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Thermo-Hydraulic Properties of the Staggered Herringbone Structure

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Title:
Thermo-Hydraulic Properties of the Staggered Herringbone Structure
Creator:
Xing, Wei
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (126 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering
Mechanical and Aerospace Engineering
Committee Chair:
MOGHADDAM,SAEED
Committee Co-Chair:
SHERIF,SHERIF AHMED
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Flow velocity ( jstor )
Friction factor ( jstor )
Geometry ( jstor )
Heat transfer ( jstor )
Heat transfer coefficients ( jstor )
Inlets ( jstor )
Microchannels ( jstor )
Nusselt number ( jstor )
Pressure reduction ( jstor )
Thermocouples ( jstor )
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
thermo-hydraulic
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Mechanical Engineering thesis, M.S.

Notes

Abstract:
Due to its superior performance in heat and mass transfer, microchannels have caught researchers attention during the past decades. In this study, an experimental study was conducted to investigate the thermohydraulic properties of a new microchannel-based geometry, the staggered herringbone structure (will be called channel-ridge structure for short). A literature review of the published studies concerning fluid flow and heat transfer in microchannels has been completed. The major heat transfer enhancement techniques and their applications in microchannels were included in this review. A thorough background on the fundamental theories on internal laminar flow was provided as well. The geometry of the new structure and its fabrication were carefully illustrated. The experimental setup and apparatus were described in details. The experiments were conducted both on flat channel and channel ridge structures, for the sake of making comparison between the two structures. It has been experimentally found that the channel-ridge geometry could lead to a 33% increase in heat transfer coefficient and only 10% higher in pressure drop, comparing to the flat channel case. A CFD analysis was followed the experiments to further study the new structure. The simulation result indicated that the heat transfer coefficient could be as high as 180% of the flat channel case. The underestimation of the experimental results was due to the off-design condition of the testing structure. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
Local:
Adviser: MOGHADDAM,SAEED.
Local:
Co-adviser: SHERIF,SHERIF AHMED.
Statement of Responsibility:
by Wei Xing.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Xing, Wei. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
969976616 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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THERMO HYDRAULIC PROPERTIES OF THE S TAGGERED HERRINGBONE STRUCTURE By WEI XING A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2014

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© 2014 Wei Xing

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To my mom

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4 ACKNOWLEDG E MENTS Acknowledgements and thanks are given to Dr. Saeed Moghaddam, Rasool Nasr , Sajjad Bigham, Abdolreza Fazeli Abhilash Paner i and all Nano structured Energy System Lab members for their guidance and support to this study. I have learned a great deal from them all.

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5 TABLE OF CONTENTS page ACKNOWLEDG E MENTS ................................ ................................ ............................... 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 NOMENCLATURE ................................ ................................ ................................ ........ 11 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 15 1.1 Microchannel Heat Exchangers ................................ ................................ ........ 15 1.2 Motivation ................................ ................................ ................................ ......... 17 1.3 Literature Review ................................ ................................ .............................. 22 1.3.1 Heat Transfer in Microchannels ................................ ............................... 22 1.3.2 Pressure Drop in Microchannels ................................ ............................. 24 1.3.3 Microchannel heat transfer enhancement ................................ ............... 27 2 FUNDAMENTAL THEORIES AND CORRELATIONS FOR LAMINAR FLOW ....... 34 2.1 Governing Equations ................................ ................................ ........................ 34 2.2 Fully Developed Flow in Circular Tubes ................................ ............................ 36 2.3 Nusselt Number and Heat Transfer Coefficient ................................ ................ 39 2.4 Entry Length Effects ................................ ................................ .......................... 42 2.5 Conclusion and Correlations for Rectangular Channels ................................ ... 44 2.6 Entry Length Effect for Rectangular Ducts ................................ ........................ 46 3 STAGGERED HERRINGBONE STRUCTURE ................................ ....................... 49 3.1 Geometry and Dimensions ................................ ................................ ............... 49 3.8 Fabrication of the Microchannel Heat Exchangers ................................ ............ 55 4 EXPERIMENTAL SETUP ................................ ................................ ....................... 59 4.1 Theory ................................ ................................ ................................ ............... 59 4.2 Test Loop ................................ ................................ ................................ .......... 61 4.3 Testing Section ................................ ................................ ................................ . 63 4.4 Experimental Apparatus ................................ ................................ .................... 67 4.4.1 Thermocouples ................................ ................................ ........................ 67 4.4.2 Flowmeter ................................ ................................ ................................ 71 4.4.3 Pressure Measurement ................................ ................................ ........... 74

