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OPTIMAL GEOMETRIC ARRANGEMENT OF UNFINNED AND
FINNED FLAT TUBE HEAT EXCHANGERS UNDER
LAMINAR FORCED CONVECTION
TAHSEEN AHMAD TAHSEEN
Thesis submitted in fulfilment of the requirements
for the award of the degree of
Doctor of Philosophy in Mechanical Engineering
Faculty of Mechanical Engineering
UNIVERSITI MALAYSIA PAHANG
2014
vi
ABSTRACT
This thesis describes the three-dimensional numerical analysis and experimental study
of the heat transfer and flow characteristics in the un-finned and finned flat tube heat
exchangers for in-line and staggered configurations. Flat tubes are vital components of
various technical applications including modern heat exchangers, thermal power plants,
and automotive radiators. The objectives of this research are to develop a numerical
code to predict the thermal–hydraulic characteristics of laminar forced convective flow,
to identify optimal spacing tube-to-tube and fin-to-fin for the maximum overall heat
transfer rate and minimum power pumping of the fan between the tube bundle and
surrounding fluid at the fixed volume and to develop a new correlation for overall heat
transfer rate and power pumping in general and optimum configurations. Conservation
equations (mass, momentum, and energy) were solved to develop code utilizing Visual-
FORTRAN based on finite volume technique to determine the temperature and velocity
fields. Subsequently, the overall heat transfer rate and power pumping among the tubes,
fins, and fluid flow were calculated. The algorithm of semi-implicit method for
pressure-linked equations was utilized to link the pressure fields with velocity. Finally,
the subsequent set of discretization equations was solved with line-by-line method of
the tri-diagonal matrix algorithm and the Gauss–Seidel’s procedure. Twelve fixed tubes
were used in the experimental setup for flat tube configurations were obtained with
these uniformly fitted tubes with a fixed volume. The experimental setups with several
arrays of tubes and fins were fabricated with the same volume. The results were
reported of the external air flow in a range of Reynolds numbers based on the hydraulic
diameter of 178 to 1,470. It can be observed from the obtained results that the
geometric optimum for tube-to-tube spacing was (St/dT 1.6) in the in-line
configuration and (St/dT 2.0) in the staggered configuration. Meanwhile, fin-to-fin
spacing was f = 0.025, according to general dimensionless variables. Up to 1.48 and
1.11 times (in-line) as well as 2.3 and 1.4 times (staggered) of heat transfer gain were
noted in the optimal configuration for the low and high Reynolds numbers. A newly
developed correlation of heat transfer rate and power pumping was then proposed.
Approximately 87.5 % of the database described the heat transfer correlation within ±
15 % for the in-line configuration. For the staggered arrangement, 82% of the deviations
were within ± 15 %. Up to 97.2 % of the database can be correlated with the proposed
power pumping correlation within ± 18 % for the in-line arrangement, and 86.2% of the
deviations were within ±15 % for the staggered arrangement. In the in-line
configuration, the mean errors of the heat transfer and power pumping correlations were
9.5 % and 12.2 %, respectively. In the staggered configuration, the mean deviation
errors of heat transfer and power pumping correlations were found to be 9.5 % and 11.1
%, respectively. The predictive correlations developed in this study for in-line and
staggered configurations can predict the heat transfer rate and power pumping of both
un-finned and finned flat tube heat exchangers, which can be applied to the design of
future heat exchangers in the industry.
