Upload
trinhthu
View
235
Download
2
Embed Size (px)
Citation preview
NUMERICAL ANALYSIS OF A FIN-TUBE PLATE
HEAT EXCHANGER WITH WINGLETS
LAFTA FLAYIH MUHSIN AL-JUHAISHI
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
v
ABSTRACT
In this presented work, numerical analysis of heat transfer and flow characteristic using
longitudinal vortex generators (LVGS) in fin and flat tube heat exchanger has been
presented. Conjugate heat transfer 3D numerical model has been developed and
successfully carried out. Rectangular winglets were set in pairs, with downstream
orientation. The effects of impact angles of (20⁰ , 30⁰, and 40⁰ ) as well as tubes and
winglets were placed in one row lined arrangement and air flow by forward
arrangement and backward arrangement. Reynolds number is ranged from 500 to 5000.
The numerical results showed that in the range of the present study, the variation of
these parameters can result in the increase of heat transfer. The study focuses on the
Influence of the different parameters of VGs on heat transfer and fluid flow
characteristics of one row lined circular-tube banks. The characteristics of average Nu
number and skin friction coefficient are studied numerically by the aid of the
computational fluid dynamics (CFD) commercial code of FLUENT ANSYS 14. The
results showed increasing in the heat transfer and skin friction coefficient with the
increasing of Re number. It has been observed that the overall Nuav number of one
circular tubes increases by 23-31% ,by 23-43% and by 23-47% with angles of (20⁰,
30°, and 40⁰) respectively, in forward arrangement and the overall Nuav number of one
circular tubes increases by 23-42%, by 23-46% and 23-52%with angles of (20⁰, 30°,
and 40⁰) respectively, in backward arrangement, with increasing in the overall average
of skin friction coefficient. Also the results showed that the rectangular winglet pairs
(RWPs) can significantly improve the heat transfer performance of the fin and-tube
heat exchangers with a moderate pressure loss penalty.
vi
ABSTRAK
Dalam ini dibentangkan kerja, analisis berangka pemindahan haba dan mengalir ciri
menggunakan penjana pusaran membujur (LVGS) di sirip dan rata tiub penukar haba
telah dibentangkan. Pemindahan haba konjugat 3D model berangka telah
dibangunkan dan berjaya dilaksanakan. Sayap lawi segi empat tepat telah ditetapkan
secara berpasangan, dengan orientasi hiliran. Kesan sudut kesan (20⁰, 30⁰, 40⁰ dan)
serta tiub dan sayap lawi diletakkan dalam satu baris berbaris susunan dan aliran
udara melalui perkiraan ke hadapan dan ke belakang perkiraan. Nombor Reynolds
adalah di antara 500 hingga 5000. Keputusan berangka menunjukkan bahawa dalam
julat kajian ini, perubahan parameter ini boleh menyebabkan peningkatan
pemindahan haba. Kajian ini memberi tumpuan kepada Pengaruh parameter yang
berbeza VGS pada pemindahan haba dan ciri-ciri aliran cecair daripada satu baris
berbaris bank bulat-tiub. Ciri-ciri purata bilangan dan geseran kulit Nu pekali dikaji
secara berangka dengan bantuan dinamik bendalir pengiraan (CFD) kod komersial
FLUENT ANSYS 14. Keputusan menunjukkan peningkatan dalam pemindahan haba
dan pekali geseran kulit dengan peningkatan jumlah Re. Ia telah diperhatikan bahawa
jumlah keseluruhan Nuav satu tiub bulat meningkat sebanyak 23-31%, oleh 23-43%
dan 23-47% dengan dengan sudut (20⁰, 30 °, dan 40⁰) masing-masing, dalam
susunan ke hadapan dan jumlah Nuav keseluruhan satu tiub bulat meningkat
sebanyak 23-42%, oleh 23-46% dan 23-52% dengan sudut (20⁰, 30 °, dan 40⁰)
masing-masing, dalam susunan ke belakang, dengan peningkatan dalam purata
keseluruhan kulit pekali geseran. Juga keputusan menunjukkan bahawa pasangan
sayap lawi segi empat tepat (RWPs) dengan ketara boleh meningkatkan prestasi
pemindahan haba daripada sirip dan-tiub penukar haba dengan kehilangan tekanan
penalti sederhana.
vii
CONTENTS
TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
CONTENTS vii
LIST OF FIGURE x
LIST OF ABBREVIATION AND SYMBOLS xvi
CHAPTER 1 INTRODUCTION
1.1 Heat Transfer Enhancement 1
1.2 Classification of Enhancement Techniques 3
1.3 Fin-Tube Heat Exchanger with Winglet 4
1.4 Problem statement 7
1.5 Project Objectives 7
1.6 Project Scopes 8
1.7 Research Significance 8
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction 9
2.2 Winglet in Tube-Fin Heat Exchanger 9
2.3 Winglets in Refrigerator Evaporator 12
2.4 Winglet-Type Vortex Generators Insert 14
CHAPTER 3 NUMERICAL METHODOLOGY
3.1 Introduction 28
3.2 Computational fluid dynamics 29
3.3 Problem-Solving with CFD 29
viii
3.4 The CFD Modelling Process 30
3.5.1 Physical Model 32
3.5.2 Governing Equations 33
3.5.3 Boundary Conditions 35
3.6 Finite Volume Method (FVM) 36
3.7 Initial test for a fin-tube plate heat exchanger with winglets 35
3.8 Fluid Flow Computation by SIMPLE Algorithm 36
3.9 Summary 37
CHAPTER 4 RESULTS AND DISCUSSIONS
4.1 Introduction 38
4.2 Calculation of Code Validation 39
4.3. Results and Discussion 40
4.4. Effect of longitudinal vortex generators LVGs 41
4.5. Reynolds number (Re) effect 43
4.6 The angle of winglets α = (20°, 30° and 40°) forward 43
4.7. The effect of Longitudinal Vortex Generators (LVGs) 47
on Skin Friction coefficient (f)
4.8 The angle of winglet α=20⁰ forward arrangement 52
(Local velocity distribution)
4.9 The angle of winglet Forward arrangements 56
(Distribution Temperature)
4.10 The angle of winglet Forward arrangements 59
(Surface Nusselt Number)
4.11 The angle of winglet Forward arrangement 62
(Local Velocity Distribution)
4.12 The angle of winglet Forward arrangements 65
(Distribution Temperature)
4.13 The angle of winglet Forward arrangements 68
(Surface Nusselt Number)
4.14 The angle of winglet forward arrangement 71
(Local velocity distribution)
4.15 The angle of winglet Forward arrangements 74
ix
(Distribution Temperature)
4.16 The angle of winglet Forward arrangements 77
(Surface Nusselt Number)
4.17 The angle of winglet (α=20°, 30° and 40°) 80
in backward arrangement
4.18 The angle of winglet α=20⁰ backward arrangement 84
(Local velocity)
4.18 The angle of winglet Backward arrangements 87
(Distribution Temperature)
4.19 The angle of winglet Backward arrangements 90
(Surface Nusselt Number)
4.20 The angle α= 30⁰ Backward arrangement 93
(Local velocity distribution)
4.21 The angle of winglet Backward arrangements 96
(Distribution Temperature)
4.22 The angle of winglet Backward arrangements 99
(Surface Nusselt Number)
4.23. Influence of the angle of attack 101
4.24 The angle α= Backward arrangement 102
(Local velocity distribution)
4.25 The angle of winglet Backward arrangements 105
(Distribution Temperature)
4.26 The angle of winglet Backward arrangements 108
(Surface Nusselt Number)
4.27 Discussion 113
4.27.1 Influence Longitudinal Vortex Generators of 113
LVGs Parameters on Heat Transfer (Nu)
CHAPTER 5 CONCLUSION AND RECOMMENDATIONS
5.1 Conclusion 114
5.2 Recommendations 116
REFERENCES 117
x
LIST OF FIGURES
NO. TITLE OF FIGURES PAGE
1.1 Fin-tubes heat exchanger 2
1.2 Flat plate fin-tubes for heat exchanger 2
1.3 Different types of flat plate fin-tubes for heat exchanger 5
1.4 Flat plate fin-tubes for heat exchanger without winglets 6
1.5 Flat plate fin-tubes for heat exchanger with vortex generator 7
1.6 Fin-tubes heat exchanger with round and oval tubes 7
3.1 The general modelling process 29
3.2 Shows schematic diagram of core region of a fin-and-tube heat 30
exchanger with RWPs.
3.3 Schematic diagram of a fin-tube heat exchanger with winglets 31
3.3 The computational domain 34
3.4 Figures (3.4, a, b, c, and d) as shown above represent initial test 36
4.1 4.1(a, b, and c): shows baseline, Forward and Backward 39
4.2 Relationship between Re and Nu 40
4.3 Distribution of the velocity through tubes bank in tube bank 41
without winglets at (V=0.464 m/s).
4.4 Shows Relation between Reynolds numbers (Re) and Nusselt numbers 42
(Nu) in baseline case
4.5 Shows Relation between Reynolds numbers (Re) and friction factor 42
(f) in baseline case
4.6 shows relation between Reynolds number (Re) and Colburn factor (j) 43
in baseline case
4.7 Shows Relation between Reynolds numbers (Re) and Nusselt numbers 44
(Nu) of baseline and α=20° forward.
4.8 Shows Relation between Reynolds numbers (Re) and Nusselt numbers 45
(Nu) of baseline and α=30° forward.
4.9 Shows Relation between Reynolds numbers (Re) and Nusselt numbers 46
(Nu) of baseline and α=40° forward.