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6 4.4.4 Thin Film Heater ................................ ................................ ...................... 75 4.4.5 Recirculating Chiller ................................ ................................ ................. 77 4.4.6 Data Acquisition System ................................ ................................ .......... 78 4.5 Experimental Procedure ................................ ................................ ................... 79 5 EXPERIME NTAL DATA DEDUCTION, ANAYLYSIS AND UNCERTAINTY ANALYSIS ................................ ................................ ................................ .............. 82 5.1 Experimental Data Reduction ................................ ................................ ........... 82 5.2 Heat Transfer Data Reduction and Analysis ................................ ..................... 82 5.2.1 Entry Length Effects ................................ ................................ ................ 85 5.2.2 Experimental Uncertainty ................................ ................................ ........ 88 5.2.3 Surface Roughness ................................ ................................ ................. 90 5.2.4 System Error ................................ ................................ ........................... 91 5.2.5 Flow Illustration ................................ ................................ ....................... 93 5.3 Pressure Drop and Friction Factor ................................ ................................ .... 95 6 COMPUTATIONAL FLUID DYNAMICS ANALYSIS ................................ ............. 103 6.1 CFD Model Establishmen t ................................ ................................ .............. 103 6.1.1 Governing Equations ................................ ................................ ............. 103 6.1.2 Geometrical model ................................ ................................ ................ 104 6.1. 3 Meshing ................................ ................................ ................................ . 105 6.1.4 Boundary Conditions ................................ ................................ ............. 107 6.1.4 Solver and Solution Controls ................................ ................................ . 108 6.2 Simulation Results and Analysis ................................ ................................ ..... 109 6.2.1 Heat Transfer Coefficient ................................ ................................ ....... 109 6.2.2 Pressure Drop and Friction Facto r ................................ ......................... 112 7 CONCLUSIONS AND RECOMMENDATIONS ................................ ..................... 116 LIST OF REFERENCES ................................ ................................ ............................. 119 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 126

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7 LIST OF TABLES Table page 1 1 Summary of published results on heat transfer in microchannels ....................... 23 1 2 Summary of published results on pressure drop in microchannels. .................... 26 1 3 Passive techniques for heat transfer enhancement ................................ ............ 28 1 4 Active techniques for heat transfer enhancement ................................ ............... 29 2 1 Fully developed Nu and Po for rectangular channels. ................................ ........ 45 2 2 Fully developed Nu for three sides heating rectangular channel ........................ 45 2 3 Developing Nu for rectangular channels with four sides heating ........................ 47 3 1 Properties of Brass alloy 260 ................................ ................................ .............. 52 4 1 Properties of water at 20°C ................................ ................................ ................ 62 4 2 AW JV 12KG flowmeter specifi cations. ................................ .............................. 73 4 3 Specifications of Omega PX409 005DWUI differential pressure transducer. ..... 75 4 4 Technical specifications of Thermof lex NES lab 900 recirculating chiller. .......... 78 6 1 Skewness and mesh quality ................................ ................................ ............. 10 6