vii
ABSTRAK
Tesis ini menerangkan tiga demensi analisa berangka dan kajian eksperimen
pemindahan haba serta ciri-ciri aliran tiub penukar haba bersirip dan tidak bersirip
dalam bentuk sususan sebaris dan susunan tak serentak. Tiub rata adalah komponen
penting dalam pelbagai aplikasi teknikal termasuk dalam penukar haba moden,
janakuasa terma, dan radiator otomotif. Penyelidikan ini bertujuan untuk menbangunkan
kod berangka bagi meramalkan ciri-ciri terma-hidraulik lamina aliran olakan paksa,
menentukan jarak optima antara tiub-tiub dan juga sirip-sirip, pada maksimum
keseluruhan kadar pemindahan haba dan minima kuasa pengepaman kipas diantara
susunan tiub dan bendalir sekitar, pada isipadu tetap dan juga membangunkan korelasi
baru kadar pemindahan haba dan kuasa pengepaman pada konfigurasi umum dan
optimum. Persamaan pengabdian (jisim, momentum dan tenaga) telah diselesaikan
untuk membangunkan kod menggunakan Visual-FORTRAN berdasarkan teknik isipadu
terhingga untuk menentukan suhu dan halaju lapangan. Seterusnya, kadar keseluruhan
pemindahan haba di kalangan tiub, sirip, dan bendalir telah dikira. Algoritma separuh-
tersirat untuk persamaan tekanan-berkaitan telah digunakan untuk menghubungkan
tekanan lapangan dengan halaju. Akhir sekali, persamaan pendiskretan set berikutnya
telah diselesaikan dengan kaedah matriks algoritma garis demi garis tiga-pepenjuru dan
tatacara Gauss-Seidel. Dua belas tiub tetap telah digunakan dalam persediaan
eksperimen untuk konfigurasi tiub rata,tiub-tiub yang dipasang seragam dengan isipadu
tetap.. Eksperimen disediakan dengan beberapa tatasusunan tiub-tiub dan sirip-sirip
telah difabrikasi pada isipadu yang sama Keputusan telah dilaporkan aliran udara luar
pada julat nombor Reynolds berdasarkan diameter hidraulik antara 178 ke 1,470. Dari
keputusan didapati geometri optimum untuk jarak tiub ke tiub adalah (St/dT 1.6) pada
konfigurasi sebaris dan (St/dT 2.0) pada konfigurasi susunan tak serentak. Sementara
itu, jarak antara sirip ke sirip adalah Πf = 0.025 mengikut pemboleh ubah umum tak
berdimensi. Gandaan pemindahaan haba sehingga 1.48 dan 1.11 kali (sebaris) dan 2.3
dan 1.4 kali (susunan tak serentak) diperhatikan adalah konfigurasi optimum bagi
nombor Reynolds yang rendah dan tinggi. Satu korelasi baru dibangunkan daripada
kadar pemindahan haba dan kuasa mengepam seterusnya telah dicadangkan. Kira-kira
87.5 % daripada pangkalan data menyifatkan korelasi pemindahan haba dalam
lingkungan ± 15 % bagi konfigurasi sebaris. Untuk susunan tak serentak, 82% daripada
sisihan berada dalam lingkungan ± 15 %. Sehingga 97.2 % daripada pangkalan data
boleh dikaitkan dengan cadangan korelasi kuasa mengepam dalam lingkungan ±18%
untuk susunan sebaris, dan 86.2% daripada sisihan berada dalam lingkungan ± 15 %
bagi susuanan tak serentak. Dalam konfigurasi sebaris, ralat min korelasi pemindahan
haba dan kuasa mengepam adalah masing-masing 9.5 % dan 12.2 %. Dalam konfigurasi
tak serentak, ralat min sisihan korelasi pemindahan haba dan kuasa mengepam masing-
masing adalah 9.5 % dan 11.1 %. Kaitan ramalan telah dibangunkan dalam kajian ini
untuk kedua-dua konfigurasi sebaris dan tak serentak yangboleh meramalkan kadar
pemindahan haba dan kuasa mengepam untuk kedua-dua penukar haba tiub rata bersirip
dan tidak bersirip yang mana ia boleh diaplikasi untuk merekabentuk penukar haba
masa depan di industri.
