OPTIMAL GEOMETRIC ARRANGEMENT OF UNFINNED AND FINNED FLAT TUBE HEAT EXCHANGERS UNDER LAMINAR FORCED CONVECTION TAHSEEN AHMAD TAHSEEN

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 (S t /d T 1.6) in the in-line configuration and (S t /d T 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 separuhtersirat 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 (S t /d T 1.6) pada konfigurasi sebaris dan (S t /d T 2.0) pada konfigurasi susunan tak serentak. Sementara itu, jarak antara sirip ke sirip adalah Π f = 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 masingmasing 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 STUDENT'S DECLARATION ACKNOWLEDGEMENTS ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES NOMENCLATURES ii iii v vi vii viii xi xii 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 126 Pumping 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 C 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 TABULATION OF SAMPLE OF EXPERIMENTAL DATA AND RESULTS D TRANSFORMATION MATRICES 260 E THREE DIMENSION DIMENSION GRID GENERATION CODE FOR IN-LINE CONFIGURATION 212 263

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 3.3 Approximation of depravities at control volume faces for any variable 4.1 Comparison between for present study and Bahaidarah et al. (2005) for the geometrical parameters and average Nusselt number. 4.2 Geometric parameters of cylinder tube heat exchanger for model validation 4.3 Grid refinement test and proportional error analysis with different grid sizes for in line and staggered configurations 4.4 Geometric parameters of flat tube heat exchanger for in-line and staggered arrangements 4.5 Constants for Dimensionless overall heat transfer rate and dimensionless power pumping correlations and determination of correlation 4.6 Coefficients for the correlations of dimensionless overall heat transfer 84 90 102 103 105 106 143 149 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) Inline (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 2.5 j-factor and fin friction with Reynolds number based on the row pitch 2.6 Mean coefficients of heat transfer for plain plate-finned tubes (571 fins/m) with the six rows 23 24 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) 3.4 The Teflon and plastic module of flat tube for in line and staggered configurations 50 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 3.9 Flat tube bundle: (a) In line and (b) Staggered configuration and (c) Side cross section view 3.10 Three-dimensional un-finned and finned flat tube heat exchanger 63 64 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 3.14 Grid generated in 2D and 3D for finned flat tube heat exchanger 3.15 Typical P-control volume in staggered and collocated grid arrangements in 2D Cartesian coordinates 3.16 Two and three dimensional control volume and neighbouring nodes in computational domain 78 81 82 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 4.2 Overall heat transfer rate against dimensionless tube spacing with varied dimensionless fin density 4.3 Dimensionless overall heat transfer rate against dimensionless tube spacing with the several dimensionless fins density 4.4 Dimensionless overall heat transfer rate versus dimensionless fins density with various dimensionless tubes spacing 4.5 Variation of overall dimensionless heat transfer rate against dimensionless tubes spacing and dimensionless fins density for various Reynolds number 4.6 Dimensionless overall heat transfer rate against Reynolds number for dimensionless tubes spacing and dimensionless fins density for in-line configuration 4.7 Dimensionless overall heat transfer rate with tube to tube spacing and dimensionless fins density against Reynolds number 4.8 Overall heat transfer rate against dimensionless tube spacing with different dimensionless fins density 4.9 The influence of tube to tube spacing and Reynolds number on the dimensionless overall heat transfer rate for different 103 109 110 112 113 115 116 118 119