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8 LIST OF FIGURES Figure page 1 1 Typical LiBr absorption refrigeration cycle. ................................ ......................... 18 1 2 Illustration of absorption for shell and tube absorber [7]. ................................ .... 19 1 3 Comparison of gradient given by different flow thickness at the same flow rat e [9]. ................................ ................................ ................................ ............... 19 1 4 Graphical illustration of staggered herringbone structure [32]. ........................... 21 1 5 Novel mircochannel heat exchanger with offset fins [69]. ................................ ... 30 1 6 Oblique fins design of a microchannel heat exchanger [70]. .............................. 30 1 7 Microchannel heat exchanger based on turning process [73]. ........................... 32 2 1 Development of velocity profile in pipe flow [77]. ................................ ................ 38 2 2 Energy balance in a finite volume of pipe flow. ................................ ................... 41 3 1 Flat channel geometry and dimensions. ................................ ............................. 49 3 2 The proposed channel ridge structure ................................ ................................ 50 3 3 Geometry and dimensions of type 1 ridge. ................................ ......................... 51 3 4 Geometry and dimensions of ty pe 2 ridge. ................................ ......................... 51 3 5 MiniTech Mill 4 CNC machine ................................ ................................ ............ 52 3 6 Testing pieces , l eft is channel ridge structure, right flat channel. ....................... 53 3 7 Detailed photo of flat channel testing piece ................................ ........................ 54 3 8 Detailed photo of the channel ridge testing piece. ................................ .............. 54 3 9 Locations of trenches on the back side of testing pieces. ................................ ... 55 3 10 Flat mills used in fabricating the testing pieces. ................................ .................. 57 3 11 Illustration of the off design structure. ................................ ................................ . 58 3 12 Actual structure made by CNC fabrication. ................................ ......................... 58 4 1 Schematic diagram of the experimental loop. ................................ ..................... 62

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9 4 2 A photograph of the experimental loop. ................................ .............................. 63 4 3 Conductive Epoxy. ................................ ................................ .............................. 64 4 4 Locations of thermocouples in the testing piece (blue circles). ........................... 65 4 5 Plexiglas cap with inlet, outlet and drain. ................................ ............................ 66 4 6 Complete picture of the testing section. ................................ .............................. 67 4 7 T Type thermocouple (probe) with Teflon type on the tip. ................................ .. 69 4 8 T Type wired thermocouples. ................................ ................................ ............. 70 4 9 Thermocouple welding machine. ................................ ................................ ........ 70 4 10 AW JV 12KG positive d isplacement flowmeter. ................................ .................. 73 4 11 Omega PX409 005DWUI differential pressure transducer. ................................ 75 4 12 Omega SRMU100306 flexible heater. ................................ ................................ 76 4 13 TDGC 0.5KM voltage regulator. ................................ ................................ ......... 76 4 14 Thermoflex NES lab 900 recirculating chiller. ................................ ..................... 77 4 15 Data acquisition system. ................................ ................................ ..................... 79 4 16 Air bubbles trapped in testing section. ................................ ................................ 80 4 17 Aculon HB AN10717 s urface modifier. ................................ ............................... 81 5 1 Experimental Nu vs Re in the flat channel testing geometry. ............................. 85 5 2 Curve fitting of the developing Nu for 3 sides heating flat channel. .................... 87 5 3 Nu vs Re with adjusted theoretical Nu. ................................ ............................... 88 5 4 Nu vs Re with adjusted Nu and error bars. ................................ ......................... 90 5 5 Heat transfer coefficient comparison between two geometries. .......................... 93 5 6 Streamlines in the flow passage. ................................ ................................ ........ 94 5 7 Velocity vectors and temperature profile of a random cross section ................... 95 5 8 Pressure drop for flat channel geometry. ................................ ............................ 98 5 9 Friction factor for flat channel geometry. ................................ .......................... 100

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10 5 10 Pressure drop comparison of two testing geometries. ................................ ...... 101 5 11 Comparison of friction factor. ................................ ................................ ............ 102 6 1 Channel ridge structure in GAMIBT. ................................ ................................ . 105 6 2 Meshed channel ridge structure in GAMBIT. ................................ .................... 107 6 3 Heat transfer coefficient comparison for C R structure. ................................ .... 110 6 4 Illustration of the off design structure. ................................ ............................... 111 6 5 Comparison of calculated heat transfer coefficients. ................................ ........ 112 6 6 Comparison of simulated and experimental pressure drop. ............................. 113 6 7 Comparison of calculated pressure drop. ................................ ......................... 114 6 8 Comparison of simulated and experimental friction factor. ............................... 115 6 9 Comparison of calculated friction factors. ................................ ......................... 115