viii
TABLE OF CONTENTS
Page
SUPERVISOR'S DECLARATION ii
STUDENT'S DECLARATION iii
ACKNOWLEDGEMENTS v
ABSTRACT vi
ABSTRAK vii
TABLE OF CONTENTS viii
LIST OF TABLES xi
LIST OF FIGURES xii
NOMENCLATURES xvi
CHAPTER I INTRODUCTION
1.1 Introduction 1
1.2 Problem Statement 3
1.3 Objectives of the Study 4
1.4 Scope of the Study 4
1.6 Organization of the Thesis 5
CHAPTER II LITERATURE REVIEW
2.1 Introduction 6
2.2 Background of Tubes Bank 7
2.3 Flow and Geometric Parameters 12
2.3.1 External Velocity of Fluid 12
2.3.2 Tube Diameter 14
2.3.3 Tube Rows 15
2.3.4 Tubes Pitch 17
2.3.5 Fins Pitch 22
2.3.6 Optimal Spacing 27
2.4 Correlations of Thermofluids 29
2.5 Flat Tube and Other Shapes 42
2.5.1 In-line and Staggered Configurations 42
2.5.2 Tubes Array between Parallel Plates 43
ix
2.6 Summary 44
CHAPTER III EXPERIMENTAL STUDY AND COMPUTATIONAL
MODELLING
3.1 Introduction 46
3.2 Strategy Frame of the Study 46
3.3 Experimental Details 48
3.3.1 Constrnction of Test Rig Details 48
3.3.2 Experimental Procedure 54
3.3.3 Experimental Approach 56
3.3.4 Experimental Uncertainty 58
3.4 Computational Modelling 62
3.4.1 Problem Description 62
3.4.2 Governing Equations 63
3.4.3 Boundary Conditions 67
3.4.4 Definition of the Performance Parameters 70
3.4.5 Numerical Solution 75
3.4.6 Pressure Correction 91
3.4.7 Solution Algorithm 95
3.4.8 Solution Procedure 97
3.4.9 Computer Programme 97
3.5 Summary 100
CHAPTER IV RESULTS AND DISCUSSION
4.1 Introduction 101
4.2 Validation of the Computational Model 101
4.3 Grid Independence Tests 104
4.4 Optimal Geometry Configuration 105
4.4.1 Overall Heat Transfer Rate 106
4.4.2 Dimensionless Pressure Drop and Dimensionless Power
Pumping
126
4.4.3 Mass Fraction Material 138
4.5 Newly Develop Correlations 140
4.5.1 Correlations for General Configuration 141
4.5.2 Correlation for Optimum configuration 148
4.6 Parametric Analysis in Optimal Geometry 155
4.6.1 Flow Field 156
x
4.6.2 Thermal Field 162
4.7 Summary 165
CHAPTER V CONCLUSIONS AND RECOMMENDATION
5.1 Introduction 166
5.2 Summary of Findings 166
5.3 Contributions of the study 168
5.4 Recommendations for Future Work 169
REFERENCES
LIST OF PUBLCATIONS
APPENDICES
A INSTRUMENT CALIBRATION 192
A.1 Calibration Wind Tunnel and Air Velocity Profile 192
A.2 Thermistor Calibration 194
B ANALYSIS OF THE EXPERIMENTAL UNCERTAINTY 196
B.1 Analysis of Uncertainty for Independent Parameters 196
B.1.1 Dimensions Uncertainty 197
B.1.2 Uncertainty Estimation of the Thermistor (Temperature) 201
B.1.3 Estimation of Flow Characteristics 204
B.2 Uncertainty for Dependent Parameters 205
B.2.1 Uncertainty Estimation of Air Properties 205
B.2.2 Estimation of Uncertainty for Overall Electrical Power
Supplier 207
B.2.3 Estimation of Uncertainty for Volumetric Heat Transfer Rate 209
B.2.4 Estimation of Uncertainty for Reynolds Number 209
B.2.5 Estimation of Uncertainty for Prandtl Number 210
B.2.7 Estimation of Uncertainty for Mass Flow Rate 210
B.2.8 Estimation of Uncertainty for Power Pumping 211
C TABULATION OF SAMPLE OF EXPERIMENTAL DATA AND
RESULTS
212
D TRANSFORMATION MATRICES 260
E THREE DIMENSION DIMENSION GRID GENERATION
CODE FOR IN-LINE CONFIGURATION
263
xi
LIST OF TABLES
Table No. Title Page
2.1 The power and constant cofficents of Nusselt number and
friction factor equations
35
2.2 The correlations constant of Sherwood number and friction loss 37
2.3 Details more correlations with condition and geometry
parameters
39
3.1 Summary of the experimental uncertainty 59
3.2 System variables of the general transport equation, the diffusion
coefficient and the source term
84
3.3 Approximation of depravities at control volume faces for any
variable
90
4.1 Comparison between for present study and Bahaidarah et al.
(2005) for the geometrical parameters and average Nusselt
number.