4.10 Shows Relation between Reynolds numbers (Re) and Nusselt 47
numbers (Nu) of baseline and α=20°, 30°, 40° forward arrangement.
xi
4.11 Shows relationship between Reynolds numbers (Re) with friction 48
factor (f) in cases baseline and α=20°, 30°, 40° forward arrangement.
4.12 Shows relationship between Reynolds number (Re) and surface heat 49
coefficient h (w/ in cases baseline and α=20°, 30°, 40°forward
arrangement.
4.13 Shows relation between Reynolds numbers (Re) with Colbrun 50
factor (f) in forward arrangement.
4.14. a Baseline Re=500 52
4.14. b =20⁰ Forward arrangement and Re=500 52
4.14. c =20⁰ Forward arrangement and Re=1000 53
4.14. d =20⁰ Forward arrangement and Re=2000 53
4.14. e: =20⁰ Forward arrangement and Re=3000 53
4.14.f: =20⁰ Forward arrangement and Re=4000 54
4.14.g: Forward arrangement and Re=5000 54
4.15.a: Baseline Re=500 56
4.15.b: =20⁰ Forward arrangement and Re=500 56
4.15. c =20⁰ Forward arrangement and Re=1000 57
4.15. d: =20⁰ Forward arrangement and Re=2000 57
4.15. e: =20⁰ Forward arrangement and Re=3000 58
4.15.f: =20⁰ Forward arrangement and Re=4000 58
4.15.g: Forward arrangement and Re=5000 59
4.16. a: Baseline Re=500 60
4.16. b: =20⁰ Forward arrangement and Re=500 60
4.16. c: =20⁰ Forward arrangement and Re=1000 61
4.16. d: =20⁰ Forward arrangement and Re=2000 61
4.16. e: =20⁰ Forward arrangement and Re=3000 61
4.16. f: =20⁰ Forward arrangement and Re=4000 62
4.16. g: Forward arrangement and Re=5000 62
4.17. a: Baseline Re=500 63
4.17. b: Forward arrangement and Re=500 ( velocity) 64
4.17. c: Forward arrangement and Re=1000 (velocity) 64
4.17. d: Forward arrangement and Re=2000 (velocity) 65
4.17. e: Forward arrangement and Re=3000 (velocity) 65
xii
4.17. f: Forward arrangement and Re=4000 (velocity) 65
4.17. g: Forward arrangement and Re=5000 (velocity) 66
4.18.a: Baseline Re=500 ( Temperature) 66
4.18.b: Forward arrangement and Re=500 (Temperature) 67
4.18. c: Forward arrangement and Re=1000 (Temperature) 67
4.18. d: Forward arrangement and Re=2000 (Temperature) 67
4.18. e: Forward arrangement and Re=3000 (Temperature) 68
4.18. f: Forward arrangement and Re=4000 (Temperature) 68
4.18. g: Forward arrangement and Re= 5000 (Temperature) 69
4.19. a: Baseline Re=500 (Nusselt number) 69
4.19. b: Forward arrangement and Re=500 (Nusselt number) 70
4.19. c: Forward arrangement and Re=1000 (Nusselt number) 70
4.19. d: Forward arrangement and Re=2000 (Nusselt number) 70
4.19. e: Forward arrangement and Re=3000 (Nusselt number) 70
4.19. f: Forward arrangement and Re=4000 (Nusselt number) 71
4.19.g: Forward arrangement and Re= 5000 (Nusselt number) 71
4.20. a: Baseline Re=500 (Velocity) 73
4.20. b: =40⁰ Forward arrangement and Re=500 (Velocity) 73
4.20. c: =40⁰ Forward arrangement and Re=1000 (Velocity) 74
4.20. d: =40⁰ Forward arrangement and Re=2000 (Velocity) 74
4.20. e: =40⁰ Forward arrangement and Re=3000 (Velocity) 74
4.20. f: =40⁰ Forward arrangement and Re=4000 (Velocity) 75
4.20. g: Forward arrangement and Re=5000 (Velocity) 75
4.21. a: Baseline Re=500 (Temperature) 76
4.21. b: Forward arrangement and Re=500 (Temperature) 76
4.21. c: Forward arrangement and Re=1000 (Temperature) 77
4.21. d: Forward arrangement and Re=2000 (Temperature) 77
4.21. e: Forward arrangement and Re=3000 (Temperature) 78
4.21. f: Forward arrangement and Re=4000 (Temperature) 78
4.21. g: Forward arrangement and Re= 5000 (Temperature) 79
4.22. a: Baseline Re=500 (Nusselt number) 79
4.22. b: Forward arrangement and Re=500 (Nusselt number) 80
4.22.c: Forward arrangement and Re=1000 (Nusselt number) 80
xiii
4.22. d : Forward arrangement and Re=2000 (Nusselt number) 80
4.22. e: Forward arrangement and Re=3000 (Nusselt number) 81
4.22. f: Forward arrangement and Re=4000 (Nusselt number) 81
4.22. g: Forward arrangement and Re= 5000 (Nusselt number) 82
4.23: Relation between Reynolds numbers (Re) and Nusselt 83
numbers (Nu) in case baseline and α=20° backward.
4.24: Shows Relation between Reynolds numbers (Re) and Nusselt 84
Numbers (Nu) in case baseline and α=30° backward.
4.25: Relation between Reynolds numbers (Re) and Nusselt 84
numbers (Nu) in case baseline and α=40° backward.
4.26: Relation between Reynolds number (Re) Nusselt number (Nu) 85
in cases baseline and α=20°, 30°, 40° backward arrangement.
4.27: Relationship between Reynolds number (Re) and surface heat 86
coefficient h(w/ ). in cases baseline and α=20°, 30°, 40°
backward arrangement
4.28. a: Baseline Re=500 (Velocity) 87
4.28. b: =20⁰ Backward arrangement and Re=500 (Velocity) 87
4.28. c: =20⁰ Backward arrangement and Re=1000 (Velocity) 88
4.28. d: =20⁰ Backward arrangement and Re=2000 (Velocity) 88
4.28. e: =20⁰ Backward arrangement and Re=3000 (Velocity) 88
4.28. f: =20⁰ Backward arrangement and Re=4000 (Velocity) 89
4.28. g : Backward arrangement and Re= 5000 (Velocity) 89
4.29. a: Baseline Re=500 (Temperature) 90
4.29. b: =20⁰ Backward arrangement and Re=500 (Temperature) 90
4.29. c: =20⁰ Backward arrangement and Re=1000 (Temperature) 91
4.29. d: =20⁰ Backward arrangement and Re=2000 (Temperature) 91
4.29. e: =20⁰ Backward arrangement and Re=3000 (Temperature) 91
4.29. f: =20⁰ Backward arrangement and Re=4000 (Temperature) 92
4.29. g: Backward arrangement and Re= 5000 (Temperature) 92
4.30. a: Baseline Re=500 (Nusselt number) 93
4.30. b : =20⁰ Backward arrangement and Re=500 (Nusselt number) 93
4.30. c: =20⁰ Backward arrangement and Re=1000 (Nusselt number) 94
4.30. d: =20⁰ Backward arrangement and Re=2000 (Nusselt number) 94
xiv
4.30. e: =20⁰ Backward arrangement and Re=3000 (Nusselt number) 94
4.30. f: =20⁰ Backward arrangement and Re=4000 (Nusselt number) 95
4.30. g: Backward arrangement and Re= 5000 (Nusselt number) 95
4.31. a: Baseline Re=500 (Velocity) 96
4.31. b: =30⁰ Backward arrangement and Re=500 (Velocity) 96
4.31. c: =30⁰ Backward arrangement and Re=1000 (Velocity) 97
4.31. d: =30⁰ Backward arrangement and Re=2000 (Velocity) 97
4.31. e: =30⁰ Backward arrangement and Re=3000 (Velocity) 97
4.31. f: =30⁰ Backward arrangement and Re=4000 (Velocity) 98
4.31. g: Backward arrangement and Re= 5000 (Velocity) 98
4.32. a Baseline Re=500 (Temperature) 99
4.32.b: Backward arrangement and Re=500 (Temperature) 99
4.32. c: Backward arrangement and Re=1000 (Temperature) 100
4.32. d: Backward arrangement and Re=2000 (Temperature) 100
4.32. e: Backward arrangement and Re=3000 (Temperature) 100
4.32. f: Backward arrangement and Re=4000 (Temperature) 101
4.32. g: Backward arrangement and Re= 5000 (Temperature) 101
4.33. a: Baseline Re=500 (Nusselt number) 102
4.33. b: Backward arrangement and Re= 500 (Nusselt number) 102
4.33. c: Backward arrangement and Re= 1000 (Nusselt number) 103
4.33. d: Backward arrangement and Re= 2000 (Nusselt number) 103
4.33. e: Backward arrangement and Re= 3000 (Nusselt number) 103
4.33. f: Backward arrangement and Re= 4000 (Nusselt number) 104
4.33. g: Backward arrangement and Re= 5000 (Nusselt number) 104
4.34. a: Baseline Re=500 (Velocity) 106
4.34. b: =40⁰ Backward arrangement and Re=500 (Velocity) 106
4.34. c: =40⁰ Backward arrangement and Re=1000 (Velocity) 107
4.34. d: =40⁰ Backward arrangement and Re=2000 (Velocity) 107
4.34. e: =40⁰ Backward arrangement and Re=3000 (Velocity) 107
4.34. f: =40⁰ Backward arrangement and Re=4000 (Velocity) 108
4.34. g: Backward arrangement and Re=5000 (Velocity) 108
4.35. a: Baseline Re=500 (Temperature) 109
4.35. b: Backward arrangement and Re=500 (Temperature) 109
xv
4.35. c: Backward arrangement and Re=1000 (Temperature) 110
4.35. d: Backward arrangement and Re=2000 (Temperature) 110
4.35. e: Backward arrangement and Re=3000 (Temperature) 111
4.35. f: Backward arrangement and Re=4000 (Temperature) 111
4.35. g: Backward arrangement and Re=5000 (Temperature) 112
4.36. a: Baseline Re=500 (Nusselt number) 112
4.36. b: Backward arrangement and Re=500 (Nusselt number) 113
4.36. c: Backward arrangement and Re=1000 (Nusselt number) 113
4.36. d: Backward arrangement and Re=2000 (Nusselt number) 114
4.36. e: Backward arrangement and Re=3000 (Nusselt number) 114
4.36. e: Backward arrangement and Re=4000 (Nusselt number) 114
4.36. g: Backward arrangement and Re= 5000 (Nusselt number) 115
4.37: Shows relationship between Reynolds number (Re)and Colburn 115
factor (j) and comparison between backward arrangement
for angles ( α=20⁰, 30⁰, and 40⁰ ).
