2.8

Abrupt contraction and expansion nonmentcluture

Error of heat balance of all test conditions

Schematic diagram of local heat transfer coefficient calculation.

59

62

64

3.1

3.2

Effects of mass flux and vapor quality on frictional pressure gradient in

rectangular multiport minichannels with fins.

Effects of mass flux and vapor quality on frictional pressure gradient in

rectangular multiport minichannels without fins

69

70

3.3 Effect of saturation temperature on frictional pressure gradient 72

3.4 Comparison of frictional pressure drop between minichannels with fins

and without fins.

73

3.5 Effects of mass flux and vapor quality on frictional pressure drop: (a)

Microfin tube; (b) Smooth tube.

75

x

3.6 Comparison of frictional pressure drop between smooth and microfin

tubes

76

3.7 Frictional pressure drop penalty factor 77

3.8 Effects of saturation temperature on Frictional pressure drop. 77

4.1 Experimental data of condensation heat transfer spread on modified

Baker two-phase flow pattern map (Scott, 1964)

81

4.2 Experimental data of condensation heat transfer overlaid on Taitel and

Dukler (1976) two-phase flow pattern map

81

4.3 Effects of mass flux and vapor quality on average heat transfer

coefficient: (a) Minichannel with fins; (b) Minichannel without fins

83

4.4 Effect of saturation temperature on average heat transfer coefficient; (a)

Minichannels with fins; (b) Minichannels without fins.

84

4.5 Comparison of average heat transfer coefficient between multiport

minichannels with and without fins: (a) G = 50 kg/m2s; (b) G = 100

kg/m2s; (c) G = 150 kg/m2s; (d) G = 200 kg/m2s.

86

4.6 Effects of mass flux and vapor quality on condensation heat transfer

coefficient in: (a) Microfins tube; (b) Smooth tube.

87

4.7 Condensation heat transfer coefficient of microfin tube compared with

condensation heat transfer coefficient of smooth tube.

88

4.8 Condensation heat transfer coefficient enhancement factor. 89

5.1 Comparison of frictional pressure drop with existing; (a) Homogeneous

Model; (b) Lockhart and Martinelli (1949) correlation; (c) Friedel (1979)

correlation; (d) Muller-Steinhagen and Heck (1986) correlation; (e)

Mishina and Hibiki (1996); (f) Wang et al. (1997); (g) Lee and Lee

(2001); (h) Koyama et al. (2003); (i) Lee and Mudawar (2005); (j)

Hwang and Kim correlation; (k) Sun and Mishima (2009); (l) Li and Wu

105

xi

(2010); (m) Zhang et al. (2010); (n) Kim and Mudawar (2012); and (o)

Jige et al. (2016) correlation.

5.2 Frictional pressure drop of the microfin tube compared with existing

correlations: (a) G = 50 kg/m2s; (b) G = 100 kg/m2s; (c) G = 200 kg/m2s

119

6.1 Comparison of experimental average heat transfer coefficient with

existing; a) Shah (1979); b) Haraguchi et al. (1994); c) Dobson and

Chato (1998); d) Wang et al. (2002); e) Koyama et al. (2003); f) Park et

al. (2011); g) Bohdal et al. (2012); h) Kim and Mudawar (2013); i) Jige

et al. (2016); and j) Shah (2016) correlation.

135

6.2 Condensation heat transfer coefficient of microfin tube compared with

existing correlations; (a) Carnavos (1980); (b) Cavallini et al. (1999); (c)

Kedzierski and Goncalves (1999); (d) Goto et al. (2003); (e) Koyama

and Yonemoto (2006).

143

7.1 Comparison of present experimental frictional pressure drop data with

proposed correlation

151

7.2 Validation of proposed frictional pressure drop correlation with available

experimental data collected from the open lituratures.

152

7.3 Comparison of experimental average heat transfer coefficient with

proposed correlations

154

7.4 Validation of proposed condensation heat transfer coefficient correlation

with available experimental data collected from the open literature.

155

xii

List of Tables

2.1 Tube charecteristics of multiport minichannels 54

2.2

2.3

2.4

Detail dimensions of the circular tube with and without microfins

Test conditions for condensation experiments

Test conditions for adiabatic experiments

56

57

57

2.5 Relationship between cC and c 60

3.1

4.1

Thermophysical properties of R134a (Lemmon et al. 2013)

Thermophysical properties of R134a (Lemmon et al. 2013)

71

85

5.1 Appropriate values of C for Lockhart and Martinelli correlation 96

5.2 Deviations of frictional pressure drop for multiport minichannels 113

5.3 Average errors and Mean absolute errors of frictional pressure drop of

microfin tube

118

6.1 Deviations of Heat transfer coefficients during condensation 134

6.2 Condensation heat transfer correlations for microfin tubes 139

6.3

7.1

Average errors and Mean absolute errors of condensation heat transfer

coefficient in microfin tube.

Two-phase frictional pressure drop data for proposed correlation

validation

142

153

7.2 Condensation heat transfer coefficient data for the proposed correlation

validation

156

xiii

Nomenclature

Aa Actual heat transfer area (m2)

An Nominal heat transfer area based on fin root diameter (m2)

Aaf

Anf

Actual flow area (m2)

Nominal flow area based on fin root diameter (m2)

Bo Bond number 2l v hg d

Cc coefficient of contraction

Cp

C

isobaric specific heat (J/kgK)

chisholm’s parameter

d

e

diameter (m)

fin height (m)

E enhancement factor

F heat transfer enhancement factor

Fr Froude number 2

2h

G

gd

f friction factor

G mass velocity (kg/m2s)

g gravitational acceleration (m/s2)

pw Wetted perimeter of tested tube (m)

h

h

h

enthalpy of refrigerant (J/kg)

enthalpy of cooling water (J/kg)

heat transfer coefficient (kW/m2K)

Nconf Confinement number

2h

l v

h

g

n

N

number of fins

number of data points

Nu Nusselt number h

l

hd

k

xiv

p pressure (Pa)

pr reduced pressure

P pressure drop (Pa)

Ph

Ga

phase change number ,p l R wi

lv

C T T

h

Galileo number 3 2

2h l

l

gd

Pr Prandtl number pC

k

Q Sensible heat gain or loss for the whole test section (J/s)

q heat transfer rate for the subsection (J/s)

q heat flux (W/m2)

Re Reynolds number hGd

Rel liquid Reynolds number (1 ) h

l

G x d

Relo liquid only flow Reynolds number h

l

Gd

Rev vapor Reynolds number h

v

Gxd

Revo vapor only flow Reynolds number h

v

Gd

Sulo liquid only flow Suratman number 2

2orl h lo

l lo

d Re

We

Suvo vapor only flow Suratman number2

2orv h vo

v vo

d Re

We

T temperature (°C)

T temperature difference (°C)

t fin tip thickness (m)

u velocity of the working fluid (m/s)

xv

u mean velocity (m/s)

We Weber number 2

h

v

G d

w

z

Width of the test section (m)

Test section wall thickness (m)

x

k

l

vapor quality

thermal conductivity (W/mK)

length of a subsection (m)

Xtt Lockhart-Martinelli parameter

0.5 0.10.91 v l

l v

x

x

z

Z

w

v

∆v

pressure drop measuring length (m)

effective heat transfer length (m)

distance between wall thermocouple (m)

specific volume (m3/kg)

specific volume difference between saturated vapor and liquid (m3/kg)

Greek letters

ξ void fraction

aspect ratio

ψ

apex angle of fin ( º )

helix angle ( º )

area ratio

angle (rad)

Φ two-phase frictional multiplier

geometry constant

HB

A

heat balance factor

Enlargement factor of surface area

surface tension (N/m)

μ dynamic viscosity (Pa s)

density (kg/m3)

shear stress (N/m2)

xvi

κ kinetic viscosity (m2/s)

Subscripts

a

al

A

A,F

A,S

adiabatic condition

aluminium

annular flow

annular with vapor shear stress

annular with surface tension

c abrupt contraction/coolant

cr

cu

Critical

copper

e abrupt expansion

eq equivalent

exp experimental

FC forced convective condensation term

F

GC

Frictional

gravity control convection term

h

HB

hydraulic diameter

heat balance

i inner

in inlet

l saturated liquid

lo

ll

lt

L

liquid-phase with total flow

laminar liquid-laminar vapor

laminar liquid-turbulent vapor

intermittent flow/lower side water flow

NC free convection condensation term

o outer

out outlet

pred predicted

R refrigerant

r

ref

reduced pressure

refrigerant

s subsection

xvii

sat saturation

tp

tt

tl

T

U

two-phase

turbulent liquid-turbulent vapor

turbulent liquid-laminar vapor

Total

upper side water flow

v

vo

saturated vapor

vapor-phase with total flow

w wall

wo outer wall surface of tested tube

wi inner wall surface of tested tube

1

CHAPTER 1

Introduction

Minichannels and small diameter microfin tubes for two-phase flow applications are

widely being used for the fabrication of compact and high performance heat

exchangers. Unlike single-phase flow system, two-phase flow system absorb far greater

amounts of heat by utilize the coolant’s combined sensible and latent heat. They are

very commonly used in air conditioning, refrigeration, automotive and heat pump

systems to improve the performance of that system. System performance enhancement

and charge of refrigerant reduction is decisive in the present day refrigeration, air

conditioning and heat pump systems.

Global warming is already underway with consequences that must be faced today as

well as tomorrow. Evidence of changes to the Earth's physical, chemical and biological

processes is now evident on every continent. The average temperature of Earth’s

atmosphere and oceans are rising due to the global warming. Since the early 20th

century, Earth's mean surface temperature has increased by about 0.8 °C, with about

two-thirds of the increase occurring since 1980 (America's Climate Choices, 2011).

According to the Intergovernmental Panel on Climate Change (IPCC) report, within the

21st century the global surface temperature is likely to rise a further 1.1 to 2.9 °C for

their lowest emissions scenario and 2.4 to 6.4 °C for their highest (Anowar Hossain,

2013, Forster et al., 2007). Therefore, the world will lose up to 39% of its land by 2100

because rising the sea level, if continue global warming (APA, University of

Wisconsin-Madison, 2007).

Air conditioning, refrigeration, automotive and heat pump sectors are prior

responsible for the man made global warming problem directly and indirectly. The

direct impacts are due to the emissions of high global warming potential refrigerants

emissions to the environment and the indirect impacts are for the greenhouse gas

emissions associated with the energy uses by those systems. Thus, the charge reduction

2

of refrigerant is very important in recent automotive, refrigeration, air conditioning and

heat pumping equipment to enhance the safety measure of flammable refrigerant and

meet the environmental concerns of using high global warming potential (GWP)

refrigerant.

Several previous study of different researchers found that the system performance

such as heat transfer is significantly empowered by either reducing the channel diameter

or employing finned tube. The use of the minichannels and small diameter microfins

tubes may imply a large reduction of the refrigerant charge of the system. Despite those

advantages, unfortunately, a higher pressure drop is obtained which may degrade the

overall efficiency of the two-phase system (Kim and Mudawar, 2012; Lopez-Belchi et

al., 2014).

The heat transfer during condensation and adiabatic frictional pressure drop for two-

phase flow system in minichannels and small diameter microfins tubes has been a

research subject for several decades. Many researchers extensively investigated two-

phase friction pressure drop and the heat transfer characteristics during condensation in

minichannels and small diameter microfins tubes experimentally and theoretically but

the information on two-phase pressure drop is still inadequate. The flow phenomena is

not clarified sufficiently yet.

Design engineers of compact and high performance heat exchangers in automotive,

refrigeration, air-conditioning and heat pump systems are facing problems to obtain

preliminary information on the heat transfer and pressure drop characteristics of two-

phase flow in minichannels and small diameter microfins tubes. Hence, the design of

the compact and high performance minichannels and microfins tube heat exchanger

essentially requires accurate predictive tools for pressure drop and heat transfer

prediction in two-phase flow.

The present study is a challenge to contribute better information and developed

prediction method of heat transfer and frictional pressure drop for the design of

compact and high performance heat exchanger.

1.1 Background

1.1.1 Minichannels

Minichannels are defined as flow passages that have hydraulic diameters in the range of

3

0.2 mm to 3 mm. The minichannel could be single or multiport as shown in Fig. 1.1 and

different in shape. There are more than 25 different geometries are studied by different

researchers (Shahsavari et al., 2012). A very few of the geometries are depicts in Fig.

1.2. The channel dimension and geometry has important effects on two-phase flow heat

transfer and pressure drop, which has been proved in a number of studies. Quite a few

classifications of channels have been proposed by different researchers based on

various criteria. Many of them have been discussed briefly by Cheng and Mewes

(2006). First definition was proposed by Shah (1986). He defined a compact heat

exchanger as an exchanger with a surface area density ratio >700 m2/m3. This limit

translates into a hydraulic diameter of <6 mm. According to this definition, the

distinction between small diameter channels and normal size channels is 6 mm.

Photo source: http://www.fcx.com

Photo source, Shabtay et al., 2014

Fig. 1.1 Examples of minichannels

4

Fig. 1.2 Cross-section of different geometry of minichannels

A most widely used classification is proposed by Kandlikar (2002) and Kandlikar and

Grande (2003) according to which:

Conventional or macro channels: dh > 3 mm

Minichannels: 3mm ≥ dh > 200 µm

Microchannels: 200 µm ≥ dh > 10 µm

Transitional channels: 10 µm ≥ dh > 1 µm

Molecular Nanochannels: 0.1 µm ≥ dh

This classification was developed mainly based on the flow of gases. They also

recommended it for both liquid as well as two-phase flow application such as boiling

and condensation flow application to provide uniformity in the channel classification.

Mehendail et al. (2000) proposed the classification of small channel dimensions in

terms of hydraulic diameter as:

Conventional or macro channels: dh > 6 mm

Compact passage channels: dh =1-6 mm

Meso channels: dh = 0.1-1 mm

Microchannels: dh = 1-100 µm

This classification is based simply on the dimensions of the channels. Although, this

classification has some acceptance.

Cheng and Wu (2006) provided a classification based on an analysis considering the

magnitude of gravity and surface tension effects as:

Star-shap Rhombus Circle Polygon Ellipse Tringle

Rectangle withround corners

Trapezoidal Square Rectangle Semi-circle Diamond

5

Conventional or macrochannels: Bo > 3.0 (Surface tension is small in compared

to gravitational force).

Minichannels: 0.05 < Bo < 3.0 (surface tension effect becomes dominant and

gravitational effect is small)

Microchannel: Bo < 0.05 (gravity effect is negligible)

Later on, Ghiaasiaan (2008) mention another classification as:

Conventional channels: dh ≥ 3 mm

Minichannels: 100 µmm ≤ dh ≤ 1000 µm

Microchannels: 10 µm ≤ dh ≤ 100 µm

This classification is also mainly based on the channels diameter and it does not

consider the effects of fluid properties.

Minichannels offers the following advantages over conventional tubes:

High thermal efficiency

Reduced pressure drop

Low refrigerant charge

Good surface temperature uniformity

Light weight

Low cost (material saving potential)

Effectiveness and compactness

Due to the above mentioned advantages, two-phase flow minichannel have gained

unprecedented popularity in many modern technologies demanding the removal of

highly concentrated heat loads from small surface areas. In recent day, minichannels in

two-phase flow has become increasingly important in many applications such as:

Industrial and automobile air conditioning, refrigeration and heat pump system

Compact heat exchanger

Biomedical instrumentation

Water cooled turbine blades

Computer data centers

Rocket nozzle cooling

Fusion reactor blanket cooling

Avionics cooling

Cooling of satellite electronics

6

Cooling of hybrid vehicle

Power electronics

Heat exchangers for hydrogen storage systems

Fig. 1.3 Examples of applications of minichannels cooling (Kim and Mudawar, 2014)

Those applications are also depicts in Fig. 1.3 collected from Kim and Mudawar, 2014.

From a practical standpoint, minichannel cooling and heating has shown great

7

versatility in design and construction, including isolated tubes, tubes that are soldered

upon a heat dissipating surface and channels that are formed into a conducting

substrate. There is also the added flexibility in minichannel shape, including circular,

rectangular, triangular, trapezoidal, diamond cross sections and so on as shown in Fig.

1.2 (Kim and Mudawar, 2014).

1.1.2 Microfins tube

Improved thermal performance of heat exchanger by enhancement technique has

become more popular and standard practices nowadays. The enhancement technique

can significantly improve the thermal efficiency of the heat exchange systems as well as

the economics of their design and operation. Generally, enhancement techniques can be

divided into two groups: namely, (1) active and (2) passive techniques. The active

techniques require external forces such as electric field, acoustic or surface vibration

whereas the passive techniques require special surface geometries such as rough surface

or extended surface etc. If two or more of these techniques are utilized together to

achieve enhancement, the term is called as compound enhancement. Both techniques

have been used by researchers for 140 years to increase heat transfer rates in heat

exchangers (Dalkilic and Wongwises, 2009). Bergeles have been identified several

enhancement techniques (Bejan & Kraus, 2003) which are given in below and their

brief description can be found in (Bejan & Kraus, 2003).

(1) Passive enhancement techniques:

Treated surfaces

Rough surfaces

Extended surfaces

Displaced enhancement devices

Swirl flow devices

Coiled tubes

Surface tension devices

Additives for liquids

Additives for gases

(2) Active enhancement techniques:

Mechanical aids

Surface vibration

8

Fluid vibration

Electrostatic fields

Injection

Suction

Jet impingement

Among the above mentioned heat transfer enhancement techniques, extended or

finned surface are perhaps the most widely used and researched enhancement technique

(Afroz, 2008). Microfin tubes are the best example of extended surface enhancement

techniques that have recently been used intensively because of their high condensation

heat transfer performance and low pressure drop.

The microfin on an internal wall surface of the tube is called microfin tube as depict

in Fig. 1.4. The microfin tube was first developed by Fujie et al. (1977) of Hitachi

Cable Ltd. As mentioned by Kim (2016). The microfin tubes have received special

attention as they significantly empowered the heat transfer coefficient with relatively

low pressure drop increases in commercial refrigeration and air conditioning

applications since the 1980s. Microfins improve the heat transfer in both two-phase and

single-phase applications, and are one of the most efficient and common heat transfer

enhancement mechanism for the heat exchangers due to their superior heat transfer

performance. The heat transfer performance of the tubes is increased in an effective

manner by the presence of the microfins on the internal wall surface of the horizontal

tubes (Dalkilic and Wongwises, 2009). The heat transfer enhancements are mainly

caused by the increase in the surface heat transfer area, surface tension effect on the

condensate drainage and induced turbulence by microfin. The refrigeration, air

conditioning and heat pumps industry is developing very compact machinery, and this

requires the use of heat exchangers with enhanced surfaces. Air cooled condensers for

refrigeration and heat pumps are manufactured with enhanced surfaces both on the

external and on the refrigerant side (Cavallini et al., 2000).

The microfin tubes are typically made of copper as it offers several advantages such as:

cost effective fabrication and assembly

Smaller size, less weight and lower material costs

Higher heat transfer coefficients

Naturally corrosion resistant metal

9

Environmentally friendly

Well suited for new refrigerants

Mechanical strength is high enough.

Fig. 1.4 Microfin tube (Photo Ref. http://www.wieland-industrierohre.de/)

Fig 1.5 Characteristic geometrical parameters of inside microfin tube (Cavallini et al.,

2000)

Typical microfin tubes available for industrial applications have an outside diameter

from 4 to 15 mm, a single set of 50-70 spiral fins with spiral angle from 6 to 30 0, fin

Fin

tip

dia

met

er (

d)

Spiral angle

Fin height

Apex angle

10

height from 0.1 to 0.25 mm, triangular or trapezoidal fin shapes with an apex angle

from 25 to 90 0 (Cavallini et al., 2000). The characteristic geometrical parameters of

microfin tubes are shown in Fig. 1.5.

A variety types of microfin tube based on the fin geometry studied by different

researchers since at the end of 1970s. The common and commercially available

microfin tubes include (Fig. 1.6-1.7):

Helical or spiral or axial grooved microfin tube

Cross-grooved microfin tube

Herringbone microfin tube

Different studies of several researchers on the microfin tubes show a heat transfer

enhancement compared to equivalent smooth tubes from 80 to 200% and over, with an

increasing pressure drop from 20 to 80% (Cavallini et al., 1999; Miyara et al., 2000; Yu

and Koyama, 1998; Kedziersky and Goncalves, 1999; Cavallini et al., 2000)

Fig. 1.6 Shabtay microfin tube (Shabtay et al., 2014)

11

Fig. 1.7 Examples of different microfin tube (Cavallini et al., 2000, 2003)

1.1.3 Two-phase Flow regimes (Flow pattern)

Flow regimes are among the most intriguing, challenging and difficult aspects of

two-phase flow and have been investigated over many decades. Two-phase flow can

form a variety of morphological flow configuration. Flow regimes are extremely

important as it strongly influence the heat and momentum transfer processes. According

to Ghiaasiaan (2008), some of the physical factors that lead to morphological variations

include the following:

The density difference between the phases; as a result the two phases respond

differently to forces such as gravity and centrifugal force;

Helical microfin tube

Cross-grooved microfin tube

Helical microfin tube Herringbone microfin tube

12

The deformability of the gas–liquid interphase that often results in incessant

coalescence and breakup processes; and

Surface tension forces, which tends to maintain one-phase dispersal.

Flow regimes and their ranges of occurrence are thus sensitive to fluid properties,

system configuration/and orientation, size scale of the system, occurrence of phase

change, and so on. Heat transfer coefficient and pressure drops are closely related to the

local two-phase flow structure of the fluid and thus two-phase flow pattern prediction is

an important aspect of modeling evaporation and condensation (Thome, 2006). To

predict heat transfer and pressure drop, it is important for designers to identify what

flow pattern exists at the local flow condition. Fig. 1.8 shows a schematic representation

of flow regimes and heat transfer coefficient variation in a horizontal minichannels

heated by a uniform heat flux.

Fig. 1.8 Schematics of flow patterns and variation of heat transfer coefficient in

minichannels with uniform circumferential heat flux (Kim and Mudawar, 2014).

In two-phase flow, different flow patterns are established at different regions of

the minichannels as the fluid undergoes a transition from vapor to liquid along the

length of the tube. Several studies already observed that the flow patterns of

minichannels are different from those observed in conventional tube due to the different

relative magnitudes of gravity, shear and surface tension forces. Those forces determine

the particular flow regime established by a given combination of liquid and gas phase

13

velocities (Coleman and Garimella, (1999, 2003)). With an order of magnitude

reduction in the channel diameter from conventional to minichannel and minichannel to

microchannel, significant changes in the two phase flow characteristics are expected.

The flow in minichannels results in the appearance of different flow regimes and some

of the flow regimes transition boundaries are also shifted. In minichannels, the

gravitational effect is insignificant so that the channel orientation no longer has a

significant effect on the two phase flow regimes (Kawahara et al., 2002). Flow regimes

in minichannels are controlled mainly by surface tension and inertia or vapor shear

forces. Based on the relative importance of the surface tension over vapor shear forces,

three overall flow regimes were identified by Shao et al., 2009, namely surface tension

dominated, vapor shear forces dominated and transitional regimes. The surface tension

forces dominate at low flow velocities corresponding to bubbly and intermittent (also

known as Taylor, segmented, slug, plug or elongated flow) flow and vapor shear forces

dominate at high velocities corresponding to annular flow.

There are many authors observed the existence of flow patterns in minichannels

(Suo and Griffith, 1964, Shao et al., 2009, Kawahara et al., 2002, Satitchaicharoen and

Wongwises, 2004, Rebrov, 2010, Coleman and Garimella, 1999, Coleman and

Garimella, 2003, Serizawa et al., 2002, Xu et al., 1999, Yang and Shieh, 2001, Zhao et

al., 2004). Most of the researchers were observed different flow patterns in horizontal

minichannel namely, bubbly flow, intermittent flow, annular flow and dispersed flow.

Bubbly flow: bubbly flow is characterized by distinct bubbles and sometimes non-

spherical bubbles of the equivalent diameter smaller than the channel diameter. Bubbly

flow is usually occurs in relatively small gas superficial velocity. Bubbles are separated

from the walls of the channel with the film of the liquid and have a wide scatter in size.

Intermittent flow: The intermittent flow is characterized by discontinuities in the

gas and liquid flow for further increasing the gas velocity. Due to further increasing the

gas velocity, the interfacial waves become large enough to wash the top of the tube.

Large amplitude waves often contain entrained bubbles. The top wall is nearly

continuously wetted by the large amplitude waves and the thin liquid films left behind

(Thome, 2006). The intermittent flow regime composite of the slug and plug flow

regimes. In plug flow, the flow regime has liquid plugs that are separated by elongated

gas bubbles. The diameters of the elongated bubbles are smaller than the tube such that

the liquid phase is continuous along the bottom of the tube below the elongated

bubbles. In slug flow, at higher gas velocities, the diameters of elongated bubbles

14

become similar in size to the channel height. The liquid slugs separating such elongated

bubbles can also be described as large amplitude waves (Thome, 2006).

Annular flow: When the mass flow rate is high enough, the condensate forms a

continuous annular film around the inside of the tube walls, almost similar to that in

vertical flow but the condensate film is thicker at the bottom than the top. The interface

between the liquid annulus and the vapor core is distributed by small amplitude waves

and droplets may be dispersed in the gas core (Thome, 2006). A significant portion of

most condensers operate in this flow regime.

Dispersed flow: with further increase of liquid superficial velocity or when the

liquid flow is turbulent and the gas phase is in either laminar flow or turbulent flow, all

the liquid may be stripped from the wall and entrained as smalled droplets in the gas

core to form the dispersed pattern. In most cases the liquid film is left in contact with

the wall (Shao et al., 2009).

1.1.4 Two-phase flow mapping

Flow pattern maps are the most widely used predictive tools for two-phase flow

pattern. A flow pattern map is used to predict the local flow pattern in a tube. The flow

pattern map is a graphical presentation that displays the transition boundaries between

the flow patterns. It is typically plotted on two-dimensional maps with coordinates

using dimensionless parameters to represent the liquid and gas velocities. The flow

pattern maps for wide variety of scales, geometric configurations, orientations and

properties are available in open literature. Baker (1954), Scott (1963), Mandhane et al.

(1974), Wambsganss et al. (1991), Kattan et el. (1998a,b,c), Xu (1999), Xu et al.

(1999), Coleman and Garimella (1999, 2003), Yang and Shieh (2001), Ould Didi et al.

(2002), Zurcher et al. (2002a,b), Thome et al. (2003), El Hajal et al. (2003), Zhao et al.

(2004), Wojtan et al. (2005a,b) and Shao et al. (2009) have all described the importance

of using flow pattern information in the determination of accurate two-phase flow

models. There are three main types of two-phase flow maps in the literature:

Baker/Mandhane type, Taitel-Dukler type, and Steiner type (Hossain, 2013). Baker

(1954) developed one of the first two-phase flow regime maps with air-water and air-oil

data in large tubes. Baker (1954) used superficial vapor mass flux times a fluid property

scaling factor on the vertical axes and superficial liquid mass flux times a different fluid

15

property scaling factor on the horizontal axis. Mandhane et al. (1974) later developed a

similar map with huge database of 5935 air water data, but used superficial gas and

liquid velocities on the horizontal and vertical axes respectively. Dobson and Chato

(1998) then made modifications to the flow map of Mandhane et al. (1974) by

multiplying the axis by the square root of the vapor to air density ratio. They observed

flow regimes with R134a, R22 and nearly azeotropic mixtures of R32/R125 condensing

inside tubes having 3.1 mm, 4.6 mm and 7.1 mm inside diameter. Taitel-Dukler (1976)

developed a mechanistic type flow map with the Lockhart- Martinelli parameter on the

horizontal axis and a modified Froude rate times a transition criteria on the vertical axis.

For typical heat exchangers, Wojtan et al. (2005a) proposed a modification of the

Kattan et al. (1998a) map, which itself is a modified Steiner (1993) map, and included

a method for predicting the onset of dry out at the top of the tube in evaporating flows.

Most of the recent two-phase flow regime maps found in the literature is Steiner

(1993) type flow maps. Ould Didi et al. (2002), Coleman and Garimella (2003), El

Hajal et al. (2003) and Wojtan et al. (2005) all use similar Steiner (1993) style flow

maps with quality on the horizontal axis and mass flux on the vertical axis. In this

research work, three well-known flow pattern maps namely, modified Baker (Scott,

1963) and Taitel-Dukler (1976) are used for plotting and visualize the experimental

data.

1.2 Literature review

1.2.1 Condensation heat transfer in minichannels

Heat transfer characteristics in single or multiport minichannels during

condensation have been strongly researched in the last fifty years. The heat transfer

characteristics in minichannles are different from those of conventional tubes. In

conventional channels, the heat transfer is dominated by vapor shear stress and

gravitational forces but in minichannels, gravitational forces are negligible. Instead of

them, surface tensions play an important role. However, several researchers extensively

investigated the condensation heat transfer characteristics in single and multiport tubes

with different shaped minichannels experimentally and theoretically in the last decade.