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11 NOMENCLATURE a rectangular channel height (m) b rectangular channel width (m) D diameter (m) D h hydraulic diameter (m) f friction factor u x direction velocity (m/s) v y direction velocity (m/s) w z direction velocity (m/s) U average velocity (m/s) p pressure (Pa) µ dynamic viscosity (Pa·s) density (kg/m 3 ) c p specific heat (kg/kJ·K) k thermal conductivity (W/m·K) T temperature (K) t time (s) h heat transfer coefficient (W/m 2 ·K) q heat flux (W/m 2 ) shear stress at wall (Pa) A area (m2) mass flow rate (kg/s) w width of a rectangular channel (mm) L length of a microchannel (mm)

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12 Nu Nussult number Re Reynolds number C R Channel ridge structure

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13 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Scien ce THERMO HYDRAULIC PROPERTIES OF THE STAGGERED HERRINGBONE STRUCTURE By Wei Xing August 2014 Chair: Saeed Moghaddam Major: Mechanical Engineering Due to its superior performance in heat and mass transfer, microchannels have on during the past decades. In this study, an experimental study was conducted to investigate the thermohydraulic properties of a new microchannel based geometry, the staggered herringbone structure (will be called channel ridge structure for short). A lit erature review of the published studies concerning fluid flow and heat transfer in microchannels has been completed. The major heat transfer enhancement techniques and their applications in microchannels were included in this review. A thorough background on the fundamental theories on internal laminar flow was provided as well. The geometry of the new structure and its fabrication were carefully illustrated. The experimental setup and apparatus were described in details. The experiments were conducted both on flat channel and channel ridge structures, for the sake of making comparison between the two structures. It has been experimentally found that the channel ridge geometry could lead to a 33% increase in heat transfer coefficient and only 10% higher in p ressure drop, comparing to the flat channel case. A CFD analysis was followed the experiments to further study the new

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14 structure. The simulation result indicated that the heat transfer coefficient could be as high as 180% of the flat channel case. The und erestimation of the experimental results was due to the off design condition of the testing structure.

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15 CHAPTER 1 INTRODUCTION 1.1 Microchannel Heat Exchangers Microchannels refer to channels which have hydraulic diameter of less than or equal to 1mm. T he cross section shape of a microchannel could be circular, rectangular, t rapezoidal and any other geometry. Due to their superior performance in heat and mass transfer, they became one of most promising research area for the recent decades. The first mic rochannel study was conducted by Tuckerman and Pease in the [1].They pointed out the benefits of enhanced heat transfer capacity when in corporating small diameter channels for cooling application in large scale circuit. They noted that as the hydraulic diameter decreases, the heat transfer properties could be enhanced significantly . In their experiment, they showed a forty times increase in heat transfer properties , such as heat transfer coefficient . As a result, t hey were able to dissipate an energy density of 7.9MW/m 2 with a maximum substrate temperature rise of 71 degree Celsius and a pressure drop of 186kPa. This is due to the scaling effect of the micro structures. In fully developed laminar flow (circular and rectangular cross section ), t he Nusselt number is a constant, which means that the heat transfer coefficient is inversely proportional the hydraulic diameter [ 2 ]. That means the less the hydraulic diameter is, the greater the heat transfer coefficient. However, according to the Naiver Stokes e quation s , the pressure drop is inversely proportional to the forth power of hydraulic diameter. As a result, the penalty of increased heat transfer is huge pre ssure drop, which would consume lot more pumping power. After the research of Tuckerman a nd Pease, a great deal of research, within the academic and industrial

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16 communities, has been conducted to investigate the physics and application of microchannel heat transfer. Since the potential of microchannel heat transfer had been realized, m uch atte ntion has been focused to verify the macroscale laws on microscale geometries, mainly the Nusselt number and pressure drop (friction factor) [ 3]. Over the pass decades, various experimental results and analysis were published. The disparities between some studies were obvious and conflicting. Recently, thanks to the advancement in microscale fabrication technologies, such as chemical etching and micro scale CNC (computer numerical controlling), manufacturing of smaller and more complicated geometries has be come possible. This led to extensive research on optimizing the channel geometry and adding additional sub structures such that enhancing the heat transfer property while lowering the pressure drop penalty [4, 5]. The main concerns in microchannel heat tr ansfer enhancement include 1). Using extended surfaces, roughened surfaces, swirl flow devise and surface vibration, 2). Decreasing the thermal boundary layer by launching flow disruption 3). using nanofluids as the working fluid due to the superior heat t ransfer properti es of nanofluids [6]. The scaling effects also influence the mass transfer due to the greater concentration gradient, compare to macroscale devices. Research concerning microchannel mass transfer has been conducted in areas such as microsca le absorption cooling system. Nasr and Moghaddam [7] experimentally studied the absorption of water vapor into LiBr solution in microchannels where the flow was constrained by superhydrophobic nanofibrous structures . Their study showed a 2.5 times increase in absorption rate, compare to the conventional shell and tube