4.38: Shows relationship between Reynolds number(Re) and friction 116
factor and comparison between backward arrangement for
angles ( α=20⁰, 30⁰, and 40⁰ ).
4.39: Shows relationship between Reynolds number (Re) Nusselt 116
number (Nu) and comparison between forward arrangement
forangles (α=20⁰, 30⁰, and 40⁰) and backward arrangement
for angles ( α=20⁰, 30⁰, and 40⁰ ).
4.40: Shows relationship between Reynolds number (Re) and friction 117
factor(f) and comparison between forward arrangement
for angles (α=20⁰, 30⁰, and 40⁰) and backward arrangement
for angles ( α=20⁰, 30⁰, and 40⁰ ).
xvi
LIST OF ABBREVIATION AND SYMBOLS
Re Reynolds number
Density of air ρ
Inlet velocity of air (m/s)
Hydraulic diameter (m)
µ Viscosity of air
L Length of heat exchanger (m)
t Fin thickness (m)
Colburn factor
Friction factor
Nu Nusselt number
Average Nusselt number
h Convection heat transfer coefficient
k Thermal Conductivity
α Angle of winglet ( )
Heat flux on the heating surface
Pr Prandtl number
P Static Pressure (pa)
D Tube diameter (m)
w width of heat exchanger (m)
H Fin pitch (m)
xvii
WL Winglet length (m)
Specific heat capacity (J/kg k)
q Heat transfer rate (w)
Central angle (m)
Distance between tube and winglet t (m)
T Temperature (k)
LVs Longitudinal vortices
LVGs Longitudinal vortex generators
RWPs Rectangular winglet pairs
VG Vortex generator
1
CHAPTER 1
INTRODUCTION
1.1 Heat Transfer Enhancement
The conversion, utilization, and recovery of energy in every industrial, commercial,
and domestic application involve a heat exchange process. Some common examples
are steam generation and condensation in power and cogeneration plants; sensible
heating and cooling of viscous media in thermal processing of chemical,
pharmaceutical, and agricultural products; refrigerant evaporation and condensation
in air-conditioning and refrigeration; gas flow heating in manufacturing and waste-
heat recovery; air and liquid cooling of engine and turbo machinery systems; and
cooling of electrical machines and electronic devices. Improved heat exchange, over
and above that in the usual or standard practice, can significantly improve the
thermal efficiency in such applications as well as the economics of their design and
operation.
The engineering cognizance of the need to increase the thermal performance
of heat exchangers, thereby effecting energy, material, and cost savings as well as a
consequential mitigation of environmental degradation had led to the development
and use of many heat transfer enhancement techniques. In the past, these methods
have been variously referred to as augmentation and intensification, among other
terms [1].
2
Enhancement techniques essentially reduce the thermal resistance in a
conventional heat exchanger by promoting higher convective heat transfer coefficient
with or without surface area increases (as represented by fins or extended surfaces).
As a result, the size of a heat exchanger can be reduced, or the heat duty of a heat
exchanger can be increased, or the pumping power requirements can be reduced, or
the exchanger’s operating approach temperature difference can be decreased [2].
Figure (1.1) fin-tube heat exchanger
Figure (1.2) flat plate fin-tubes for heat exchanger
The latter is particularly useful in thermal processing of biochemical, food,
plastic, and pharmaceutical media to avoid the thermal degradation of the end
product. On the other hand, heat exchange systems in spacecraft, electronic devices,
3
and medical applications, for example, may rely primarily on the enhanced thermal
performance for their successful operation.
1.2 Classification of Enhancement Techniques
Sixteen different enhancement techniques have been identified by Bergles [2],
which can be classified broadly as passive and active techniques.
A list of the various methods or devices under each of these two categories is
given in Table (1-1(. The primary distinguishing feature is that, unlike active
methods, the passive techniques do not require direct input of external power.
Table (1-1) Classification of various heat transfer enhancement techniques [2].
Passive Techniques Active Techniques
Treated surface Mechanical aids
Roughness surface Surface vibration
Extended surface Fluid vibration
Displaced enhancement devices Electrostatic fields
Swirl flow devices Injection
Coiled tubes Suction
Surface tension devices Jet impingement
Additives for liquids
Additives for gases
Compound Enhancement
Two or more passive and/or active techniques
that are employed together
Generally, they use surface or geometrical modifications to the flow channel, or
incorporate an insert, material, or additional device. Except for extended surfaces
which increase the effective heat transfer surface area, these passive schemes
promote higher heat transfer coefficients by disturbing or altering the existing flow
behaviour. This, however, is accompanied by an increase in the pressure drop.
In the case of active techniques, the addition of external power essentially
4
facilitates the desired flow modification and the concomitant improvement in the rate
of heat transfer. The use of two or more techniques (passive and/or active) in
conjunction constitutes a compound enhancement.
The effectiveness of any of these methods is strongly dependent on the mode of
heat transfer (single-phase free or forced convection, pool boiling, forced convection
boiling or condensation, and convective mass transfer) and type and process
application of the heat exchanger. In considering their specific applications, a
descriptive characterization of each of the 16 techniques is useful in assessing their
potential.
1.3 Fin-Tube Heat Exchanger with Winglet
Tube-fin heat exchangers are mostly employed as gas-to-liquid exchangers.
Nowadays, many applications such as chemical, petroleum industries, thermal
processing systems in automotive, refrigeration and air conditioning are found for
tube-fine exchangers. Depending on the fin type, these exchangers are referred to as
finned tube exchangers (having normal fins on individual tube) and tube-fin
exchangers (having flat continuous fins). In these exchangers, the fins can be plain,
wavy, or interrupted, while round, flat and oval tubes may be used. A tube-fin
exchanger with flat fins is referred to as a plate finned tube, Figure (1.3).
5
Figure (1.3) different types of flat plate fin-tube for heat exchanger
Apart from the flow structure, geometrical parameters such as tube form (round or
flat tube). Arrangement (in line or staggered), and tube and fin spacing are effective
in the performance of these exchangers. For example, with an inline arrangement, the
horseshoe vortices may not be generated in front of the tubes of the second and the
other rows, while in the staggered arrangement, the horseshoe vortices appear in
front of each tube, which can influence the flow structure on the large area of the fin.
In recent years, vortex generators such as fins, ribs, wings etc. have been successfully
used for heat transfer enhancement of the modern thermal systems. Vortex
generators form secondary flow by swirl and destabilize the flow. They generate the
6
longitudinal vortices and create rotating and secondary flow in the main flow which
can raise turbulent intensity, mix the warm and cold fluid near and in the centre of
channel and increase the heat transfer in the heat exchangers. A lot of investigations
were mainly focused on circular-tube-fin and oval-tube-fin with mounted and
punched longitudinal vortex generators to enhance the heat transfer [3–14].
Figure (1.4) flat plate fin-tubes for heat exchanger without winglets
Figure (1.5) flat plate fin-tubes for heat exchanger with vortex generator
The energy transfer outside tube of economizers in coal-fired boilers needs more
attention and usually faces two significant problems: low heat transfer efficiency of
the gas, and serious tube erosion caused by ash and particles from coal combustion.
Recently, longitudinal vortex generators (LVGs) and dimples have been proved to
7
have a high performance in shell-side gas heat transfer enhancement. Zhang et al.
[15], [16] A typical finned flat and round tube bank with vortex generators is
presented in Fig(1.6) .
Figure (1.6) Fin-tubes heat exchanger with Round tubes and oval tubes
1.4 Problem statement
During my work 23 years experience in cement plant, we have found many problems
related to the subjects .There are many departments in the cement plant, such as
(Cement Mill, Raw mill, Rotary Kiln, and Air Compressors).
For this study we have chosen a problem in a cooling system for the Journal bearing
found in Cement Mill, symmetro gear box and main motor .This problem needs high
efficiency cooling systems, the same work principal with heat exchangers.
Therefore the principal of work in this research will be to increase the efficiency of
heat exchanger by using winglets.
1.5 Project Objectives
This numerical study includes
a) Study the effect of winglets in fin-tube heat exchanger.
b) Exam the effect of different Reynolds number on thermal and flow felid. The
ranges of Reynolds number are (500, 1000, 2000, 3000, 4000, and 5000).