The available studies on heat transfer characteristics in minichannels during

condensation are summarized below:

16

Thome et al. (2003) developed a new flow pattern based model for condensation

heat transfer in the horizontal tube of diameter ranging from 3.1 to 21.4 mm based on

simplified flow structures of the flow regimes and also considered the effect of liquid-

vapor interfacial roughness. The model predicted experimental database, contained

4621 data points from 15 fluids of different flow regimes reasonably.

Koyama et al. (2003a, b) experimentally measured the condensation heat transfer

coefficients of R134a in two multiport tubes having eight channels and nineteen

channels with 1.1 mm and 0.8 mm hydraulic diameters at the saturation temperature 60

C. They proposed a correlation for heat transfer coefficient by combining convective

and film condensation term based on the same functional form as the correlation of

Haraguchi et al. (1994). The author also concluded that the heat transfer enhancement

effect of micro-fins is mainly due to the enlargement of heat transfer area.

Agarwal et al., (2010) carried out experiments of HFC134a condensation heat

transfer in six non-circular horizontal multiport tubes whose hydraulic diameter ranged

from 0.424 to 0.839 mm. The channels included barrel-shaped, N-shaped, rectangular,

square, triangular extruded tubes, and a channel with a W-shaped corrugated insert that

yielded triangular minichannels. They developed correlation for heat transfer during

condensation in horizontal non-circular minichannels and suggested to use annular flow

based model for square, barrel-shaped and rectangular channels, while the mist-flow

based model for channels with sharp corners.

Goss and Passos (2013) experimentally studied the convective condensation of

R134a inside eight horizontal and parallel tubes of 0.77 mm diameter. Their results

show that mass velocity and vapor quality have an important influence on the heat

transfer coefficient. The consideration that all of the resistance to heat transfer is due to

the conduction through the liquid film is a good approximation, mainly for xv < 0.95.

Kim et al. (2003) performed an experimental investigation of condensation heat

transfer in a smooth multiport minichannel with 1.56 mm hydraulic diameter and in a

microfin multiport minichannel with 1.41 mm hydraulic diameter using R410A and

R22 as working fluids. Results showed that the effect of surface drainage on the fin

surface is more pronounced for R22 than R410A because of smaller Weber umber. In

addition, they modified Yang and Webb (1997) correlation to predict microfins tube

data adequately.

Wang et al. (2002) investigated the condensation heat transfer and flow regime

17

measurements of R134a in a rectangular multiport minichannel with a hydraulic

diameter of 1.46 mm. Existing correlations were failed to predict their experimental

data. The author developed a correlation by weighting the regime-specific correlations

with an annular flow length fraction to account for the effect of flow regime transitions

over a range of condenser flow conditions.

Wang and Rose (2005, 2006) theoretically investigated the film condensation heat

transfer from a vapor flowing in horizontal non-circular minichannel. They developed a

theoretical model based on fundamental analysis which assumes laminar condensate

flow on the channel walls and takes account of the effects of the interfacial shear stress,

surface tension, and gravity. The author presented results for fluids of R134a, R22, and

R410A in square and triangular section minichannels in the range of hydraulic diameter

0.5-5 mm.

Yang and Webb (1997) proposed a semi empirical model by considering the effects

of vapor share and surface tension forces to predict the condensation heat transfer inside

multiport minichannel having microgrooves. At low mass velocity, surface tension

force is effective in enhancing the condensation heat transfer as long as the fin tips are

not flooded by condensate. The surface tension effect is strongly depends on the fin

geometry. The flow is vapor share controlled and contribution of surface tension is very

small at high mass velocity.

Park and Hrnjak (2009) investigated the CO2 flow condensation heat transfer in

multiport tubes of 0.89 mm hydraulic diameter at low temperature. They were measured

at mass velocity from 200 to 800 kg/m2s, saturation temperature of -15 and -25 0C, and

wall sub-cooling temperature from 2 to 4 0C. The author observed that the measured

heat transfer coefficient increased with the increase of mass fluxes and vapor qualities,

whereas it is almost independent of wall sub-cooling.

Yang and Webb (1996) conducted experiments of condensation heat transfer using

R12 in a flat extruded aluminum plain tube of hydraulic diameter 2.63 mm and microfin

tube of hydraulic diameter of 1.56 mm. The condensation heat transfer coefficient in

both plain and microfin tubes increases with increasing heat flux. The authors propose

that the heat transfer coefficients in a microfin tube are slightly greater than that of plain

tubes due to the surface tension drainage force becomes effective and provide additional

enhancement, which is apparently additive to the effect caused by vapor shear. This

effect is not so strong at high mass velocity.

Sakamatapan et al., (2013) conducted experiments of condensation heat transfer

18

characteristics of R134a in multiport minichannels have fourteen channels with a 1.1

mm hydraulic diameter and eight channels with a 1.2 mm hydraulic diameter. Results

showed that the heat transfer coefficient increased with the increase of heat flux, mass

flux and vapor quality but decreased as saturation temperature increases. They found

that when the hydraulic diameter is decreased; the heat transfer coefficients increased

up to 15%.

Kim and Mudawar (2013) proposed a new universal approach to predict the

condensation heat transfer coefficient for predominantly annular flows, and slug and

bubbly flows in mini/microchannels. The proposed approach is capable of tackling

many fluids with different thermophysical properties, flow parameters and broad ranges

of all geometry with hydraulic diameter from 0.424 to 6.22 mm. The author amassed a

consolidated database consisting of 4045 condensation data points from 28 sources for

mini/microchannels. The data points consists of 1964 data points for single channel

from 17 sources and 2081 data points for multiport channel from 13 sources includes 17

different working fluids.

Derby et al. (2012) experimentally measured the condensation heat transfer

coefficients of R134a in 1 mm square, triangular and semi-circular multiport

minichannels with smaller measurement uncertainties. The author concluded that the

mass flux and vapor quality had significant effects on condensation process but

saturation temperature, heat flux and channel shape had no significant effects.

Illan-Gomez et al., (2015) investigated the flow condensation heat transfer

coefficients of R1234yf and R134a in a minichannel multiport tube of 1.16 mm

hydraulic diameter. The test were conducted over a range of mass flux 350 to 940

kg/m2s and saturation temperature range of 30 to 55 0C. Test results showed that the

thermal conductivity, density ratio and viscosity ratio are playing an important role in

the variation of the heat transfer coefficient. The refrigerant R134a has shown higher

heat transfer coefficient than its potential substitute refrigerant R1234yf. The variation

of saturation temperature and mass flux produces similar effects in both refrigerants.

Cavallini et al. (2005) investigated the pressure drop and condensation heat transfer

characteristics of R134a and R410A in a multiport minichannel with 1.4 mm hydraulic

diameter. They have been compared their data against models available in the literature.

All of the existing models were failed to predict the experimental heat transfer

coefficient at high values of mass velocity and high values of the dimensionless gas

velocity.

19

Cavallini et al. (2006) reviewed experimental works on condensation flow regimes;

heat transfer and pressure drop in minichannels of different cross-section geometries

with hydraulic diameters ranging from 0.4 to 3 mm. They compared the available

experimental data for high pressure refrigerant (R410A), medium pressure refrigerant

(R134a) and low pressure refrigerant (R236ea) with semi-empirical and theoretical

models developed for conventional and minichannels. Based on the review and

experimental data, they discussed and evaluated opportunity for a new heat transfer

model for condensation in minichannels. In the new model, they considered the effects

of the entrainment rate of droplets from the liquid film.

Cavallini et al. (2011) reported an experimental data for condensation heat transfer

and adiabatic frictional pressure drop of the refrigerants R32 and R245fa in a single

circular minichannel of inside diameter 0.96 mm. The author’s compared the

experimental heat transfer data with predicting models to provide a guideline for design

of minichannel condenser. They concluded that most of the experimental data points of

condensation heat transfer coefficient were shear stress dominated.

Del Col et al. (2010) experimentally measured the local heat transfer coefficients

during condensation of R1234yf and R134a in a single circular minichannel of 0.96 mm

inside diameter. The refrigerant R1234yf displayed lower heat transfer coefficients that

R134a at the same operation conditions.

Shah (2016a) presented a correlation for heat transfer during condensation in

horizontal single and multiport mini/microchannels of many shapes with hydraulic

diameter from 0.10 to 2.8 mm. They collected 1017 data points from 31 source

covering 13 fluids. The author suggested a simple new boundary between conventional

channels and minichannels for condensation heat transfer.

Shah (2016b) proposed two alternative comprehensive correlations for heat transfer

during condensation in plain conventional channels and micro/minichannels in all

orientations. Both correlations were developed by modifying the Shah (2009)

correlation. They have been validated both the correlations with a database contained

4063 data points collected from 67 source that includes 33 fluids, diameters 0.10 to 49.0

mm, various shapes and all orientations.

Zhang et al. (2012) experimentally investigated condensation heat transfer and

pressure drop of R22, R410A and R407C in two single round tubes with inner diameter

of 1.088 mm and 1.289 mm. The results indicated that condensation heat transfer

coefficients increase with mass flux and vapor quality, increasing faster in the high

20

vapor quality region. They compared the experimental data with the correlations for

large diameter tubes and minichannels. Almost all of the correlations for large diameter

tubes overestimated the experimental data. The correlations for minichannels showed

better prediction but still had large discrepancy.

Lui et al. (2013) conducted experimental measurements of condensation heat

transfer and pressure drop of R152a in circular and square minichannel with hydraulic

diameters of 1.152 mm and 0.952 mm, respectively. The results showed that the

condensation heat transfer and pressure drop increase with mass flux and vapor quality

while decrease with the saturation temperature in both tubes. The author observed that

the square minichannel showed higher heat transfer coefficient than the circular

minichannel due to the effect of surface tension.

Zhang et al. (2015) presented a comprehensive review of correlations for heat

transfer during condensation in horizontal conventional tube and minichannels. They

compiled a database containing 2563 data points of condensation heat transfer,

including 1462 data points for conventional tube and 1101 for minichannels from 26

sources covering 17 working fluids. Total 28 correlations including 7 correlations for

minichannels were evaluated using compiled database. The evaluation results indicated

that more attention is needed to improve the prediction method for minichannels.

Zhang et al (2016) numerically investigated the heat transfer and pressure drop

characteristics during condensation for R410A in minichannels with hydraulic

diameters of 0.25, 1, and 4 mm, respectively at different saturation temperatures. The

results indicated that the heat transfer coefficients and pressure drop increase with

increasing mass flux and vapor quality and decreasing with tube diameter and saturation

temperature. The shear dominated flow regime was observed at higher mass flux, vapor

quality and in smaller diameter tube. Further, the author proposed a new correlation

based on numerical simulation.

Heo et al. (2013) investigated the in-tube condensation heat transfer characteristics

of CO2 in three different rectangular minichannels of hydraulic diameters 1.5, 0.78 and

0.68 mm having 7, 23 and 19 numbers of ports, respectively. The author’s found that

the condensation heat transfer coefficients increased with the decrease in hydraulic

diameter. Increasing and decreasing the heat transfer coefficient at critical vapor quality

was also observed in minichannel of hydraulic diameter 0.78 mm. The existing models

for the prediction of heat transfer coefficients over predicted the experimental data

except Thome et al. (2003) model.

21

Oh and Son (2011) carried out experimental study on the condensation heat transfer

of R22, R134a and R410A in a single circular horizontal copper minichannel of 1.77

mm inner diameter. The results showed that the condensation heat transfer coefficient

of R410A was higher than that of R22 and R134a at the same test condition. Most of

the existing correlations whose were proposed for conventional tube and minichannels

failed to predict their experimental data reasonably.

Huai and Koyama (2004) experimentally studied the local characteristics of heat

transfer and pressure drop of CO2 during condensation in a multiport extruded

aluminum minichannel with 1.31 mm equivalent diameter having 10 circular channels.

The results indicated that the heat transfer coefficient in the two-phase region is higher

than that in the single-phase and mass flux has significant effect on condensation heat

transfer characteristics. During the comparison of experimental data with previous

existing correlations, the authors were observed large discrepancies.

Shin and Kim (2004) developed a new experimental technique to measure the

condensation heat transfer and pressure drop of R134a in a horizontal single round

minichannel with an inner diameter of 0.691 mm. The authors concluded that the

condensation heat transfer increased with the refrigerant quality as expected except for

low mass fluxes. The comparisons of experimental data with existing heat transfer

coefficient revel that all of the correlations failed to predict the experimental data

reasonably.

Shin and Kim (2005) presented an experimental study of condensation heat transfer

characteristics of R134a in horizontal single circular minichannels (d =0.493, 0.691,

and 1.067 mm) and rectangular minichannels (dh =0.494, 0.658, and 0.972 mm). The

tests were conducted over a mass flux range of 100-600 kg/m2s, a heat flux range of 5-

20 kW/m2, and at saturation temperature of 40 0C. The heat flux was shown

insignificant effects on heat transfer coefficient and pressure drop. A clear

enhancement of heat transfer coefficients was observed as the hydraulic diameter

decreased. All of the existing correlations failed to predict the experimental data.

Jige et al. (2016) performed the experimental study of condensation heat transfer

characteristics of refrigerants R134a, R32, R1234ze (E), and R410A in a horizontal

rectangular multiport minichannel of hydraulic diameter 0.85 mm. The tests were

performed for mass flux from 100 to 400 kg/m2s and a saturation temperature from 40

to 60 0C. The author clarified the effects of mass velocity, vapor quality, saturation

temperature, refrigerant properties and hydraulic diameter of a rectangular channel on

22

condensation. The authors concluded that the effects of the vapor shear stress and

surface tension on the condensation heat transfer surpass the gravity effect with

decreasing channel size. Particularly, in the case of low mass velocity, the condensate

film is attracted to the corners of the cross sectional area in the rectangular

minichannels because of the effect of the surface tension. Therefore, the condensate

film is kept thin between the corners for comparatively low vapor quality. The authors

also proposed a model for condensation heat transfer in rectangular minichannels

considering the flow patterns and effects of vapor shear and surface tension.

Recently, Rahman et al. (2017) reported an experimental study of condensation heat

transfer of R134a in horizontal rectangular multiport minichannel with and without fins

having 20 channels with hydraulic diameters of 0.64 and 0.81 mm, respectively. The

measurements were done over a mass flux range from 50-200 kg/m2s and at saturation

temperature of 30 and 35 0C, respectively. The authors found that the condensation heat

transfer coefficient of R134a tended to increases with increasing mass flux and vapor

quality in both minichannels with and without fin. The heat transfer coefficient is

increases faster at higher vapor quality. The saturation temperature has significant

influence on heat transfer coefficient which decreases with increasing the saturation

temperature. The heat transfer coefficient of rectangular multiport minichannel with

fins was approximately 10-39% higher than those of rectangular multiport minichannel

without fin for the same operating conditions due to the surface tension force. They

compared their experimental data with ten well known correlations that were developed

for the conventional tube, minichannels and microchannels. All of the existing

correlations were failed to capture the experimental heat transfer coefficient data within

a high degree of accuracy. In addition, the author proposed a new correlation to predict

the experimental data. The proposed correlation agreed well with the experimental data

with mean average error 17.4%.

1.2.2 Two-phase pressure drop in minichannels

In the last seventy years, much experimental and analytical research were devoted

to measuring the two-phase frictional pressure drop in small diameter tubes and

minichannels of circular or rectangular geometry with single or multiport channels

configurations. Very few of them will be reviewed here.

Yang and Webb (1996) measured an adiabatic single-phase and two-phase pressure

23

drop of R12 flowing in 1.56 and 2.64 mm hydraulic diameters extruded aluminum with

and without fin tube, respectively. The frictional pressure gradient of tube with fin was

higher than that of the tube without fin at same test conditions. Their works showed that

the pressure drop is dominated by vapor shear in both tube with and without fins. The

author also developed the pressure drop correlation on the basis of equivalent mass

velocity concept according to Akers et al. (1959).

Revellin and Thome (2007) experimentally measured an adiabatic two-phase

frictional pressure drop of R134a and R245fa in two sizes of circular minichannels

having inner diameters of 0.509 mm and 0.790 mm. Similar to the classic Moody

diagram in single-phase flow, they distinguished three different zones for laminar,

transition and turbulent flow. Only the turbulent zone was best predicted by the Muller-

Steinhagen and Heck (1986) correlation. They also proposed a new homogeneous two-

phase frictional pressure drop model for a limited range of application.

Koyama et al. (2003) investigated the pressure drop characteristics of R134a in four

types of multiport minichannel tubes. They found that the Friedel (1979) correlation

was able to predict well their data, except at low mass velocity. They also developed a

new model for frictional pressure drop based on the Mishima and Hibiki

(1996) correlation.

Zhang and Webb (2001) measured adiabatic two-phase flow pressure drops for R-

134a, R-22 and R-404a flowing in a multi-port extruded aluminum tube with a

hydraulic diameter of 2.13 mm, and in two copper tubes having inside diameters of 6.25

and 3.25 mm, respectively. They found that the Friedel correlation did not predict the

two-phase data accurately, especially for high reduced pressure. Using the data taken in

their present and in a previous study, a new correlation for two-phase friction pressure

drop in small tubes was developed by modifying the Friedel correlation.

Tran et al. (2000) carried out an experimental study of two-phase flow pressure drop

of R134a, R12 and R113 at six different pressures in two round tube (2.46 mm and 2.92

mm inside diameter) and one rectangular channel (2.40 mm hydraulic diameter). The

data were compared with the large-tube correlations but all of the correlations were

failed to predict the experimental data.

Li and Wu (2010, 2011) collected the experimental data of adiabatic two phase

pressure drop in micro/minichannels for both single and multiport channel

configurations covering 12 fluids for a wide range of operational conditions and

channel dimensions. Based on the whole database, the Bond number and the Reynolds

24

number were introduced to modify the Chisholm parameter to develop a new generalize

correlation for the two-phase pressure drop. To indicate the relative importance of

surface tension, a particular trend was observed with the Bond number that

distinguished the entire database into three ranges.

Lee and Lee (2001) presented an experimental study of two-phase pressure drop of

water and air through horizontal rectangular channels having hydraulic diameter 0.78

mm, 1.91 mm, 3.64 mm and 6.67 mm, respectively. The authors found that the pressure

drop increased with increase in superficial velocities of the liquid and gas but decrease

with hydraulic diameter. They expressed the two-phase frictional multiplier using the

Lockhart-Martinelli type correlation with the modification on parameter C considering

the effects of mass flux and channel dimension.

Agarwal and Garimella (2009) measured the pressure drop and presented a multiple

flow-regime model during condensation of refrigerant R134a in horizontal minichannel.

Condensation pressure drop were measured in two circular and six noncircular channels

having hydraulic diameter from 0.42 mm to 0.8 mm.

Cavallini et al. (2005) experimentally studied the frictional pressure drop

characteristics in multiport minichannel of hydraulic diameter 1.4 mm during adiabatic

two-phase flow of R134a, R236ea and R410A. In their study, R410A presents a

significantly lower pressure drop in comparison with R134a and R236ea at the same

operating conditions. The low pressure fluid R236ea shows the highest pressure

gradient among the three fluids. The experimental data were compared against several

models available in the literature, finding that the correlations by Friedel et al., Zhang

and Webb, Mishima and Hibiki, and Mueller-Steinhagen and Heck are in good

agreement with the R134a experimental data. All of the correlations were failed to

predict the R410A data. The R236ea data are in good agreement with the predictions by

Mueller-Steinhagen & Heck (1986).

Cavallini et al. (2009) presented a model for calculation of the frictional pressure

gradient during condensation or adiabatic liquid-gas flow inside minichannels with

different surface roughness. The researchers used new experimental frictional pressure

gradient data associated to single-phase flow and adiabatic two-phase flow of R134a

inside a single horizontal mini tube with rough wall in their modelling to account for

the effects of surface roughness. It was a Friedel based model and it took into account

fluid properties, tube diameter, mass flux, vapor quality, reduced pressure, entrainment

ratio and surface roughness. With respect to the flow pattern prediction capability, they

25

built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and

mist flow were here predicted. However, they extended the suggested procedure to the

intermittent flow in minichannels and applied it also with success to horizontal macro

tubes.

Bohdal et al. (2012) performed the experimental investigation of condensation

pressure drop of R134a, R404a and R407C refrigerants in circular minichannels with

internal diameter 0.31-3.30 mm. They found that the pressure drop in a two-phase flow

during condensation of refrigerants depends on the refrigerant type, process parameters

and the structure of two-phase flow. The authors compared the experimental results

with the correlations proposed by other researcher. Based on the experimental results,

the authors developed a new correlation for the calculation of the local value of the

frictional pressure drop in the range of two-phase flow structures.

Zhang et al. (2010) explored alternative correlations of two-phase friction pressure

drop and void fraction by applying the artificial neural network for round and

rectangular minichannels based on the separated flow and drift-flux model. They

collected 2201 data points for adiabatic and diabetic conditions from 13 source covering

9 working fluids and hydraulic diameters from 0.007 mm to 6.25 mm.

Kim and Mudawar (2012) developed a new universal approach to predict a two-

phase frictional pressure drop for adiabatic and condensing mini/microchannel flow

based on 7115 data points from 36 sources consisting 17 working fluids. In their

universal approach, they incorporated appropriate dimensionless relations in a separated

flow model to account for both small channel size and different combinations of liquid

and vapor states. This approach is shown to provide excellent predictions of the entire

consolidated database and fairly uniform accuracy against all parameters of the

database. It is also capable of tackling single and multiple channels as well as situations

involving significant flow deceleration due to condensation.

Kim and Mudawar (2013) also proposed a new technique to predict the frictional

pressure gradients for saturated flow boiling considering a consolidated database

consisting 2378 data points which were amassed from 16 sources. The database

considered data for both single and multiport channel, consists of 9 working fluids,

hydraulic diameters from 0.349 to 5.35 mm, mass velocities from 33 to 2738 kg/m2s,

liquid-only Reynolds numbers from 156 to 28,010, qualities from 0 to 1, reduced

pressures from 0.005 to 0.78. A separated flow technique previously developed by the

authors for adiabatic or condensation mini/micro-channel flows is modified to account

26

the different flow structure between boiling and adiabatic or condensing flows.

Lopez-Belchi et al. (2014) experimentally studied condensing two-phase frictional

pressure drop inside a minichannel having 1.16 mm hydraulic diameter with R1234yf,

R134a and R32. They analyzed experimental data to show the effect of saturation

temperature, mass fluxes, vapor quality and fluid properties on pressure drop. In

addition, they presented a new correlation model for “C” calculation.

Jige et al. (2016) investigated the condensation heat transfer and adiabatic pressure

drop characteristics of refrigerants R134a, R32, R1234ze (E) and R410A in a 0.85 mm

hydraulic diameter horizontal rectangular multiport minichannel. They concluded that

the frictional pressure drop increases with decreasing hydraulic diameter due to the

increase in shear stress with increasing velocity gradient. Moreover, they developed the

frictional pressure drop correlation for multiport tube considering the effect of channel

geometry.

Tapia and Ribatski (2017) conducted an experimental investigation on the effects of

refrigerant and channel geometry on the frictional pressure drop during condensing

two-phase flow in minichannels. The researchers used 4 refrigerants, R134a, R1234ze

(E), R1234yf and R600a as a working fluid and three cross-sectional geometries

namely, circular, square and triangular sections as minichannels with hydraulic

diameters 1.1 mm, 0.868 mm and 0.634 mm, respectively. The author concluded that

the two-phase frictional pressure drop for R600a is higher compared to the other fluids.

Moreover, the two-phase frictional pressure drop gradient of R1234ze(E) is higher than

that of R134a and R1234yf. Highest pressure drop were also observed for the triangular

geometry followed by square and circular geometries. Based on the 1468 experimental

data points, they proposed a new predictive method for two-phase friction pressure drop

using Muller-Steinhagen and Heck (1986) model.

Recently, Rahman et al. (2017) examined the experimental adiabatic two-phase

frictional pressure drop of R134a in rectangular multiport minichannel with and without

fins having 20 channels with hydraulic diameters of 0.64 mm and 0.81 mm,

respectively. The pressure drop measurements were done over the mass flux range of

50–200 kg/m2s, saturation temperature range of 20–35 °C, and inlet vapor quality range

of 0.1–0.9. The effects of mass flux, saturation temperature, inlet vapor quality and

channel geometry on frictional pressure drop were clarified. The results discovered that

the mass flux, inlet vapor quality, saturation temperature and channel geometry play an

important role in increasing or decreasing the two-phase frictional pressure drop. The

27

present experimental data were compared with available existing well known frictional

pressure drop correlation. In addition, the researcher developed a validated new two-

phase frictional pressure drop correlation considering the effects of inertia, viscous

force, fluid properties, channel geometry and surface tension.

1.2.3 Condensation heat transfer and pressure drop in microfin tube

Condensation heat transfer and pressure drop in microfin tube has been a research

subject since the end of 1970s due to higher heat transfer enhancement with low

pressure drop. Some of the available studies are reviewed here:

Koyama and Yonemoto (2006) performed experimental studies on condensation

heat transfer and pressure drop of R22, R123 and R134a in eleven different horizontal

microfin tubes. They developed the heat transfer correlations using Yu and Koyama

(1998) correlation based on the void fraction.

Yu and Koyama (1998) conducted an experimental study on condensation heat

transfer of pure refrigerant R134a, R123 and R22 in microfin tubes. The authors

concluded that the local condensation heat transfer characteristics in a horizontal

microfin tube were found to be about 2 times higher than those of a smooth tube with

the same inner diameter. This enhancement seems mainly caused by the enlargement

ration of heat transfer area. By considering the enlargement ratio of heat transfer area, a

modified correlation, from the correlation of Haraguchi et al. (1994) for smooth tubes,

was proposed for the condensation heat transfer in microfin tube with pure refrigerant.

Nozu et al (1998) measured pressure drop during condensation of CFC11 in

horizontal helical microfin tubes and proposed a correlation Eq. (3.1.20) for the local

frictional pressure gradient in which the effect of refrigerant mass velocity was

introduced on the basis of the flow regime consideration.

Goto et al. (2003) experimentally measured the condensation heat transfer

coefficients of R410A and R22 in five different internally helical microfins and

herringbone microfins tubes of about 8.0 mm outer diameter. The obtained results

indicated that the condensation heat transfer coefficients of the herringbone microfins

tube are twice as large as those of helical one. The authors developed a new empirical

correlations based on Koyama and Yu (1996) correlations for both the helical and

herringbone microfins tube to predict the condensation heat transfer coefficients of

28

R410A and R22.

Newell and Shah (1999) recommended a method of predicting two-phase pressure

drop inside helical microfin tubes where they multiplied smooth tube pressure drop

correlation of Souza and Pimenta (1995) with a pressure drop penalty factor.

Han and Lee (2005) experimentally studied the condensation heat transfer and

pressure drop characteristics of refrigerants R134a, R22 and R410A in four different

microfin tubes with 4.0, 5.1, 6.46, and 8.92 mm inside diameters, respectively. The

effects of mass flux, vapor quality and refrigerants on condensation were clarified in

terms of the heat transfer enhancement factor and the pressure drop penalty factor. The

dependence of heat transfer enhancement factors with vapor quality and mass flux

showed similar trend as those of the pressure drop penalty factors. In addition, the

authors proposed a correlation for condensation heat transfer coefficients and frictional

pressure drops in an annular flow regime for microfin tube based on the experimental

data and the heat-momentum analogy.

Mori et al. (1999) measured the frictional pressure gradient of R410A inside a

herringbone microfin tube varying the mass velocity 100-500 kg/m2s. They used

adiabatic condition for measuring the pressure drop and the inlet saturation temperature

was 50 0C. Their data can be used for necessary comparison of two-phase frictional

multiplier as they use adiabatic condition. For the fixed test section length they supplied

the liquid-vapor mixture of the refrigerant maintaining constant quality and mass

velocity and measured the frictional two-phase pressure drop.

Honda et al. (2005) showed the experimental results that described the effects of

mass flux and condensation temperature difference on the local condensation heat

transfer characteristics of R407C in a horizontal microfin tube having 6.35 mm outside

diameter. The experiments were performed over a range of mass velocity of 50-300

kg/m2s, at the saturation temperature of 40 0C, and condensation temperature difference

of 1.5, 2.5 and 4.5 K.

Jung et al. (2004) performed an experiment on flow condensation heat transfer

coefficients of R22, R134a, R407C and R410A inside horizontal plain and microfin

tube of 9.52 mm outside diameter. The condensation heat transfer coefficients of R134a

and R410A in plain tube were similar to those of R22 while the heat transfer coefficient

of R407C was 11-15% lower than those of R22. In microfin tube, the condensation heat

transfer coefficients of R134a were similar to those of R22 while the heat transfer

coefficient of R407C and R410A were 23-53% and 10-21% lower than those of R22.

29

The different heat transfer characteristics between tested refrigerants were mainly

because of different fluid properties and flow pattern. The authors observed 2-3 times

higher heat transfer coefficients in microfin tube than those of a plain tube. They also

concluded that the condensation heat transfer enhancement factor decreased as the mass

flux increased for all the tested refrigerants.