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17 absorption mode. However, for a microchannel device, its excessive pressure drop and difficulty in fabrication somehow fades its future. Given the pros and cons for microchannel technology, various studies have been conducted in the past decades. However, before getting into any of the details about past studies, it is quite necessary to present and clarify the motivation of the study. 1.2 Motivation Apart from heat and momentum transfer, ma ss transfer is the most important transport phenomena used in many industries. One of most commonly used mass transport is the absorption of species into a liquid absorbent. This process has been widely used in many technologies, such as absorption heat pu mps [7 15], liquid desiccant based dehumidification [16 21], purification of the natural gas streams [22 26]. Absorbing water vapor into LiBr (lithium bromide) solution is the most important process in the absorption refrigeration cycle , since it determine s the capacity and compactness of a system . Due to the slow diffusion rate of water vapor being absorbed by LiBr solution, the whole process is limited. Furthermore, heat would be generated in the absorption process, which further slows the absorption rate . Before discussing the details concerning the absorption process of water/LiBr pair, it would be necessary to provide an overview of the absorption refrigeration cycle. The Absorption Cycle was invented in 1846 by Ferdinand Carré for the purpose of produc ing ice with heat input. Compare to the conventional vapor compression cycle, the absorption cycle produces cooling and/or heating with thermal input and minimal electric input. A LiBr absorption cycle consists of a condenser, an expansion valve, an evapor ator, an absorber, solution pump and a generator (also referred as desorber). They a re connected as a closed loop (s hown in Fig ure 1 1) .

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18 Figure 1 1 . Typical LiBr absorption refrigeration cycle. The cycle works in the followi ng order. Heat is applied to the generator, which contains a solution of LiBr/water, rich in water. The heat causes high pressure water vapor to desorb from the solution. Heat can either come from combustion of a fuel or waste heat from engine exhaust, oth er industrial processes, solar heat, or any other heat source. The high pressure water vapor flows into a condenser, typically cooled by outdoor air. The water vapor condenses into a high pressure liquid, releasing heat which can be used as output heat. Th is heat could be used as heating living space (this is the heat source for absorption heat pump) . The high pressure liquid water goes through a restriction (usually an expansion valve), to the low pressure side of the cycle. This liquid, at low pressures, boils or evaporates at room temperature in the evaporator. The boiling or evaporation is a n endothermic process. This provides the cooling or refrigeration product. The low pressure vapor flows to the absorber, which contains a LiBr rich solution obtained from the generator. In the whole cycle, the most limiting process for this cycle is the absorption process happened in the absorber. The conventional absorbers are shell and tube heat exchanger . Concerning this type of

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19 absorber, a number of experimental an d numerical studies have conducted to evaluate and enhance the absorption performance [ 27 31] . It is widely recognized that the thick solution film impedes the absorption rate (Figure 1 2). Figure 1 2 . Illustration of absorpt ion for shell and tube absorber [7]. Concentration gradient, which is the driving force of the process, is lowered due to thick solution film . It could be easily seen from Figure 1 3 that decreased flow thickness , at the same flow rate, yields greater grad ient. Furthermore, thick solution film also deceases the temperature gradient, which darkens the heat transfer process. Figure 1 3 . Comparison of gradient given by different flow thickness at the same flow rate [9]. Recently, it has been proved by Yu et al . [ 9 ] that the rate of the absorption process could be enhanced by controlling the solution flow thickness. By utilizing