8
c) Investigating the Nusselt number, friction factor for fin-tube heat exchanger with
winglet and without winglet.
d) Study the effect of forward and backward arrangement of winglet in fin-tube heat
exchanger
1.6 Project Scopes
Scope of this research is numerical studies of enhance heat transfer in fin- tube heat
exchanger with and without winglet, and this work can be summarized as follows :
a) Investigation numerically of enhance heat transfer in fin- tube heat exchanger.
b) Investigation numerically of effects of different Reynolds number on fin- tube
heat exchanger, heat transfer coefficient, Nusselt number and distribution of
temperature in tubes.
c) Study the effect of forward and back ward arrangement of winglets
1.7 Research Significance
The heat transfer enhancement can reduce the size and cost for heat exchanger by
using vortex generator element in the fin. Air-cooled condensers (ACCs) with
obvious water conservation benefit can be an important alternative for power plant
near coal mines where water source is of shortage. In direct air-cooled condensers of
power generating units, the ambient air replaces water as cooling medium. The
previous studies show that longitudinal vortex generators generate higher heat
transfer enhancement for the same pressure penalty than transverse vortex generators
in detail a base configuration with embedded rectangular vortex generators in
internal flow.
9
CHAPTER 2
LITERATURE SURVEY
2.1 Introduction
The purpose of this literature review is to go through the main topics of interest.
The enhancement of heat transfer by using a winglet in fin tube heat exchanger is the
subject of growing importance in myriad industrial applications; hence the fin- tube
heat exchanger has been the subject of several studies. This literature review will
address a number of experimental and theoretical studies which focused on the air
side performance of fin- tube heat exchanger. The experimental and numerical
studies carried out in order to cover the enhancement in heat transfer by using
winglet in a fin- tube heat exchanger in all applications and the effect of
configurations for heat exchangers.
2.2. Winglet in Tube-Fin Heat Exchanger
He et al [17] investigated numerically the effect of rectangular winglet pairs (RWPs)
on heat transfer enhancement and pressure loss penalty for fin-and-tube heat
exchangers. The rectangular winglet pairs RWPs were placed with a special
orientation for the purpose of enhancement of heat transfer with low Reynolds
number flow. The numerical study involved three-dimensional flow and conjugate
heat transfer in the computational domain, which was set up to model the entire flow
channel in the air flow direction. The effects of attack angle of rectangular winglet
10
pairs RWPs, row-number of RWPs and placement of RWPs on the heat transfer
characteristics and flow structure were examined in detail. It was observed that the
longitudinal vortices caused by RWPs and the impingement of RWPs-directed flow
on the downstream tube were important reasons of heat transfer enhancement for fin-
and-tube heat exchangers with RWPs. It was interesting to find that the pressure loss
penalty of the fin-and-tube heat exchangers with RWPs can be reduced by altering
the placement of the same number of RWPs from inline array to staggered array
without reducing the heat transfer enhancement. The results showed that the
rectangular winglet pairs (RWPs) were significantly improved the heat transfer
performance of the fin and-tube heat exchangers with a moderate pressure loss
penalty.
Huisseune et al [18] studied the influence of delta winglet vortex generators
on heat transfer enhancement on air-side of a round-tube heat exchanger with
louvered fins. The contribution of five important design parameters to the thermal
hydraulic performance of the compound heat exchanger was numerically
investigated. Knowing which parameters have the biggest influence is important for
the optimization. At high inlet velocities the performance was mainly determined by
the louvers, while at lower inlet velocities also the delta winglet geometry had a
significant contribution. To validate the simulations, an aluminum compound heat
exchanger was made and tested in a wind tunnel. The experimental result showed
that the friction factor decreased with increased Reynolds number.
Huisseune et al [19] examined numerically the effects of punching delta
winglet vortex generators on Performance enhancement of a louvered fin heat
exchanger. The delta winglet vortex generators into the louvered fin surface in the
near wake region of each tube were numerically investigated using computational
fluid dynamics (CFD). The delta winglet vortex generators cause three important
mechanisms of heat transfer enhancement.
First, due to the swirling motion of the generated vortices, hot air is removed from
the tube wake to the mainstream regions and vice versa. Second, the induced wall-
normal flow locally thins the boundary layer, which also enhances the heat transfer.
Third, the size of the wake zones is reduced because the flow separation from the
tube surface is delayed.
11
Lei et al [20] examined the effects of vortex generators on heat transfer and
pressure drop of an oval heat exchanger by using computational fluid dynamics
(CFD) method. The Reynolds numbers based on fin collar outside diameter varied
from 600 to 2600.From the results, it was found that the delta-winglet vortex
generator with an attack angle of 20° and an aspect ratio of 2 provided the best
integrated performance over the range of Reynolds number computed.
Tian et al [21] investigated numerically the effects of delta winglets on air-
side heat transfer and fluid flow characteristics of wavy fin-and-tube heat exchanger.
The three-dimensional simulations were performed with renormalization-group
(RNG) k 3 model to lay the foundation for the design of the high-performance heat
exchanger. The wavy fin-and-tube heat exchangers which had three-row round tubes
in staggered or inline arrangements were studied. The numerical results showed that
each delta winglet generates a downstream main vortex and a corner vortex. For the
in-line array, the longitudinal vortices enhance the heat transfer not only on the fin
surface in the tube wake region but also on the tube surface downstream of the delta
winglet; for the staggered array, longitudinal vortices were disrupted at the first wavy
trough downstream from the delta winglet and only develop a short distance along
the main-flow direction, and the vortices mainly enhance the heat transfer of the fin
surface in the tube wake region. The longitudinal vortices generated by delta winglet
caused considerable augmentation of heat transfer performance for wavy fin-and-
tube heat exchanger with modest pressure drop penalty.
Tiwari et al [22] studied Heat transfer enhancement in cross-flow heat
exchangers using oval tubes and multiple delta winglets. A three-dimensional study
of laminar flow and heat transfer in a channel with built-in oval tube and delta
winglets was carried out through the solution of the complete Navier–Stokes and
energy equations using a body-fitted grid and a finite-volume method. Oval tubes
were used in place of circular tubes, and delta-winglet type vortex generators in
various configurations were mounted on the fin-surface. An evaluation of the
strategy is attempted in this investigation. The investigation is carried out for
different angles of attack of the winglets to the incoming flow for the case of two
winglet pairs. The variation of axial location of the winglets is also considered for
one pair of winglets mounted in common-flow-down configuration. The results
12
indicate that vortex generators in conjunction with the oval tube showed definite
promise for the improvement of fin–tube heat exchangers.
2.3. Winglets in Refrigerator Evaporator
Sommers et al [23] studied the influence of longitudinal vortex generation
heat transfer enhancement on the fin surface of a heat exchanger. The single row of
delta-wing vortex generators was applied to a refrigerator evaporator with a fin
spacing of 8.5 mm both along the leading edge and at a location halfway along the
flow length for a total of 108 vortex generators. Heat transfer and pressure drop
performance were measured before and after to determine the effectiveness of the
vortex generator under frosting conditions. The heat transfer enhancement
monotonically increased with air velocity and results in a small pressure drop penalty
that is incommensurate with the achieved enhancement. The heat transfer coefficient
is observed to lie between 26-51 W/m2-K for the enhanced evaporator and between
16-26 W/m2-K for the baseline evaporator. Two different performance evaluation
criteria are calculated and both show that the enhanced evaporator outperforms the
baseline specimen for Reynolds numbers greater than approximately 700-750.
2.4 Winglet-Type Vortex Generators Insert
Wua and Tao [24] studied numerically the impact of delta winglet vortex
generators on the heat transfer enhancement and lower pressure loss of a novel fin-
tube surface with two rows of tubes in different diameters. Numerical simulation
results showed that the fin-tube surface with first row tube in smaller size and second
row tube in larger size can lead to an increase of heat transfer and decrease of
pressure drop in comparison with the traditional fin-tube surface with two rows of
13
tubes in the same size. It was clearly noted that the delta winglet pairs could bring
about a further heat transfer enhancement and pressure drop decrease through the
careful arrangement of the location, size and attack angle of delta winglet pairs either
in ‘‘common flow up’’ or ‘‘common flow down’’ configurations. It was also
observed that the utilization of delta winglet vortex generators led to develop more
compact, higher heat transfer efficiency, lower fan power and quieter heat exchanger
of refrigeration and air condition system.
Habchi et al. [25] carried out three dimensional numerical study of heat
transfer in vortex generator-type multifunctional heat exchangers. The first category
were rows of trapezoidal vortex generators in different arrangements; in the second
category the vortex generators were fixed at certain distance from the tube wall, and
the third category had vortex generator rows between which a row of small
protrusions were inserted on the tube wall. The study was conducted for turbulent
vortical flow with Reynolds numbers were varied between 7500 and 15,000 and
constant wall temperature Tw = 360 K. It was also noted that the counter-rotating
vortex pair start to develop from the leading edge of the vortex generator and reaches
maximum intensity near the trailing edge. The total turbulence kinetic energy reaches
its maximum near the trailing edge of the vortex generator due to the decrease in the
shear layer intensity by viscous forces. The longitudinal variation of local Nusselt
number computed on different HEV cross sections showed the advantage of using
protrusions between two successive vortex generator rows, since they increased the
local heat transfer by increasing the temperature gradients and vortices very close to
the heated wall.
Lawson and Thole [26] studied experimentally the effect of a louvered fin
heat exchanger with used practical delta winglets on heat transfer augmentation
along the tube wall. From the results, it was clearly noted that the utilization of delta
winglets with louvered fins provided augmentations in heat transfer along the tube
wall as high as 47% with a corresponding increase of 19% in pressure losses.