Kedzierski and Goncalves (1999) presented the local convective condensation heat

transfer measurements of refrigerants R134a, R410A, R125 and R32 in a microfin tube

of 9.5 mm outer diameter. The refrigerant R32 exhibited the higher heat transfer due to

its higher thermal conductivity. The authors proposed a single expression correlation

from the measured convective condensation Nusselt number for all of the tested

refrigerants. The correlation was shown to predict existing condensation Nusselt

numbers for microfin tubes from the literature acceptably well excluding the Nusselt

numbers for microfin tubes with cross-grooves. They found that the microfins enhanced

the heat transfer with a combination of liquid-vapor interface mixing and turbulent

mixing near the wall. Moreover, surface tension drainage and swirl effects are

presumed to have little influence on the heat transfer.

Cavallini et al. (2003) reviewed some research relating to condensation inside and

outside smooth and enhanced tubes. They concluded that within smooth circular tubes,

adequate predicting procedures for heat transfer are in general available to designers,

even in the presence of lubricating oils. Experimental data are needed for condensation

of halogenated refrigerants near the critical temperature to possibly extend the

confidence on available design tools. In addition, condensation of CO2 at low

temperature should be investigated to help designing cascade systems with this natural

refrigerant.

Dalkilic and Wongwises (2009) reviewed a large number of existing studies of heat

transfer and pressure drop during in-tube condensation according to the tube orientation

(horizontal, vertical, inclined tubes) and tube geometry (smooth and enhanced tubes),

flow pattern studies of condensation, void fraction studies, and refrigerants with the

effect of oil.

Kim and Shin (2005) experimentally investigated the condensation heat transfer of

R22 and R410A in a horizontal smooth and seven different microfin tubes having 9.52

mm outer diameter. The authors found that the average heat transfer coefficient of the

microfin tube was 1.7-3.19 times higher than that of the smooth tube. This is mainly

due to the larger heat transfer area of microfin tube.

30

Miyara et al. (2003) studied the effects of fin height and helix angle on

condensation heat transfer inside five types of horizontal herringbone microfin tubes.

The authors found that the heat transfer in herringbone microfin tubes is approximately

2-4 times higher than that of the helical microfin tubes under high mass velocity

conditions. The authors suggested that the fin height is better to be 0.18 mm or smaller.

The larger helix angle yields higher heat transfer coefficient and larger pressure drop.

Although the heat transfer enhancement is degraded for shorter fin or smaller helix

angle, it is still higher than that of a conventional helical microfin.

Miyara and Otsubo (2002) carried out an experiment on condensation heat transfer

of R410A in a smooth tube, a helical microfin tube and three different herringbone

microfin tubes, respectively. They found in their study that micro fins were working at

fin-diverging parts in order to remove liquid and they were working at fin-converging

parts in order to collect liquid in the herringbone micro fin tube. Thinning the film at

the diverging parts and mixing the liquid at the converging parts increase the heat

transfer. The removal of the liquid and collection by herringbone micro fins does not

take effect in the low mass velocity region but only in the high mass velocity region.

Kim et al. (2009) investigated the condensation heat transfer of CO2 at low

temperature inside a horizontal smooth and microfin tubes with 5.0 mm and 4.34 mm

outer diameter, respectively. The test was conducted over a mass flux range of 200-800

kg/m2s and at saturation temperatures of -25 0C and -15 0C, respectively. The effects of

various factors on the heat transfer coefficient and enhancement factor were analyzed.

Based on the average enhancement factors and penalty factors, they discovered that the

internally finned geometry do not always guarantee the superior in tube condensation

performance of the microfin tube in refrigeration and air-conditioning systems. Due to

the complexity, variety of fin geometry and flow mechanisms all most all of the

existing correlations were failed to predict the experimental data.

Sapali and Patil (2010) experimentally investigated the heat transfer coefficients

during condensation of R134a and R404A in a smooth and microfin tubes having inner

diameters of 8.56 mm and 8.96 mm, respectively. The experimental results indicated

that the average heat transfer coefficients increase with mass flux but decrease with

increasing temperature for both tubes. The authors found that the average heat transfer

coefficients of R134a and R404A in microfin tube were 1.5-2.5 and 1.3-2 times higher

than that in smooth tube, respectively.

Son and Oh (2012) investigated the heat transfer characteristics of CO2 during

31

condensation in a horizontal smooth and microfin tube at higher saturation temperature

of 20-30 0C. The outer diameters of the tested smooth and microfin tubes were 6.35 and

5.0 mm, respectively. The experimental results indicated that the annular flow almost

dominated the condensation flow in both tubes. The heat transfer coefficients for the

microfin tube were higher than those for the smooth tube in the entire vapor quality

range approximately 1.006 to 1.48 times. The enhancement of condensation heat

transfer were mainly due to the large effective heat transfer area in microfin tube,

turbulence induced in the liquid film and the surface tension effect on the liquid

drainage. The author’s found that most of the existing correlations failed to predict the

experimental data. Furthermore, they suggested necessity to develop accurate and

reliable correlation to predict condensation heat transfer coefficients at high saturation

temperatures in the horizontal smooth and microfin tubes.

Wang et al. (2002) presented a modified model of film condensation from

previously proposed theoretical models in horizontal microfin tubes. The surface

tension force in stratified flow regime and the interfacial shear stress in the annular flow

regime were incorporated in the modified model to describe the characteristics of

condensing two-phase flow more accurately.

Wang et al. (2003) performed a comprehensive comparison of eight previously

proposed correlations with available experimental data for the frictional pressure drop

during condensation of refrigerants of R11, R123, R134a, R22, R32, R125 and R410A

inside eight helical microfin tubes with mass velocity from 78 to 459 kg/m2s. The

results show that the overall root means square deviations of relative residuals of

frictional pressure drop for all tubes and all refrigerants taking together decreased in the

order of the correlations of Nozu et al. (1998), Newell and Shah (1999), Kedzierski and

Goncalves (1997, 1999), Cavallini et al. (1997), Goto et al. (2001), Choi et al. (2001),

Haraguchi et al. (1993), Goto et al. (2001). The best among those correlations is Goto et

al. (2001) which shows r.m.s relative deviation of 23.6%.

Li et al. (2012) performed an experimental study of condensation characteristics

and pressure drop of R22 inside five different microfin tubes with 5.0 mm outer

diameter. The results suggested that the small hydraulic diameter tube (among five

different tubes) has the highest heat transfer coefficient and pressure drop penalty. The

mass flux has nonlinear relation with the condensation heat transfer coefficients for 2

different microfin tubes. The complex nonlinear mass flux effect may be explained by

the complex interactions between microfins and fluid, including liquid drainage by

32

surface tension and interfacial turbulence. Most of the existing correlations were failed

to predict their experimental data accurately.

Wu et al. (2014) experimentally studied convective condensation inside one smooth

tube and six microfin tubes of different geometries. They concluded that the heat

transfer coefficient in the microfin tubes decreases at first and then increases or flattens

out gradually as mass flux decreases due to the surface tension and interfacial

turbulence effects.

Kim (2016) experimentally investigated the condensation heat transfer and pressure

drop of R410A in a 7.0 mm OD smooth and microfin tube at low mass flux. He found

that the heat transfer coefficient of the microfin tube shows a minimum behavior with

the mass flux. Below the mass flux of 100 kg/m2s, the heat transfer coefficient

decreases as mass flux increases. The flow pattern was stratified below the mass flux

100 kg/m2s and the condensation induced by surface tension by microfins. The flow

pattern was annular at high mass flux and condensation induced by share stress.

Therefore, the heat transfer coefficients increased as mass flux increased.

Recently, Rahman et al. (2017) conducted an experimental study of adiabatic

pressure drop and condensation heat transfer characteristics of refrigerant R134a in a

small diameter smooth and microfin tubes. The outer diameters of the tested smooth

and microfin tubes were 2.5 mm. The authors performed this test in the mass flux range

of 50 to 200 kg/m2s, range of vapor quality of 0 to 1 and range of saturation temperature

of 20 to 35 0C. They found that both the condensation heat transfer coefficient and

frictional pressure drop were increases with the mass flux and vapor quality but the

frictional pressure drop decreases with saturation temperature. The microfin tube has

slightly influence on the frictional pressure gradients. The frictional pressure drop of the

microfin tube was higher than those of smooth tube about 10-15%. The higher heat

transfer coefficient was obtained in microfin tube about 2-68%. The present

experimental data were compared with the existing well-known condensation heat

transfer and frictional pressure drop models available in the open literature. The Goto et

al. (2001) pressure drop correlation gives fairly good prediction with 26.1% mean

absolute error. The heat transfer correlation of Cavallini et al. (1999) can predict the

present experimental heat transfer data reasonably.

33

1.3 Objectives of the present research

Through the literature review, it is clear that the results of different studies shown

different effects. That suggests needs for systematically measured heat transfer and

pressure drop data to understand the phenomenon of condensation in minichannels and

microfin tubes and developing models. Although, heat transfer and frictional pressure

drop has been a research subject for several decades and many researchers extensively

investigated the heat transfer and pressure drop characteristics in minichannels and

large diameter microfin tubes experimentally and theoretically. But consistent

information on heat transfer and pressure drop characteristics in multiport rectangular

minichannels and small diameter microfin tubes are still inadequate. Hence, the design

of high performance multiport rectangular minichannels and small diameter microfin

tubes heat exchanger essentially requires accurate predictive tools for heat transfer

coefficient and pressure drop prediction in two-phase flow. The main objectives of the

present studies are:

1. To investigate the effects of all of the involved parameters such as mass

velocity, vapor quality and saturation temperature on adiabatic frictional

pressure drop characteristics of two-phase flow inside rectangular multiport

minichannels experimentally.

2. To developed a new frictional pressure drop prediction model for rectangular

multiport minichannel based on the experimental data and validate with the

existing data available in open literature

3. To investigate the effects of all of the involved parameters such as mass

velocity, vapor quality and saturation temperature on condensation heat transfer

coefficients of two-phase flow inside rectangular multiport minichannels

experimentally.

4. To developed a new heat transfer coefficient during condensation prediction

model for rectangular multiport minichannels based on the experimental data

and validate with the existing data available in open literature

5. To investigate the effects of all of the involved parameters on frictional pressure

drop of R134a inside small diameter microfin tube experimentally.

6. To investigate the effects of all of the involved parameters on condensation heat

transfer coefficients of R134a inside small diameter microfin tube

experimentally.

34

1.4 Overview of the thesis

This thesis is organized as follows:

The present chapter presents the fundamental background, literature reviews and outline

of the objectives of the research and the method used. In the background, the

fundamentals of the minichannels, microfin tubes, flow regime and flow regimes maps

have been discussed inherit. In the literature survey, previous studies relating to heat

transfer and pressure drop have been discussed.

The description of the experimental setup and experimental methodology together with

data reduction and uncertainty measurement are presented in Chapter 2.

Chapter 3 addresses the experimental results of two-phase frictional pressure drop at

adiabatic condition inside rectangular multiport minichannels and microfin tube.

Chapter 4 reports the experimental results of condensation heat transfer of R134a in

rectangular multiport minichannels and microfin tubes.

Chapter 5 contains a review of some of the models available in the open literature for

frictional pressure drop prediction in both minichannels and microfin tubes. The chapter

also contains the comparison of present experimental frictional pressure drop data with

review models.

Chapter 6 presents a review of some of the models available in the open literature for

condensation heat transfer prediction in both minichannels and microfin tubes. The

chapter also contains the comparison of present experimental heat transfer coefficients

data with review models.

Chapter 7 reports a new frictional pressure drop and condensation heat transfer

coefficient prediction models. Both models are validating using the existing pressure

drop and heat transfer data available in open literature.

Finally, Chapter 8 presents the summary and concluding remarks of all findings of the

present research together with future recommendations.

35

References

Afroz, H. M. M., 2008. Prediction method of single-phase and two-phase pressure drop

inside microfin tubes, PhD Thesis, Saga University, Japan.

Agarwal, A., Bandhauer, T. M., Garimella, S., 2010. Measurement and modeling of

condensation heat transfer in non-circular microchannel, International Journal of

Refrigeration 33, 1169-1179.

Agarwal, A., Garimella, S., 2009. Modeling of pressure drop during condensation in

circular and noncircular microchannels, Journal of Fluids Engineering 131,

0113021-0113028.

Akers, W. W., Deans, H. A., Crosser, O. K., 1959. Condensation heat transfer within

horizontal tubes, Chem. Eng. Prog. Symp. Ser 55, 171-176.

America's Climate Choices. Washington, D.C.: The National Academies Press. 2011.

p. 15. "ANSI/ASHRAE Addendum ak to ANSI/ASHRAE Standard 34-

2007". Standards AddendaANSI/ASHRAE Standard 34-2007, Designation and

Safety Classification of Refrigerants. American Society of Heating, Refrigerating

and Air-Conditioning Engineers, Inc. 1791 Tullie Circle NE, Atlanta, GA 30329.

2010.02.24. ISSN 1041-2336. Retrieved 2011.12.18.

Anowar Hossain, M., 2013. Heat transfer and pressure drop during in-tube

condensation and evaporation of low GWP refrigerant mixtures, PhD thesis, Saga

University, Japan.

Baker, O., 1954. Simultaneous flow of oil and gas, Oil and Gas Journal 53, 185-195.

Bejan, A., Kraus, A. D., 2003. Heat Transfer Handbook, John Wiley & Sons, 1029-

1130.

Bohdal, T., Charun, H., Sikora, M., 2012. Pressure drop during condensation of

refrigerants in pipe minichannels, Archives of Thermodynamics 33 (1), 87-106.

36

Cavallini, A., Bortolin, S., Col, D. D., Matkovic, M., Rossetto, L., 2011. Condensation

heat transfer and pressure losses of High and Low pressure refrigerant flowing in a

single circular minichannel, Heat Transfer Engineering 32 (2), 90-98.

Cavallini, A., Col, D. D., Doretti, L., Matkovic, M., Rossetto, L., Zilio, C., 2005.

Condensation heat transfer and pressure gradient inside multiport minichannels,

Heat Transfer Engineering 26 (3), 45-55.

Cavallini, A., Col, D.D, Matkovic, M., Rossetto, L., 2009. Frictional pressure drop

during vapor–liquid flow in minichannels: modelling and experimental evaluation,

Internal Journal of Heat and Fluid Flow 30, 131–139.

Cavallini, A., Col, D.D., Doretti, L., Matkovic, M., Rossetto, L., Zilio, C., 2005. Two-

phase frictional pressure gradient of R236ea, R134a and R410A inside multi-port

mini-channels, Experimental Thermal and Fluid Science 29, 861–870.

Cavallini, A., Del Col, D., Doretti, L., Longo, G. A., Rossetto, L., 2000. Heat transfer

and pressure drop during condensation of refrigerants inside horizontal enhanced

tubes, International Journal of Refrigeration 23, 4-25.

Cavallini, A., Del Col, D., Doretti, L., Longo, G. A., Rossetto, L., 1997. Pressure drop

during condensation and vaporization of refrigerants inside enhanced tubes, Heat

and technology 15 (1), 3-10.

Cavallini, A., Doretti, L., Matkovic, M., Rossetto, L., 2006. Update on condensation

heat transfer and pressure drop inside minichannels, Heat Transfer Engineering 27

(4), 74-87.

Cavallini, A., Gensi, G., Del Col, D., Doretti, L., Longo, G. A., Rossetto, L., Zilio, C.,

2003. Condensation inside and outside smooth and enhanced tubes- a review of

recent research, International Journal of Refrigeration 26, 373-392.

Cheng, L., Mewes, D., 2006. Review of two-phase flow and flow boiling of mixtures in

small and mini channels, International Journal of Multiphase Flow 32, 183–207.

37

Choi, J. Y., Kedzierski, M. A., Domanski, P. A., 2001. Generalized pressure drop

correlation for evaporation and condensation in smooth and microfin tubes, In:

Proc. Of IIF-IIR Commision B1, Paderborn, Germany, B4, 9-16.

Coleman, J. W., Garimella, S., 1999. Characterization of two-phase flow patterns in

small diameter round and rectangular tubes, International Journal of Heat and Mass

Transfer 31, 2689-2881.

Coleman, J. W., Garimella, S., 2003. Two-phase flow regimes in round, square and

rectangular tubes during condensation of refrigerant R134a, International Journal of

Refrigeration 26, 117–128.

Dalkilic, A. S., Wongwises, S., 2009. Intensive literature review of condensation inside

smooth and enhanced tubes, International Journal of Heat and Mass Transfer 52,

3409-3426.

Derby, M., Lee, H. J., Peles, Y., Jensen, M. K., 2012. Condensation heat transfer in

square, triangular and semi-circular minichannels, International Journal of Heat and

Mass Transfer 55 187–197.

El Hajal, J., Thome, J.R., Cavalini, A., 2003. Condensation in horizontal tubes, part 1:

two-phase flow pattern map, International Journal of Heat and Mass Transfer 46,

3349-3363.

Forster, P.M.F., Ramaswamy, V., Artaxo, P., Berntsen, T., Betts, R., Fahey, D.W.,

Haywood, J., Lean, J., Lowe, D.C., Myhre, G., Nganga, J., Prinn, R., Raga, G.,

Schulz M., Van Dorland, R., (2007). Changes in Atmospheric Constituents and in

Radiative Forcing, IPCC: Climate Change 2007: The Physical Science

Basis. Contribution of Working Group I to the Fourth Assessment Report of the

Intergovernmental Panel on Climate Change (https://www.ipcc.ch/pdf/ assessment-

report/ar4/wg1/ar4-wg1-chapter2.pdf).

38

Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and

vertical two-phase pipe flow, European Two-phase Group Meeting, Ispra, Italy,

Paper E2.

Fujie, K., Itoh, N., Kimura, H., Nakayama, N., Yanugidi, T., 1977. Heat transfer pipe,

US Patent 4044479, Hitachi Ltd.

Ghiaasiaan, S. M., 2008. Two-phase flow, Boiling and Condensation, in conventional

and miniature systems, Cambridge University Press, 3rd chapter.

Gomez, F. I., Belchi, A. L., Cascales, J. R. G., Garcia, F. V., 2015. Experimental two-

phase heat transfer coefficient and frictional pressure drop inside mini-channels

during condensation with R1234yf and R134a, International Journal of

Refrigeration 51, 12-23.

Goss Jr., G., Passos, J. C., 2013. Heat transfer during the condensation of R134a inside

eight parallel microchannels, International Journal of Heat and Mass Transfer 59, 9-

19.

Goto, M., Inoue, N., Yonemoto, R., 2003. Condensation heat transfer of R410A inside

internally grooved horizontal tubes, International Journal of Refrigeration 26, 410-

416.

Han, D., Lee, K. J., 2005. Experimental study on condensation heat transfer

enhancement and pressure drop penalty factors in four microfin tubes, International

Journal of Heat and Mass Transfer 48 3804–3816.

Haraguchi, H., Koyama, S., Esaki, J., Fujii T., 1993. Condensation heat transfer of

refrigerants HCFC134a, HCFC123 and HCFC22 in a horizontal smooth and a

horizontal microfin tube, In: Proc. 30th National Symp. of Japan, Yokohama, 343-

345.

Haraguchi, H., Koyama, S., Fujii, T., 1994. Condensation of Refrigerants HCFC22,

HFCI34a and HCFC123 in a Horizontal Smooth Tube (2nd Report, Proposals of

39

Empirical Expressions for Local Heat Transfer Coefficient), Trans. JSME 60, 245-

252 (in Japanese).

Heo, J., Park, H., Yun, R., 2013. Comparison of condensation heat transfer and pressure

drop of CO2 in rectangular microchannels, International Journal of Heat and Mass

Transfer 65 719–726.

Honda, H., Wijayanta, A. T., Takata, N., 2005. Condensation of R407C in a horizontal

microfin tube, International Journal of Refrigeration 28, 203-211.

Hossain, M. A., 2013. Heat transfer and pressure drop during in-tube condensation and

evaporation of low GWP refrigerant mixtures, PhD thesis, Saga University.

Huai, X., Koyama, S., 2004. An experimental study of carbon dioxide condensation in

minichannels, Journal of Thermal Science 13 (4), 358-365.

Jige, D., Inoue, N., Koyama, S., 2016. Condensation of refrigerants in a multiport tube

with rectangular minichannels, International Journal of Refrigeration 67, 202-213.

Jige, D., Inoue, N., Koyama, S., 2016. Condensation of refrigerants in a multiport tube

with rectangular minichannels, International Journal of Refrigeration 67, 202-213.

Jung, D., Cho, Y., Park, K., 2004. Flow condensation heat transfer coefficients of R22,

R134a, R407C and R410A inside plain and microfin tubes, International Journal of

Refrigeration 27, 25-32.

Kandlikar, S.G., 2002. Fundamental issues related to flow boiling in minichannels and

microchannels, Experimental Thermal and Fluid Science 26 (2–4), 389–407.

Kandlikar, S.G., Grande,W.J., 2003. Evolution of microchannel flow passages –

thermohydraulic performance and fabrication technology. Heat Transfer

Engineering 24 (1), 3–17.

40

Kattan, N., Thome, J. R., and Favrat, D. 1998a. Flow Boiling in Horizontal Tubes, 1:

Development of a Diabatic Two-Phase Flow Pattern Map, Journal of Heat Transfer,

120, 140–147.

Kattan, N., Thome, J. R., and Favrat, D. 1998b. Flow Boiling in Horizontal Tubes, 2:

New Heat Transfer Data for Five Refrigerants, Journal of Heat Transfer, 120, 148–

155.

Kawahara, A., Chung, P. M. Y., Kawaji, M., 2002. Investigation of two-phase flow

pattern, void fraction and pressure drop in a microchannel, International Journal of

Multiphase Flow 28, 1411-1435.

Kedzierski, M. A., Goncalves, J. M., 1997. Horizontal convective condensation of

alternative refrigerants within a micro-fin tube [NISTIR 6095] Gaithersburg (MD

USA), National Institute of Standard and Technology (NIST).

Kedzierski, M. A., Goncalves, J. M., 1999. Horizontal Convective condensation of

alternative refrigerants within a microfin tube, Enhanced Heat Transfer 6, 161-178.

Kim, M. H., Shin, J. S., 2005. Condensation heat transfer of R22 and R410A in

horizontal smooth and microfin tubes, International Journal of Refrigeration 28,

949-957.

Kim, N. H., 2016. Condensation heat transfer and pressure drop of R‑410A in a 7.0 mm

O.D. microfin tube at low mass fluxes, Heat Mass Transfer, Doi 10.1007/s00231-

016-1789-2.

Kim, N. H., 2016. Condensation heat transfer and pressure drop of R‑410A in a 7.0 mm

O.D. microfin tube at low mass fluxes, Heat Mass Transfer, doi 10.1007/s00231-

016-1789-2.

Kim, N. H., Cho, J. P., Kim, J. O., Youn, B., 2003. Condensation heat transfer of R22

and R410A in flat aluminum multi-channel tubes with or without micro-fins,

International Journal of Refrigeration 26, 830-839.

41

Kim, S. M., Mudawar, I., 2013. Universal approach to predicting heat transfer

coefficient for condensing mini/micro-channel flow, International Journal of Heat

and Mass Transfer 56 238–250.

Kim, S. M., Mudawar, I., 2014. Review of databases and predictive methods for heat

transfer in condensing and boiling mini/micro-channel flows, International Journal

of Heat and Mass Transfer 77, 627–652.

Kim, S.M. and Mudawar, I., 2012. Universal approach to predicting two-phase

frictional pressure drop for adiabatic and condensing mini/micro-channel flows,

International Journal of Heat and Mass Transfer 55, 3246–3261.

Kim, S.M. and Mudawar, I., 2013. Universal approach to predicting two-phase

frictional pressure drop for mini/micro-channel saturated flow boiling, International

Journal of Heat and Mass Transfer 58, 718–734.

Kim, Y. J., Jang, J., Hrnjak, P. S., Kim, M. S., 2009. Condensation heat transfer of

carbon dioxide inside horizontal smooth and microfin tubes at low temperatures,

Journal of Heat Transfer 131, 021501-1-021501-10.

Koyama, S. Yu, J., 1996. Condensation heat transfer of pure refrigerant inside an

internally grooved horizontal tube, In: Proc. of The JAR Annual Conference, 173–6.

Koyama, S., Kuwahara, K., Nakashita, K., 2003. Condensation of refrigerant in a

multiport channel, Proceedings of the First International Microchannel and

Minichannels, ASME, 193–205.

Koyama, S., Kuwahara, K., Nakashita, K., 2003b. Condensation of refrigerant in a

multi-port channel, Proceedings of ICMM2003, Microchannels and Minichannels,

April 24-25, Rochester, New York, USA.

Koyama, S., Kuwahara, K., Nakashita, K., Yamamoto, K., 2003a. An experimental

study on condensation of refrigerant R134a in a multi-port extruded tube,

International Journal of Refrigeration 26, 425-432.

42

Koyama, S., Yonemoto, R., 2006. Experimental study on condensation of pure

refrigerants in horizontal microfin tube – Proposal of correlations for heat transfer

coefficient and frictional pressure drop, Proceedings of International Refrigeration

and Air Conditioning Conference, Purdue, USA, July 17-20.

Lee, H.J., Lee, S.Y., 2001. Pressure drop correlations for two-phase flow within

horizontal rectangular channels with small heights, International Journal of

Multiphase Flow 27, 783–796.

Li, G. Q., Wu, Z., Li, W., Wang, Z., Wang, X., Li, H. X., Yao, S. C., 2012.

Experimental investigation of condensation in microfin tubes of different

geometries, Experimental Thermal and Fluid Science 37, 19-28.

Li, W., Wu, Z., 2010. A general correlation for adiabatic two-phase pressure drops in

micro/mini-channels, International Journal of Heat and Mass Transfer 53, 2732–

2739.

Li, W., Wu, Z., 2011. Generalized adiabatic pressure drop correlations in evaporative

micro/mini-channels, Experimental Thermal and Fluid Science 35, 866–872.

Liu, N., Li, J. M., Sun, J., Wang, H. S., 2013. Heat transfer and pressure drop during

condensation of R152a in circular and square microchannels, Experimental Thermal

and Fluid Science 47, 60-67.

Lopez-Belchi, A., Illan-Gomez, F., Vera-Garcia, F., Garcia-Cascales, J. R., 2014.

Experimental condensing two-phase frictional pressure drop inside mini-channels.

Comparisons and new model development, International Journal of Heat and Mass

Transfer 75, 581-591.

Mandhane, J.M., Gregory, G.A., Aziz, K., 1974. A flow pattern map for gas-liquid flow

in horizontal and inclined pipes, International Journal of Multiphase Flow 1, 537-

553.

43

Mehendail, S.S., Jacobi, A.M., Shah, R.K., 2000. Fluid flow and heat transfer at micro-

and meso-scales with application in heat exchanger design. Appl. Mech. Rev. 53

(7), 105–116.

Mishima, M., Hibiki, T., 1996. Some characteristics of air–water two-phase flow in

small diameter vertical tubes, International Journal of Multiphase Flow, 22, 703-

712.

Miyara, A., Ostubo, Y., Ohtsuka, S., Mizuta, Y., 2003. Effects of fin shape on

condensation in herringbone microfin tubes, International Journal of Refrigeration

26, 417-424.

Miyara, A., Otsubo, Y., 2002. Condensation heat transfer of herringbone microfin

tubes, International Journal of Thermal Science 41, 639-645.

Mori, H., Yoshida, S., Oishi, K., Yoshihara, T., 1999. In: Proc. JAR Annual conference,

97-100 (in Japanese).

Newell, T. A., Shah, R. K., 1999. Refrigerant heat transfer, pressure drop, and void

fraction effects in microfin tubes, In: Proc. 2nd Int. Symp. on two-phase flow and

experimentation, Edizioni ETS, Italy, 3, 1623-1639.

Nozu, S., Katayama, H., Nakata, H., Honda, H., 1998. Condensation of a refrigerant

CFC11 in horizontal microfin tubes (Proposal of a correlation equation for frictional

pressure gradient), Experimental Thermal and Fluid Science 18, 82-96.

Oh, H. K., Son, C. H., 2011. Condensation heat transfer characteristics of R22, R134a

and R410A in a single circular microtube, Experimental Thermal and Fluid Science

35, 706-716.

Ould Didi, M.B., Kattan, N., Thome, J.R., 2002. Prediction of two-phase pressure

gradients of refrigerants in horizontal tubes, International Journal of Refrigeration

25, 935-947.

44

Park, C. Y., Hrnjak, P., 2009. CO2 flow condensation heat transfer and pressure drop in

multi-port microchannels at low temperatures, International Journal of Refrigeration

32, 1129-1139.

Rahman, M. M., Kariya, K., Miyara, A., 2017. Comparison and development of new

correlation for adiabatic two-phase pressure drop of refrigerant flowing inside a

multiport minichannels with and without fins, International Journal of Refrigeration

82, 119-129.