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20 microchannel based absorber, the solution thickness could be well controlled by the channel geometry. Fo [ 7 ] experimentally demonstrated that the LiBr solution flow could be constrained by superhydrophobic nanofibrous membranes. As a result, its absorption characteristics could be manipulated through independen t control of the flow thickness and velocity. Through this approach, a significant increase in absorption rate versus the falling film absorption technology was achieved. They did a n experimental parametric study in which the role of solution flow thickne ss, the water pressure difference between vapor phase and solution, solution inlet temperature and solution flow rate was investigated . It has been proved that decreasing the solution film thickness could largely enhance the absorption rate. The absorption rate could also be increased by having greater flow velocity inside the channel and it is linearly varied with the pressure potential. From the ir optimized configuration of their experiments, an approximately 2.5 times increase in absorption rate was obse rved compare to the conventional type of absorber. More importantly, the conventional shell and tube heat exchanger takes a lot of space, which makes the absorption refrigeration cycles be almost impossible to be implemented in civil use. Their study shows that it is promising to build compact absorbers with superior performance. The performance of the microchannel based absorption has been further enhanced. Bigham et al . [ 32] achieved even greater absorption rate by adding micro structures at the bottom o f microchannels. The micro structures added are staggered herringbone structures (will be called ridges for short). This is shown in Figure 1 4. By having such structures on the bottom of the flow passage, the laminar streamline will be

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21 stretched and fold ed within the solution film. During this process, vortices were generated by the interruption caused by the micro structures. The vortices continuously bring the concentrated solution from the bottom and middle of the flow to the top at the vapor solution interface. T his leads to significant increase in absorption rate. From their simulation result, the absorption rate could be increased as much as 2.5 times than the flat channel case. Figure 1 4 . Graphical illustration of st aggered herringbone structure [32]. The secondary structure, which creates vortices and modifies the streamlines, must have positive effect on heat transfer due to the enhanced mixing. The goal of this work is to independently study the heat transfer prope rties and pressure drop of the channel ridge geometry and compare its performance with the case of flat channel (no secondary micro structures added). Before starting the research, a literature re view regarding the recent research of microchannel heat tra nsfer and fluid flow is provided. This review first goes through some of the early works aiming at validate the fundamental laws on micro scale. Then, works concerning microchannel heat transfer enhancement would be reviewed.

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22 1.3 Literature Review 1.3.1 He at Transfer in Microchannels conducted to investigate the physics of microchannel heat transfer as well as the validity of macroscal e laws on microscale structures[33 35]. Wu and Little [ 36] tested rectangular microchannels and found that the Nusselt number varied with Reynolds number in the laminar regime. This was one of the first studies that predicted a higher Nusselt number for microchannels when compared to conventional equations. Al so, in the data provided by Choi et al . [37], the Nusselt number was dependent of Reynolds number in the laminar flow regime. They also proposed that in the turbulent flow regime, the experimental Nusselt number is higher than the calculation from the Ditt us Boelter e quation. The same higher than expected result was also confirmed by Rahman and Gui [38 , 39]. Similar to the previous studies, Yu et al . [ 40] also obtained greater Nusselt numbers in their experimental results , comparing to the conventional theo ry . Adams et al. [41] performed experiments on microchannels in the turbulent regime and found their heat transfer coefficients to be higher than predicted by theoretical turbulent equations. Nusselt numbers in excess of theoretical predictions were also f ound by Celata et al. [ 42 ] and Bucci et al. [43] through experimental work. Recently, Jung and Kwak [44] number to be a function of both the Reynolds number and the aspect ratio in the laminar regime. However, not all researchers have found huge differences between experimenta l results and theoretical predictions in the heat transfer properties. Harms et al. [ 45 ] performed experiments on an array of microchannels and determined that local Nusselt