102
4.2 Geometric parameters of cylinder tube heat exchanger for model
validation
103
4.3 Grid refinement test and proportional error analysis with
different grid sizes for in–line and staggered configurations
105
4.4 Geometric parameters of flat tube heat exchanger for in-line and
staggered arrangements
106
4.5 Constants for Dimensionless overall heat transfer rate and
dimensionless power pumping correlations and determination of
correlation
143
4.6 Coefficients for the correlations of dimensionless overall heat
transfer
149
4.7 Constants for the correlations of dimensionless power pumping 152
xii
LIST OF FIGURES
Figure No. Title Page
2.1 The configurations of finned round and flat tube heat exchanger 8
2.2 The configurations of round tube banks heat exchanger (a) In-
line (b) staggered, and (c) side view
9
2.3 The nomenclature of staggered tube bundle configuration 19
2.4 The heat transfer and friction characteristics of a four-row plain
plate heat exchanger for several fin pitches
23
2.5 j-factor and fin friction with Reynolds number based on the
row pitch
24
2.6 Mean coefficients of heat transfer for plain plate-finned tubes
(571 fins/m) with the six rows
25
3.1 Flow chart of research methodology 47
3.2 A photograph for the experimental setup 49
3.3 Schematic diagram of experimental setup with dimensions
(mm)
50
3.4 The Teflon and plastic module of flat tube for in–line and
staggered configurations
51
3.5 The thermistor assembly 54
3.6 Flow chart of the steps in the experimental work 57
3.7 Flow chart of the steps for finding the experimental uncertainty 61
3.8 Flat tube surface area better compare with classical circular
tube shape
63
3.9 Flat tube bundle: (a) In–line and (b) Staggered configuration
and (c) Side cross section view
64
3.10 Three-dimensional un-finned and finned flat tube heat
exchanger
65
3.11 A typical 3D computational domains and boundary conditions 69
3.12 Coordinate system for the flat tube bank in (a) Physical domain 76
xiii
of in–line arrangement, (b) Physical domain of staggered
arrangement and (c) Computational domain
3.13 Relationship between the physical and computational domain in
2D and 3D plane
78
3.14 Grid generated in 2D and 3D for finned flat tube heat
exchanger
81
3.15 Typical P-control volume in staggered and collocated grid
arrangements in 2D Cartesian coordinates
82
3.16 Two and three–dimensional control volume and neighbouring
nodes in computational domain
85
3.17 Separation of the two-dimensional control volume 89
3.18 Flow chart of the computer programme 99
4.1 Comparison between the current numerical results with
previous published experimental results for the overall heat
transfer rate
103
4.2 Overall heat transfer rate against dimensionless tube spacing
with varied dimensionless fin density
109
4.3 Dimensionless overall heat transfer rate against dimensionless
tube spacing with the several dimensionless fins density
110
4.4 Dimensionless overall heat transfer rate versus dimensionless
fins density with various dimensionless tubes spacing
112
4.5 Variation of overall dimensionless heat transfer rate against
dimensionless tubes spacing and dimensionless fins density for
various Reynolds number
113
4.6 Dimensionless overall heat transfer rate against Reynolds
number for dimensionless tubes spacing and dimensionless fins
density for in-line configuration
115
4.7 Dimensionless overall heat transfer rate with tube–to–tube
spacing and dimensionless fins density against Reynolds
number
116
4.8 Overall heat transfer rate against dimensionless tube spacing
with different dimensionless fins density
118
4.9 The influence of tube–to–tube spacing and Reynolds number on
the dimensionless overall heat transfer rate for different
119
xiv
dimensionless fins density
4.10 Dimensionless overall heat transfer rate against dimensionless
fins density for various tube–to–tube spacing for staggered
configuration
121
4.11 Trends of dimensionless overall heat transfer rate with
dimensionless fins density and tube–to–tube spacing for
different Reynolds number
122
4.12 Influence of Reynolds number on dimensionless overall heat
transfer rate for tube–to–tube spacing and dimensionless fins
density on staggered configuration
124
4.13 Effect of Reynolds number on dimensionless overall heat
transfer rate for dimensionless fins density and tube–to–tube
spacing on staggered configuration
125
4.14 Dimensionless pressure drop with dimensionless tubes spacing
for several dimensionless fins density
128
4.15 Dimensionless power pumping against dimensionless tubes
spacing for different dimensionless fins density
129
4.16 Influence of dimensionless fins density on dimensionless power
pumping with dimensionless tubes spacing for various
Reynolds numbers
131
4.17 Influence of Reynolds number on dimensionless power
pumping with dimensionless fins density for various tube–to–
tube spacing
132
4.18 Dimensionless pressure drop against dimensionless tubes
spacing for different dimensionless fins density
134
4.19 Variation of dimensionless power pumping with dimensionless
tubes spacing for different dimensionless fins density
135
4.20 Effect of dimensionless fins density on dimensionless power
pumping with dimensionless fins density for different Reynolds
numbers
137
4.21 Influence of Reynolds number on dimensionless power