Rahman, M. M., Kariya, K., Miyara, A., 2017. Experimental investigation of

condensation heat transfer and adiabatic pressure drop characteristics inside a

microfin and smooth tube, International Journal of Air-Conditioning and

Refrigeration 25 (3), 1750027-1-1750027-11.

Rahman, M. M., Kariya, K., Miyara, A., 2018. An experimental study and development

of new correlation for condensation heat transfer coefficient of refrigerant inside a

multiport minichannel with and without fins, International Journal of Heat and Mass

Transfer 116, 50-60.

Rebrov, E. V., 2010. Two-phase flow regimes in microchannels, Theoretical

Foundations of Chemical Engineering 44 (4), 355-367.

Revellin, R., Thome, J. T., 2007. Adiabatic two-phase frictional pressure drops in

microchannels, Experimental Thermal and Fluid Science 32, 673-685.

Sakamatapan, K., Kaew-On, J., Dalkilic, A. S., Mahian, O., Wongwises, S., 2013.

Condensation heat transfer characteristics of R-134a flowing inside the multiport

minichannels, International Journal of Heat and Mass Transfer 64, 976-985.

Sapali, S. N., Patil, P. A., 2010. Heat transfer during condensation of HFC-134a and R-

404A inside of a horizontal smooth and micro-fin tube, Experimental Thermal and

Fluid Science 34, 1133–1141.

45

Satitchaichroen, P., Wongwises, S., 2004. Two-phase flow pattern maps for vertical

upward gas-liquid flow in mini-gap channels, International Journal of Multiphase

Flow 30, 225-236.

Scott, D.S., 1963. Properties of cocurrent gas-liquid flow, Advances in Chemical

Engineering 4, 199-276.

Sempertegui-Tapia, D. F., Ribatski, G., 2017. Two-phase frictional pressure drop in

horizontal micro-scale channels: Experimental data analysis and prediction method

development, International Journal of Refrigeration 79, 143-163.

Serizawa, A., Feng, Z., Kawara, Z., 2002. Two-phase flow in microchannels,

Experimental Thermal and Fluid Science 26, 703-714.

Shabtay, Y., Black, J., Kraft, F., 2014. New copper-based heat exchangers for

alternative refrigerants, 15th International Refrigeration and Air Conditioning

Conference, July 14-17, Paper No. 2570, Purdue, USA.

Shah, M. M., 2009. An improved and extended general correlation for heat transfer

during condensation in plain tubes. HVAC&R Res 15 (5), 889–913.

Shah, M. M., 2016a. A correlation for heat transfer during condensation in horizontal

mini/micro channels, International Journal of Refrigeration 64, 187-202.

Shah, M. M., 2016b. Comprehensive correlations for heat transfer during condensation

in conventional and mini/micro channels in all orientations, International Journal of

Refrigeration 67, 22-41.

Shah, R.K., 1986. Classification of heat exchangers. In: Kakac, S., Bergles, A.E.,

Mayinger, F. (Eds.), Heat Exchangers: Thermal Hydraulic Fundamentals and

Design. Hemisphere Publishing Corp., Washington DC, 9–46.

46

Shahsavari, S., Tamayol, A., Ejeang, E., Bahrami, M., 2012. Convective heat transfer in

microchannels of noncircular cross sections: an analytical approach, Journal of Heat

Transfer 134, 091701-1-10.

Shao, N., Gavriilidis, A., Angeli, P., 2009. Flow regimes for adiabatic gas-liquid flow

in mirochannels, Chemical Engineering Science 64 (11), 2749-2761.

Shin, J. S., Kim, M. H., 2004. An experimental study of condensation heat transfer

inside a mini-channel with a new measurement technique, International Journal of

Multiphase Flow 30, 311-325.

Shin, J. S., Kim, M. H., 2005. An experimental study of flow condensation heat transfer

inside circular and rectangular mini-channel, International Journal of Multiphase

Flow 26 (3), 36-44.

Son, C. H., Oh, H. K., 2012. Condensation heat transfer characteristics of CO2 in a

horizontal smooth and microfin tube at high saturation temperatures, Applied

Thermal Engineering 36, 51-62.

Suo, M., Griffith, P., 1964. Two-phase flow in capillary tubes, Transactions of the

ASME, 576-582.

Thome, J. R., Hajal, J. E., Cavallini, A., 2003. Condensation in horizontal tubes, part 2:

new heat transfer model based on flow regimes, International Journal of Heat and

Mass Transfer 46, 3365–3387.

Thome, J.R., 2006. Engineering Data Book III, Chapter 13th.

Thome, J.R., El Hajal, J., Cavallini, A., 2003. Condensation in horizontal tubes, part 2:

new heat transfer model based on flow regimes, International Journal of Heat and

Mass Transfer 46, 3365-3387.

Tran, T. N., Chyu, M. C., Wambsganss, M. W., France, D. M., 2000. Two-phase

pressure drop of refrigerants during flow boiling in small channels: an experimental

47

investigation and correlation development, International Journal of Multiphase Flow

26, 1739-1754.

Wambsganss, M. W., Jendrzjczyk, J. A., France, D. M., 1991. Two-phase flow patterns

and transitions in a small, horizontal, rectangular channel, International Journal of

Multiphase flow 17 (3), 327-342.

Wang, H. S., Honda, H., Nozu, S., 2002. Modified theoretical models of film

condensation in horizontal microfin tubes, International Journal of Heat and Mass

Transfer 45, 1513–1523.

Wang, H. S., Rose, J. W., 2005. A theory of film condensation in horizontal noncircular

section microchannels, Transection of ASME, Journal of Heat Transfer 127, 1096-

1105.

Wang, H. S., Rose, J. W., 2006. Film condensation in horizontal microchannels: Effect

of channel shape, International Journal of Thermal Science 45, 1205-1212.

Wang, H. S., Rose, J. W., Honda, H., 2003. Condensation of refrigerants in horizontal

microfin tubes: comparison of correlations for frictional pressure drop, International

Journal of Refrigeration 26, 461–472.

Wang, W. W. W., Radcliff, T. D., Christensen, R. N., 2002. A condensation heat

transfer correlation for millimeter-scale tubing with flow regime transition,

Experimental Thermal and Fluid Science 26, 473-485.

Wojtan, L., Ursenbacher, T., Thome, J.R., 2005a. Investigation of flow boiling in

horizontal tubes: Part I-A new diabatic two-phase flow pattern map, International

Journal of Heat and Mass Transfer 48, 2955-2969.

Wojtan, L., Ursenbacher, T., Thome, J.R., 2005b. Investigation of flow boiling in

horizontal tubes: Part II-Development of a new heat transfer model for stratified-

wavy, dryout and mist flow regimes, International Journal of Heat and Mass

Transfer 48, 2970-2985.

48

Wu, Z., Sunden, B., Wang, L., Li, W., 2014. Convective condensation inside horizontal

smooth and microfin tubes, Journal of Heat Transfer 136, 0515041-05150411.

Xu, J. L., Cheng, P., Zhao, T. S., 1999. Gas-liquid two-phase regimes in rectangular

channels with mini/micro gaps, International Journal of Multiphase Flow 25, 411-

432.

Xu, J., 1999. Experimental study on gas-liquid two-phase flow regimes in rectangular

channels with mini gaps, International Journal of Heat and Fluid Flow 20, 422-428.

Yang, C. Y., Shieh, C. C., 2001. Flow pattern of air-water and two-phase R-134a in

small circular tubes, International Journal of Multiphase Flow 27, 1163-1177.

Yang, C. Y., Webb, R. L., 1996. Condensation of R12 in small hydraulic diameter

extruded aluminum tubes with and without micro-fins, International Journal of Heat

and Mass Transfer 39, 791-800.

Yang, C. Y., Webb, R. L., 1997. A predictive model for condensation in small

hydraulic diameter tubes having axial microfins, Transection of ASME, Journal of

Heat Transfer 119, 776-782.

Yang, C.Y., Webb, R. L., 1996. Friction pressure drop of R-12 in small hydraulic

diameter extruded aluminum tubes with and without micro-fins, International

Journal of Heat and Mass Transfer 39, 801-809.

Yu, J., Koyama, S., 1998. Condensation heat transfer of pure refrigerants in microfin

tubes, Proceedings of International Refrigeration and Air Conditioning Conference,

Purdue, USA, Paper 431.

Yu, J., Koyama, S., 1998. Condensation heat transfer of pure refrigerants in microfin

tubes, International Refrigeration Conference, Purdue University, 325-330.

49

Zhang, H. Fang, X., Shang, H., Chen, W., 2015. Flow condensation heat transfer

correlations in horizontal channels, International Journal of Refrigeration 59, 102-

114.

Zhang, H. Y., Li, J. M., Liu, N., Wang, B. X., 2012. Experimental investigation of

condensation heat transfer and pressure drop of R22, R410A and R407C in mini-

tubes, International Journal of Heat and Mass Transfer 55, 3522-3532.

Zhang, J., Li, W., Minkowycz, W. J., 2016. Numerical simulation of condensation fpr

R410A at a different saturation temperature in mini/micro tubes, Numerical Heat

Transfer, Part A: Applications 69 (5), 464-478.

Zhang, M., Webb, R. L., 2001. Correlation of two-phase friction for refrigerants in

small-diameter tubes, Experimental Thermal and Fluid Science 25, 131-139.

Zhang, W., Hibiki, T., Mishima, K., 2010. Correlations of two-phase frictional pressure

drop and void fraction in mini-channel, International Journal of Heat and Mass

Transfer 53, 453–465.

Zhao, J., Liu, G., Li, B., 2004. Two-phase patterns in a square minichannel, Journal of

Thermal Science 13 (2), 174-178.

Zurcher, O., Farvat, D., Thome, J.R., 2002a. Development of a diabatic two-phase flow

pattern map for horizontal flow boiling, International Journal of Heat and Mass

Transfer 45, 291-301.

Zurcher, O., Farvat, D., Thome, J.R., 2002b. Evaporation of refrigerants in a horizontal

tube: and improved flow pattern dependent heat transfer model compared to

ammonia data, International Journal of Heat and Mass Transfer 45, 303-317.

50

CHAPTER 2

Experimental Methods

The experimental test facility, the test sections, data reduction procedures and

measurements uncertainty analysis will be described in the present chapter. A new

experimental test facility was constructed in the MIYARA & KARIYA Thermal

Energy Engineering Lab, Department of Mechanical Engineering at the Saga

University, Japan. The main purpose of this test facility construction is to measure the

heat transfer and pressure drop during condensation and vaporization of refrigerants

inside horizontal rectangular multiport minichannels, smooth tubes and microfin tubes.

In this test facility, three different test sections have been installed in parallel mode as

shown in Fig. 2.1. The first one consists of a microfin tubes, second one consists of a

rectangular multiport minichannels with fins and third one consists of a rectangular

multiport minichannels without fins.

Fig. 2.1 a photograph of the test sections.

51

2.1 Experimental Facility

2.1.1 Experimental Apparatus

The experimental setup has been specifically fabricated to measure the heat transfer

and pressure drop of refrigerants during condensation and boiling. Fig. 2.2 shows the

schematic diagram of the experimental apparatus used in this study. The experimental

test facility consists of a test section, refrigerant loop, cooling/heating water loop, sub-

cooling loop and data acquisition system. The liquid refrigerant is pumped by an

independently controlled gear pump magnetically coupled to a variable speed electric

motor through a filter, mixer, preheaters, sight glass tube, test section, cooler and

accumulator. To complete the cycle, refrigerant from the cooler is then recirculated,

collected in an accumulator and returned to the refrigerant pump. The pump is also used

to set the mass flow rate measured by a Coriolis-effect mass flow meter. Any dust and

foreign materials contained in the refrigerant are separated through the strainer installed

after the pump.

For the condensation, the quality of refrigerant before entering the test section is

controlled by first pre-heater and superheat by second pre-heater. The hot refrigerant (in

the thermodynamic state known as a superheated vapor and it is at a temperature and

pressure at which it can be condensed with typically available cooling water) is then

enter the test section to get experimental data in the vapor quality range 0-1. The test

section consists of a tube-in-tube heat exchanger where the tested refrigerant is

cooled/heated using cooling/heating water flowing in a closed cooling/heating loop.

Cooling/heating water kept at a constant temperature is supplied to the test section from

the cooling/heating unit with constant flow rate. After the test section, refrigerant flows

through the cooler, where the refrigerant is fully subcooled by the brine which is kept at

a constant temperature in the heat source unit. Three mixing chambers are installed at

the inlet of first preheater and test section and outlet of the test section to measure the

bulk temperature of refrigerant. The system pressure of the test apparatus is controlled

by the accumulator. The absolute pressure transducer, differential pressure transducer

and K-type thermocouple at various positions and sight glass at inlet and outlet of the

test section are installed as shown in Fig. 2.2 to monitor the refrigerant’s state. All of

the signals from the pressure transducer and thermocouples are collected by a, Keithley

52

3706, data acquisition system. The whole test apparatus is well insulated with special

attention given to the test section.

Fig. 2.2 Schematic diagram of the experimental apparatus

2.1.2 The test sections

Four test sections have been used in the different experimental investigations, two

are rectangular multiport minichannels and others two is circular tube with and without

fins.

2.1.1.1 Multiport minichannels with and without fins

Fig. 2.3 depicts the schematic diagram of the multiport minichannels. The test

Heating

water bath

53

section for the multiport rectangular minichannels consists of horizontally installed

aluminum rectangular multiport minichannels without fins having 20 channels in 0.813

mm hydraulic diameter and aluminum rectangular multiport minichannels with fins

having 20 channels in 0.645 mm hydraulic diameter, two heder and six cooling water

channel. The photographs and details of the test tube are presented in Fig. 2.3-2.4 and

Table 2.1. The both test tubes are made of aluminum alloy. The hydraulic diameters dh

of rectangular multiport minichannels are calculated as follows:

4h

p

Ad

w (2.1)

Where A and wp are the total cross-sectional area and wetted perimeter length of the

tube, respectively.

There are 8 fins inside the each channel inner surface (2 fins on each side of the

inner surface) of the rectangular multiport minichannel with fins. The fin size is

mentioned in Fig 2.4. The cooling water channels are attached on both upper and

bottom side of the test section. Each cooling water channel is subdivided by three

subsections. Mixing chamber is installed at the inlet and the outlet of the each water

channel to measure the bulk water temperature as shown in Fig. 2.2. The length of each

subsection is 250 mm. The cooling water channels are designed as a rectangular

channel and used to supply heat flux to the tested tubes. The total length of the each test

section is 852 mm and effective cooling length is 750 mm. A differential pressure

transducer with calibrated accuracy of ±0.1 kPa is installed in the header to measure the

pressure difference. The inlet and outlet refrigerant temperature are measured by two K-

type thermocouples with calibrated accuracy of ±0.03K installed in the inlet and outlet

mixing chambers The inlet and outlet pressure are measured by two absolute pressure

transducer with calibrated accuracy of ±0.1 kPa inserted in the inlet and outlet mixing

chambers. Twenty four T-type thermocouples with a calibrated accuracy of ±0.03K are

attached at four points along the multiport minichannel outer wall of each subsection,

both upper and bottom side, to measure the outer wall temperature. For measuring the

inlet and outlet cooling water temperatures, K-type thermocouples with calibrated

accuracy of ±0.03K are also installed at inlet and outlet of each subsection of the water

channel.

54

Table 2.1 Tube characteristics of multiport minichannels

Multiport

Minichannel

Tube

Width

(mm)

Tube

Thickness

(mm)

Outer

tube thickness

(mm)

Tube

Inner

pillar thickness

(mm)

No. of

channel

Channel

Width

Channel

Height

Hydraulic

diameter

(mm)

With fins 19.0 2.0 0.37 0.30 20 0.61 1.24 0.64

Without fins 19.0 2.0 0.37 0.30 20 0.62 1.24 0.81

Fig. 2.3 Test section (Multiport minichannels)

55

Fig. 2.4 Photograph of the test tube

2.1.1.2 Smooth and microfin tubes

Fig. 2.5 illustrates the schematic diagram of the test section for the circular tube

with and without fins. The details dimensions of the test tube are summarized in Table

2.2. The test section consists of horizontally installed copper tube, two headers and

three cooling water channels. The test tubes are small-diameter circular tubes with and

without microfins. The equivalent diameter of the tube with microfins is 2.68 mm. The

equivalent diameter of the microfins tube is calculated as follows:

4eq

Ad

(2.2)

where A is the flow area of refrigerant.

The inner diameter of a tube without microfins is 2.14 mm. The cooling water

channels are designed as a tube in tube heat exchanger and used to supply heat flux to

the tested tubes. The total length of the each test section is 852 mm and effective

cooling and heating length is 744 mm. A differential pressure transducer with calibrated

accuracy of ±0.1 kPa is installed in the header to measure the pressure difference. The

inlet and outlet refrigerant temperature are measured by two K-type thermocouples with

calibrated accuracy of ±0.03K installed in the inlet and outlet mixing chambers. The

56

inlet and outlet pressure are measured by two pressure transducer with calibrated

accuracy of ±0.1 kPa inserted in the inlet and outlet mixing chambers. For measuring

the inlet and outlet cooling water temperatures, K-type thermocouples with calibrated

accuracy of ±0.03 K are also installed at the inlet and outlet of each subsection of the

water channel.

Table 2.2 Detail dimensions of the circular tube with and without microfins

Circular tube with microfins

Circular tube without fins

Outer diameter, do 3.0 mm 2.5 mm Inner diameter, di - 2.14 mm Diameter at fin root, dr 2.7 mm - Diameter at fin tip, dt 2.5 mm - Equivalent diameter, de 2.68 mm - Fin height, e 0.1 mm - No. of fins, n 25 - Apex angle, γ 330 - Helix angle, ψ 100 -

Fig. 2.5 Test section (Circular tube)

2.1.3 Range of test conditions

The experiments covered a wide range of test conditions for all test section studied in

the present work to investigate the effect of the following parameters on the

experimental condensation heat transfer coefficients and frictional pressure drop: the

57

mass velocity, saturation temperature, vapor quality, and tube geometry. Table 2.3 and

Table 2.4 listed the range of the test conditions of the present research for condensation

and adiabatic experiments, respectively.

Table 2.3 Test conditions for condensation experiments

Test Section Minichannel

with fins

Minichannel

without fin Smooth tube Microfin tube

Channel

Diameter dh = 0.64 mm dh = 0.81 mm di = 2.14 mm deq = 2.68 mm

G [kg/m2s] 50-200 50-200 50-200 50-200

Tsat (C) 30, 35 30, 35 30 30

x 0.1-0.9 0.1-0.9 0.1-0.9 0.1-0.9

Table 2.4 Test conditions for adiabatic experiments

Test Section Minichannel

with fins

Minichannel

without fin Smooth tube Microfin tube

Channel

Diameter dh = 0.64 mm dh = 0.81 mm di = 2.14 mm deq = 2.68 mm

G [kg/m2s] 50-200 50-200 50-200 50-200

Tsat (C) 20, 30, 35 20, 30, 35 20, 30, 35 30

x 0.1-0.9 0.1-0.9 0.1-0.9 0.1-0.9

58

2.2 Data reduction

2.2.1 Two-phase frictional pressure drop

The two-phase pressure drop is composed of pressure drop due to momentum change or

acceleration (deceleration), gravity or static, abrupt contraction, abrupt expansion, and

friction. The gravitational or static pressure drop is zero due to horizontal flow. The

pressure drop due to momentum change or acceleration (deceleration) was not included

in the measured pressure drop as the pressure drop was obtained at adiabatic conditions.

Therefore, the total measured pressure drop TP at adiabatic condition is expressed as

the sum of frictional pressure drop FP , pressure drop due to the abrupt contraction

cP and expansion eP at the inlet and outlet of the test section,

T F c eP P P P (2.3)

The pressure drop due to abrupt contraction and expansion in the headers should be

taken into account in addition to the pressure drop in the channel. In the case of a

sudden contraction and enlargement in the cross-sectional area of the pipe flow

separation occurred and the general method used in single-phase flow is still applicable

to a one-dimensional separated two-phase flow (Collier and Thome, 1994). Fig. 2.6

depicts a two-phase flow passing through a sudden contraction and expansion. The

subscript 1, 2 and 3 has been used to denote the conditions at planes 1, 2 and 3,

respectively as laid in Fig. 2.6.

59

Fig. 2.6 Abrupt contraction and expansion nomenclature.

According to Collier and Thome (1994), the pressure drop due to the abrupt contraction

is given by

22

2

1 11 1 1

2l v

c

c c l

G v vP x

C v

(2.4)

And the pressure drop in the case of sudden expansion is given by

2 2

2 (1 )1 ( )

(1 )v

e e e l

l

vx xP G v

v

(2.5)

where, δ is the area ratio ( 1 2 2 3/ , /c eA A A A ) and the coefficient of contraction, Cc

is a function of δ. Perry (1963) suggested the relationship between Cc and δc as listed in

Table 2.5.

The void function is assumed as a constant and calculated by the homogeneous

model.

1

11 v

l

x

x

(2.6)

60

The pressure drop due to abrupt contraction and abrupt expansion was found to be less

than 2% of the total two phase pressure drop.

Table 2.5 Relationship between cC and c

1

c 0 0.2 0.4 0.6 0.8 1.0

cC 0.586 0.598 0.625 0.686 0.790 1.0

2

11

cC

0.5 0.45 0.36 0.21 0.07 0

The vapor quality before entering the test section is expressed as:

outh hx

h h

(2.7)

out in

Wh h

G

(2.8)

The saturated liquid enthalpy, h and enthalpy of saturated vapor, h at the preheater

outlet are calculated with its temperature. The K-type thermocouple at outlet of the

preheater gives the refrigerant temperature. The enthalpy of refrigerant before the

preheater is calculated with its bulk temperature and pressure. The amount of heat, W,

is supplied by the electricity into the preheater in the direct heating method. The

experimental study was conducted at adiabatic condition (the temperature of flowing

refrigerant in the test section and water flowing upper and lower side of the test section

was same). The vapor quality does not change along the test section because no further

heat is added to the refrigerant flowing in the test section.

61

Then from the experimental frictional pressure drop, the experimental two-phase

frictional multiplierl is obtained, based on Lockhart-Martinelli (1949) method, from

the following equation as:

2l

F l

PP

z z

(2.9)

where F

P

z

is the frictional pressure gradient for the two-phase flow; l

P

z

is the

frictional pressure gradient when only liquid flows through the test tube.

The value of l

P

z

is estimated by

222 1l

l h l

f G xP

z d

(2.10)

where the friction factor lf is calculated by Colburn’s Eq. for single-phase flow in a

tube.

0.2

0.046

Rel

l

f (2.11)

2.2.2 Condensation heat transfer

The sectional two-phase average local heat transfer coefficient of each thermocouple

location, i (i=1, 2, 3,…………..,12), during the condensation of R134a in horizontal

rectangular multiport minichannels with and without fins was calculated by

,

,

stp i

R,i wi i

qh

T T

(2.12)

where sq is the heat flux of each subsection based on the actual heat transfer surface

area inside the channel, ,R iT is the refrigerant temperature inside the channel and ,wi iT is

the inner wall temperature.

62

The heat flux of each subsection is calculated as

c HBs

p

qq

w Z

(2.13)

To get better data reduction, sq is modified by HB due to the error of heat balance as

shown in Fig. 2.7.

Fig. 2.7 Error of heat balance of all test conditions

The heat transfer rate of the coolant side of each subsection is

, ,( )c c s out s inq m h h (2.14)

The heat balance factor, HB is

RHB

c

Q

Q (2.15)

The sensible heat gain of the coolant of the whole test section is

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

50100200

-10%

50 100 150 200

QR [

kW

]

QC [kW]

G [kg/m2s]

+10%

Minichannels

G [kg/m2s]

Microfin and smooth tubes

63

[ ( )] [ ( )]c c out in U c out in LQ m h h m h h (2.16)

The heat release of refrigerant of the whole test section is

( )R R out inQ m h h (2.17)

The inner wall temperature, ,wi iT of the multiport minichannel at each thermocouple

location was calculated from the measured outer wall temperature and the heat flux

using one-dimensional Fourier’s heat conduction equation

, ,s

wi i wo i

al

q zT T

w Z k

(2.18)

In the case of horizontal microfins and smooth circular tubes, the inner wall temperature

was calculated by

0

, ,

ln

2

s

iwi i wo i

cu

dq

dT T

z k

(2.19)

The refrigerant temperature at each thermocouple location, ,R iT , was determined from

the corresponding saturation pressure assuming saturated state. The pressure drop in the

test section was recorded by a differential pressure transducer. Based on the recorded

pressure drop, a new frictional pressure drop correlation was developed in order to

identify the saturation conditions on each thermocouple location. The local heat transfer

coefficient calculation process for multiport minichannel is schematically depicted in

Fig 2.8.

64

Fig. 2.8 Schematic diagram of local heat transfer coefficient calculation

The refrigerant equivalent vapor quality at each thermocouple location is given by

,b i l

i

v l

h hx

h h

(2.20)

Where, ,b ih is the local enthalpy at each test section wall thermocouple location. The

local enthalpy of each thermocouple location “i” was obtained from the local enthalpy

in the location “i-1” using the following equation:

, ,i 1R

b i b

R

q wh h

l m

(2.21)

For the first thermocouple location Eq. (2.9) becomes:

,1 ,R

b b in

R

q wh h

l m

(2.22)

The i+1th point local enthalpy of a thermocouple point is the ith point local enthalpy

of the next thermocouple point.

The thermodynamic properties and transport properties of R134a were obtained

from NIST REFPROP 9.1 (Lemmon et al., 2013).

65

2.3 Experimental measurement uncertainties analysis

The experiments were conducted over a range of test conditions. The effects of different

parameters on the condensation heat transfer and adiabatic pressure drop were clarified.

The vapor quality, mass flux and saturation temperature were varied. The experimental

uncertainty of the condensation heat transfer and adiabatic pressure drop were

calculated following the method by JCGM 100 (2008). The experimental uncertainty is

consisted of two parts, type A uncertainty that derives from repeated observation and

type B uncertainty that derives from instruments calibration and manufacturer’s

specifications. The resulting u of each parameter x is expressed as:

2 2

A Bu x u x u x (2.23)

The combined standard uncertainty is obtained by combining the standard uncertainty

of the measured quantities 1 2, ,....., Nx x x , through a functional relationship f as follows:

1 2, ,.........., Ny f x x x (2.24)

2

2

1

N

ii i

fu y u x

x

(2.25)

The expanded uncertainty U is obtained by multiplying the combined uncertainty u (y)

by a coverage factor k = 2 with a level of confidence of 95%.

U u y k (2.26)

The uncertainty analysis of heat transfer coefficient can be carried out based on the

basic equation of condensation heat transfer mentioned in Eq. 2.12.

2 2 2

2 2 2s wi R

s wi R

h h hu h u q u T u T

q T T

(2.27)

66

Similarly, the uncertainty analysis of frictional pressure drop can be carried out from

the basic equation of frictional pressure drop calculation as mentioned in Eq. 2.3.

2 22

2 2 2F F FF T c e

T c e

P P Pu P u P u P u P

P P P

(2.28)

67

References

Collier, J. G., Thome, J. R., 1994. Convective Boiling and Condensation, Third edition,

Oxford University Press, Oxford, UK.

JCGM 100, 2008. Evaluation of measurement data-Guide to the expression of

uncertainty in measurement.

Lemmon, E.W., Huber, M.L., McLinden, M.O., 2013. Reference Fluid Thermodynamic

and Transport Properties, In: NIST Standard Reference Database 23, REFPROP,

Version 9.1, Gaithersburg, April.

Lockhart, R.W., Martinelli, R.C., (1949). Proposed Correlation of Data for Isothermal

Two-Phase, Two-Component Flow in Pipes. Chemical Engineering Progress 45, 39-

48.

Perry, 1963. Chemical Engineers Handbook, 4th Edition, McGraw-Hili, 5-30.

68

CHAPTER 3

Two-phase Frictional Pressure Drop Analysis

The two-phase frictional pressure drop of R134a in horizontal rectangular multiport

minichannels and microfin tubes at the adiabatic condition is analyzed and discussed in

this chapter. The experimental study conducted over the mass flux range of 50-200

kg/m2s, vapor quality range of 0 to 0.9 and at the saturation temperature of 20, 30 and

35 0C, respectively.

3.1 Two-phase frictional pressure drop in rectangular multiport

minichannels with and without fins

3.1.1 Effect of the mass flux and vapor quality

The analysis of an experimental pressure drop results reveals several important

trends. Most notably, the mass flux and vapor quality has shown significant effect. Fig.

3.1 and Fig. 3.2, respectively shows the effects of mass flux and vapor quality on the

frictional pressure drop in rectangular multiport minichannel with and without fins. The

frictional pressure drop in both multiport minichannels significantly increases with

increasing mass flux and vapor quality. Starting from the beginning with a vapor quality

of 0.1, frictional pressure drop increases almost nearly linearly for all of the vapor

quality range. The increase of the frictional pressure gradient is mainly due to the

higher vapor shear stress which increases with increasing mass flux and vapor quality.