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23 numbers can be accurately predicted in microchannels by conventional correlations with reasonable deviation . Qu and Mudawar [46] did both experiments and numerical simulations on microchannels with different depths in the laminar flow regime. They found that the Navier Stokes and energy equations could predict the fluid thermal and dyna mic behavior in microchannels. Lee et al. [47] investigated the heat transfer characteristics of rectangular copper microchannels with widths ranging from 194 to 534 large range of Reynolds numbers from 300 to 3500. A numerical analysis was also completed to validate their test results. They also found that Na v i er Stokes e quations could be accurate in microchannel analysis, although care must be taken to use the proper theoretical or empirical correlation. Many of the empirical correlations availa ble did not match with their experimental data. However, their numerical analysis showed good agreement with their experimental results in the laminar regime. They indicated that considerations of entrance regions and turbulent transitions must be accounte d for. Moreover, various review articles have summarized the experimental results and empirical correlations on heat transfer in microchannles [48, 49]. Table1 1 concludes the important published studies and their results. Table 1 1 . Summary of published results on heat transfer in microchannels Reference Parameters Conclusions on validity of conventional theory Wu and Little [36] w=89 92µm b=493 572µm L=28,30mm Re=400 20,000 Measured Nusselt numbers higher than conventional co rrelations for both laminar and turbulent flows Choi et al. [37] D = 3 81.2µm L = 24 52 mm Re = 20 25,000 Measured Nusselt numbers higher than correlations for turbulent flow; exhibit Re dependence for laminar flow

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24 Table 1 1. Continued Reference P arameters Conclusions on validity of conventional theory Yu et al. [40] D = 19 102µm L = 24 52 mm Re = 2500 20,000 Measured Nusselt numbers higher than correlation for turbulent flow Peng et al. [50] w = 100 300µm L = 50mm Re = 50 4000 Measured Nusselt n umbers lower than correlation for laminar flow; higher for turbulent flow although trend correctly captured by correlation Adams et al. [41] D = 760µm L = 63.5 mm Re = 2600 23,000 Measured Nusselt numbers higher than correlation for turbulent flow Ravigu rurajan and Drost [51] w = 270µm b = 1000µm L = 20.5 mm Re = 120 1300 Measured heat transfer coefficients higher than laminar prediction Harms et al. [45] w = 25µm b = 1000µm L = 25mm Re = 173 12,900 Measured local Nusselt numbers in good agreement with laminar prediction Qu et al. [52] Dh = 62 169µm Re < 1400 Nusselt numbers lower than CFD prediction Celata et al. [53] D = 130 290µm Re = 100 6000 Measured Nusselt numbers not adequately predicted by correlations for laminar and turbulent flows It cou ld be concluded that the conventional is suitable for predicting the heat transfer characteristics in microchannels. The deviations from the early studies were mainly caused by instrumentation and experimental uncertainties. Other than instrumentation and experimental uncertainties, surface roughness could also be source for the greater heat transfer coefficient. 1.3.2 Pressure Drop in Microchannels The early studies on pressure drop showed that the pressure drop was greater than the prediction brought by the conventional theory. Wu and Little [36] conducted gas flow experiment and found that the friction factor is higher than the prediction by the Navier Stokes equation. The same trend was also confirmed by the experiment

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25 conducted by Peng and Peterson [34, 54 ]. They tested microchannels with hydraulic on hydraulic diameter and channel aspect ratio. Possible reasons for the excessive pressure drop might be experimental uncertain ties and the hydraulic entrance effects. Recently, more studies which confirmed the validity of conventional theory on microchannels have been published. Xu et al. [55] conducted experiments on microchannels with hydraulic diameter of 344 low Reynolds number (20) to turbulent regime of Reynolds number up to 4000. The result showed good agreement with the laminar theory. Judy et al. [56] conducted experiments on pressure drop in microchannels of circular and square cross sections with hydrau working fluids, such as distilled water, methanol and isopropanol. No distinguishable deviation from conventional theory was found in Reynolds number from 8 to 2300. Qu and Mudawar [46] found t hat friction factor data from their experiments with theory. For other type of cross section, Wu and Cheng [57, 58] tested trapezoidal microchannels and found that the convent ional Navier Stokes equation could predict the friction factor with a reasonable accuracy. However, when the surface roughness increases, deviations from conventional theory were observed. Mala and Li [59] tested circular microtubes with high relative rou ghness, and they found that as the relative roughness increased, the friction factor in the laminar regime grew higher. Guo and Li [60] indicated from their experiments on microchannels with high relative roughness that friction factors increased with rela tive