pumping against dimensionless fins density for different
dimensionless tubes spacing
138
4.22 Mass fraction of un–finned and tube configurations with tube–
to–tube spacing and dimensionless fin density
139
4.23 Correlation and relative error of predicted dimensionless 144
xv
overall heat transfer rate for in–line arrangement
4.24 Correlation and relative error of predicted dimensionless
overall heat transfer rate for staggered arrangement
145
4.25 Correlation and relative error of predicted dimensionless power
pumping with an in–line arrangement
146
4.26 Correlation and relative error of predicted dimensionless power
pumping with a staggered arrangement
147
4.27 Comparison between the prediced dimensionless overall heat
transfer rate with experimental results for the optimal tube–to–
tube spacing
150
4.28 Comparison between the prediced dimensionless overall heat
transfer rate with experimental results for the optimal
dimensionless fins density
151
4.29 Comparison dimensionless power pumping correlation with
experimental results for the optimal tube–to–tube spacing
153
4.30 Comparison of the dimensionless power pumping correlation
with experimental results for the optimal dimensionless fin
density
154
4.31 Dimensionless velocity profiles at section behind each tube
along the flow direction with Reynolds number on the optimal
tubes spacing for in–line configuration
157
4.32 Dimensionless velocity profiles at section behind each tube
along the flow direction with Reynolds number on the optimal
tubes spacing for staggered configuration
158
4.33 Mean streamlines patterns with Reynolds number in the optimal
tubes spacing for in–line configuration
160
4.34 Mean streamlines patterns with Reynolds number in the optimal
tubes spacing for staggered configuration
161
4.35 Isotherm floods patterns with Reynolds number at the optimal
tube–to–tube spacing in an in–line configuration
163
4.36 Isotherm floods patterns with Reynolds number at the optimal
tube–to–tube spacing in staggered configuration
164
xvi
NOMENCLATURES
Symbol Description and Unit
2D Two dimensional
3D Three dimensional
A Area, m2
Ac Cross-sectional area
BFC Body fitted coordinates
CFD Computational fluid dynamic
CV Control volume
CVFEM Control-volume finite element method
cp Specific heat, J/(kg K)
d Diameter of round tube, m
Dh Hydraulic diameter, m
dL Longitudinal diameter of flat tube, m
dT Transverse diameter of flattened tube, m
E Input voltage, Volt
Er Relative error
FVM Finite volume methods
G1, G2, G2 Contravariant velocity components
GE Governing equations
GIT Grid independency test
Hy Array height, m
HEM Heat exchanger module
HRSG Heat recovery steam generator
xvii
I Input current, A
J Jacobian of the transformation
k Thermal conductivity of air, W/(m K)
L Array width, m
LES Large eddy simulation
Ecm Air mass flow rate entering one elemental channel, kg/s
M Node number of the grid in -direction
MEr Mean relative error
N Node number of the grid in -direction
nf Fins number
p Pressure, Pa
pf Fins pitch, m
PDE Partial differential equation
PFTHE Plain fin-and-tube heat exchangers
qin Input heat, W
Qq Overall heat transfer rate, W
R2 Coefficient of determination
RTD Resistance temperature detector
S Source term
SIMPLE Semi-implicit methods pressure-linked equation
SOR Gauss-Seidel successive over relaxation
St Tubes spacing, m
Stotal Total source terms
,S Source term due to nonorthogonality
xviii
S Source term of
t Tube thickness, m
T Temperature, oC
Average temperature, oC
T* Dimensionless temperature
TDMA Tri–diagonal matrix algorithm
u*,v*,w* Dimensionless velocity components
u,v,w Velocity components, m/s
Wx Array length, m
x*, y*, z* Dimensionless Cartesian coordinates
x, y, z Cartesian coordinates, m
pH Power pumping, W
Dimensionless Groups
Nu Average Nusselt number
qQ~
Dimensionless overall thermal conductance
~ Dimensionless overall thermal conductance
*TS Dimensionless spacing between rows of tubes
*sm~ Dimensionless mass of solid material (mass fraction)
f Friction factor
j Colburn factor
Nu Nusselt number
Pr Prandtl number
Re Reynolds number
pH~
Dimensionless power pumping
xix
Greek Symbols
,, Coefficients of transformation
Dimensionless fin density in direction z
Underrelaxation factor of
Diffusion coefficient
Δp Pressure drop, Pa
Δp* Dimensionless pressure drop in cross flow
Δx, Δy, Δz Dimensions of the computational cell
ε Emissivity
μ Dynamic viscosity, N s/m2
ρ Density, kg/m3
, Curvilinear coordinates
σ Slandered deviation
General dependent variable
Subscripts and superscripts
" Corrected values
* Dimensionless quantity
** Uncorrected values
1 First node to the wall
a Air
e, w, n, s, b, t Adjacent faces to the main point P
E, W, N, S, B, T Adjacent points to the main point P
f Fin
h Hydraulic
xx
i Inside
i, j, k Index notations or coordinate direction identifiers
in Inlet, Input
L Longitudinal
Max Maximum value
o Outside
out Outlet
T Transverse
s Surface
t Tube
to Total
w Tube wall
CHAPTER I
INTRODUCTION
1.1 INTRODUCTION
Substantial research effort has been exerted to improve the efficiency of heat
exchangers because of the widespread use of these devices in industrial, transportation,
and domestic applications, including thermal power plants, means of transport, heating
and air conditioning systems, electronic equipment, and space vehicles (Incropera et al.