The vapor shear stress increases with increasing vapor flow velocity which increases as

mass flux and vapor quality increases. Similar trends are also observed some previous

studies by Hwang and Kim (2006), Pamitran et al. (2010), Park and Hrnjak (2007) and

Sakamatapan et al (2014).

69

Fig. 3.1 Effects of mass flux and vapor quality on frictional pressure gradient in

rectangular multiport minichannels with fins

0

5

10

15

20

25

30

50 100 150 200

P

/z)

F [

kP

a/m

]

Minichannel with fins (dh= 0.64 mm) G [kg/m2s]

R134a, Tsat

= 30 0C

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

Vapor quality

P

/z)

F [

kP

a/m

]

R134a, Tsat

= 35 0C

Minichannel with fins (dh= 0.64 mm)

50 100 150 200

G [kg/m2s]

70

Fig. 3.2 Effects of mass flux and vapor quality on frictional pressure gradient in

rectangular multiport minichannels without fins.

3.1.2 Effect of saturation temperature

Saturation temperature also plays an influential role in two-phase frictional pressure

drop. In order to investigate the effect of saturation temperature on the frictional

pressure drop, experimental investigation was conducted by changing the saturation

temperature from 20 0C to 35 0C at mass flux 50, 100 and 200 kg/m2s, respectively as

shown in Fig. 3.3. There is no noticeable change in frictional pressure drop with

0

5

10

15

20

25

30

P

/z)

F [

kPa/

m]

R134a, Tsat

= 30 0C

Minichannel without fins (dh= 0.81 mm) G [kg/m2s]

50 100 150 200

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

P

/z)

F [

kPa/

m]

Vapor quality

R134a, Tsat

= 35 0C

Minichannel without fins (dh= 0.81 mm) G [kg/m2s]

50 100 150 200

71

saturation temperature at low mass flux. However, at high mass fluxes, the

experimental results confirmed that the saturation temperature had a significant effect

on frictional pressure drop which decreased with increasing saturation temperature. The

physical explanation of these effects is that the saturation temperature changes fluid

properties such as viscosity, density and surface tension as well as shear stress. When

increasing the saturation temperature, the viscosity ratio /l v , density ratio /l v

and surface tension decreases as a consequence the frictional pressure drop decreases.

The physical properties of selected working refrigerant are shown in Table 3.1. The

frictional pressure drop trend is fully consistent with Revillin and Thome (2007),

Pamitran et al. (2010) and Sakamatapan et al (2014).

Table 3.1 Thermophysical properties of R134a (Lemmon et al., 2013)

Tsat

[0C] ρl

[kg/m3] ρv

[kg/m3] l

v

µl

[µPa s] µv

[µPa s] l

v

σ

[mN/m]

20 1225.90 27.65 44.34 207.75 11.48 18.09 8.71

30 1188.00 37.37 31.79 183.47 11.90 15.41 7.40

35 1168.10 43.22 27.02 172.33 12.12 14.21 6.76

72

Fig. 3.3 Effect of saturation temperature on frictional pressure gradient

0

5

10

15

20

25

30

P

/z)

F [

kP

a/m

]

R134a, G = 50 kg/m2s

Minichannel with fins (dh= 0.64 mm) T

sat [0C]

20 30 35

0

5

10

15

20

25

35

P

/z)

F [

kP

a/m

]

Tsat

[0C]

20 30

Minichannel with fins (dh= 0.64 mm)

R134a, G = 100 kg/m2s

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

Tsat

[0C]

20 30 35

P

/z)

F [

kP

a/m

]

Vapor quality

Minichannel with fins (dh= 0.64 mm)

R134a, G = 200 kg/m2s

73

3.1.3 Effect of channel hydraulic diameter

The comparisons of the frictional pressure gradient were conducted between

rectangular minichannel with fins and without fin of hydraulic diameters of 0.64 mm

and 0.81 mm with same outer dimension and similar tested conditions, as shown in Fig.

3.4.

Fig. 3.4 Comparison of frictional pressure drop between minichannels with fins and

without fins.

0

5

10

15

20

25

30

100 150 200

100 150 200

(P

/z)

F [

kP

a/m

]

Minichannel with finsG [kg/m2s]

G [kg/m2s]Minichannel without fin

Tsat

=30 0C

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

100 150 200

100 150 200

(P

/z)

F [

kP

a/m

]

Vapor quality

G [kg/m2s]Minichannel with fins

G [kg/m2s]Minichannel without fin

Tsat

=35 0C

74

The experimental results exhibited that the frictional pressure drop of the multiport

minichannel with fins is 1.08-1.25 times higher than that of multiport minichannel

without fin for the same tested condition. At low mass velocity, the effect was not

notable. The effect is increasing with increasing the mass velocity. The smaller

hydraulic diameter tube offers higher frictional pressure drop due to the higher wall

shear stress which increases with increasing velocity gradients. The velocity gradiants

decreases with decreasing channel hydraulic diameter. This trend was strongly

supported by Revellin and Thome (2007), Sakamatapan et al. (2014) and Jige et al.

(2016).

3.2 Two-phase frictional pressure drop in circular microfins and

smooth tubes

The adiabatic two-phase frictional pressure drop of R134a in horizontal circular

microfins and smooth tubes are analyzed and discussed in this section. The

experimental study conducted over the mass flux range of 50-200 kg/m2s, vapor quality

range of 0 to 0.9 and at the saturation temperature of 20, 30 and 35 0C, respectively.

3.2.1 Influence of mass flux and vapor quality

Two phase frictional pressure drop at the adiabatic condition for microfin and

smooth tube are stated in Fig. 3.5 (a) and Fig. 3.5 (b). For both tubes, the frictional

pressure drop increases with mass flux and vapor quality. These are general trends of

two-phase frictional pressure drop (Collier and Thome, 1994). The increase of frictional

pressure drop is due to the effects of higher shear stress and momentum that leads to an

increase in wall shear stress as a result frictional pressure drop increases. The frictional

pressure drop mainly depends on the wall shear stress between liquid phase and tube

wall and the interfacial shear stress between liquid and vapor phases. Roughly speaking,

these shear stresses are strongly affected by the velocity gradient of each phase. The

larger bulk velocity of the liquid phase allows the larger velocity gradient of the liquid

phase near the tube wall, which results in the increase of wall shear stress. Similarly,

since the liquid-vapor interface acts like a tube wall to the vapor phase, the increase of

75

velocity difference between the liquid and vapor phases causes the increase of

interfacial shear stress (Kim et al., 2008).

Fig. 3.5 Effects of mass flux and vapor quality on frictional pressure drop: (a) Microfin

tube; (b) Smooth tube.

0 0.2 0.4 0.6 0.8 1.00

4

8

12

16

20

50 100 200

(P

/z)

F [

kPa/

m]

Vapor quality

R134a, Tsat

= 20 0C Microfin tube

G [kg/m2s]

a)

0 0.2 0.4 0.6 0.8 1.00

4

8

12

16

20

(P

/z)

F [

kPa/

m]

Vapor quality

R134a, Tsat

= 20 0C Smooth tube

G [kg/m2s]

50 100 200

b)

76

3.2.2 Influence of microfins

The frictional pressure drop in smooth and microfin tube at similar experimental

condition was compared to identify the effects of internal fins on pressure drop. The

result overlaid in Fig. 3.6, shows that the frictional pressure drops of microfin tube is

higher than those of smooth tube approximately 6% to 29%. This is due to the internal

geometry. Pressure drop penalty factor, the ratio of pressure drop between microfin and

smooth tube at the same condition, are presented in Fig. 3.7. Figure 3.7 shows that the

pressure drop penalty factor increases as vapor quality increases and mass flux has an

insignificant effect.

Fig. 3.6 Comparison of frictional pressure drop between smooth and microfin tubes

3.2.3 Influence of saturation temperature

In order to investigate the influence of saturation temperature on the frictional

pressure drop, experimental investigation was conducted by changing the saturation

temperature from 20 0C to 35 0C at mass flux 200 kg/m2s, as shown in Fig. 3.8. It was

found that the saturation temperature had a significant effect on frictional pressure

gradient which decreased with increasing saturation temperature. The reason is that the

0 0.2 0.4 0.6 0.8 1.00

4

8

12

16

20

Microfin tube

G [kg/m2s] 50 100 200

50 100 200

(P

/z)

F [

kPa/

m]

Vapor quality

Smooth tube

G [kg/m2s]

R134a, Tsat

= 20 0C

77

saturation temperature changes the viscosity as well as shear stress. The physical

explanation of these effects is same as with the multiport minichannels.

Fig. 3.7 Frictional pressure drop penalty factor

Fig. 3.8 Effects of saturation temperature on Frictional pressure drop.

0 0.2 0.4 0.6 0.8 1.01

1.2

1.4

1.6

1.8

2.0

50 100 200

Pre

ssur

e dr

op p

enal

ty f

acto

r

Vapor quality

G [kg/m2s]

0.0 0.2 0.4 0.6 0.8 1.00

4

8

12

16

20

20 30 35

(P

/z)

F [

kP

a/m

]

Vapor quality

Tsat

[0C]Smooth tube (d = 2.14 mm)

G = 200 kg/m2s

78

3.3 Conclusions

An adiabatic two-phase frictional pressure drop charecteristics of R134a in two

rectangular multiport minichannels with fins and without fin and microfin tube were

investigated experimentally for different mass velocity and saturation temperature. The

effects of mass velocity, vapor qualities, saturation temperature and channel geometry

on the frictional pressure drop were analyzed and discussed.

The main conclusions are as follows:

1. The experimental frictional pressure gradiants in both multiport minichannels

and microfin tube increase with mass velocitie and vapor quality and decrease

with saturation temperature.

2. The hydraulic diameter of the multiport minichannel has significant influence on

the frictional pressure gradients which increases with decreasing hydraulic

diameter of the minichannles.

3. The microfin tube has slightly influence on the frictional pressure gradients. The

frictional pressure drop of the microfin tube was higher than those of smooth

tube about 10-15%.

79

References

Collier, J. G., Thome, J. R., 1994. Convective Boiling and Condensation, Third edition,

Oxford University Press, Oxford, UK.

Hwang, Y. W., and Kim, M. S., 2006. The pressure drop in microtubes and the

correlation development, International Journal of Heat and Mass Transfer 49, 1804–

1812.

Jige, D., Inoue, N., Koyama, S., 2016. Condensation of refrigerants in a multiport tube

with rectangular minichannels, International Journal of Refrigeration 67, 202-213.

Kim, Y. J., Jang, J., Hrnjak, P. S., Kim, M. S., 2008. Adiabatic horizontal and vertical

pressure drop of carbon dioxide inside smooth and microfin tubes at low

temperatures, Journal of Heat Transfer 130, 111001-1-111001-10.

Pamitran, A. S., Choi, K. I., Oh, J. T., Hrnjak, P., 2010. Characteristics of two-phase

flow pattern transitions and pressure drop of five refrigerants in horizontal circular

small tubes, International Journal of Refrigeration 33, 578–588.

Park, C. Y., Hrnjak, P. S., 2007. CO2 and R410A flow boiling heat transfer, pressure

drop, and flow pattern at low temperatures in a horizontal smooth tube, International

Journal of Refrigeration 30, 166–178.

Revellin, R., Thome, J. R., 2007. Adiabatic two-phase frictional pressure drops in

microchannels, Experimental Thermal and Fluid Science 31, 673-685.

Sakamatapan, K., and Wongwises, S., 2014. Pressure drop during condensation of

R134a flowing inside a multiport minichannel. International Journal of Heat and

Mass Transfer 75, 31-39.

80

CHAPTER 4

Condensation Heat Transfer

The local heat transfer coefficient has been measured in horizontal rectangular

multiport minichannels and circular tube with and without fins during condensation of

R134a. The experiments have been conducted over the entire range of vapor quality at

mass flux range of 50 to 200 kg/m2s and saturation temperature between 20 to 35 0C.

The effect of different parameters on the condensation heat transfer coefficient has been

explored in this topic.

4.1 Condensation heat transfer in rectangular multiport minichannels

with and without fins

Many researchers’ already stated that the heat transfer mechanism during the

condensation process is strongly dependent on the flow pattern inside the channels.

Several experimental investigations were performed to developed information on the

flow patterns of condensing flow and the operating conditions (Soliman, 1986).

Therefore, to identify the flow pattern the present experimental data were overlaid on

two most widely used existing flow pattern map proposed by Scott (1964) and Taitel

and Dukler (1976) as illustrate in Fig. 4.1 and Fig. 4.2, respectively. Most of the present

experimental data points are lapse in the annular flow, annular-wavy and annular-slug

flow transition zone on modified Baker flow pattern map shown in Fig. 4.1, while few

data obtained at low vapor quality (x < 0.26) points fall into the slug and plug flow

region. In the Taitel and Dukler flow pattern map illustrate in Fig. 4.2, most of the

current data are fall in the annular flow region, although very few data obtained at low

vapor quality (x < 0.19) lapse into the intermittent flow region.

81

Fig. 4.1 Experimental data of condensation heat transfer spread on modified Baker two-

phase flow pattern map (Scott, 1964)

Fig. 4.2 Experimental data of condensation heat transfer overlaid on Taitel and Dukler

(1976) two-phase flow pattern map

10-3 10-2 10-1 100 101 102 103 104100

101

102

103

104

Multiport minichannel

Annular

10-3

10-2

10-1

100

101

Stratified Smooth

Bubbly

IntermittentStratified-Wavy

with fins without fin

Fr G

or

T

K

X

82

4.1.1 Effect of mass velocity and vapor quality

In order to investigate the effect of different parameters on heat transfer coefficient,

the local heat transfer coefficient of R134a in horizontal rectangular minichannels with

and without fins are measured and discussed as an average value over the entire length

of the test section. The experimental results were obtained for different mass fluxes

from 50 to 200 kg/m2s and at saturation temperature of 30 0C and 35 0C. Fig. 4.3 (a) and

Fig. 4.3 (b) illustrate the local heat transfer coefficient variation along the tube with

respect to the vapor quality, (1-x) of R134a in horizontal rectangular multiport

minichannels with and without fins at 35 0C saturation temperature for different mass

flux. For all mass fluxes and both the multiport minichannels with and without fins,

experimental results display that the average heat transfer coefficient decreases as the

condensation progresses.

The heat transfer coefficient decreases much fasters at high vapor quality (x > 0.5)

in both minichannels. The heat transfer coefficient decreases due to the increase of

thermal resistance of condensate and decrease of shear stress of the vapor and liquid

phase. Sakamatapan et al. (2013) observed the similar phenomenon. They explained the

mechanism as the velocity of the vapor and liquid phases is high at high vapor quality.

Therefore, the shear stress at the interface between the vapor and liquid film is higher

than that at low vapor quality. The shear stress is increases due to higher turbulence at

the interface between the vapor and liquid film, which lead to a corresponding increase

in the condensation heat transfer coefficient. Furthermore, as expected, the average heat

transfer coefficient significantly increases with mass flux in both minichannels

illustrates in Fig 4.3. The facts suggest that the condensation heat transfer is dominated

by the force convection as well as the shear stress. This effect is more important at low

vapor qualities. The tested range of vapor quality was 0.1 to 0.9. The vapor quality was

not reached higher than 0.9 for all mass fluxes. From the general theory, it is expected

that the heat transfer coefficient fall after higher vapor quality than 0.9, in that situation

the liquid film almost disappears and the flow is more similar to single vapor flow with

a decrease in heat transfer coefficient (Belchi, 2014).

83

Fig. 4.3 Effects of mass flux and vapor quality on average heat transfer coefficient: (a)

Minichannel with fins; (b) Minichannel without fins

4.1.2 Effect of saturation temperature

The influence of saturation temperature on the average heat transfer coefficient was

investigated by changing the saturation temperature at constant mass flux and heat flux.

Fig. 4.4 depicts the effect of saturation temperature on experimental average heat

transfer coefficient of R134a at mass flux of 150 kg/m2s. The experimental result

indicates that the average heat transfer coefficient is increase with decreasing saturation

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

200

50 100 150

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

R134a, Tsat

= 35 0CMinichannel with fins G [kg/m2s]

a)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

200

G [kg/m2s]Minichannel without fin

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

50 100 150

R134a, Tsat

= 35 0C

b)

84

temperature. The reason is that the saturation temperature changes the system pressure

as well as the thermal and transport properties of refrigerant. The viscosity ratio and

density ratio increases (as mentioned in Table 4.1) with decreasing saturation

temperature which increases the shear stress. The surface tension and thermal

conductivity of liquid film also increases with decreasing saturation temperature as

shown in Table 4.1. Therefore, this occurrence makes the heat transfer coefficient

higher.

Fig. 4.4 Effect of saturation temperature on average heat transfer coefficient; (a)

Minichannels with fins; (b) Minichannels without fins.

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

30 35

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

R134aG = 150 kg/m2s

Multiport minichannel with finsT

sat [0C]

a)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

30 35

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2K

]

1-x

R134aG = 150 kg/m2s

Multiport minichannel without fin

Tsat

[0C]

b)

85

Table 4.1 Thermophysical properties of R134a (Lemmon et al. 2013)

Tsat

[0C]

ρl

[kg/m3]

ρv

[kg/m3]

l

v

µl

[µPa s]

µv

[µPa s]

l

v

σ

[mN/m]

kl

[W/mK]

30 1188.00 37.37 31.79 183.47 11.90 15.42 7.40 0.079

35 1168.10 43.22 27.02 172.33 12.12 14.21 6.76 0.076

4.1.3 Effect of minichannels diameter

The comparisons of average heat transfer coefficient were conducted between

multiport minichannels with and without fins of hydraulic diameters of 0.64 mm and

0.81 mm with same outer dimension and similar tested condition as depicts in Fig. 4.5.

At saturation temperature of 35 0C and mass flux of 50, 100, 150 and 200 kg/m2s,

respectively, results indicate (in Fig. 4.5) that heat transfer coefficient of rectangular

multiport minichannel with fins is higher than the rectangular multiport minichannel

without fin about average 39% at higher vaper quality (x > 0.3). According to Yang and

Webb (1996), the enhancement is attributed to the effect of surface tension drainage

force. The surface tension force acts to maintain a smaller film thickness on the groove

fin than exists on the surface of the smooth tube. At low vapor quality (x < 0.3), the

heat transfer coefficient for the multiport minichannels with fins is higher than of

multiport minichannel without fin about 10-15%. This trend is also supported by Yang

and Webb (1996).

The tube outer diameter, channel width and channel height in both tube are similar. Due

to the fins inside the channel, the tube hydraulic diameter is reduced. Because of the

fins inside the channel, the actual heat transfer surface area is increased. The

augmentation ratio, the ratio of actual heat transfer surface area between minichannel

with fins and without fin, is the main cause of heat transfer enhancement.

86

Fig. 4.5 Comparison of average heat transfer coefficient between multiport

minichannels with and without fins: (a) G = 50 kg/m2s; (b) G = 100 kg/m2s; (c) G = 150

kg/m2s; (d) G = 200 kg/m2s.

4.2 Condensation heat transfer in circular microfins and smooth tube

4.2.1 Effect of mass fluxes and vapor quality

Fig. 4.6 shows the average condensation heat transfer coefficient as a function of

vapor quality with variation of mass fluxes for the microfin and smooth tubes. As

expected, the heat transfer coefficient is decreased as condensation proceeded. Fig. 4.6

also showed that the heat transfer coefficient was significantly increased with mass

flux. These trends are usual in case of in tube condensation (Collier and Thome, 1994,

Ghiaasiaan, 2008). The heat transfer coefficient decreases because the vapor shear

stresses decreases and the thermal resistance of the condensate increases. If the mass

velocity or vapor quality increases the void fraction in a tube also increases. If the void

fraction increases, more surface will be exposed to vapor and liquid film become

thinner which yielding a high heat transfer coefficient (Collier and Thome, 1994, Kim,

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

with fins without fin

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

R134a, Tsat

= 35 0C

G = 50 kg/m2s

Multiport minichannelsa)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

with fins without fin

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2K

]

1-x

R134a, Tsat

= 35 0C

G = 100 kg/m2s

Multiport minichannelb)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

with fins without fin

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

R134a, Tsat

= 35 0C

G = 150 kg/m2s

Multiport minichannelc)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

with fins without fin

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

R134a, Tsat

= 35 0C Multiport minichannel

G = 200 kg/m2s

d)

87

2016). This enhancement is mainly due to the major effect of the contribution of forced

convection condensation heat transfer at the tube wall.

Fig. 4.6 Effects of mass flux and vapor quality on condensation heat transfer coefficient in:

(a) Microfin tube; (b) Smooth tube.

4.2.2 Effect of tube diameter

The comparison of measured heat transfer coefficients between smooth and microfin

tube has been done in this study and overlaid in Fig. 4.7.

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

G = 50 kg/m2s, q = 7 kW/m2

G = 100 kg/m2s, q = 12 kW/m2

G = 200 kg/m2s, q = 16 kW/m2

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

Microfin tube (deq

= 2.68 mm)R134a, Tsat

= 30 0Ca)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

G = 50 kg/m2s, q = 7 kW/m2

G = 100 kg/m2s, q = 12 kW/m2

G = 200 kg/m2s, q = 16 kW/m2

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

Smooth tube (di = 2.14 mm)R134a, T

sat = 30 0C

b)

88

Fig. 4.7 Condensation heat transfer coefficient of microfin tube compared with

condensation heat transfer coefficient of smooth tube.

0

5

10

15

20

25

30

q = 7 kW/m2

Tsat

= 30 0C Microfin tube (d

eq = 2.68 mm)

Smooth tube (di = 2.14 mm)

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

G = 50 kg/m2s

R134a

0

5

10

15

20

25

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2K

] R134aT

sat = 30 0C

G = 100 kg/m2sq = 12 kW/m2

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

Hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

1-x

R134aT

sat = 30 0C

G = 200 kg/m2sq = 16 kW/m2

89

It can be seen from Fig. 4.7 that the heat transfer coefficient for the microfin tube are

greater than those of smooth tube in the whole quality range about 2-68%.The reason is

that the surface tension effect on liquid drainage which formed a very thin liquid film on

the surface of microfin. Fig. 4.8 depicts the heat transfer enhancement factors varied with

mass fluxes and vapor quality. The heat transfer enhancement factor is defined as the ratio

of the heat transfer coefficient of the microfin tube to that of smooth tube at the same

condition. The heat transfer enhancement factors significantly increases with increasing

mass fluxes due to the contribution of forced convection condensation heat transfer as

mentioned earlier. With increasing the mass flux the turbulence created by fin grooves also

increased which enhance the heat transfer enhancement factor. This trend is fully

consistent with the Sapali and Patil (2010). In the case of low vapor quality region, the

heat transfer coefficient is almost same in both the smooth and microfin tube.

Fig. 4.8 Condensation heat transfer coefficient enhancement factor.

0 0.2 0.4 0.6 0.8 11

1.2

1.4

1.6

1.8

2.0

50 100 200

Hea

t tr

ansf

er e

nh

ance

men

t fa

cto

r

1-x

G [kg/m2s]

90

4.3 Conclusions

Condensation heat transfer characteristics were experimentally investigated inside

two horizontal rectangular multiport minichannels and microfin tube for different mass

velocity and saturation temperature. The effects of mass flux, vapor quality, saturation

temperature and channel diameter of the tube on heat transfer coefficient were

examined and discussed. Based on the experimental study, the main findings of the

present investigation can be summarized as follows:

1. The average heat transfer coefficient of R134a during condensation tended to

increases with increasing mass flux and vapor quality in both multiport

minichannels and microfin tube.

2. The saturation temperature has significant influence on heat transfer coefficient

which decreases with increasing the saturation temperature. The reason is the

thermal conductivity of liquid film which decreases with increasing saturation

temperature.

3. The heat transfer coefficient of rectangular multiport minichannel with fins is

approximately 10-39% higher than those of rectangular multiport minichannel

without fin for the same operating conditions due to the surface tension force.

4. The higher heat transfer coefficients were obtained in microfin tube then that of

smooth tube about 2-68%.

91

References

Belchi, E. A. L., 2014. Characterization of heat transfer and pressure drop in

condensation processes within minichannel tubes with last generation of

refrigeration fluids, PhD thesis.

Collier, J. G., Thome, J. R., 1994. Convective boiling and condensation, 3rd edn,

Oxford University Press, Oxford.

Ghiaasiaan, S. M., 2008. Two-phase flow, boiling and condensation, Cambridge

University Press, Cambridge.

Kim, N. H., 2016. Condensation heat transfer and pressure drop of R410A in a 7.0 mm

O.D. microfin tube at low mass fluxes, Heat Mass Transfer, doi 10.1007/s00231-

016-1789-2.

Lemmon, E.W., Huber, M.L., McLinden, M.O., 2013. Reference Fluid Thermodynamic

and Transport Properties-REFPROP, Version 9.1, NIST Standard Reference

Database 23, Gaithersburg, April.

Sakamatapan, K., Kaew-On, J., Dalkilic, A. S., Mahian, O., Wongwises, S., 2013.

Condensation heat transfer characteristics of R-134a flowing inside the multiport

minichannels, International Journal of Heat and Mass Transfer 64, 976-985.

Sapali, S. N., Patil, P. A., 2010. Heat transfer during condensation of HFC-134a and

R404A inside of a horizontal smooth and microfin tube, Experimental Thermal and

Fluid Science 34, 1133-1141.

Scott, D. S., 1964. Properties of cocurrent gas-liquid flow, Advances in Chemical

Engineering 4, 199-277.

92

Soliman, H. M., 1986. The mist-annular transition during condensation and its influence

on the heat transfer mechanism, International Journal of Multiphase flow 12, 277-

288.

Taitel, Y., Dukler, A. E., 1976. A model for predicting flow regime horizontal and near

horizontal gas-liquid flow, AIChE Journal 22, 47-55.

Yang, C. Y., Webb, R. L., 1996. Condensation of R12 in small hydraulic diameter

extruded aluminum tubes with and without micro-fins, International Journal of Heat

and Mass Transfer 39, 791-800.

93

CHAPTER 5

Comparison of two-phase frictional pressure drop

Accurate prediction of frictional pressure drop is an essential requirement for the design

of any heat exchanger. In the last sixty seven years, several theoretical models and

empirical correlation have been proposed for the pressure drop prediction. However, in

the following chapter the experimental data of frictional pressure drop for multiport

minichannels and microfins tube were compared against existing models available in

the open literature. The frictional pressure drop of rectangular multiport minichannels is

compared with fifteen models including homogeneous model developed for both

conventional and minichannels. Whereas, the frictional pressure drop of microfins tube

are compared with seven correlations developed for conventional channel smooth and

microfins tube. The 288 experimental data points are used for the comparison. The

criterion used for the evaluation is the mean absolute error (MAE) and average error

(AE), listed in Table 5.2, which are calculated using the following equations:

,pred ,exp

1 ,exp

1 NF F

i F

P PMAE

N P

(5.1)

,pred ,exp

1 ,exp

1 NF F

i F

P PAE

N P

(5.2)

Actually, the average error is used to identify either a correlation has an under-

prediction or over-prediction.

5.1 Models review and comparison of frictional pressure drop in

multiport minichannels with the well-known correlations

94

5.1.1 Models review

First of all, a bibliography research has been made to find the well-known and

renowned correlations available to calculate frictional pressure drop in rectangular

multiport minichannels.

5.1.1.1 Correlations developed for convensional channel

The following correlations were developed specially for frictional pressure drop

prediction in convensional tube.

5.1.1.1.1 Homogeneous model (Thome, 2006)

The homogeneous model assumes that the two phases to flow as a single phase

possessing mean fluid properties. It is charecterized by suitably averaged properties of

the liquid and vapor phase. The homogeneous model is also known as the friction factor

or fog flow model (Collier and Thome, 1994). By considering the homogeneous model,

the frictional pressure drop can be expressed as a function of the two phase friction

factor, tpf as:

22 tp

F h tp

f GP

z d

(5.3)

The two-phase friction factor can be expressed in terms of the two-phase Reynolds

number by the Blasius equation as follows:

0.25

16for 2000

0.079for 2000

tp

tp

tp

tp

tp

ReRe

f

ReRe

(5.4)

Thome (2006) suggested that the homogeneous model is not suitable for mass flux

less than 2000 kg/m2s and at low reduced pressure.

95

5.1.1.1.2 Lockhart and Martinelli correlation (1949)

The frictional pressure drop is typically predicted using separated flow models. The

Lockhart and Martinelli (1949) was proposed the first separated flow model to predict

the frictional pressure drop for isothermal two-phase flow and after that the separated

flow model has been continuously developed by many researchers. The separated flow

model considers the two-phase are artificially flow separately into two streams, namely

liquid and vapor. In this model, each stream is assumed to travel at a mean velocity.

The Lockhart and Martinelli (1949) method is the original method that predicted the

two-phase frictional pressure drop based on a two-phase multiplier for the liquid-phase

or the vapor-phase, respectively (Thome, 2006).

2l

F l

P P

z z

(5.5)

2v

F v

P P

z z

(5.6)

The liquid-phase and vapor-phase pressure gradiants are obtained from

222 1l

l h l

f G xP

z d

(5.7)

2 22 v

v h v

f G xP

z d

(5.8)

The single-phase friction factors of the liquid-phase, lf and vapor-phase, vf are

calculated as follows with their respective physical properties.