Comparisons of measured heat transfer coefficients with and without piercings
indicate that piercings reduce average heat transfer augmentations, but it significantly
increases with respect to no winglets present. It was also observed that the negative
effects of piercings only occurred before the turnover louver, where the winglets
were angled towards the tube wall. Piercings interfered with the winglet influence
14
causing the larger Nusselt number augmentations after the turnover louver for the
pierced louvered fin configurations. Flow passing through the piercings. Friction
factor tests indicated that piercings decreased the friction factors through the test
section relative to the solid louvered fin configuration. Flow through the piercings
caused less shear at the interface between the louver-directed flow and channel-
directed flow regimes.
Ling et al. [27] carried out numerical study on heat transfer and pressure drop
for fin-and-tube heat exchangers with rectangular winglet-type pairs (RWPs) vortex
generators under low Reynolds number flow. The rectangular winglet-type pairs
RWPs were placed with a special orientation for the purpose of enhancement of heat
transfer. The effects of attack-angle of RWPs, row-number of RWPs and placement
of RWPs on the heat transfer characteristics and flow structure were examined. It
was found that the pressure loss penalty of the fin-and-tube heat exchangers with
RWPs could be reduced by altering the placement of the same number of RWPs
from inline array to staggered array without reducing the heat transfer enhancement.
The results showed that the rectangular winglet pairs (RWPs) significantly improved
the heat transfer performance of the fin-and-tube heat exchangers with a moderate
pressure loss penalty. The staggered-RWPs array provided further reduce the
pressure loss penalty due to the asymmetric arrangement of the vortex generators. It
was expected that the staggered-RWPs array could further reduce the pressure loss
penalty with increase of the Reynolds number.
Lemouedda et al. [28] investigated numerically the effect of angle of attack
of delta-winglet vortex generators in a plate-fin-and-tube heat exchanger. The
optimal angles of attack of the delta-winglets were investigated based on the Pareto
optimal strategy. The angle of attack of a pair a delta-winglet-type VGs mounted
behind each tube was varied between β = -90° and +90°. Three circular tube rows
with inline and staggered tube arrangements were investigated for Reynolds numbers
from 200 to 1200. The results showed that increased the performance of plate-fin
and-tube heat exchangers with used the delta-winglets as heat transfer enhancement
elements. It was found that the used of winglet vortex generators led to increase the
heat transfer in regions of poor heat transfer rate such as the wake regions behind the
tubes by directing a part of the fluid of the mainstream towards these regions.
15
Jiong et al. [29] studied numerically the effect of a slit fin-and-tube heat
exchanger with longitudinal vortex generators on the heat transfer and fluid flow
characteristics. The 3-D numerical simulation was performed on laminar flow of air.
They compared the characteristics of heat transfer and fluid flow for the slit fin and-
tube heat exchanger with longitudinal vortex generators with the heat exchanger with
X-shape arrangement slit fin and heat exchanger with rectangular winglet
longitudinal vortex generators. In front of the first tube, the span-average Nusselt
number abruptly increased due to the formation of horseshoe vortices, which brings
about better mixing and enhances heat transfer in this region. For the slit fin, the
enhanced heat transfer effect of strips led the span-average Nusselt number larger
than the plain fin in this region. A little peak occurs at the downstream of the first
strip as the effect of the longitudinal vortices. The heat transfer performance and
friction factor of slit fin-and-tube heat exchanger with longitudinal vortex generator
is 15.8% and 4.2% larger than that of heat exchanger with X-Arrangement slit fin
and heat exchanger with rectangular winglet longitudinal vortex generators.
Eiamsa-ard and Promvonge [30] studied experimentally the behaviors of
turbulent tube flow through a straight tape with double-sided delta wings (T-W) on
the heat transfer rate and friction factor. They studied the effect of the double-sided
delta wings with forward/backward-wing arrangement, delta wings with alternate
axis (T-WA), three wing-width ratios and wing-pitch ratios on Nusselt number (Nu)
and friction factor f. The overall walls of the tested tube were exposed to a uniform
heat-flux at turbulent air flow over a range of 4000 < Re <20000 .Experimental
results showed that the Nusselt number increased with the reduction of pitch ratio
due to higher turbulence intensity. For the B-wing and F-wing, it was found that the
friction factor get higher values for larger wing-width ratio. It was observed that the
friction factor decreased with decreased wing-width ratios due to lower turbulence
intensity and friction near the tube wall. It was also noted that the thermal
performance factor increased as increased the wing-width ratio. As found, the heat
transfer rate and thermal performance factor of the F-wing were found to be higher
than those of the B-wing. The mean Nusselt number values of the delta wings with
alternate axis (T-WA) was higher than that of the T-W delta wings because of the
high strength of the turbulence intensity in the tube and the better mixing of fluid
16
caused by the interruption of wing elements or alternate axis planes .
Wu et al. [31] studied experimentally and numerically the effect of pair of
delta winglet longitudinal vortex generator punched directly from the plates at attack
angles of 15º, 30º, 45º and 60º on the heat transfer in rectangular channels with air as
a fluid. Experimental results showed that the average Nusselt number on the surfaces
of plate increased with increased of the attack angle of delta winglet pair compared
with that of plain plate without delta winglet pair. The average Nusselt number of the
plate with attack angle of 60º was slightly higher than that of plate with attack angle
of 45º. The average Nu for the plate with delta winglet pair at β=15º increased by 8-
11%, those at β=30º, 45º, 60º increased by 15-20%, 21-29%, 21-34%, respectively at
the experimental range. The average Nu increased with the increase of the Re in the
channel for all cases. Punched vortex generators directly from the fins of heat
exchanger are not only convenient to implement, but it is also beneficial to enhance
the integral heat transfer of the both surfaces of the practical fin due to the transverse
flow through the punched holes.
Kotcioglu et al. [32] studied the second law analysis and heat transfer in a
cross-flow heat exchanger with a new winglet-type vortex generator. The
experimental data showed an increase in the heat transfer enhancement from 15% to
30% and also an increase in the pressure-loss penalty from20% to 30%, in a
comparison with and without vortex generators, respectively. The effectiveness
values of the HX with and without the convergent divergent longitudinal vortex
generator (CDLVG) generators containing gaps for the passage of fluid into the
channel was obtained up to 68-80%, compared to a cross-flow heat exchanger HX
with empty tubes in cross-flow. It was also found that the pressure loss reduced as
the velocity increased; nevertheless the reduction is rather small. Due to the
irreversibility, the motion of mixed fluid in the channels, the number of channels and
the vortex generator surface affect the variation on the cross-flow heat exchanger HX
that increased heat transfer area on both exhaust air and supply air sides, leading to a
higher heat transfer and pressure drop and also increasing the entropy generation
number.
Hiravennavar et al. [33] studied numerically the laminar flow over a delta
17
winglet pair in a channel at various Reynolds numbers and winglet thicknesses. They
solved the three-dimensional, unsteady, incompressible Navier– Stokes equations
and the energy equation by numerical simulation. Three types of parametric were
studied the channel without winglet, with one winglet and a winglet pair, variation of
Reynolds number in case of winglet pair and variation of the thickness of winglet for
the case of winglet pair. It was observed that the Nusselt number Nu was higher for
the case with winglet pair as compared to single winglet case. At the end of the
channel the winglet pair case showed increased of 66.6% in Nusselt number as
compared to the plane channel case and 33.1% as compared to the single winglet
case. It was noted that the enhancement in heat transfer by a winglet pair was twice
that of a single winglet. It was also showed that influence of the thickness of winglet
on the Nusselt number as the thickness of the winglets increased the Nusselt number
Nu increased.
Chen and Hsu [34] investigated theoretically and experimentally the average
heat transfer coefficient and fin efficiency on the fin of annular-finned tube heat
exchangers in natural convection for various fin spicing. The radiation and
convection heat transfer coefficients were simultaneously taken into consideration in
this study. The heat transfer coefficient on this annular circular fin was assumed to be
non-uniform. Thus, the whole annular circular fin was divided into several sub-fin
regions in order to predict the average heat transfer coefficient and fin efficiency
from the knowledge of the ambient temperature, tube temperature and fin
temperature recordings at several selected measurement locations. The results
showed that the average heat transfer coefficient value increased with increasing the
fin spacing (S), and the fin efficiency decreased with increasing the fin spacing.
Chen and Hsu [35] studied theoretically and experimentally the average heat
transfer coefficient and fin efficiency on a vertical annular circular fin of finned-tube
heat exchangers for various fin spacing in forced convection. The distribution of the
heat transfer coefficient on the fin was assumed to be non-uniform, thus the whole
annular circular fin was divided into several sub-fin regions in order to predict the
average heat transfer coefficient and fin efficiency values. The results showed that
the effect of the fin spacing (S) on the average heat transfer coefficient value could
be negligible when the S value exceeded about 0.018 m. The average heat transfer
18
coefficient value increased with increasing the air speed Vair for 1 m/s ≤ Vair ≤ 5 m/s
(1550 ≤ Red ≤ 7760) and increasing the fin spacing for 0.005 m ≤ S ≤ 0.018 m. The
fin efficiency value decreased with increasing Vair for 1 m/s ≤ Vair ≤ 5 m/s and
seemed to be not very sensitive to the fin spacing.