2011). Increasing the efficiency of heat exchangers would greatly reduce the cost,
space, and materials required in their use (Bejan and Kraus, 2003). The demand for
increased supply of energy continues to increase in all facets of society. The answer to
this demand is the intelligent use of available energy. The utilization of available energy
to optimize industrial processes has been a popular research topic in recent years
because of the extensive use of heat exchangers in industrial applications, such as tube
arrangements, un-finned and finned systems, refrigeration, air conditioners, and heaters
(Webb and Kim, 2007). The heat exchanging equipment in these devices must be
designed such that they can be accommodated by the devices that enclose them.
Therefore, an optimized heat exchanger would provide maximum heat transfer for a
given space (Bejan, 2000; Bejan and Lorente, 2008). Such equipment strikes a balance
between reduction in size or volume and maintenance and enhancement of its
performance.
Improving the performance of heat exchangers is important because of the
economic and environmental effects of these devices. The loss incurred during
operation can be reduced by rationalizing the use of available energy. The volume
incurred by the array of tube heat exchangers should be fixed. Heat exchangers must be
2
fitted according to available space (Bejan, 2000) through a process called volume
constrained optimization. In this process, the optimal spacing between tubes of known
geometry is determined in a manner that maximizes the overall heat transfer (thermal
conductance) between the array and the surrounding fluid. The development of cooling
techniques for electronic packages is a common example of basic optimization.
Considerable effort has been exerted to determine the optimal spacing for various
geometric configurations, be it natural or forced convection (Bar–Cohen and Rohsenow,
1984; Bejan, 2004; Bejan and Sciubba, 1992; Kim et al., 1991; Knight et al., 1991,
1992; Ledezma et al., 1996; Matos et al., 2004).
Flat tubes are vital components in various technical devices, including modern
heat exchangers and automotive radiators. Although many researchers have studied
fluid flow and heat transfer in objects of various shapes, flat tubes have not been fully
investigated (Bahaidarah, 2004). Flat tubes have been recently incorporated into
automotive air conditioning evaporators and condensers. Their cost has been reduced
because of the developments in automotive brazed aluminum manufacturing technology
(Min and Webb, 2004; Webb and Kim, 2007). Compared with circular tube heat
exchangers, flat tube heat exchangers have lower air–side pressure drop and higher air–
side heat transfer coefficients. Given their smaller wake area, flat tube heat exchangers
are likely to have lower pressure drop than circular tube heat exchangers. The same
reason accounts for the smaller amount of vibration and noise in flat tube heat
exchangers than in circular tube heat exchangers (Bahaidarah, 2004). The external heat
transfer coefficient of the tube as well as the pressure drop of the fluid flowing
externally are the most critical design variables of tubular heat exchangers (Webb and
Kim, 2007). From nuclear reactors to refinery condensers, various energy conversion
and chemical reaction systems have been installed with tubular heat exchangers in them.
Tube configurations have been reported to positively affect heat transfer (Nishiyama et
al., 1988; Wung et al., 1986)
Determining the optimal geometry is important to maximize the volumetric heat
transfer under the volumetric constraint and reduce the pressure drop (power pumping).