0.25

0.079l

l

fRe

(5.9)

0.25

0.079v

v

fRe

(5.10)

The corresponding two-phase multipliers for liquid and vapor phase are obtained

96

2

2

11 for 4000l l

tt tt

CRe

X X (5.11)

2 21 for 4000v tt tt lCX X Re (5.12)

where ttX is the Martinelli parameter in the turbulent flow regimes defined as

0.5 0.10.91 v l

tt

l v

xX

x

(5.13)

The value of C in Eqs. 5.11 and 5.12 mainly depends on the flow regimes. The

appropriate values of C are listed in Table 5.1.

Table 5.1 Appropriate values of C for Lockhart and Martinelli correlation

Liquid Vapor C

Turbulent Turbulent 20

Laminar Turbulent 12

Turbulent Laminar 10

Laminar Laminar 5

5.1.1.1.3 Friedel Correlation (1979)

The Friedel correlation (1979) is one of the most accurate two-phase frictional

pressure drop correlation. The correlation was obtained based on a two-phase multiplier

using a large database of two-phase frictional pressure drop consisted 25000 data points.

The database consists of air-water, air-oil and R12 as working fluids.

2lo

F lo

P P

z z

(5.14)

22 lo

lo h l

f GP

z d

(5.15)

97

0.2240.7822 2

0.045 0.035

3.24 11 l vo

lo

v lo

x x Hfx x

f Fr We

(5.16)

0.91 0.19 0.722

2, , 1h l v v

h tp tp v l l

G dGFr We H

gd

(5.17)

5.1.1.1.4 The Müller-Steinhagen and Heck correlation (1986)

Müller-Steinhagen and Heck (1986) proposed a two-phase frictional pressure drop

correlation by optimizing an empirical interpolation between all vapor flow and all

liquid flow. The authors checked the reliabilities of the correlation against a databank

containing 9300 data points of frictional pressure drop for various working fluids and

flow conditions. The database covered the diameter range of tube from 4 mm to 392

mm and working fluids of air-water, air-oil, hydrocarbon, R11, R12 and R22.

1/3 3(1 )F vo

P PE x x

z z

(5.18)

2lo vo lo

P P PE x

z z z

(5.19)

5.1.1.1.5 The Wang et al. correlation (1997)

Wang et al. (1997) developed a correlation based on a two-phase multiplier by

considering flow pattern for adiabatic frictional pressure drop of R22, R134a and

R401C. The Wang et al. (1997) correlation as follows:

For 200G kg/m2s

2l

F l

P P

z z

(5.20)

2

2

11l

C

X X (5.21)

2.15 5.1

6 0.128 0.9384.566 10 l llo

v v

vC X Re

v

(5.22)

98

For 200G kg/m2s

2v

F v

P P

z z

(5.23)

2 0.62 2.451 9.4 0.564v X X (5.24)

5.1.1.2 Correlations developed for minichannels

The following models were developed specially for friction pressure drop prediction

in minichannels.

5.1.1.2.1 The Mishima and Hibiki correlation (1996)

The authors proposed the correlation based on two-phase multiplier using the

Lockhart and Martinelli model. They modified the Chisholm’s parameter, C as a

dependable function of tube inner diameter.

2l

F l

P P

z z

(5.25)

2

2

11l

C

X X (5.26)

31921(1 )idC e (5.27)

5.1.1.2.2 The Lee and Lee correlation (2001)

The authors proposed a set of correlations to predict the two-phase frictional

pressure drop through horizontal rectangular minichannels. The correlation is the

Lockhart and Martinelli type. They modified the Chisholm’s parameter, C to take

account of the channel hydraulic diameter and the flow rates of the vapor and liquid.

8 1.317 0.719 0.5576.833 10ll loC Re (5.28)

0.4510.408tt loC Re (5.29)

2 0.7266.185 10lt loC Re (5.30)

99

0.1743.627tl loC Re (5.31)

where l lj

and

2l

l hd

(5.32)

5.1.1.2.3 The Koyama et al. correlation (2003)

Koyama et al (2003) developed a simple correlation based on the Mishima and

Hibiki correlation (1995). The authors modified the two-phase multiplier to takeing an

account of the surface tension effects as follows:

2v

F v

P P

z z

(5.33)

0.17

2 0.6 21 13.17 1 Bolv tt tt

v

e X X

(5.34)

2 ( )h l vd gBo

(5.35)

0.5 0.10.91 v l

tt

l v

xX

x

(5.36)

5.1.1.2.4 The Lee and Mudawar correlation (2005)

Lee and Mudawar (2005) proposed a correlation that incorporates the effects of

surface tension and liquid viscosity in the separated flow model as two-phase multiplier

for liquid-phase and vapor-phase. The authors were developed two separate correlations

for C based on the flow states of the liquid and vapor as follows:

For laminar flow of liquid and laminar flow of vapor

0.047 0.602.16vv lo loC Re We (5.37)

For laminar flow of liquid and turbulent flow of vapor

0.25 0.231.45vv lo loC Re We (5.38)

100

5.1.1.2.5 The Hwang and Kim correlation (2006)

Hwang and Kim (2006) developed the two-phase flow frictional pressure drop

correlation in the form of the Lockhart-Martinelli correlation. The authors included the

effect of the Reynolds number, surface tension and tube diameter in thire proposed

correlation. They developed the correlation based on their experimental data of R134a

in three circular minichannels with inner diameters of 0.244, 0.43 and 0.792 mm at

adiabatic condition. The correlation as follows:

2l

F l

P P

z z

(5.39)

2

2

11l

C

X X (5.40)

0.452 0.32 0.820.227 Rel confC X N (5.41)

2

( )conf

l v

dN

g

(5.42)

5.1.1.2.6 The Sun and Mishima correlation (2009)

The authors proposed a model based on 2092 experimental data points of two-phase

frictional pressure drop which were collected from 18 sources. The working fluid

includes R134a, R22, R410A, R407C, R404A, R123, R236ea, R245fa, R507, CO2,

water and air. The data points covered the hydraulic diameter ranges from 0.506 to 12

mm. Sun and Mishima (2009) modified Chisholm correlation which showed best

performance in the turbulent region.

2l

F l

P P

z z

(5.43)

For 2000 and 2000l vRe Re

2

2

11l

C

X X (5.44)

0.15326 1 1 exp

1000 0.27 0.8l

conf

ReC

N

(5.45)

101

For 2000 and 2000l vRe Re

2

1.19 2

11l

C

X X (5.46)

0.4 0.51

1.79 v

l

Re xC

Re x

(5.47)

5.1.1.2.7 The Zhang et al. correlation (2010)

This correlation was proposed by applying the artificial neural network based on

2201 experimental data points of 18 fluids collected from 13 sources. The databank

covered the hydraulic diameter ranges from 0.07 to 6.25 mm. Zhang et al. (2010)

modified the Mishima and Hibiki correlation and proposed the new Chisholm

parameter C for minichannel using the non-dimensional Laplace constant as follows:

2l

F l

P P

z z

(5.48)

2

2

11l

C

X X (5.49)

21 1 exp( 0.142 / )confC N (5.50)

5.1.1.2.8 The Li and Wu correlation (2010)

The authors presented a general correlation for adiabatic two-phase frictional

pressure drop in minichannels based on the collected database having 769 data points.

They collected those data points from the literature for both multi and single channel

configuration covering 12 fluids for a wide range of operational conditions and channel

hydraulic diameter from 0.148 to 3.25 mm. Li and Wu (2010) modified the Chisholm

parameter of two-phase multipliers by introducing the Bond number and the Reynolds

mumber as follows:

2l

F l

P P

z z

(5.51)

102

2

2

11l

C

X X (5.52)

For 1.5Bo

0.4511.9C Bo (5.53)

For 1.5 11Bo

0.560.5109.4 lC BoRe

(5.54)

where, 2

l v hg dBo

(5.55)

5.1.1.2.9 The Kim and Mudawar correlation (2012)

Kim and Mudawar (2012) proposed a universal approach to predict two-phase

frictional pressure drop in single and multiport minichannels having differents

geometrical configurations. They developed Lockhart and Martinelli type correlation

based on 7115 frictional pressure drop data points collected from 36 sources covering

17 working fluids, hydraulic diameters from 0.0695 to 6.22 mm, mass velicities from

4.0 to 8528 kg/m2s and reduced pressure pressures from 0.0052 to 0.91. The Chisholm

parameter, C of various combinations of Reynolds number, Weber number, Suratman

number and density ratio were developed for each of the four combinations of flow

regimes as follows:

2l

F l

P P

z z

(5.56)

where,

2

2

11l

C

X X (5.57)

/

/l

v

P zX

P z

(5.58)

103

222 1l

l l h

f G xP

z d

(5.59)

2 22 v

v v h

f G xP

z d

(5.60)

1

0.25

0.2

16 for 2000

0.079 for 2000 20000

0.046 for 20000

k k

k k k

k k

Re Re

f Re Re

Re Re

(5.61)

5.1.1.2.10 The Jige et al. correlation (2016)

The authors presented a new condensation frictional pressure drop correlation for

multiport tube. They proposed the correlation based on their measured experimental

data of rectangular multiport minichannels having 0.85 mm hydraulic diameter. In this

correlation, they considered the effect of channel geometry using the two-phase

multiplier and frictional pressure drop for a vapor phase with total flow. The correlation

is as follows:

2vo

F vo

P P

z z

(5.62)

where

22 vo

vo h v

f GP

z d

(5.63)

1.25 0.75

2 1.8 1.8 0.68 0.43(1 ) 0.65 (1 )v lo l vvo

l vo v l

fx x x x

f

(5.64)

The values of the friction factor of vapor phase and liquid phase are obtained by

1

0.2

for 1500

0.046for 1500

h

vh

v

vo

h

vh

v

GdC

Gd

fGd

Gd

(5.65)

104

1

0.2

for 1500

0.046for 1500

h

lh

l

lo

h

lh

l

GdC

Gd

fGd

Gd

(5.66)

The value of channel geometry constant, C1 is determined as follows:

1 16 for circular channelsC

2 3 4 51 24 1 1.355 1.947 1.701 0.956 0.254 for rectangular channelsC

5.1.2 Comparison of experimental frictional pressure drop of minichannels

with existing correlations

The present experimental data of frictional pressure drop were compared against the

existing well-known pressure drop correlations proposed by Homogeneous Model

(Thome, 2006), Lockhart and Martinelli (1949), Friedel (1979), Muller-Steinhagen and

Heck (1986), Mishima and Hibiki (1996), Wang et al. (1997), Lee and Lee (2001),

Koyama et al. (2003), Lee and Mudawar (2005), Hwang and Kim (2006), Sun and

Mishima (2009), Li and Wu (2010), Zhang et al.(2010), Kim and Mudawar (2012) and

Jige et al. (2016), as shown in Figs. 5.1(a)-5.1(l). The existing well-known pressure

drop correlations are already discussed above.

The correlation of Friedel (1979) and Muller-Steinhagen and Heck (1986) for

relatively large diameter circular tubes and Lockhart and Martinelli (1949), Sun and

Mishima (2009), Li and Wu (2010), Zhang et al. (2010) and Kim and Mudawar (2012)

for single and multiport minichannels were proposed based on a wide range of

consolidated databases.

105

Fig. 5.1 Comparison of frictional pressure drop with existing; (a) Homogeneous Model;

(b) Lockhart and Martinelli (1949) correlation; (c) Friedel (1979) correlation; (d)

Muller-Steinhagen and Heck (1986) correlation; (e) Mishina and Hibiki (1996); (f)

Wang et al. (1997); (g) Lee and Lee (2001); (h) Koyama et al. (2003); (i) Lee and

Mudawar (2005); (j) Hwang and Kim correlation; (k) Sun and Mishima (2009); (l) Li

and Wu (2010); (m) Zhang et al. (2010); (n) Kim and Mudawar (2012); and (o) Jige et

al. (2016) correlation.

100

101

102

100

101

102

50 100 150 200

(P

/z)

F, P

red

icte

d [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

G [kg/m2s]Minichannel with fins

50 100 150 200

Homogeneous model

+30%

-30%

Minichannel without finG [kg/m2s]

a)

100 101 102

100

101

102

b)

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

G [kg/m2s] Minichannel without fin

-30%

+30%

50 100 150 200

G [kg/m2s] Minichannel with fins

Lockhart and Martinelli (1949)

50 100 150 200

106

Fig. 5.1- (continued)

100 101 102

100

101

102

(P

/z)

F, P

red

icte

d [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

50 100 150 200

+30%

-30%

Minichannel without finG [kg/m2s]

50 100 150 200

Friedel (1979)c)

100 101 102

100

101

102

(P

/z)

F, P

redi

cted

[kP

a/m

]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

50 100 150 200

+30%

-30%

Minichannel without fin

50 100 150 200

G [kg/m2s]

Muller and Heck (1986)d)

100 101 102

100

101

102

50 100 150 200

50 100 150 200

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

+30%

-30%

Minichannel without finG [kg/m2s]

Mishima and Hibiki (1996)e)

107

Fig. 5.1- (continued)

100 101 102

100

101

102

50 100 150 200

50 100 150 200

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

G [kg/m2s]Minichannel with fins +30%

-30%

Minichannel without finG [kg/m2s]

Wang et al. (1997)f)

100

101

102

100

101

102

(P

/z)

F, P

redic

ted

[kP

a/m

]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

50 100 150 200

+30%

-30%

Minichannel without finG [kg/m2s]

50 100 150 200

Lee and Lee (2001)g)

100 101 102

100

101

102

(P

/z)

F,

Pre

dic

ted

[k

Pa/

m]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

50 100 150 200

+30%

-30%

Minichannel without finG [kg/m

2s]

50 100 150 200

Koyama et al. (2003)h)

108

Fig. 5.1- (continued)

100

101

102

100

101

102

(P

/z)

F, P

redic

ted

[kP

a/m

]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

50 100 150 200

Lee and Mudawar (2005)i)

+30%

-30%

50 100 150 200

G [kg/m2s] Minichannel without fin

100

101

102

100

101

102

(P

/z)

F, P

redic

ted

[kP

a/m

]

(P/z)F, Experimental [kPa/m]

Minichannel with finsG [kg/m2s]

50 100 150 200

+30%

-30%

Minichannel without finG [kg/m2s]

50 100 150 200

Hwang and Kim (2006)j)

100 101 102

100

101

102

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

G [kg/m2s] Minichannel without fin

50 100 150 200

Sun and Mishima (2009)

-30%

+30% Minichannel with finsG [kg/m2s]

50 100 150 200

k)

109

Fig. 5.1- (continued)

100 101 102

100

101

102

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

Li and Wu (2010)

50 100 150 200

G [kg/m2s] Minichannel without fin

-30%

+30%Minichannel with finsG [kg/m2s]

50 100 150 200

l)

100 101 102

100

101

102

Minichannel with fins

(P

/z)

F, P

redic

ted [

kP

a/m

]

G [kg/m2s] 50 100 150 200

+30%

-30%

Minichannel without finG [kg/m2s]

50 100 150 200

Zhang et al. (2010)

(P/z)F, Experimental [kPa/m]

m)

100 101 102

100

101

102

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

50 100 150 200

G [kg/m2s]Minichannel with fins +30%

-30%

Minichannel without finG [kg/m2s]

50 100 150 200

Kim and Mudawar (2012)n)

110

Fig. 5.1- (continued)

Lee and Lee (2001) and Hwang and Kim (2006) proposed the correlations based on

the experimental data of adiabatic flow in small diameter rectangular and circular tubes.

Whereas, the Koyama et al. (2003) and Jige et al. (2016) were developed the frictional

pressure drop correlations based on the experimental data on condensation flow in the

rectangular multiport minichannels.

The homogeneous model is enough accurate to predict experimental data of

rectangular multiport minichannels with fins as shown in Fig. 5.1 (a) with mean

absolute error 15.6%. But this model under-predicted the experimental data of

minichannels without fin, especially at mass velocity 50 and 200 kg/m2s.

The Lockhart and Martinelli (1949) correlation showed good prediction for

experimental data of minichannels with fins with 29.9% mean absolute error but

underestimated the experimental data of minichannels without fin with mean absolute

error 15.5%. The predicted results are presented in Fig. 5.1 (b).

The correlation of Friedel (1979) is compared with the present data and the results

are depicted in Fig. 5.1 (c). The correlation was consistently under-predicted the

experimental results of both minichannels with mean absolute error of 43%. The

discrepancy between experimental and predicted data may be due to the important

difference between the diameter considered by the authors and that studied in the

present study.

100 101 102

100

101

102

G [kg/m2s]

Minichannel without fin

50 100 150 200

50 100 150 200

(P

/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

Jige et al. (2016)

Minichannel with fins +30%

-30%

G [kg/m2s]

o)

111

As seen in Fig. 5.1 (d), the correlation of Muller-Steinhagen and Heck (1986)

correlation consistently over-estimated the present experimental data for both

minichannels with 40.2% mean absolute error. This correlation may be over-estimate

the experimental data because the diameter range considered by the authors. The

authors was developed the correlation for tubes diameter range from 4 -392 mm.

The comparison of present experimental results with the correlation of Mishima and

Hibiki (1996) is depicted in Fig. 5.1 (e). As seen in the figure, the correlation is highly

under-predicted present experimental results. The mean absolute error of prediction is

41.2%. The under-prediction may be because of Chisholm parameter that was

developed by the authors only based on the tube diameter for air-water flows.

As seen in Fig. 5.1 (f), the Wang et al. (1997) correlation is completely failed to

predict the present experimental data for both minichannels with fins and without fin.

The mean absolute error of the prediction is 56.1% as listed in Table 5.2. The

correlation is unable to predict the present experimental results because it was

developed for conventional circular tube.

The results of the comparison with the Lee and Lee (2001) correlation are presented

in Fig. 5.1 (g). The correlation had shown slightly under-prediction at low mass velocity

and slightly over-estimation at high mass velocity with mean absolute error 28.9 %.

Fig. 5.1 (h) presented comparison of present experimental results with the correlation of

Koyama et al. (2003). The correlation predicts the results very well with little under-

estimation at low mass velocity but mean absolute error of the comparison is within

15.4%.

The correlation of Lee and Mudawar (2005) is not able to predict present

experimental data correctly. The results of comparison are depicted in Fig. 5.1 (i). As

seen in figure, the model clearly overestimated and underestimated over the whole

range studied.

As seen in Fig. 5.1 (j) and (k), the Hwang and Kim (2006) and Sun and Mishima

(2009) correlations are predicted the experimental data accurately for high mass

velocity. Both the correlations, can predict experimental data of low mass velocity with

slightly under-estimation. The error of prediction increases with decreasing mass

velocity as show in Fig. 5.1 (j) and (k). The mean absolute errors of the comparison are

25.5% and 22.4%, respectively.

112

The Li and Wu (2010) correlation predicted the experimental data fairly good but

slightly under-predicts few data, especially at low mass flux for both minichannels with

mean absolute error 17.3%. The comparison is depicted in Fig. 5.1 (l).

The comparison of present experimental results with the correlation of Zhang et al.

(2010) is overlaid in Fig. 5.1 (m). The correlation showed good prediction at high mass

velocity for both minichannels but failed to predict the experimental data for low mass

velocity. This correlation predicted the experimental data with mean absolute error of

29.8%.

The correlation of Kim and Mudawar (2012) was compared with the present

experimental data of both minichannels. The predicted results are presented in Fig. 5.1

(n). The correlation greatly under-estimates present experimental data with mean

absolute error of 42.4%.

As seen in Fig. 5.1 (o), the correlation of Jige et al. (2016) accurate enough to

predict the present experimental but showed under-estimation at low frictional pressure

drop values which correspond to low mass velocity and high vapor quality. This

correlation can predict frictional pressure drop data with mean absolute error of 20.6%.

The compared results of each correlation are listed in Table 5.2 in the form of average

error (AE) and mean absolute error (MAE).

113

Table 5.2 Deviations of frictional pressure drop for multiport minichannels

Correlation

Minichannel

with fins

Minichannel

without fin All data

AE

(%)

MAE

(%)

AE

(%)

MAE

(%)

AE

(%)

MAE

(%)

Homogenous model 4.8 15.6 -20.8 22.1 -8.0 18.8

Lockhart and Martinelli (1949) -29.0 29.9 -11.2 15.5 -20.1 22.7

Friedel (1979) -36.6 41.8 -20.1 44.3 -28.3 43.0

Muller-Steinhagen and Heck (1986) 23.4 28.2 51.5 52.3 37.4 40.2

Mishima and Hibiki (1996) -22.4 32.3 -50.1 50.1 -36.2 41.2

Wang et al. (1997) -51.8 51.5 -60.5 60.5 -56.1 56.1

Lee and Lee (2001) 2.0 24.6 25.5 33.1 13.7 28.9

Koyama et al.(2003) -17.6 19.3 -7.9 11.6 -12.7 15.4

Lee and Mudawar (2005) -15.5 26.8 -31.2 35.1 -23.3 30.9

Hwang and Kim (2006) -35.0 35.0 -12.6 15.9 -23.8 25.5

Sun and Mishima (2009) -22.3 24.2 -19.2 20.6 -20.7 22.4

Zhang et al. (2010) 3.0 25.7 -33.9 33.9 -15.1 29.8

Li and Wu (2010) -18.5 21.1 -12.4 13.5 -15.4 17.3

Kim and Mudawar (2012) -50.4 51.7 -33.2 33.2 -41.8 42.4

Jige et al. (2016) 5.8 21.3 0.2 20.0 3.0 20.6

5.2 Models review and comparison of frictional pressure drop in

microfins tube with the well-known correlations

5.2.1 Models review

The experimental frictional pressure drop datapoints were compared with the

following models briefly reviewed here.

5.2.1.1 The Miyara et al. correlation (2000)

114

The authors proposed a frictional pressure drop correlation in the same manner of

Haraguchi et al. (1994) for herringbone microfin tube. The correlation was correlated

with the two-phase multiplier and Lockhart-Martinelli parameter as follows:

2v

F v

P P

z z

(5.67)

where

2 2

0.2

0.092

/v v i i v

P G x

z d Gxd

(5.68)

0.35

1/21.2 1.65 tt

v

i v l v

GX

gd

(5.69)

0.5 0.10.91 v l

tt

l v

xX

x

(5.70)

5.2.1.2 The Koyama and Yonemoto correlation (2006)

Koyama and Yonemoto (2006) developed the Lockhart-Martinelli type frictional

pressure drop correlation based on their experimenta data of 6.51 mm inner diameter

microfin tube, Miyara’s (2003) data and Haraguchi’s data. The correlation is as follows:

2v

F v

P P

z z

(5.71)

where,

2 22 v

v i v

f G xP

z d

(5.72)

0.2

0.046

/v

i v

fGd x

(5.73)

0.05 0.51 1.2v ttFr X (5.74)

i v l v

GFr

gd

(5.75)

115

5.2.1.3 The Müller-Steinhagen and Heck correlation (1986)

The authors developed a two-phase frictional pressure drop correlation for smooth

tube by optimizing an empirical interpolation between all vapor flow and all liquid flow.

The Müller-Steinhagen and Heck (1986) checked the reliabilities of the correlation

against a database containing 9300 data points of frictional pressure drop for various

working fluids and flow conditions. The database covered the diameter range of tube

from 4 mm to 392 mm and working fluids of air-water, air-oil, hydrocarbon, R11, R12

and R22. This correlation is given by:

1/3 3(1 )F vo

P PE x x

z z

(5.76)

where

2lo vo lo

P P PE x

z z z

(5.77)

22 vo

vo h v

f GP

z d

(5.78)

22 lo

lo h l

f GP

z d

(5.79)

5.2.1.4 The Goto et al. correlation (2001)

The correlation was developed by these authors utilizes a single-phase multiplier

based on vapor phase. They used their measured experimental frictional pressure drop

data for condensation and evaporation of R410A and R22 inside a convensional spiral

groove tube having 7.30 mm mean inned diameter. The following equation was

suggested by the authors:

2v

F v

P P

z z

(5.80)

where

22 ( )v

v h v

f GxP

z d

(5.81)

116

0.791 1.64v ttX (5.82)

4 0.53

0.20

2 0.21

3

1.47 10 for 2000 2600

0.046 for 2600 6500

1.23 10 for 6500 12700

9.20 10 for 12700<

v v

v vv

v v

v

Re Re

Re Ref

Re Re

Re

(5.83)

5.2.1.5 The Haraguchi et al. correlation (1994)

They proposed an empirical correlation for the local frictional pressure drop during

condensation of R22, R134a and R123 inside a horizontal smooth tube having 8.4 mm

inner diameter. The proposed the Lockhart-Martinelli type correlation as follows:

2v

F v

P P

z z

(5.84)

Where

2 2

0.2

0.092

/v v i i v

P G x

z d Gxd

(5.85)

0.75

0.35

0.51 0.5

( )v tt

h v l v

GX

gd

(5.86)

5.2.1.6 The Olivier et al. correlation (2004)

Olivier et al. (2004) proposed this correlation by modifiying the Carnavos

correlation (1980) to predict the frictional pressure drop of R22, R407C and R134a in

convensional smooth tube, helical and herringbone microfin tube during condensation.

The frictiona pressure drop was obtained by the product of the liquid-phase pressure

drop and two-phase multiplier as follows:

2l

F lo

P P

z z

(5.87)

where

117

2

1.655

7.2421.376l

ttX (5.88)

22 [ (1 )]lo

lo h l

f G xP

z d

(5.89)

0.5

0.750.2

20.046 1 sec

cosh

lo l

e h

d entf Re

d d

(5.90)

5.2.1.7 The Kedzierski and Goncalves correlation (1999)

The authors suggested using the Pierre’s semi-empirical equation to predict the

pressure drop. They proposed a correlation of friction factor prediction by regression

analysis based on the experimental data of microfin tube. This correlation was

developed as a dependable fuction of fin height, tube diameter and Reynolds number as

follows:

0 2

0i

i

F h

f v vPv v G

z d

(5.91)

Where

0.2111/ 4.16 532 /3 32.275 10 9.33 10 exp0.003

re d

r

ef Re

d

(5.92)

lvxh

g z

(5.93)

5.2.2 Comparison of experimental frictional pressure drop of microfins

tube

In order to validate the experimental procedure, the experimental frictional pressure

drops of the microfin tube were compared with the seven most widely used pressure

drop correlations proposed by Muller and Heck (1986), Haraguchi et al. (1993),

Kedzierski and Goncalves (1999), Miyara et al. (2000), Goto et al. (2001), Olivier et al.

(2004) and Koyama and Yonemoto (2006). The Muller and Heck (1986) correlation

118

was developed for smooth tube and other six correlations were developed for microfin

tube. The compared frictional pressure drop results of adiabatic pressure drop in the

microfin tube are shown in Table 5.3.

At mass flux 50 kg/m2s, the correlation of Haraguchi et al. (1993) and Miyara et al.

(2000) showed fairly good prediction and other correlations were greatly under

predicted. The Goto et al. (2001) correlation can predict the present experimental

friction pressure drop for mass flux 100 and 200 kg/m2s within an acceptable limit of

error as presented in Fig. 5.2 (b) and (c). Except the Kedzierski and Goncalves (1999)

correlation, other correlations can predict the present pressure drop of mass flux 100

kg/m2s within a certain limit of error. At mass flux 200 kg/m2s, all of the correlation,

except Goto et al. (2001) correlation, completely failed to predict the present data. The

average errors and mean absolute errors are listed in table 5.3.

Table 5.3 Average errors and Mean absolute errors of frictional pressure drop of

microfin tube

Correlation AE

(%)

MAE

(%)

Miyara et. al (2000) -27.2 24.7

Koyama and Yonemoto (2006) -20.0 30.4

Muller and Heck (1986) -39.7 44.1

Goto et al. (2001) -24.4 26.1

Haraguchi et al. (1993) -15.8 20.7

Olivier et al. (2004) -39.0 32.4

Kedzierski and Goncalves (1999) -35.2 30.8

119

Fig. 5.2 Frictional pressure drop of the microfin tube compared with existing

correlations: (a) G = 50 kg/m2s; (b) G = 100 kg/m2s; (c) G = 200 kg/m2s.