Choi et al. [36] investigated experimentally the heat transfer characteristics of
discrete plate finned-tube heat exchangers with large fin pitches. Thirty-four heat
exchangers were tested with variations of fin pitches, the number of tube rows, fin
alignment, and vertical fin space. The Colburn j-factor of the discrete plate finned-
tube exchanger was analyzed as a function of coil geometry and then compared with
that of the continuous plate finned-tube heat exchanger. For fin pitches of 7.5–15
mm, the Colburn j-factors of the discrete plate finned-tube heat exchangers were 6.0–
11.6% higher than those of the continuous plate finned-tube heat exchangers. The j-
factor of the discrete plate finned-tube heat exchangers decreased with the rise of the
number of tube rows. As the number of tube rows increased, the j-factor decreased
more severely in the continuous plate finned-tube heat exchangers than in the
discrete plate finned-tube heat exchangers. The j-factor for the staggered fin
alignment was at least 5.5% higher than that of the inline fin alignment in the
discrete plate finned tube heat exchangers. For the inline fin alignment, the j-factor
increased with the increase of vertical fin space, but the increase of the j-factor
became negligible for vertical fin space greater than 4 mm. For the staggered fin
alignment, the effects of vertical fin space on the j-factor were almost negligible at
all Reynolds numbers.
Nagarani and Mayilsamy [37] investigated and analyzed experimentally the
heat transfer rate and efficiency for circular and elliptical annular fins for different
environmental conditions. It was found that the elliptical fin efficiency was more
than that of the circular fin. The heat transfer coefficient depends upon the space,
time, flow conditions and fluid properties. If there are changes in the environmental
conditions, there are changes in the heat transfer coefficient and efficiency also.
Alam et al. [38] reviewed the use of tabulators in different forms of ribs,
baffles, delta winglets, obstacles, vortex generator, rings and perforated
blocks/baffles is an effective way to improve the performance of heat exchangers and
19
solar air heaters. Investigators studied the effect of these tabulators for heat transfer
and friction characteristics in air ducts. Based on their view it was found that
perforation in ribs/baffles/blocks and combination of combined rib and delta winglet
leads to the better thermo-hydraulic performance. The correlation presented by
various investigators, in terms of non-dimension al parameters for heat transfer and
friction factor in solar air heater sand heat exchanger shave also been presented.
Du et al [39] studied experimentally the heat transfer and resistance
characteristics of two finned oval-tube heat exchangers (HE1: Double rows of tubes,
HE2: Three rows of tubes.) inclined towards the air incoming flow direction. Four air
inlet angles (90, 60, 45 and 30) were investigated separately to acquire the heat
transfer and pressure drop performances for Reynolds number ranging from 1300 to
13,000. The experimental correlations of Nusselt number and resistance coefficient
of the air side were obtained, and the comprehensive comparisons of heat transfer
performance were carried out. The results showed that whether the heat transfer
performance for heat exchangers positioned obliquely was improved was depended
on their inclined angles.
Du et al. [40] studied numerical Punched longitudinal vortex generators
(LVGs) were employed to enhance air-side heat transfer on the wavy fin surface of
flat tube used in direct air-cooled condenser. The heat transfer enhancement of four
types of the longitudinal vortex generators with different attack angles were
compared by numerical simulations. It was found that the delta winglet pair with
attack angle 25 could reach the greatest performance evaluation criteria (PEC) under
the conditions of the inlet air flow velocity varied from 1 m/s to 5 m/s. The
influences of locations on the wavy fin surface and the row number of the
longitudinal vortex generators were also discussed. One delta winglet pairs at the
middle of the wavy fin surface and the minimum row number, n = 1, with the
average PEC is 1.23, had the best heat transfer performance of all conditions. as well
as the numerical simulations verified that the delta winglet pairs can generate
obvious longitudinal vortex pairs at the down-sweep zone, which can enhance the
heat transfer between the cooling air flow and heated wall surface with acceptable
pressure loss.
Gawande et al.[41] studied numerically the performance characteristics of a
20
solar heater and heat exchangers by using artificial roughness in different forms
shapes and sizes. Artificial roughness was provided in the form of different
geometries such as ribs, dimple shape roughness, wire mesh, baffles, delta winglets
etc. To determine the effect of these geometries on thermal performance of solar
heaters and heat exchangers, several experimental and numerical studies had been
carried out by various researchers. An attempt had been made to review various
roughness element geometries employed in solar air heaters and heat exchangers in
terms of heat transfer, friction factor and flow simulation techniques. Correlations
developed for heat transfer and friction factor for different roughness geometries by
various investigators in solar air heaters were present.
Gholami et al [42] investigated numerically the heat transfer enhancement
and pressure loss penalty for fin-and-tube compact heat exchangers with the wavy-up
and wavy-down rectangular winglets in low Reynolds number flow. The rectangular
winglets were used with a particular wavy form for the purpose of enhancement of
air side heat transfer performance of fin-and-tube compact heat exchangers. The
effect of Reynolds numbers from 400 to 800 and angle of attack of 30° of wavy
rectangular winglets were also examined. The effects of using the wavy rectangular
winglet, conventional rectangular winglet configuration and without winglet as
baseline configuration, on the heat transfer characteristics and flow structure were
studied and analysed in detail for the inline tube arrangements. The results showed
that the wavy rectangular winglet can significantly improve the heat transfer
performance of the fin-and-tube compact heat exchangers with a moderate pressure
loss penalty. It was also clearly found that the numerical results of the wavy winglet
had significant effect on the heat transfer performance and also, this augmentation
was more important for the case of the wavy-up rectangular winglet configuration.
Hasanpour et al [43] reviewed that the enhancing of heat transfer mechanisms
were used in many industrial applications like heat exchanger, air conditioning,
chemical reactors and refrigeration systems. Therefore several techniques had been
promoted to enhance heat transfer rate and to decrease the size and cost of equipment
especially the heat exchangers. One of the leading tools used in passive heat transfer
methods mainly at turbulence flow was twisted tape inserts.
21
Khoshvaght et al [44] studied experimentally a comparative evaluation of
seven common configurations of channels used in plate-fin heat exchangers. All the
channels, including plain, perforated, offset strip, louvered, wavy, vortex-generator,
and pin, were fabricated and tested experimentally. The working fluid was water, and
Reynolds number range was varied from 480 to 3770. To evaluate the performance
of these channels and also selected an optimum plate-fin channel, three mostly used
energy-based performance evaluation criteria were employed. The results were
presented as plots of dimensional and non-dimensional parameters. The results of the
studied channels, the vortex-generator channel showed a significant enhancement in
the heat transfer coefficient and a proper reduction in the heat exchanger surface
area. Therefore, it could be applied as a high quality interrupted surface in the plate-
fin heat exchangers. Moreover, the wavy channel displayed an optimal performance
at low Reynolds numbers.
Li et al [45] investigated numerically a radiantly arranged LVGs enhanced
fin-and-tube structure to enhance air side heat transfer. The arrangement of LVGs is
totally different from existing publications. In the proposed structure there exist 12
winglets around each tube. The attack angles are 50, 50, 50, 50, 70 and 110,
respectively. The height ends of the winglets were further away from the tube, while
the closed point ends of winglets were close to the tube wall. Heat transfer and
pressure drop performance was compared with other three structures: an arc-shaped
wavy fin-and-tube surface, a common-flow down LVGs enhanced fin-and-tube
surface and a plain plate fin-and-tube surface. The results showed that the 12
winglets form five local passages which could guide the moving fluid from the main
flow to the tube wall, leading to some impinging effect or reducing the wake region
behind the tube. The performance evaluation of the four structures was conducted by
using the newly proposed ln (Nue/Nuo) vs. ln (fe/fo) plot based on energy saving. It
was found that the proposed radiantly arranged LVGs enhanced fin and- tube surface
was the best. The field synergy principle is adopted to analyse the four structures and
it was found that the domain averaged synergy angle of the proposed radiantly
arranged LVGs enhanced structure was significantly less than that of other three
cases. Finally characteristics of the proposed fin and- tube surface with five tubes
were investigated at five fin pitches and compared with the wavy structure of six
tubes at the same other conditions.
22
Ranut et al [46] studied numerically the Optimization of heat exchangers, as a
consequence of their vital role in several industries and applications, has attracted a
lot of interest in the last years, and in particular the necessity of improving their
performances is well recognized. The coupling of optimization techniques with
Computational Fluid Dynamics (CFD) had demonstrated to be a valid methodology
for easily explore this work; a CFD-based shape optimization of a tube bundle in
cross flow was presented, as a natural extension of the work.
Saha et al [47] investigated numerically the performance of a plate-fin heat
exchanger with an emphasis on acquiring fundamental understanding of the relation
between local flow behaviour and heat transfer augmentation mechanism. Numerical
simulations were performed in a rectangular channel containing built-in longitudinal
vortex generators on the bottom wall arranged periodically both in the stream wise
and span wise directions. Two types of vortex generators, namely, rectangular
winglet pair (RWP) and delta-winglet pair (DWP) with two different flow
arrangements, common-flow-up (CFU) and common-flow-down (CFD) had been
explored to assess the influence of shape and flow arrangements on heat transfer
enhancement. The basic mechanisms of flow structure and heat transfer
characteristics had been examined with the help of secondary velocity vectors,
streamlines, and temperature contours. Additionally, the mechanism of the local heat
transfer augmentation had been explained using a novel concept called the field
synergy principle. The performance of the vortex generators had been compared
based on integral quantities such as Nusselt number, pressure loss, performance
evaluation factor and domain averaged synergy angle. The computations reveal
enhanced mixing of fluid between the wall layer and the core due to strong
secondary flows produced by vortex generators. The performance analysis indicates
that the RWP was more effective in terms of heat transfer enhancement as compared
to DWP. The field synergy analysis showed that the sites with higher Nusselt number
are associated with smaller synergy angle or better coordination between the velocity
vector and the temperature gradient.