In this study, the geometric parameters were first identified to initiate the optimization
3
of the overall heat transfer rate among the tubes and the air free stream. The following
two geometric parameters were identified in the arrangement.
i) tube-to-tube spacing, tS
ii) fin-to-fin spacing, fp
1.2 PROBLEM STATEMENT
The increase in heat transfer gain and decrease in pressure drop in any tube bank
configuration using a heat exchanger are important considerations for the design
regardless of the tube shape (Canhoto and Reis, 2011; Knight et al., 1992). The
reduction in volume for the thermal system is also important. The main problem in these
applications (thermal system) is how to disperse heat and reduce pumping power. The
principal parameters involved are tube and fin spacing. Many studies have investigated
heat transfer and fluid flow in cross flow over several tube shapes. Furthermore, the
optimal spacing (optimum design) in circular and elliptic tubes has been extensively
studied. However, the optimal spacing in flat tubes has not been fully studied. This
study aims to determine the optimum spacing (tube-to-tube and fin-to-fin) for un-finned
and finned flat tube heat exchangers with both in-line and staggered configurations.
Several parameters affect the rate of heat transfer and pressure drop; these parameters
include external fluid velocity, tube diameter, tube spacing, and fin spacing (Hsieh and
Jang, 2012; Jin et al., 2013). Therefore, the present study attempts to address the
optimal arrangement of un-finned and finned flat tube heat exchangers for laminar
forced convection under fixed volume. Both in-line and staggered configurations are
considered. The maximum overall heat transfer rate and minimum pumping power are
presented at the optimal spacing of tubes and fins. The correlations of heat transfer
density rate and pumping power for general and optimal arrangements are also
calculated. This study contributes to the technical aspect of heat exchanger applications.
4
1.3 OBJECTIVES OF THE STUDY
The objectives of the present work are summarized as follows:
i) To develop a numerical code to predict the thermal–hydraulic characteristics
of laminar forced convective flow over 3D un-finned and finned flat tube
bank heat exchangers with in-line and staggered configurations.
ii) To analyze the heat transfer and flow characteristics in un-finned and finned
flat tube bank heat exchangers.
iii) To identify optimum arrangements (tube and fin spacing) to maximize the
overall heat transfer rate and minimize the pumping power in a specific fixed-
volume configuration.
iv) To develop a new correlation for overall heat transfer rate and pumping
power in general and optimum configurations.
1.4 SCOPE OF THE STUDY
This thesis attempts to analyze the heat transfer and flow characteristics in un-
finned and finned flat tube bundles and to evaluate the optimum design. The optimum
design should yield maximum heat transfer (cooling or heating) under a fixed volume
while reducing the pressure drop and pumping power of flow. The optimum design can
be established by determining the optimum spacing between tubes and fins. The key
steps of study are as follows.
i) Analysis is performed on the air side of the un-finned and finned flat tube heat
exchangers (external flow).
ii) The cross-flow arrangement is considered.
iii) The flow is considered a steady, laminar forced convection incompressible flow
in the 2D and 3D domain.
iv) Both in-line and staggered configurations are considered in this study.
v) Experimental work is conducted to provide a set of data for the validation of the
simulation model as well as previous numerical and experimental studies under
several geometrical and flow parameters.
5
1.5 ORGANIZATION OF THE THESIS
This thesis is arranged in a manner that clarifies the subject from all aspects; it
provides details on the facts, observations, arguments, and procedures to achieve the
objectives. The thesis contains five chapters. The thesis introduction presents the
following in the specified order: the importance of using flat tubes, the problem
statement, the main objectives, and the scope. Chapter II describes and discusses studies
related to the objectives of the present study. Chapter III is divided into two main
sections: experimental work and computational models. The first section of this chapter
presents the experimental equipment, followed by the details of the setup of all
equipment, test modules, and instrument calibration, including an open-circuit low-
speed wind tunnel and a thermistor. The second section lists the suppositions and
describes the mathematical model for the physical problem of un-finned and finned flat
tube banks. This section includes problem description, the governing equations, the
generated grid, and the numerical solution. The results and discussion of the 2D and 3D
models for both in-line and staggered un-finned and finned flat tube banks are presented
in Chapter IV. This chapter also contains the validations and comparisons of the
experimental and simulation results. The simulation results are evaluated and validated
in light of the empirical data. The development of new correlations for overall heat
transfer rate and pumping power is also presented in this chapter. The main findings and
discussions are presented in Chapter V. Some recommendations for future research are
also provided in this chapter. The last section of this thesis contains the references and
appendices related to instrument calibration, experimental uncertainty, and tabulation of
the experimental results.