xiv dimensionless fins density 4.10 Dimensionless overall heat transfer rate against dimensionless fins density for various tube to tube spacing for staggered configuration 4.11 Trends of dimensionless overall heat transfer rate with dimensionless fins density and tube to tube spacing for different Reynolds number 4.12 Influence of Reynolds number on dimensionless overall heat transfer rate for tube to tube spacing and dimensionless fins density on staggered configuration 4.13 Effect of Reynolds number on dimensionless overall heat transfer rate for dimensionless fins density and tube to tube spacing on staggered configuration 4.14 Dimensionless pressure drop with dimensionless tubes spacing for several dimensionless fins density 4.15 Dimensionless power pumping against dimensionless tubes spacing for different dimensionless fins density 4.16 Influence of dimensionless fins density on dimensionless power pumping with dimensionless tubes spacing for various Reynolds numbers 4.17 Influence of Reynolds number on dimensionless power pumping with dimensionless fins density for various tube to tube spacing 4.18 Dimensionless pressure drop against dimensionless tubes spacing for different dimensionless fins density 4.19 Variation of dimensionless power pumping with dimensionless tubes spacing for different dimensionless fins density 4.20 Effect of dimensionless fins density on dimensionless power pumping with dimensionless fins density for different Reynolds numbers 4.21 Influence of Reynolds number on dimensionless power pumping against dimensionless fins density for different dimensionless tubes spacing 4.22 Mass fraction of un finned and tube configurations with tube to tube spacing and dimensionless fin density 121 122 124 125 128 129 131 132 134 135 137 138 139 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 4.25 Correlation and relative error of predicted dimensionless power pumping with an in line arrangement 4.26 Correlation and relative error of predicted dimensionless power pumping with a staggered arrangement 4.27 Comparison between the prediced dimensionless overall heat transfer rate with experimental results for the optimal tube to tube spacing 4.28 Comparison between the prediced dimensionless overall heat transfer rate with experimental results for the optimal dimensionless fins density 4.29 Comparison dimensionless power pumping correlation with experimental results for the optimal tube to tube spacing 4.30 Comparison of the dimensionless power pumping correlation with experimental results for the optimal dimensionless fin density 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 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 4.33 Mean streamlines patterns with Reynolds number in the optimal tubes spacing for in line configuration 4.34 Mean streamlines patterns with Reynolds number in the optimal tubes spacing for staggered configuration 4.35 Isotherm floods patterns with Reynolds number at the optimal tube to tube spacing in an in line configuration 4.36 Isotherm floods patterns with Reynolds number at the optimal tube to tube spacing in staggered configuration 145 146 147 150 151 153 154 157 158 160 161 163 164

xvi NOMENCLATURES Symbol 2D 3D Description and Unit Two dimensional Three dimensional A Area, m 2 A c BFC CFD CV CVFEM Cross-sectional area Body fitted coordinates Computational fluid dynamic Control volume Control-volume finite element method c p Specific heat, J/(kg K) d D h d L d T E Er FVM G 1, G 2, G 2 GE GIT Hy HEM HRSG Diameter of round tube, m Hydraulic diameter, m Longitudinal diameter of flat tube, m Transverse diameter of flattened tube, m Input voltage, Volt Relative error Finite volume methods Contravariant velocity components Governing equations Grid independency test Array height, m Heat exchanger module Heat recovery steam generator

xvii I J Input current, A Jacobian of the transformation k Thermal conductivity of air, W/(m K) L LES Array width, m Large eddy simulation m Ec Air mass flow rate entering one elemental channel, kg/s M MEr N n f p Node number of the grid in -direction Mean relative error Node number of the grid in -direction Fins number Pressure, Pa p f PDE PFTHE q in Qq R 2 RTD S SIMPLE SOR S t S total Fins pitch, m Partial differential equation Plain fin-and-tube heat exchangers Input heat, W Overall heat transfer rate, W Coefficient of determination Resistance temperature detector Source term Semi-implicit methods pressure-linked equation Gauss-Seidel successive over relaxation Tubes spacing, m Total source terms S, Source term due to nonorthogonality

xviii S t T Source term of Tube thickness, m Temperature, o C Average temperature, o C T* Dimensionless temperature TDMA u*,v*,w* u,v,w W x x*, y*, z* Tri diagonal matrix algorithm Dimensionless velocity components Velocity components, m/s Array length, m Dimensionless Cartesian coordinates x, y, z Cartesian coordinates, m H p Power pumping, W Dimensionless Groups Nu Q ~ q * Q ~ q * S T * m ~ s f j Nu Pr Re H ~ p Average Nusselt number Dimensionless overall thermal conductance Dimensionless overall thermal conductance Dimensionless spacing between rows of tubes Dimensionless mass of solid material (mass fraction) Friction factor Colburn factor Nusselt number Prandtl number Reynolds number Dimensionless power pumping

xix Greek Symbols,, Coefficients of transformation Dimensionless fin density in direction z Underrelaxation factor of Diffusion coefficient Δp Δp* Δx, Δy, Δz ε Pressure drop, Pa Dimensionless pressure drop in cross flow Dimensions of the computational cell Emissivity μ Dynamic viscosity, N s/m 2 ρ Density, kg/m 3, 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 h Fin Hydraulic

xx i Inside i, j, k Index notations or coordinate direction identifiers in L Max o out T s t to w Inlet, Input Longitudinal Maximum value Outside Outlet Transverse Surface Tube Total 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, S t ii) fin-to-fin spacing, pf 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 fixedvolume 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 unfinned 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 lowspeed 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, P 1 and transverse pitch, P 2 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)