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30a) Experimental Miyara et al. (2000) Koyama and Yonemoto (2006) Muller and Heck (1986) Goto et al. (2001) Haraguchi et al. (1993) Olivier et al. (2004) Kedzierski and Goncalves (1999)

(P

/z)

F [

kP

a/m

]

Vapor quality

R134a, Tsat

= 20 0CMicrofin tube

G = 50 kg/m2s

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30b) Experimental Miyara et al. (2000) Koyama and Yonemoto (2006) Muller and Heck (1986) Goto et al. (2001) Haraguchi et al. (1993) Olivier et al. (2004) Kedzierski and Goncalves (1999)

(P

/z)

F [

kP

a/m

]

Vapor quality

G = 100 kg/m2sR134a, T

sat = 20 0C

Microfin tube

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30 Experimental Miyara et al. (2000) Koyama and Yonemoto (2006) Muller and Heck (1986) Goto et al. (2001) Haraguchi et al. (1993) Olivier et al. (2004) Kedzierski and Goncalves (1999)

(P

/z)

F [

kP

a/m

]

Vapor quality

G = 200 kg/m2sR134a, T

sat = 20 0C

Microfin tubec)

120

5.3 Conclusions

For the comparison of experimental frictional pressure drop data, several of the most

widely used existing frictional pressure drop models are reviewed in this chapter. Some

convensional tubes models and other specially developed for minichchannels are

considered for the comparison of frictional pressure drop in rectangular multiport

minichannels. Five existing correlations those were developed for convensional

microfin tubes are also considered for the prediction of frictional pressure drop in

microfin tube. The experimental frictional pressure gradient was compared with those

reviewed correlations. Some correlations over-predicted, some are under-predicted and

few correlations captured the correct frictional pressure drop within the limits of

experimental error. All of the existing correlations were failed to capture the present

experimental frictional pressure drop with a high degree of accuracy.

121

References

Carnavos, T. C., 1980. Heat transfer performance of internally finned tubes in turbulent

flow, Heat transfer Engineering 1, 32-37.

Collier, J. G., Thome, J. R., 1994. Convective Boiling and Condensation, Third edition,

Oxford University Press, Oxford, UK.

Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and

vertical two-phase pipe flow, in: European Two-phase Group Meeting, Ispra, Italy,

Paper E2.

Goto, M., Inoue, N., Ishiwatari, N., 2001. Condensation and evaporation heat transfer of

R410A inside internally grooved horizontal tubes. International Journal of

Refrigeration 24, 628-638.

Haraguchi H, Koyama S, Fujii T. Condensation of refrigerants HCFC22, HFC134a and

HCFC123 in a horizontal smooth tube (1st report, proposal of empirical expressions

for the local frictional pressure drop). Trans JSME (B) 1994;60(574):239–44 [in

Japanese].

Hwang, Y.W. and Kim, M.S., 2006. The pressure drop in microtubes and the

correlation development, International Journal of Heat and Mass Transfer 49, 1804–

1812.

Jige, D., Inoue, N., Koyama, S., 2016. Condensation of refrigerants in a multiport tube

with rectangular minichannels, International Journal of Refrigeration 67, 202-213.

Kedzierski, M.A., Goncalves, J.M., 1999. Horizontal convective condensation of

alternative refrigerants within a microfin tube, Journal of Enhanced Heat Transfer 6,

161-178.

122

Kim, S.M. and Mudawar, I., 2012. Universal approach to predicting two-phase

frictional pressure drop for adiabatic and condensing mini/micro-channel flows.

International Journal of Heat and Mass Transfer 55, 3246–3261.

Koyama, S., Kuwahara, K., Nakashita, K., 2003. Condensation of refrigerant in a

multiport channel, In: Proceedings of First International Microchannel and

Minichannels, ASME, 193-205.

Koyama, S., Yonemoto, R., 2006. Experimental study on condensation of pure

refrigerants in horizontal microfin tube-proposal of correlations for heat transfer

coefficient and frictional pressure drop, International Refrigeration and Air

Conditioning Conference, Purdue, R133.

Lee, H.J. and Lee, S.Y., 2001. Pressure drop correlations for two-phase flow within

horizontal rectangular channels with small heights, International Journal of

Multiphase Flow 27, 783–796.

Lee, J. and Mudawar, I., 2005. Two-phase flow in high-heat-flux micro-channel heat

sink for refrigeration cooling applications: Part I––pressure drop characteristics,

International Journal of Heat and Mass Transfer 48, 928–940.

Li, W. and Wu, Z., 2010. A general correlation for adiabatic two-phase pressure drop in

micro/mini-channels, International Journal of Heat and Mass Transfer 53, 2732–

2739.

Lockhart, R.W. and Martinelli, R.C., 1949. Proposed correlation of data for isothermal

two-phase, two-component flow in pipes, Chemical Engineering Progress 45, 39–

48.

Mishima, K., Hibiki, T., 1995. Effect of inner diameter on some characteristics of air-

water two-phase flows in capillary tubes, Transection of JSME (B) 61(589), 99–106

[in Japanese].

123

Mishima, M. and Hibiki, T., 1996. Some characteristics of air–water two-phase flow in

small diameter vertical tubes, Internal Journal of Multiphase Flow 22, 703–712.

Miyara, A., Otsubo, Y., Ohtsuka, S., Mizuta, Y., 2003. Effects of fin shape on

condensation in herringbone microfin tubes, International Journal of Refrigeration

26, 417-424.

Miyara, A., Nonaka, K., Taniguchi, M., 2000. Condensation heat transfer and flow

pattern inside a herringbone-type micro-type tube, International Journal of

Refrigeration 23, 141-152.

Müller-Steinhagen, H. and Heck, K., 1986. A simple frictional pressure drop correlation

for two-phase flow in pipes, Chemical Engineering Progress 20, 297–308.

Olivier, J. A., Liebenberg, L., Kedzierski, M. A., Meyer, J. P., 2004. Pressure drop

during condensation inside horizontal smooth, helical microfin, and herringbone

microfin tubes, Journal of Heat Transfer 126, 687-696.

Sun, L. and Mishima, K., 2009. Evaluation analysis of prediction methods for two-

phase flow pressure drop in mini-channels, Internal Journal of Multiphase Flow 35,

47–54.

Thome, J.R., 2006. Engineering Data Book III, Chapter 13th.

Wang, C. C., Chiang, C. S., Lu, D. C., 1997. Visual observation of two-phase flow

pattern of R22, R134a and R407C in a 6.5 mm smooth tube, Experimental Thermal

and Fluid Science 15, 395-405.

Zhang, W., Hibiki, T., Mishima, K., 2010. Correlations of two-phase frictional pressure

drop and void fraction in mini-channel, International Journal of Heat and Mass

Transfer 53, 453–465.

124

CHAPTER 6

Comparison of Condensation Heat transfer

For practical application such as design of compact and high performance heat

exchanger, accurate prediction of heat transfer coefficient is a crucial obligation. There

are several theoretical models and empirical correlations have been proposed by many

researchers in the last decade. However, due to the complexity of two-phase flow, it is

quite difficult to predict the experimental data accurately over a broad range of

operating conditions and parameter. In the following chapter, the experimental heat

transfer coefficients data were compared with ten widely used and renowned

correlations, which suggested for conventional tube, minichannels and microchannels.

The 213 experimental data points are used for the comparison. The criterion used for

the evaluation is the mean absolute error (MAE) and average error (AE), listed in Table

6.1, which are calculated using the following equations:

,pred ,exp

1 ,exp

1 Ntp tp

i tp

h hMAE

N h

(6.1)

,pred ,exp

1 ,exp

1 Ntp tp

i tp

h hAE

N h

(6.2)

Actually, the average error is used to identify either a correlation has an under-

prediction or over-prediction.

6.1 Models review and comparison of heat transfer coefficients in

minichannels with existing correlations

125

6.1.1 Models review

First of all, a bibliography research has been made to find the most widely used and

renowned correlations available to calculate condensation heat transfer coefficient in

rectangular multiport minichannels.

6.1.1.1 Correlations developed for conventional tube

The following correlations were developed specially for the condensation heat

transfer coefficient prediction in conventional tube.

6.1.1.1.1 The Shah correlation (1979)

The author presented a simple dimensionless model to predict the film condensation

heat transfer coefficient based on 474 experimental data points collected from the

literature. The data points includes water, R11, R12, R22, R113, ethanol, benzene,

methanol, toluene and trichloroethylene as working fluids during condensation in

horizontal, vertical and inclined tubes with ranges of diameters from 7 to 40 mm.

0.040.760.8

0.38

3.8 11tp l

r

x xh h x

p

(6.3)

0.8 0.40.023 ll l l

kh Re Pr

d

(6.4)

6.1.1.1.2 The Haraguchi et al. correlation (1994)

Haraguchi et al. (1994) developed an empirical correlation for the heat transfer

coefficient based on the turbulent liquid film theory and Nusselt’s theory. They used

their measured condensation heat transfer coefficients of R134a, R22 and R123 in an 8

mm diameter horizontal conventional smooth circular tube. This model includes the

effects vapor shear stress and gravity forces.

ltp

h

Nukh

d (6.5)

126

2 2FC GCNu Nu Nu (6.6)

where

0.77 0.80.0152 1 0.6 vFC l l

tt

Nu Re PrX

(6.7)

0.25

0.725 l lGC

Ga PrNu H

Ph

(6.8)

0.75

0.351 0.5( )

v tt

h v l v

GX

gd

(6.9)

0.1( ) 10 1 8.9 1H (6.10)

1

( / ) 0.4(1 ) /11 0.4 0.6

1 0.4(1 ) /v l v

l

x xx

x x x

(6.11)

6.1.1.1.3 The Dobson and Chato correlation (1998)

The authors proposed a two-phase heat transfer coefficient correlation in terms of

refrigerants properties and Martinelli parameter. They used experimental heat transfer

coefficient of the refrigerants R134a, R12, R22 and near-azeotropic blends of

R32/R125 in 50/50 percent and 60/40 percent compositions during condensation in

horizontal smooth circular tubes with diameters ranging from 3.14 to 7.04 mm. Donson

and Chato (1998) suggested the following model for annular flow regimes:

0.8 0.4

0.89

2.220.023 1 l

tp l l

tt h

kh Re Pr

X d

(6.12)

6.1.1.2 Correlations developed for minichannels and microchannels

The following models were developed specially for the condensation heat transfer

coefficient prediction in minichannels and microchannels.

6.1.1.2.1 The Wang et al. correlation (2002)

127

Two correlations, each representing the physics of the specific phase distribution

was proposed by these authors. The first one is for the annular flow based on the

frictional multiplier and dimensionless boundary layer temperature. The second one is

for stratified flow. For stratified flow, the film wise condensation and single-phase

forced convective heat transfer models were combined with straightforward void

fraction weighting. They developed this model based on their experimental local

convective heat transfer and flow regime measurements of R134a during condensation

inside a horizontal rectangular multiport minichannels of 1.46 mm hydraulic diameter.

Heat transfer correlation for annular flow regime:

1.6650.6792 0.2208

2

1.376 80.0274 tt

annular l l

tt

XNu Pr Re x

X

(6.13)

Heat transfer correlation for stratified flow regime:

1stratified film convectionNu Nu Nu (6.14)

Where

12/3

11 v

l

x

x

(6.15)

1/43

0.555 lv l l v hfilm

l l sat wall

gh dNu

k T T

(6.16)

0.8 0.40.023convection l lNu Re Pr (6.17)

Heat transfer correlation for combined flow regime:

ltp

h

Nukh

d (6.18)

1annular annular annular stratifiedNu f Nu f Nu (6.19)

Where

128

in transition

annular

in out

x xf

x x

(6.20)

6.1.1.2.2 The Koyama et al. correlation (2003)

The authors proposed this model using the experimental data of R134a during

condensation in two different multiport extruded minichannels having 8 channels with

1.11 mm hydraulic diameter and 19 channels with 0.8 mm hydraulic diameter. They

modified the Haraguchi et al. (1994) correlation by replacing two-phase multiplier with

Mishima and Hibiki (1995) as follows:

ltp

h

Nukh

d (6.21)

2 2FC GCNu Nu Nu (6.4)

where

0.77 0.80.0152 1 0.6 vFC l l

tt

Nu Re PrX

(6.22)

1/4

0.725 l lGC

Ga PrNu H

Ph

(6.23)

0.3192 21 21 1 hdv tt tte X X (6.24)

0.1 4( ) 10 1 1 1.7 10 1loH Re

(6.25)

1

( / ) 0.4(1 ) /11 0.4 0.6

1 0.4(1 ) /v l v

l

x xx

x x x

(6.26)

3 2

2h l

l

gdGa

(6.27)

l sat wi

lv

Cp T TPh

h

(6.28)

1,h h

l lo

l l

G x d GdRe Re

(6.29)

129

6.1.1.2.3 The Park et al. correlation (2011)

The Perk et al. modified the Koyama et al. correlation based on their experimental

data of R1234ze(E), R134a and R236fa during condensation in multiport minichannel

of 1.45 mm hydraulic diameter.

The modified equations are:

1.37 0.70.0055 vFC l l

tt

Nu Pr ReX

(6.30)

0.25

0.850.746(1 ) ( )Bo l l lGC

Ga PrNu e H

Ph

(6.31)

They followed Koyama et al. (2003) for other equations.

6.1.1.2.4 The Bohdal et al. correlation (2012)

The authors proposed this correlation with the use of mathematical statistics

principles. They selected the model’s parameter by quasi-Newton and simplex

methods. To develop the correlation, the authors used their own experimental data of

R134a, R407C and R404A during condensation in 9 circular minichannels with internal

diameters of 0.31, 0.45, 0.64, 0.98, 1.40, 1.60, 1.94, 2.30 and 3.30 mm, respectively.

0.266

0.258 0.495 0.28825.0841

ltp l l r

h

kxh Re Pr p

- x d

(6.32)

6.1.1.2.5 The Kim and Mudawar correlation (2013)

Kim and Mudawar (2013) proposed a universal approach to predict the heat transfer

coefficient during condensation in minichannels based on a consolidated databank

consisting of 4045 data points. They collected those data points from 28 sources. The

databank consists of data points of 17 different working fluids and single and multiport

minichannels covering hydraulic diameters from 0.424 to 6.22 mm.

130

0.69 0.34 0.2

0.50.69 0.34 2 7 0.38 1.39 2 0.2

0.048 / for > 7

(0.048 / ) (3.2 10 ) for 7

l l v tt tttp h

l l l v tt l vo tt

Re Pr X We Xh d

k Re Pr X Re Su We X

(6.33)

where,

0.64 0.3 0.039 0.4

0.79 0.157 2 0.084 0.3 0.039 0.4

2.45 / [ (1 1.09 ) ] for 1250

0.85 [( / ) ( / )] / [ (1 1.09 ) ] for 1250v vo tt l

v tt v l l v vo tt l

Re Su X ReWe

Re X Su X Re

--

-------------------------------------------------------------------------------------------------- (6.34)

2 21v CX X (6.35)

2 2(1 ) /l l v vX f v x f v x (6.36)

1

0.25

1

16 for 2000

0.079 for 2000 20000

0.046 for 20000

p p

p p p

p p

Re Re

f Re Re

Re Re

(6.37)

where the subscript p denotes l or v for liquid-phase and vapor-phase, respectively.

0.03 0.1 0.35

4 0.17 0.5 0.14

0.59 0.19 0.36

5 0.44 0.5 0.48

0.39 ( / ) if 2000and 2000

8.7 10 ( / ) if 2000and 2000

0.0015 ( / ) if 2000and 2000

3.5 10 ( / ) if

lo vo l v l v

lo vo l v l v

lo vo l v l v

lo vo l v

Re Su Re Re

Re Su Re ReC

Re Su Re Re

Re Su Re

2000and 2000l vRe

(6.38)

2

1, , ,hv h h h

vo lo l v

v l l v

Gd xd Gd Gd xSu Re Re Re

(6.39)

6.1.1.2.6 The Shah correlation (2016)

The author presented a correlation for heat transfer during condensation in

horizontal minichannels based on a database contained 1017 data points collected from

31 sources. The collected database covered 13 working fluids and single and multiport

minichannel with different shape of hydraulic diameter ranges from 0.10 to 2.8 mm.

Shah (2016) suggested the following equations:

131

0.62

1.249 1

if 100and 0.98( 0.263)

if 20and 0.95(1.254 2.27 )

if neither of the above conditions is satisfied

l vo v

tp N vo v

l N

h We J Z

h h We J Z

h h

(6.40)

where,

0.3685 0.2363 2.144

0.817 0.11 1.128 1l l vl lo l

v v l

h h x Pr

(6.41)

0.8 0.40.023 llo lo l

h

kh Re Pr

d

(6.42)

31/3

21.32 l l v l

N lo

l

g kh Re

(6.43)

2h

vo

v

G dWe

(6.44)

v

h v l v

xGJ

gd

(6.45)

0.8

0.4 1

1rZ p

x

(6.46)

6.1.1.2.7 The Jige et al. correlation (2016)

This model was developed for predicting heat transfer coefficient during

condensation in rectangular multiport minichannels considering the flow patterns,

effects of vapor shear stress and surface tension. The authors used their own

experimental condensation heat transfer data of refrigerants R134a, R32, R1234ze(E),

and R410A in a horizontal rectangular multiport minichannels with hydraulic diameter

of 0.85 mm. The considered the annular flow regimes for high vapor quality region and

intermittent flow regimes for low vapor quality region.

The heat transfer for intermittent flow was obtained by using the correlation of

forced single-phase liquid flow as follows:

132

2/3

2 3

10002

for 2000

1 12.7 12

8.23(1 1.891 2.220 0.894 ) for 2000

ll l

l

L ll

l

fRe Pr

ReNu f

Pr

Re

(6.47)

The heat transfer for annular flow regimes was obtained by combining the effects of

the vapor shear stress and surface tension using the same function form of the

Haraguchi et al. (1994) correlation, which considered the effects of the vapor shear

stress and gravity.

3 3 1/3, ,( )A A F A SNu Nu Nu (6.48)

where,

0.4 0.3 0.5, 0.6 0.06

1vo l

A F l l l vo

v

Nu Re Pr Re fx

(6.49)

0.25

, 0.51 l h lvA S

l l R wi

d hNu

k T T

(6.50)

Two-phase multiplier:

1.25 0.75

1.8 1.431.8 0.681 0.65 1l lo l vvo

v vo v l

fx x x x

f

(6.51)

Friction factor for vapor-phase:

0.2

if 1500

0.046if 1500

h

vh

v

vo

h

vh

v

Gd

Gd

fGd

Gd

(6.52)

133

Friction factor for liquid-phase:

0.2

if 1500

0.046if 1500

h

lh

l

lo

h

lh

l

Gd

Gd

fGd

Gd

(6.53)

where is the channel geometry constant which was obtained by

2 3 4

16 for Circular channels

24(1 1.355 1.947 1.701 0.956 ) for Rectangular channels

(6.54)

Finally, the heat transfer during condensation in rectangular multiport minichannels was

calculated by:

1tp h

A L

l

h dNu Nu Nu

k (6.55)

Where the void fraction is calculated by the homogeneous model as:

1 v

l

x

x x

(6.56)

6.1.2 Comparison with existing correlations

In the present experimental study, the average heat transfer coefficients in multiport

minichannels were compared against correlations discussed above.

The Shah (1979) correlation greatly over-predicted the experimental data for both

minichannels except few data for x > 0.7 as stated in Fig. 6.1 (a). This is because the

correlation was developed for conventional circular tube. Although, the Haraguchi et al.

(1994) correlation was developed for conventional circular tube but the correlation

predicted present data relatively good for mass fluxes 200 and 150 kg/m2s as shown in

Fig. 6.1 (b) and it failed to captured the data for low mass fluxes. Fig. 6.1 (c) and Fig.

6.1 (d), respectively shown that the correlation of Dobson and Chato (1998) and Wang

134

et al. (2002) consistently underestimated the present experimental data for both test

section. The Dobson and Chato (1998) and Wang et al. (2002) correlations were

proposed for conventional tube and minichannel.

The correlation of Koyama et al. (2003) and Park et al. (2011) predicted better but

slightly under predicted the present experimental data for both test section as depicts in

Fig. 6.1 (e) and 6.1 (f), respectively. They developed their correlations by modifying

Haraguchi et al. (1994) correlation for rectangular minichannels. As stated in Fig. 6.1

(g), the Bohdal et al. (2012) correlation failed to captured the present experimental data

for mass fluxes 50-150 kg/m2s but predicted well data for mass flus 200 kg/m2s.

According to Fig. 6.1 (h)-6.1 (j), the correlation of Kim and Mudawar (2013), Jige

et al. (2016) and Shah (2016) provides comparatively good prediction but the accuracy

slightly deteriorated for few data. A detailed comparison of average error and mean

absolute error are summarized in Table 6.1.

Table 6.1 Deviations of Heat transfer coefficients during condensation

Correlation

Minichannel

with fins

Minichannel

without fin All data

AE

(%)

MAE

(%)

AE

(%)

MAE

(%)

AE

(%)

MAE

(%)

Shah (1979) 63.0 63.1 81.8 81.9 72.4 72.5

Haraguchi et al.

(1994) 11.28 27.56 16.9 30.9 14.0 29.3

Dobson and Chato

(1998) -27.8 30.1 -23.8 26.2 -25.8 28.1

Wang et al. (2002) -44.0 42.8 -51.2 48.5 -47.6 45.6

Koyama et al. (2003) -34.35 34.1 -24.7 27.7 -29.5 30.9

Park et al. (2011) -42.5 40.5 -35.7 35.8 -39.1 38.1

Bohdal et al. (2012) 30.2 40.4 28.0 36.2 29.1 38.3

Kim and Mudawar

(2013) 3.2 30.9 5.0 25.7 4.1 28.3

Shah (2016) -23.1 28.2 2.8 26.0 -10.1 27.1

Jige et al. (2016) -6.23 30.1 -19.0 28.2 -12.6 29.1

135

Fig. 6.1 Comparison of experimental average heat transfer coefficient with existing; a)

Shah (1979); b) Haraguchi et al. (1994); c) Dobson and Chato (1998); d) Wang et al.

(2002); e) Koyama et al. (2003); f) Park et al. (2011); g) Bohdal et al. (2012); h) Kim

and Mudawar (2013); i) Jige et al. (2016); and j) Shah (2016) correlation.

100 101 102

100

101

102

with fins without fin

G [kg/m2s]

Shah (1979)

50 100 150 200

50 100 150 200

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

Multiport minichannels

-30%+30%

a)

100 101 102

100

101

102b)

50 100 150 200

50 100 150 200

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

G [kg/m2s]Multiport minichannels with fins without fin

Haraguchi et al. (1994)

-30%+30%

136

Fig. 6.1 – (continued)

100 101 102

100

101

102c)

50 100 150 200

50 100150 200

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

G [kg/m2s]Multiport minichannels with fins without fin

Dobson and Chato (1998)

-30%+30%

100

101

102

100

101

102

d)

-30%+30%

50 100 150 200

50 100 150 200

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

Wang et al. (2002)

G [kg/m2s]Multiport minichannels with fins without fin

100

101

102

100

101

102

e)

50 100 150 200

50 100 150 200

Pre

d.

hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

G [kg/m2s]Multiport minichannels with fins without fin

Koyama et al. (2003)

-30%+30%

137

Fig. 6.1 – (continued)

100 101 102

100

101

102f)

50 100 150 200

50 100 150 200

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2K

]

Expt. heat transfer coefficient [kW/m2K]

Park et al. (2011)

G [kg/m2s]Multiport minichannels with fins without fin

-30%+30%

100

101

102

100

101

102

50 100 150 200

50 100 150 200

50 100 150 200P

red

. h

eat

tran

sfer

co

effi

cien

t [k

W/m

2 K]

Expt. heat transfer coefficient [kW/m2K]

Bohdal et al. (2012)

Multiport minichannels G [kg/m2s]

with fins without fin

-30%+30%

g)

100

101

102

100

101

102

50 100 150 200

50 100 150 200P

red. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

Kim and Mudawar (2013)

Multiport minichannels G [kg/m2s]

with fins without fin

-30%+30%

h)

138

Fig. 6.1- (continued)

100

101

102

100

101

102

50 100 150 200

50 100 150 200

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

G [kg/m2s]Multiport minichannels with fins without fin

Jige et al. (2016)

-30%+30%

i)

100

101

102

100

101

102

50 100 150 200

50 100 150 200

Pre

d. h

eat

tran

sfer

coe

ffic

ient

[kW

/m2K

]

Expt. heat transfer coefficient [kW/m2K]

Shah (2016)

Multiport minichannels G [kg/m2s]

with fins without fin

-30%+30%

j)

139

6.2 Comparison of condensation heat transfer coefficients in microfin

tube with existing correlations

The present experimental condensation heat transfer coefficient data on the microfin

tube were compared with five widely used available correlations of Koyama and

Yonemoto, 2006; Kedzierski and Goncalves, 1999; Carnavos, 1980; Cavallini et al.,

1999; and Goto et al, 2003, respectively that were particularly developed for predicting

heat transfer coefficient in microfin tube. The existing condensation heat transfer

correlations are listed in Table 6.2. The compared errors and results of the correlations

are stated in Table 6.3 and Fig. 6.2, respectively.

Table 6.2 Condensation heat transfer correlations for microfin tubes

Author(s) Correlation Remarks

Carnavos

(1980)

0.1 0.5

30.8 0.40.023 sec

h

l

af nl l

nf a

hdNu

k

A ANu Re Pr

A A

dh = 3.91-22.7

mm, air, water,

ethylene glycol-

water, Horizontal

Cavallini et al.

(1999)

tp t

l

h dNu

k

0.260.8 0.34 20.05 eq l W vNu Re Pr Rx Bo Fr

Where

0.5

4 1 l

v

eq

t l

G x x

Red

l Pll

l

CPr

k

2vo

v

r

uFr

gd

8

l rW

eg dBo

n

di = 6.14-15.87

mm, Pure

refrigerant,

azeotropic and

zeotropic

refrigerant

mixtures, 7

working fluids,

Horizontal

microfin tubes,

300 data points

140

Table 6.2 – (continued)

2 1 sin

2

cos 12

cos

r

x

en

d

R

Kedzierski

and

Goncalves

(1999)

ltp

h

Nukh

d

0.235 0.308 2.7084.94 xl l vNu Re Pr S

Where

2 21.16 0.887

10log

x x

cr cr

p p

p p

v lv

v vS

v

1v lv xv x v

d = 3.14-7.04 mm,

R134a, R124, R32,

R410A (R32/R125,

50/50% mass),

Horizontal

microfins tube

Goto et al.

(2003)

ltp

h

Nukh

d

2 2( FC NCNu Nu Nu

Where

0.25

0.25

( )0.725 l

NC

A l

Ga PrHNu

Ph

0.1 0.1

0.70.7431

v lFC v l

tt v

xNu f Re

X x

4 0.53

0.20

3 0.21

3

1.47 10 for 2000 2600

0.046 for 2600 6500

1.23 10 for 6500 12700

9.20 10 for 12700<

v v

v vv

v v

v

Re Re

Re Ref

Re Re

Re

0.791.0 1.64v ttX

dm = 7.18, 7.22,

7.27, 7.30 mm,

R410A, R22,

horizontal,

microfins tubes

141

Table 6.2 – (continued)

Koyama and

Yonemoto

(2006)

ltp

i

Nukh

d

2 2( FC NCNu Nu Nu

0.1

0.5 0.52.121

lFC v v l l

v

xNu f Re Pr

x

0.25

0.5 0.1

( )1.98 l

NC

A l

Ga PrHNu

Bo Ph

Where

l v iP t gdBo

2 3

2l i

l

g dGa

Pl sat wil

lv

C T TPh

h

0.05 0.51 1.2v ttFr X

v l v i

GFr

gd

0.5

0.750.2

0.046

sec

v

af

v

nf

fA

ReA

0.110 1 8.9 1H

di = 6.25-8.37 mm,

11 microfins tubes.

R22, R134a, R123,

142

Table 6.3 Average errors and Mean absolute errors of condensation heat transfer coefficient in microfin tube.

Correlation AE

(%)

MAE

(%)

Carnavos (1980) -85.3 80.8

Cavallini et al. (1999) -26.5 26.9

Kedzierski and Goncalves (1999) -31.8 32.1

Goto et al. (2003) -36.0 34.5

Koyama and Yonemoto (2006) -18.8 24.8

The Carnavos (1980) correlation greatly underestimated the present data as depict in

Fig. 6.2 (a) with mean average error 80%. The correlations of Koyama and Yonemoto

(2006) and Goto et al. (2003) can predict accurately data only for mass flux 100 kg/m2s

and 50 kg/m2s as stated in Fig. 6.2 (e) and (d), respectively. But their correlations

slightly under predicted others data as overlaid in Fig. 6.2 (e) and (d). The Kedzierski

and Goncalves (1999) correlation also slightly underestimated the present experimental

data with mean average error 32.1% as shown in Fig. 6.2 (c).

The Cavallini et al. (1999) correlation showed the best prediction with mean

absolute errors of 26.9%. Cavallini et al. (1999) model can predict present experimental

data accurately for mass flux 100 kg/m2s and 200 kg/m2s but failed to predict data for

mass flux 50 kg/m2s as depicted in Fig. 6.2 (b). Poor prediction by existing correlations

may be attributed due to the lack of low mass flux data in the consideration database

during correlation development.

143

Fig. 6.2 Condensation heat transfer coefficient of microfin tube compared with existing

correlations; (a) Carnavos (1980); (b) Cavallini et al. (1999); (c) Kedzierski and

Goncalves (1999); (d) Goto et al. (2003); (e) Koyama and Yonemoto (2006).