CHAPTER II
LITERATURE REVIEW
2.1 INTRODUCTION
There has been a significant amount of research work carried out to improve the
efficiency of heat exchangers. The reason for these efforts is that heat exchangers have a
widespread use in industrial, transportation as well as domestic applications such as
thermal power plants, means of transport, heating and air conditioning systems,
electronic equipment and space vehicles (Manglick, 2003). Because of their extensive
use, increase in their efficiency would consequently reduce cost, space and materials
required drastically (Brauer, 1964; Manglick, 2003). The aforementioned research work
includes a focus on the choice of working fluids with high thermal conductivity,
selection of their flow organization and high effective heat transfer surfaces constructed
from high-conductivity materials.
This chapter shows a general review of the heat transfer and fluid flow
characteristics of a tube banks heat exchanger and discusses the effect on the
thermofluid characteristics of several parameters: the frontal velocity of fluid, tube
diameter, tube configuration, tube rows, tube spacing, fin spacing, and tube shape. The
optimum tube-to-tube and fin-to-fin spacing with the maximum heat transfer rate and
minimum pressure drop are also presented. A highlight of the most important
correlations for heat transfer and fluid flow in a tube banks heat exchanger is provided.
The other specific shapes (flat tube) and confinement of the tube between parallel plates
are outlined were reviewed. The chapter also shows and describes the gaps in the
research which may be considered by new studies and suggests future work. Finally,
this chaper presents the significant conclusions.
7
2.2 BACKGROUND OF TUBES BANK
The general configurations of un-finned and finned tube banks heat exchangers
were presented in Figures 2.1 and 2.2. Both in–line and staggered configurations of tube
as well as the circular and flat tubes shape are illustrated. In general, one fluid flows
over the tubes array, while a other fluid at the different temperature moves through the
tubes. The rows of tube at the in-line and staggered arrangements in the flow direction
of fluid (i.e., inlet velocity of air u∞) are as shown in Figures 2.2(a) and (b). The
characteristics of configuration by the diameter of tube such as d, for circular tube and
tansverse tube diameter of flat tube as well as by the longitudinal pitch, P1 and
transverse pitch, P2 the distance between centres of tube. Beale and Spalding (1999)
carried out a numerical investigation of transient incompressible flow in in-line square,
rotated square, and staggered tube banks for the Re number range of 30 ≤ Re ≤ 3,000
and ratio of pitch to diameter of 2:1. The drag lift, pressure drop, and heat transfer
coefficient were calculated. A calculation procedure for a 2D elliptic flow is applied to
predict the pressure drop and heat transfer characteristics of laminar and turbulent flows
of air across tube banks. The theoretical results of the model are compared with
previously published experimental data (Wilson and Bassiouny, 2000). A 2D numerical
study of the laminar steady state flow in a circular tube banks heat exchanger was
carried out for low Reynolds number numbers (Li et al., 2003; Odabaee et al., 2012).
The flow in a bundle of elliptical cylinders was investigated both numerically and
experimentally (Tang et al., 2009; Yianneskis et al., 2001).
The momentum and energy equations have been solved by using a finite
difference method. The effect of the Nusselt number on the surface of the tube was
recorded by Juncu (2007). The importance of heat transfer and fluid flow appearances
of tube banks in the design of heat exchangers is well known (Žukauskas, 1972).
Comprehensive experimental (Kang et al., 1994; Khan et al., 2004; Yao and Zhu, 1994),
numerical studies (Jayavel and Tiwari, 2009; Marchi and Hobmeir, 2007; Rahmani et
al., 2006; Wilson and Bassiouny, 2000) and both experimental and numerical studies
(Nishimura, 1991; Rodgers et al., 2008; Sumner, 2010) of circular tube banks have been
done previously. The numerical analysis of laminar forced convection in a 2D steady
8
(a) In-line classic tube shape (b) Staggered classic tube shape
(c) In-line flat tube (d) Staggered flat tube
Figure 2.1: The configurations of finned round and flat tube heat exchanger (Adopted
form).
Source: Webb and Kim (2005)