Sun et al [48] tested experimentally and numerically the effect of elliptical
tube in finned-tube heat exchangers (FTHE). Most of the previous studies evaluated
the two tube shapes only based on the air-side performance of FTHE, and did not
consider any interaction effect of the axis ratio with other parameters. among seven
23
design factors including number of rows, axis ratio, transversal tube pitch,
longitudinal tube pitch, fin pitch, air velocity, water volumetric flow rate. Response
surface analysis was used to evaluate the axis ratio effect on the overall thermal
hydraulic performance which was quantified by the heat transfer rate per unit power
consumption. The results showed that the axis ratio strongly interacted with air
velocity and water volumetric flow rate. The increase of axis ratio improved the
overall thermal hydraulic performance at higher air velocity or lower water
volumetric flow rate, but the opposite effect was observed at lower air velocity or
higher water volumetric flow rate.
Tarlet et al [49] studied experimentally a first and second law analysis of the
heat transfer characteristics of a mini shell-and tube heat exchanger equipped with
multi-scale distributor/collector. Experiments of heat exchanger with or without
transverse baffles installed in the shell side were conducted, under laminar flow
conditions (average channel Re number between 8 and 100). The temperature field at
the shell side was obtained by using infrared thermograph. The effects of transverse
baffles on the thermal performance and entropy generation of the heat exchanger
system were quantified and discussed. Experimental results show that the integration
of multi-scale branched distributor and collector guarantees uniform flow distribution
among parallel tubes. The installation of baffles provides a locally cross flow and
globally counter current flow arrangement so that the recirculation, passive zones can
be largely eliminated. Enhancement of heat transfer has been verified by first law
(global heat transfer coefficient) and second law (entropy generation) analyses.
Xuehong et al [50] investigated by numerical study the effect of composite
fin and advantage of longitudinal vortex generator and slit fin, respectively. The
performance of air-side heat transfer and fluid flow was investigated by numerical
simulation for Reynolds number ranging from Re = 304 to 2130. Stepwise
approximation method is applied on the mesh generation for the irregular domains of
delta winglets and slit fins. The mechanism for augmenting heat transfer was also
analysed based on the local fluid field, field synergy principle and entrance
dissipation principle. The numerical results showed that some eddies are developed
behind the X-shaped slit and delta winglet, which produce some disruptions to fluid
flow and enhance heat transfer; compared with plain fin and slit fin, it was found that
24
the composite fin had better heat transfer performance. By applying on the field
synergy principle and entrance dissipation principle to analyse the composite fin, the
results showed that composite fin was improved the synergy of temperature gradient
and velocity fields, and its equivalent thermal resistance was smaller and its
irreversibility of heat transfer is lower.
Yamashita et al [51] studied experimentally a new type of heat exchanger, in
which flue gas flows inside thin tubes and cool water is on the shell side, was
proposed to develop the performance and compactness of shell and tube type heat
exchangers for latent heat recovery from flue gas. The experimental heat transfer
characteristics of single tubes were systematically investigated to determine the
effects of tube diameter (1.0-5.0 mm) and length (7 -100 mm). Furthermore, a
correlation between the non-dimensional bulk mean temperature and the ratio of
effective tube length to the thermal entrance region was proposed and was correlated
well with the measurement data. Prediction of the heat exchanger performance using
this correlation was possible. As a result, it was found that the using mini-tubes is
remarkably effective to reduce the size of heat exchanger due to enhancement of heat
transfer coefficient and enlargement of heat transfer surface. The volume with 1 mm
inner diameter of tubes was approximately 5 present of that with 5 mm in diameter.
Zhao et al [52] numerically studied the heat transfer performance and reduce
erosion of economizers in coal-fired power plants. The heat transfer and erosion
characteristics was tested for the single H-type finned oval tube with enhanced heat
transfer structures including bleeding dimples, longitudinal vortex generators
(LVGs), and compound dimple-LVG. The results showed that the oval tube with
compound LVG-dimple achieved the highest overall heat transfer performance while
the oval tube with LVG works most efficiently in the anti-wear performance. Then
based on the H-type finned oval tube, the LVG structure on the first row of tubes
together with hemisphere protrusions design, while the compound LVG-dimple on
the rest tubes were also simulated. The optimized H-type finned oval tube bank heat
exchanger was demonstrated of high performance on both heat transfer and anti-
wear.
Zhou et al [53] studied experimentally the performance of plane and curved
winglet (rectangular, trapezoidal and delta) vortex generators (VGs) with and without
110
REFERENCES
[1] R. M. Manglik ''Heat transfer Enhancement '', Handbook of Heat Transfer,
(Adrian Bejan and Allan D. Kraus), Wiley & Sons, Inc, Hoboken, New
Jersy, Chapter 14, pp. 1029-1130, 2003.
[2] W.J.Marner and A.E. Bergles. “Augmentation of highly viscous laminar
heat transfer inside tubes with constant wall temperature Experimental
Thermal and Fluid Science, Volume 2, Issue 3, July 1989 pp 252–267
[3] M. Sohal, J. O’Brien, Improving air-cooled condenser performance
usingwinglets and oval tubes in a geothermal power plant, Geotherm. Res.
Counc. Trans. 25 (2001) 1–7.
[4] S. Tiwari, D. Maurya, G. Biswas, V. Eswaran, Heat transfer enhancement in
cross-flow heat exchangers using oval tubes and multiple delta winglets, Int.
J Heat Mass Transfer 46 (15) (2003) 2841–2856.
[5] P. Chu, Y. He, Y. Lei, L. Tian, R. Li, Three-dimensional numerical study on
finand–oval-tube heat exchanger with longitudinal vortex generators, Appl.
Therm. Eng. 29 (2009) 859–876.
[6] A. Joardar, A. Jacobi, A numerical study of flow and heat transfer
enhancement using an array of delta-winglet vortex generators
in a fin-and-tube heat exchanger, J. Heat Transfer 139 (2007)
1156–1168.
[7] C. Lin, Y. Liu, J. Leu, Heat transfer and fluid flow analysis for plate-fin and
oval tube heat exchangers with vortex generators, Heat Transfer Eng. 29
(2008) 588–596.
[8] Y. Chen, M. Fiebig, N. Mitra, Conjugate heat transfer of a finned oval
tubewith a punched longitudinal vortex generator in form of delta winglet–
parametric investigations of the winglet, Int. J. Heat Transfer 41 (1998)
3961–3978.
[9] Y. Chen, M. Fiebig, N. Mitra, Heat transfer enhancement of a finned oval
tube with punched longitudinal vortex generators in line, Int. J. Heat
Transfer 41(1998) 4151–4166.
[10] Y. Chen, M. Fiebig, N. Mitra, Heat transfer enhancement of finned oval
111
tubes with staggered punched longitudinal vortex generators, Int. J. Heat
Transfer 43 (2000) 417–435.
[11] G. Biswas, K. Torii, D. Fujii, K. Nishino, Numerical and experimental
determination of flow structure and heat transfer effects of longitudinal
vortices in a channel flow, Int. J. Heat Mass Transfer 39 (1996) 3441–
3451.
[12] F. Dupont, C. Gabillet, P. Bot, Experimental study of the flow in a compact
heat exchanger channel with embossed-type vortex generators, J. Fluids
Eng. 125(2003) 701–709.
[13] A. Jain, G. Biswas, D. Maurya, Winglet-type vortex generators with
commonflow-up configuration for fin-tube heat exchangers, Numer. Heat
Transfer, Part A 43 (2003) 201–219.
[14] M. Gupta, K. Kasana, R. Vasudevan, A numerical study of the effect on
flow structure and heat transfer of a rectangular winglet pair in a plate fin
heat exchanger, Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 223
(2009) 2109–2115.
[15] X.B. Zhao, G.H. Tang, X.W. Ma, Y. Jin, W.Q. Tao “Numerical investigation
of heat transfer and erosion characteristics for H-type finned oval tube
with longitudinal vortex generators and dimples” Applied Energy 127
(2014) 93–104.
[16] Zhang YH, Wu X, Wang LB, Song KW, Dong YX, Liu S. “Comparison of
heat transfer performance of tube bank fin with mounted vortex generators
to tube bank fin with punched vortex generators”.Exp Thermo Fluid .
33(2008)58–66.
[17] Ya-Ling He , Pan Chu, Wen-Quan Tao, Yu-Wen Zhang, Tao Xie “Analysis
of heat transfer and pressure drop for fin-and-tube heat exchangers with
rectangular winglet-type vortex generators”. Applied Thermal Engineering
(2012)p 1-14.
[18] Henk Huisseune , Christophe T’Joen, Peter De Jaeger, Bernd Ameel, Sven
De Schampheleire, Michel De Paepe “Performance analysis of a
compound heat exchanger by screening its design parameters” Applied
Thermal Engineering (2013).p 490-501.
[19] Henk Huisseune , Christophe T’Joen, Peter De Jaeger, Bernd Ameel,Sven
De Schampheleire a, Michel De Paepe “Performance enhancement of a
112
louvered fin heat exchanger by using delta winglet vortex generators”
International Journal of Heat and Mass Transfer (2013) 475–487.