100 101 102

100

101

102

a)

Pre

d. H

eat

tran

sfer

coef

fici

ent

[kW

/m2 K

]

Expt. Heat transfer coefficient [kW/m2K]

G [kg/m2s 50 100 200

+30%

-30%

Carnavos (1980)

100 101 102

100

101

102

b)

Pre

d. H

eat

tran

sfer

coef

fici

ent

[kW

/m2 K

]

Expt. Heat transfer coefficient [kW/m2K]

Cavallini et al. (1999)

50 100 200

G [kg/m2s +30%

-30%

100 101 102

100

101

102

c)

Pre

d. H

eat

tran

sfer

coef

fici

ent

[kW

/m2K

]

Expt. Heat transfer coefficient [kW/m2K]

50 100 200

G [kg/m2s

Kedzierski and Goncalves (1999)

+30%

-30%

100

101

102

100

101

102

d)

Pre

d. H

eat

tran

sfer

coef

fici

ent

[kW

/m2 K

]

Expt. Heat transfer coefficient [kW/m2K]

G [kg/m2s 50 100 200

+30%

-30%

Goto et al. (2003)

100 101 102

100

101

102

50 100 200

Pre

d. H

eat

tran

sfer

coef

fici

ent

[kW

/m2 K

]

Expt. Heat transfer coefficient [kW/m2K]

G [kg/m2s

Koyama and Yonemoto (2006)

+30%

-30%

e)

144

6.3 Conclusions

Ten most widely used well-known correlations that were developed for the

conventional tube and minichannels and five correlations for microfin tubes are

reviewed and compared with experimental heat transfer coefficients, respectively.

Among them, some correlations over-predicted, some are under-predicted and few

correlations captured the correct heat transfer coefficient within the limits of

experimental error. All of the existing correlations were failed to capture the present

experimental heat transfer coefficient within a high degree of accuracy.

145

References

Bohdal, T., Charun, H., Sikora, M., 2012. Heat transfer during condensation of

refrigerants in tubular minichannels, Archives of Thermodynamics 33 (2), 3-22.

Carnavos, T. C., 1980. Heat transfer performance of internally finned tubes in turbulent

flow, Heat transfer Engineering 1, 32-37.

Cavallini, A., Del Col, D., Doretti, L., Longo, G.A., Rossetto, L., 1999. A new

computational procedure for heat transfer and pressure drop during refrigerant

condensation inside enhanced tubes, Journal of Enhanced Heat Transfer 6, 441–456.

Dobson, M. K., Chato, J. C., 1998. Condensation in smooth horizontal tubes, Journal of

Heat Transfer 120, 192-213.

Goto, M., Inoue, N., Yonemoto, R., 2003. Condensation heat transfer of R410A inside

internally grooved horizontal tubes, International Journal of Refrigeration 26, 410–

416.

Haraguchi, H., Koyama, S., Fujii, T., 1994. Condensation of refrigerants HCFC 22,

HFC 134a and HCFC 123 in a horizontal smooth tube (2nd report, proposals of

empirical expressions for the local heat transfer coefficient) Trans. JSME 60, 245-

252 (in Japanese).

Kedzierski, M.A., Goncalves, J.M., 1999. Horizontal convective condensation of

alternative refrigerants within a microfin tube, Journal of Enhanced Heat Transfer 6,

161-178.

Kim, S. M., Mudawar, I., 2013. Universal approach to predicting heat transfer

coefficient for condensing mini/micro-channel flow, International Journal of Heat

and Mass Transfer 56, 238-250.

146

Koyama, S., Kuwahara, K., Nakashita, K., Yamamoto, K., 2003. An experimental study

on condensation of refrigerant R134a in a multi-port extruded tube, International

Journal of Refrigeration 26, 425-432.

Koyama, S., Yonemoto, R., 2006. Experimental study on condensation of pure

refrigerants in horizontal microfin tube-proposal of correlations for heat transfer

coefficient and frictional pressure drop, International Refrigeration and Air

Conditioning Conference, Purdue, R133.

Mishima, K., Hibiki, T., 1995. Effect of inner diameter on some characteristics of air-

water two-phase flows in capillary tubes, Transection of JSME (B) 61(589), 99–106

[in Japanese].

Park, J. E., Farahani, F. V., Consolini, L., Thome, J. R., 2011. Experimental study on

condensation heat transfer in vertical minichannels for new refrigerant R1234ze(E)

versus R134a and R236fa, Experimental Thermal and Fluid Science 35, 442-454.

Shah, M. M., 1979. A general correlation for heat transfer during film condensation

inside tube, International Journal of Heat and Mass Transfer 22, 547–556.

Shah, M. M., 2016. A correlation for heat transfer during condensation in horizontal

mini/micro channels, International Journal of Refrigeration 64, 187–202.

Wang, W. W. W., Radcliff, T. D., Christensen, R. N., 2002. A condensation heat

transfer correlation for millimeter-scale tubing with flow regime transition,

Experimental Thermal and Fluid Science 26, 473-485.

147

CHAPTER 7

Development of New Correlations

For the design of compact and high performance heat exchanger, it is essential to

develop an accurate model for the prediction of frictional pressure drop and heat

transfer coefficients in rectangular multiport minichannels. All of the existing pressure

drop and heat transfer correlations discussed in Chapter 5 and Chapter 6, somehow

shown a slightly over or underestimation of the experimental results. In this chapter the

experimental data are correlated to develop an accurate model for the prediction of two-

phase frictional pressure drop and condensation heat transfer coefficient.

7.1 Development of new pressure drop correlation for minichannels

Adiabatic and diabetic two-phase pressure drop can be predicted based on either the

homogeneous model or the separated flow model. The simplest approach to the

prediction of two-phase flows is homogeneous model, which assume that the phases are

thoroughly mixed and can be treated as a single-phase flow. However, the homogenous

method is not suitable for mass flux less than 2000 kg/m2s and at low reduced pressure

(Thome, 2006). Whereas, in separated flow model the phase is considered to be flowing

separately. The frictional pressure drop in two-phase flows is typically predicted using

separated flow models. The first separated flow model was proposed for isothermal

two-phase flow pressure drop by Lockhart and Martinelli (1949) and then followed by

many others. Chisholm (1967) developed a theoretical basis for the Lockhart-Martinelli

correlation for two-phase flow. Later on, Friedel (1979), Muller-Steinhagen and Heck

(1986), Jung and Radermacher (1989), Wang et al. (1997) proposed a simple model for

two-phase frictional pressure drop prediction in macro-channels. Among them, Friedel

(1979) and Muller-Steinhagen and Heck (1986) correlations were developed using a

large data bank containing 25,000 and 9300 measurements of frictional pressure drop

148

for a variety of fluids and conditions respectively. Those models are widely used in

conventional theory to predict frictional pressure drop in macro-channels, many recent

authors (Choi et al., 2008; Xu et al., 2012) have reported the ability of these correlations

to estimate with reasonable accuracy the frictional pressure drop in mini-channels

(Lopez-Belchi et al., 2014).

In the last few years, many studies have developed pressure drop correlation on

the basis of the Lockhart and Martinelli (1949), Chisholm (1967), Friedel (1979)

correlations. Choi et al. (2008), Pamitran et al.(2010) and Kim and Mudawar (2013)

proposed a new correlation on the basis of the Lockhart-Martinelli method. Mishima

and Hibiki (1996), Yu et al. (2002), Kawahara et al. (2002), Sun and Mishima (2009)

and Zhang et al. (2010) developed pressure drop correlations on the basis of the

Chisholm (1967) correlation. The Chang et al. (2000), Chen et al. (2001), and Zhang

and Webb (2001) developed pressure drop correlation on the basis of the Friedel (1979)

correlation. Revellin and Thome (2007) developed a new homogenous two-phase

frictional pressure drop model with a limited range of application. Most of the

researchers developed their correlation for high mass velocity and minichannels without

fins.

However, in the present analysis separated flow model will be used for the

development of new correlation to predict frictional pressure drop in minichannels. In

the separated flow model empirical correlations two-phase multiplier and single-

phase flow pressure drop are needed.

The two-phase multipliers are defined as:

2 Fl

l

P

z

P

z

(7.1)

2 Fv

v

P

z

P

z

(7.2)

2 Flo

lo

P

z

P

z

(7.3)

149

2 Fvo

vo

P

z

P

z

(7.4)

Hence, the frictional pressure drop can be calculated from two-phase multiplier as

follows:

2

22 1l

l

F l h

f G xP

z d

(7.5)

2

2 2 vv

F v h

f GxP

z d

(7.6)

22 2 lolo

F lo h

f GP

z d

(7.7)

22 2 vovo

F vo h

f GP

z d

(7.8)

Any of the above mentioned separated flow model can be used to predict the two-

phase frictional pressure drop inside minichannels if two-phase multiplier is available.

The present analysis considers the Eq. (7.5) for two-phase frictional pressure drop in

rectangular multiport minichannels. It is necessary to develop a model for determining

the two-phase multiplier. Therefore, a new approach is developed to improve the

accuracy of frictional pressure drop prediction of two-phase flow in rectangular

multiport minichannels with and without fins. The present correlation is developed for

multiport tube with and without fin considering the effect of channel geometry (Jige et

al., 2016), reduced pressure (Kim and Mudawar, 2012; Zhang et al., 2010), Reynolds

number and Weber number based on the Lockhart and Martinelli (1949) model. Lee

and Mudawar (2005) assumed that the added complexity of two-phase flow in a

minichannel is the net result of interactions between inertia, viscous force, and surface

tension. These interactions can be added by Reynolds and Weber number. The reduced

pressure is introduced to consider the variation of fluid properties with saturation

temperature (Kim and Mudawar, 2012).

150

The new two-phase frictional pressure drop correlation for adiabatic flow in rectangular

multiport minichannel with and without fins is as follows:

The two-phase frictional pressure drop was calculated by

2l

F l

P P

Z Z

(7.9)

The two-phase frictional pressure drop multiplier

2

2

11l

tt tt

C

X X (7.10)

The Martinelli parameter, Xtt, can be obtained as:

0.5 0.10.91 v l

tt

l l vv

xP PX

Z Z x

(7.11)

where the Chisholm’s parameter, C is adjusted by least square method with a new

dimensionless parameter based on the present experimental frictional pressure drop data

as

0.31

0.35 0.25 0.09 0.09(1 ) tp tp

c

PC x x Re We

P

(7.12)

Where λ is the constant value depends on the channel geometry (Jige et al., 2016). The

value of λ for circular channel is 16 and for rectangular channels, it’s calculated using

the equation of the Shah and London (1978).

3 52 424 1 1.355 1.947 1.701 0.956 0.254 (7.13)

2h

tp

tp

G dWe

(7.14)

151

htp

tp

GdRe

(7.15)

The two-phase mixture viscosity and density were calculated by the equations of

MacAdames et al. (1942).

1 1

tp v l

x x

(7.16)

1 1

tp v l

x x

(7.17)

However, the newly proposed correlation can predict the present experimental data

well on the whole with an average deviation of -2.3% and mean deviation of 17.4%, as

shown in Fig. 7.1. The proposed correlation can predict 99% of the data point within the

±30% error limits.

Fig. 7.1 Comparison of present experimental frictional pressure drop data with

proposed correlation

100

101

102

100

101

102

(P/z)

F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

G [kg/m2s] 50 100 150 200

Proposed correlation

Minichannel without fin

-30%

+30%Minichannel with finsG [kg/m2s]

50 100 150 200

152

Moreover, the new prediction method has also been validated with the available

data collected from open literature listed in Table 7.1. Figure 7.2 shows a comparison

between the present correlation and frictional pressure drop data of single-channel tube

and multiport tubes (Jige et al., 2016; Revellin and Thome, 2007; Hwang and Kim,

2006; Zhang and Weeb, 2001). The comparison has been done with data of seven

working fluids covering circular and rectangular tube of diameter from 0.244 to 3.25

mm. The proposed correlation will be applicable for mass flux from 50 to 2000 kg/m2s,

vapor quality from 0.03 to 0.98 and reduced pressure from 0.10 to 0.80, respectively.

The newly develop correlation showing good agreement with the present experimental

data and some researcher’s data in the single and multiport tubes with rectangular

minichannels with and without fins and circular channel.

Fig. 7.2 Validation of proposed frictional pressure drop correlation with available

experimental data collected from the open literatures.

100 101 102 103 104

100

101

102

103

104

Present study Jige et al. (2016) Revellin and Thome (2007) Hwang and Kim (2006) Zhang and Wedd (2001)

(P/z)F, P

redic

ted [

kP

a/m

]

(P/z)F, Experimental [kPa/m]

+30%

-30%

153

Table 7.1 Two-phase frictional pressure drop data for proposed correlation validation

Author (s) Channel

geometry* dh

[mm] Fluid (s)

Mass flux [kg/m2s]

Test mode

No. of data point

Jige et al. (2016)

R Multi, H

0.85

R134a, R410A

R1234ze(E) R32,

100-500 Con. 198

Revellin and Thome (2007)

C Single, H

0.509 0.709

R134a, R245fa

1200-2000 A 160

Hwang and Kim (2006)

C Single, H

0.244 0.43 0.792

R134a 140-950 A 80

Zhang and Webb (2001)

C Single/ R Multi,

H

2.13 3.25

R134a, R22, R404A

400-1000 A 65

* C: circular, R: rectangular, H: horizontal; Con.: Condensation; A: Adiabatic

7.2 Development of new heat transfer correlation for minichannels

For practical application such as design of heat exchangers, the experimental data

essential to correlate empirically to determine the heat transfer coefficient. Due to the

variety in operating conditions and complex characteristics of two-phase flow, all the

existing correlations discussed in previous chapter somehow shown a slightly over or

underestimation of the present experimental heat transfer coefficient of condensing

flow. From the present experimental data, the authors discovered that the heat transfer

coefficients were strongly dependent on mass flux, vapor quality, saturation

temperature, and channel geometry. Most of the experimental heat transfer coefficient

data points were laps in the annular flow. Therefore, a new annular flow condensation

heat transfer correlation was developed using the same functional form as the Kim and

Mudawar (2013) to improve the accuracy of the heat transfer coefficient prediction of

two-phase flow in horizontal rectangular multiport minichannels with and without fins.

The reduced pressure and vapor quality were introduced in the present correlation to

consider the variation of fluid properties with saturation temperature. Lee and Mudawar

(2005) assumed that the added complexity of two-phase flow in a minichannel is the net

result of interactions between inertia, viscous force, and surface tension. These

interactions were added by Reynolds and Prandtl number.

154

The following two-phase heat transfer coefficient correlation for condensing flow in

horizontal rectangular multiport minichannel with and without fins is obtained by fitting

the values of exponents:

0.1 0.09

0.11 0.45

1v l

tp l l

cr tt h

kp xh Re Pr

p x X d

(7.18)

where, the two-phase pressure drop multiplier of vapor flow is obtained by

2 21v tt ttCX X (7.19)

The Lockhart- Martinelli parameter, Xtt and Chisholm’s parameter, C is obtained by

following Eq. 7.3-7.4.

However, the newly proposed correlation can predict the present experimental data

well under all operating conditions with an average error of -6.9% and mean average

error 17.4%, as shown in Fig. 7.3. The proposed correlation can predict 99% of the data

point within the ±30% error limits.

Fig. 7.3 Comparison of experimental average heat transfer coefficient with proposed

correlations

100 101 102

100

101

102

50 100 150 200

50 100 150 200

Pre

d. h

eat

tran

sfer

co

effi

cien

t [k

W/m

2 K]

Expt. heat transfer coefficient [kW/m2K]

Proposed correlation

Multiport minichannels G [kg/m2s]

with fins without fin

-30%+30%

155

Furthermore, the newly developed correlation for heat transfer coefficient of

condensing flow has also been validated with the available data listed in Table 6. Those

data was collected from the open literature. In the present study, total 750 condensation

heat transfer data points for minichannels were amassed from seven sources (Agarwal

et al., 2010; Yang and Webb, 1996; Jige et al., 2016; Derby et al., 2012; Webb, 1999;

Kim et al., 2003; Belchi et al., 2015). Figure 7.4 depicts a comparison between the

present correlation and available experimental data. The comparison has been done with

data of seven working fluids covering circular, rectangular, square, triangular and semi-

circular multiport minichannels with and without fins of diameter from 0.424 to 2.637

mm. The proposed correlation has been validated with data for mass flux range of 50

kg/m2s to 8000 kg/m2s, vapor quality range of 0 to 1 and reduced pressure range of

0.10 to 0.80, respectively. The newly proposed correlation showed good agreement

with the present experimental data and some previous condensing flow data of seven

different refrigerants in multiport minichannels with and without fins as presented in

Fig. 7.4.

Fig. 7.4 Validation of proposed condensation heat transfer coefficient correlation with

available experimental data collected from the open literature.

100 101 102

100

101

102

Present studyAgarwal et al. (2010)Jige et al. (2016)Kim et al. (2003)Belchi et al. (2015)Darby et al. (2012)Webb (1999)Yang and Webb (1996)

Pre

d. hea

t tr

ansf

er c

oef

fici

ent

[kW

/m2 K

]

Expt. heat transfer coefficient [kW/m2K]

-30%+30%

156

Table 7.2 Condensation heat transfer coefficient data for the proposed correlation

validation

Author (s) Channel

geometry*

dh

[mm] Fluid (s)

Mass flux

[kg/m2s]

No. of

data

points

Agarwal et al.

(2010)

R Multiport,

WF, H

0.424-

0.839 R134a 300-750 153

Yang and Webb

(1996)

R, Multiport,

WF/F, H

2.637,

1.564 R12 400-1400 35

Jige et al.

(2016)

R Multiport,

WF, H 0.85

R134a,

R1234ze(E)

R32,

100-400 235

Derby et al.

(2012)

S, T, SC,

Multiport,

WF, H

1.0 R134a 75-450 60

Webb

(1999)

R, Multiport,

WF, H 1.33 R134a 255-327 15

Kim et al.

(2003)

R Multiport,

WF/F, H

1.41,

1.56 R22, R410A 200-600 45

Belchi et al.

(2015)

R Multiport,

WF, H 1.16 R32, R410A 100-8000 160

* C: circular, R: rectangular, WF: without fin, F: with fins, S: square, T: triangular, SC:

semi-circular, H: horizontal

157

7.3 Conclusions

For the prediction of frictional pressure drop and condensation heat transfer

coefficient, two new correlations have been proposed in order to predict the

experimental results accurately. The newly proposed frictional pressure drop correlation

predicted the present experimental data well under all operating conditions with an

average error of -2.3% and mean absolute error of 17.4%. The proposed heat transfer

coefficient correlation also showed good prediction under all operation conditions with

an average error of -6.9% and mean absolute error of 17.4%. The proposed correlations

can predict 99% of the present experimental results within the ±30% error limits. The

newly proposed correlations also showed good agreement with some previous frictional

pressure drop and condensing heat transfer coefficients data of different refrigerants in

single and multiport minichannels.

158

References

Agarwal, A., Bandhauer, T. M., Garimella, S., 2010. Measurement and modeling of

condensation heat transfer in non-circular microchannels, International Journal of

Refrigeration 33, 1169-1179.

Belchi, A. L., Gomez, F. I., Cascales, J. R. G., Garcia, F. V., 2015. Heat transfer

coefficient during condensation inside a minichannel multiport tube with R32 and

R410A as working fluids, Science and Technology for the Built Environment 21,

535-544.

Chang, Y.J., Chiang, S.K., Chung, T.W., Wang, C.C., 2000. Two phase frictional

characteristics of R-410A and air–water in a 5 mm smooth tube. ASHRAE

Transactions DA-00-11-3, 792–797.

Chen, I.Y., Yang, K.S., Chang, Y.J., Wang, C.C., 2001. Two-phase pressure drop of

air– water and R-410A in small horizontal tubes, International Journal of

Multiphase Flow 27, 1293–1299.

Chisholm, D., 1967. A theoretical basis for the Lockhart–Martinelli correlation for two-

phase flow, International Journal of Heat and Mass Transfer 10, 1767–1778.

Choi, K.I., Pamitran, A.S., Oh, C.Y., Oh, J.T., 2008. Two-phase pressure drop of R-

410A in horizontal smooth minichannels, International Journal of Refrigeration 31,

119-129.

Derby, M., Lee, H. J., Peles, Y., Jensen, M. K., 2012. Condensation heat transfer in

square, triangular, and semi-circular mini-channels, International Journal of Heat

and Mass Transfer 55, 187-197

Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and

vertical two-phase pipe flow, in: European Two-phase Group Meeting, Ispra, Italy,

Paper E2.

159

Hwang, Y.W., Kim, M.S., 2006. The pressure drop in microtubes and the correlation

development, International Journal of Heat and Mass Transfer 49, 1804–1812.

Jung, D.S., Radermacher, R., 1989. Prediction of pressure drop during horizontal

annular flow boiling of pure and mixed refrigerants, International Journal of Heat

and Mass Transfer 32, 2435–2446.

Kawahara, A., Chung, P.M.Y., Kawaji, M., 2002. Investigation of two-phase flow

pattern, void fraction and pressure drop in a minichannel, Internal Journal of

Multiphase Flow 28, 1411–1435.

Kim, N. H., Cho, J. P., Kim, J. O., Youn, B., 2003. Condensation heat transfer of R-22

and R-410A in flat aluminum multi-channel tubes with or without micro-fins,

International Journal of Refrigeration 26, 830-839.

Kim, S. M., Mudawar, I., 2013. Universal approach to predicting heat transfer

coefficient for condensing mini/micro-channel flow, International Journal of Heat

and Mass Transfer 56, 238-250.

Kim, S.M., Mudawar, I., 2012. Universal approach to predicting two-phase frictional

pressure drop for adiabatic and condensing mini/micro-channel flows. International

Journal of Heat and Mass Transfer 55, 3246–3261.

Kim, S.M., Mudawar, I., 2013. Universal approach to predicting two-phase frictional

pressure drop for mini/micro-channel saturated flow boiling. International Journal

of Heat and Mass Transfer 58, 718–734.

Lee, J., Mudawar, I., 2005. Two-phase flow in high-heat-flux micro-channel heat sink

for refrigeration cooling applications: Part I––pressure drop characteristics,

International Journal of Heat and Mass Transfer 48, 928–940.

Lockhart, R.W. and Martinelli, R.C., 1949. Proposed correlation of data for isothermal

two-phase, two-component flow in pipes, Chemical Engineering Progress 45, 39–

48.

160

Lopez-Belchi, A., Illan-Gomez, F., Vera-Garcia, F., Garcia-Cascales, J. R., 2014.

Experimental condensing two-phase frictional pressure drop inside mini-channels.

Comparisons and new model development. International Journal of Heat and Mass

Transfer 75, 581-591.

McAdams, W.H., Woods, W.K., Heroman, L.C., 1942. Vaporization inside horizontal

tubes, II. Benzene–oil mixture, Transaction of the ASME 64, 193–200.

Mishima, M., Hibiki, T., 1996. Some characteristics of air–water two-phase flow in

small diameter vertical tubes, Internal Journal of Multiphase Flow 22, 703–712.

Müller-Steinhagen, H., Heck, K., 1986. A simple frictional pressure drop correlation for

two-phase flow in pipes, Chemical Engineering Progress 20, 297–308.

Pamitran, A.S., Choi, K.I., Oh, J.T., Hrnjak, P., 2010. Characteristics of two-phase flow

pattern transitions and pressure drop of five refrigerants in horizontal circular small

tubes, International Journal of Refrigeration 33, 578-588.

Revellin, R., Thome, J.R., 2007. Adiabatic two-phase frictional pressure drops in

microchannels, Experimental Thermal Fluid and Science 31, 673–685.

Shah, R.K., London, A.L., 1978. Laminar flow forced convection in ducts. In:

Advances Heat Transfer, Academic Press, New York. (Chapter 3).

Sun, L., Mishima, K., 2009. Evaluation analysis of prediction methods for two-phase

flow pressure drop in mini-channels, Internal Journal of Multiphase Flow 35, 47–

54.

Thome, J.R., 2006. Engineering Data Book III, Chapter 13th.

Wang, C.C., Chiang, C.S., Lu, D.C., 1997. Visual observation of two-phase flow

pattern of R-22, R-134a, and R-407C in a 6.5-mm smooth tube, Experimental

Thermal and Fluid Science 15, 395–405.

161

Webb, R. L., 1999. Prediction of condensation and evaporation in micro-fin and micro-

channel tubes, Heat transfer Enhancement of Heat Exchangers, 529-550.

Xu, Y., Fang, X., Su, X., Zhou, Z., Chen, W., 2012. Evaluation of frictional pressure

drop correlations for two-phase flow in pipes, Nuclear Engineering and Design 253,

86–97.

Yang, C. Y., Webb, R. L., 1996. Condensation of R12 in small hydraulic diameter

extruded aluminum tubes with and without micro-fins, International Journal of Heat

and Mass Transfer 39, 791-800.

Yu, W., France, D.M., Wambsganss, M.W., Hull, J.R., 2002. Two-phase pressure drop,

boiling heat transfer, and critical heat flux to water in a small-diameter horizontal

tube, Internal Journal of Multiphase Flow 28, 927–941.

Zhang, M., Webb, R.L., 2001. Correlation of two-phase friction for refrigerants in

small-diameter tubes, Experimental Thermal Fluid and Science 25, 131–139.

Zhang, W., Hibiki, T., Mishima, K., 2010. Correlations of two-phase frictional pressure

drop and void fraction in mini-channel, International Journal of Heat and Mass

Transfer 53, 453–465.

162

CHAPTER 8

Conclusions and recommendations

8.1 Conclusions

An adiabatic frictional pressure drop and condensation heat transfer characteristics

of R134a flowing inside a rectangular multiport minichannels with fins having 20

channels with a hydraulic diameter of 0.64 mm, rectangular multiport minichannels

without fin having 20 channels with a hydraulic diameter of 0.81 mm and small

diameter microfin tube with an equivalent diameter of 2.68 mm were investigated

experimentally. The effects of mass flux, vapor quality, saturation temperature and

channel geometry of the tube on the frictional pressure drop and condensation heat

transfer were examined and clarified. Based on the experimental study, the main

findings of the present investigation can be summarized as follows:

1. The frictional pressure drop of R134a significantly increases with the mass flux

and vapor quality in both rectangular multiport minichannels and microfin tube.

2. The frictional pressure drop of R134a decreases with saturation temperature.

3. The hydraulic diameter of the minichannel has significant influence on the

frictional pressure gradients which increases with decreasing hydraulic diameter

of the minichannles. The frictional pressure drop of multiport minichannel with

fins was 1.08-1.25 times higher than that of multiport minichannel without fin.

4. The microfin tube has slightly influence on the frictional pressure gradients. The

frictional pressure drop of the microfin tube was higher than those of smooth

tube about 10-15%.

5. The average heat transfer coefficient of R134a during condensation tended to

increases with increasing mass flux and vapor quality in both rectangular

minichannels and microfin tube. The heat transfer coefficient is increases faster

at higher vapor quality (x > 0.5).

163

6. The saturation temperature has significant influence on condensation heat

transfer coefficient which decreases with increasing the saturation temperature.

The reason is the thermal conductivity of liquid film which decreases with

increasing saturation temperature.

7. The heat transfer coefficient of rectangular multiport minichannel with fins is

approximately 10-39% higher than those of rectangular multiport minichannel

without fin for the same operating conditions due to the surface tension force.

8. The higher heat transfer coefficients were obtained in microfin tube about 2-

68% than that of smooth tube at the same operating condition.

9. The experimental frictional pressure drops of rectangular multiport

minichannels were compared with fifteen widely used existing well known

correlations that were developed for the conventional and minichannels. Some

correlations over-predicted, some are under-predicted and few correlations

captured the correct frictional pressure drop within the limits of experimental

error.

10. The frictional pressure drops of microfin tube were compared with seven

existing well-known correlations. Among them, the Goto et al. correlation gives

fairly good prediction with 26.1% mean absolute error.

11. The experimental heat transfer coefficients were compared with ten well-known

correlations that were developed for the conventional tube, minichannels and

microchannel. Among them, some correlations over-predicted, some are under-

predicted and few correlations captured the correct heat transfer coefficient

within the limits of experimental error.

12. A new correlation for the prediction of frictional pressure drop and condensation

heat transfer coefficients in rectangular multiport minichannels were proposed

based on the experimental results. Both correlations agreed well with the present

measured data and available data in the open literature.

164

8.2 Future works

Some recommendations for future works based on the present work are as follows:

1. Further research is still needed before the fundamentals of condensation heat

transfer in minichannels and small diameter microfin tubes are fully understood.

To achieve that goal, it is needed to expand the present experimental database.

2. Better design tools to correctly predict the frictional pressure drop and

condensation heat transfer coefficients in small diameter microfin tubes still

need to be developed.

3. A new database has been obtained for pressure drop and condensation in

minichannels and microfin tube for high pressure refrigerant R134a. It is

therefore recommended that new condensation heat transfer coefficient and

frictional pressure drop measurement experiments be extended to other medium

pressure and low pressure pure and mixture refrigerant.

4. In the same test section, the research work also can be extended to observe

evaporation characteristics with the same refrigerant.