[20] Yong-Gang Lei, Ya-Ling He, Li-Ting Tian, Pan Chu, Wen-Quan Tao
“Hydrodynamics and heat transfer characteristics of a novel heat
exchanger with delta-winglet vortex generators” Chemical Engineering
Science (2010)p1551–1562.
[21] Liting Tian, Yaling He, Yubing Tao, Wenquan Tao “A comparative study
on the air-side performance of wavy fin-and-tube heat exchanger with
punched delta winglets in staggered and in-line arrangements”
International Journal of Thermal Sciences .(2009) p1765–1776.
[22] S. Tiwari, D. Maurya, G. Biswas, V. Eswaran. “Heat transfer enhancement
in cross-flow heat exchangers using oval tubes and multiple delta
winglets”. International Journal of Heat and Mass Transfer. (2003) p
2841–2856.
[23] J.M. Wua, W.Q. Tao,“Impact of delta winglet vortex generators on
the perfor-mance of a novel fin-tube surfaces with two rows of
tubes in different diameters”, Energy Conversion and Management
vol.52 ,2011,pp 2895–2901.
[24] C.Habchi, S.Russeil, D. Bougeard, J. Harion, T. Lemenand, D.Valle, H.
Peerhossaini,“Enhancing heat transfer in vortex generator-type
multifunctional heat exchangers”, Applied Thermal Engineering ,vol.38
,2012,pp 14–25.
[25] M. J.Lawson, K.A. Thole, “Heat transfer augmentation along the tube
wall of a louvered fin heat exchanger using practical delta winglets”, Int.
Comm. in Heat and Mass Transfer ,vol.51 , 2008, pp 2346–2360.
[26] Ya-Ling He, Pan Chu, Wen-Quan Tao, Yu-Wen Zhang, T. Xie,“Analysis
of heat transfer and pressure drop for fin-and-tube heat exchangers with
rectangular winglet-type vortex generators”, Applied Thermal
Engineering, 2012. In Press.
[27] A. Lemouedda ,M. Breuer , E. Franz , T. Botsch , A.Delgado, “Optimization
of the angle of attack of delta-winglet vortex generators in a plate-fin-and-
tube heat exchanger”, Int. J. of Heat and Mass Transfer ,vol.53 ,2010,pp
5386–5399.
[28] J. Li, S. Wanga, J. Chen , Y. Lei, “Numerical study on a slit fin-and-tube
heat exchanger with longitudinal vortex generators”, Int. J. of Heat and
Mass Transfer, vol.54,2011, pp 1743–1751.
[29] S. Eiamsa-ard, P. Promvonge, “Influence of Double-sided Delta-wing
Tape Insert with Alternate-axes on Flow and Heat Transfer Characteristics
113
in a Heat Exchanger Tube”, Fluid Flow and Transport Phenomena, vol.19 ,
2011,pp 410–423.
[30] J. M. Wu, W.Q. Tao, “Effect of longitudinal vortex generator on heat
transfer in rectangular channels”, Applied Thermal Engineering, vol.37,
2012, pp 67–72.
[31] I. Kotcioglu, S. Caliskan, A. Cansiz, S. Baskaya, “Second law analysis and
heat transfer in a cross-flow heat exchanger with a new winglet-type
vortex generator”, Energy ,vol.35 ,2010,pp 3686–3695.
[32] P. Promvonge, S. Eiamsa-ard, “Heat transfer and turbulent flow friction in
a circular tube fitted with conical-nozzle turbulators”, Int. J. of Heat and
Mass Transfer, vol. 34, 2007, pp 72–82.
[33] J.M. Wua, W.Q. Tao,“Impact of delta winglet vortex generators on the
perfor-mance of a novel fin-tube surfaces with two rows of tubes in
different diameters”, Energy Conversion and Management ,vol.52
,2011,pp 2895–2901.
[34] C.Habchi, S.Russeil, D. Bougeard, J. Harion, T. Lemenand, D.Valle, H.
Peerhossaini,“Enhancing heat transfer in vortex generator-type
multifunctional heat exchangers”, Applied Thermal Engineering ,vol.38
,2012,pp 14–25.
[35] Han Taw Chen, Wei-Lun Hsu, Estimation of heat transfer co efficient on
the fin of annular finned tube heat exchangers in natural convection for
various fin spacings, International Journal of Heat & Mass Transfer (2007)
1750-1761.
[36] Choi, Jong Min; Kim, Yonghan; Lee, Mooyeon; Kim, Yongchan. Applied
Thermal Engineering vol. 30 issue 2-3 February, 2010. p. 174-180
[37] N.Nagarani and K. Mayilsamy (2010). "EXPERIMENTAL HEAT
TRANSFER ANALYSIS ON ANNULAR CIRCULAR AND
ELLIPTICAL FINS." International Journal of Engineering Science and
Technology 2(7): 2839-2845
[38] Alam, Tabish; Saini, R.P.; Saini, J.S. Renewable and Sustainable Energy
Reviews vol. 31 March, 2014. p. 289-304
[39] X.P. Du, M. Zeng, Z.Y. Dong “Wang Experimental study of the effect of
air inlet angle on the air-side performance for cross-flow finned oval-tube
heat exchangers” Experimental Thermal and Fluid Science. 52 (2014) pp
146–155
114
[40] Xiaoze Du, Lili Feng, Li Li, Lijun Yang, Yong ping Yang “Heat transfer
enhancement of wavy finned flat tube by punched longitudinal vortex
generators.
[41] Vipin B.Gawande, A.S.Dhoble,D.B.Zodpe “Effect of roughness geometries
on heat transfer enhancement in solar thermal systems – A review”
32(2014) pp347–378
[42] A.A. Gholami, Mazlan A.Wahid, H.A. Mohammed “Heat transfer
enhancement and pressure drop for fin-and-tube compact heat
exchangers with wavy rectangular winglet-type vortex generators”
International Communications in Heat and Mass Transfer 54
(2014) 132–140
[43] A. Hasanpour, M. Farhadi , K. Sedighi “A review study on twisted tape
inserts on turbulent flow heat exchangers: The overall enhancement ratio
criteria” International Communications in Heat and Mass Transfer 55
(2014) 53–62
[44] M. Khoshvaght-Aliabadi, F. Hormozi, A. Zamzamian “Role of channel
shape on performance of plate-fin heat exchangers: Experimental
assessment” International Journal of Thermal Sciences 79 (2014) 183e193,
[45] M.J. Li, W.J. Zhou, J.F. Zhang, J.F. Fan, Y.L. He, W.Q. Tao “Heat transfer
and pressure performance of a plain fin with radiantly arranged winglets
around each tube in fin-and-tube heat transfer surface” International
Journal of Heat and Mass Transfer 70 (2014) 734–744
[46] Paola Ranut , Gábor Janiga , Enrico Nobile , Dominique Thévenin “Multi-
objective shape optimization of a tube bundle in cross-flow” International
Journal of Heat and Mass Transfer 68 (2014) 585–598
[47] Pankaj Saha, Gautam Biswas , Subrata Sarkar “Comparison of winglet-
type vortex generators periodically deployed in a plate-fin heat exchanger
– A synergy based analysis” International Journal of Heat and Mass
Transfer 74 (2014) 292–305
115
[48] Lei Sun, Chun-Lu Zhang “Evaluation of elliptical finned-tube heat
exchangerperformance using CFD and response surface methodology”
International Journal of Thermal Sciences 75 (2014) 45e53
[49] Dominique Tarlet, Yilin Fan, Stéphane Roux, Lingai Luo “Entropy
generation analysis of a mini heat exchanger for heat transfer
intensification” Experimental Thermal and Fluid Science 53 (2014) 119–
126
[50] Wu Xuehong, Zhang Wenhui, Gou Qiuping, Luo Zhiming, Lu Yanli
“Numerical simulation of heat transfer and fluid flow characteristics of
composite fin” International Journal of Heat and Mass Transfer 75 (2014)
414–424
[51] Junpei Yamashita, Yoshio Utaka “Improved performance of secondary heat
exchanger for latent heat recovery from flue gas using mini-tubes” Applied
Thermal Engineering 67 (2014) 230e239
[52] X.B. Zhao, G.H. Tang X.W. Ma, Y. Jin, W.Q. Tao “Numerical
investigation of heat transfer and erosion characteristics for H-type
finned oval tube with longitudinal vortex generators and dimples”
Applied Energy 127 (2014) 93–104
[53] Guobing Zhou*, Zhizheng Feng “Experimental investigations of heat
transfer enhancement by plane and curved winglet type vortex
generators with punched holes” International Journal of Thermal
Sciences 78 (2014) 2635
[54] Anderson, John D. (1995). Computational Fluid Dynamics: The Basics
with Applications. Science/ Engineering/Math. McGraw-Hill Science.
[55] Patankar, Suhas (1980). Numerical Heat Transfer and Fluid
Flow.Hemisphere Series on Computational Methods in Mechanics and
Thermal Science.Taylor & Francis.
[56] M.Venturino, P.Rubini, “Coupled fluid flow and heat transfer analysis of
steel reheat furnaces”, School of Mechanical Cranfield University, 1995.
[57] R. S. Vajjha, D. K. Das, D. P. Kulkarni, “Development of new correlations
for convective heat transfer and friction factor in turbulent regime for
116
nanofluids”,Int. J.of Heat and Mass Transfer,vol. 53, 2010,pp4607.4618
[58] M. Corcione, “Empirical correlating equations for predicting the effective
thermal conductivity and dynamic viscosity of nanofluids”, Energy
Conversion and Management, vol.52, 2011, pp 789–793.