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26 roughness. Tu and Hrnjak [61] performed friction factor experiments on both smooth and rough microchannels, and they found that their results were well predicted by laminar theory on the smooth channel test. However, the rough channel that they tested showed different behavior. The friction factor increased with the Reynolds number. Table 1 2 reviews the important results of published studies on pressure drop inside microchannels. Table 1 2 . Summary of published results on p ressure drop in microchannels. Reference Parameter/material Conclusions on comparison with Navier Stokes Urbanek et al. [62] D= 12, 25um/Silicon 5 30% increase in fRe; dependent on fluid temperature Papautsky et al. [63, 64] D= 44, 57um/ Metal Re = 0.00 1 120 10 20% increase in fRe Mala et al. [65] D= 51 169um/Silicon R= 0 1500 0 40% increase in fRe Pfahler et al. [66] D= 0.5 40um/Silicon Re < 100 0 30% decrease in fRe with fluid type, channel diameter; Re dependence observed Yu et al. [40] D= 52um/Sil icon Re= 300 2000 19% decrease in fRe Peng and Peterson [50] D= 133 143um/Stainless Steel Re= 100 3000 fRe increased for some diameters, decreased for other; dependent on Re Peng et al. [67] D= 133 368um/Stainless Steel Re= 100 800 fRe increased for som e diameters, decreased for others; dependent on Re In summary, the conventional laminar theory could be readily applied to smooth microchannels with reasonable accuracy. The main source of deviation might be experimental error and hydraulic entry effect. However, as the surface roughness increases, distinguishable deviations were observed by a number of researchers. It could be concluded that the surface roughness does play an important role in pressure

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27 drop for rough channels. More investigations are nee ded to further study the effects of surface roughness on pressure drop. 1.3.3 Microchannel heat transfer enhancement Since the early research on microchannel heat transfer physics, more and more attention have been paid to enhance the performance of microc hannels. Specifically, due to the scaling effect discussed earlier, researchers are devoted to improve the heat transfer performance while paying less for the pressure drop penalty. Bergles et al. [68] characterized the heat transfer augmentation technique s as passive and active techniques. Passive techniques refer to the techniques that change the channel geometry such that the fluid flow passage will be affected. As a result, a greater surface to volume ratio will be reached to enhance the heat transfer. On the other hand, the pressure drop penalty would not be so huge. Typical passive techniques include increasing the surface roughness, flow disruptions, channel curvature, re entrant obstructions, and secondary flow. Active techniques refer to the techni ques that incorporates external motions to enhance the flow mixing and thus augment the heat transfer, such as vibration, electrostatic fields, flow pulsation and variable roughness structures. Steinke et al. [ 4] s ummarized these techniques and evaluated t he feasibility on these techniques on micro or mini channels. The passive enhancement techniques are summarized in Table 1 3, while the active ones are summarized in Table 1 4.

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28 Table 1 3 . Passive techniques for heat transfer enhancement Enhanceme nt technique Conventional channel Minichannel microchannel Surface Roughness Roughness structure remains in boundary layer; provides early transition to turbulence Use different surface treatments, roughness structures can remain in boundary layer and protrude into bulk flow Can achieve with various etches; roughness structures may greatly influence flow field Flow Disruptions Using twisted tape, coiled wires, offset strip fins; fairly effective Can extend conventional methods here; offset strip fins, some twisted tapes, small gauge wire Can use sidewall or in channel; optimize geometry for minimal impact on flow Channel Curvature Not practical due to large radius of curvature; has been demonstrated in D h = 3.33 mm More possible tha n conventional; incorporate return bends for compact heat exchangers Most practical; achievable radius of curvature; large number of serpentine channels Re entrant Obstructions Effect not as prevalent; bulk flow reaches fully developed flow quickly; harde r to return flow to developing state Can incorporate structures to interrupt flow; header design could contribute to pre existing turbulence Short paths make for dominate behavior; can incorporate opportunities to maintain developing flows Secondary Flows Flow obstructions can generate secondary flows; combination of inserts and obstructions Could use jets to aid in second flow generation; combination of inserts and obstructions Can fabricate geometries to promote mixing of fluid in channel Out of Plane M ixing Not very effective; space requirements prohibitive Possible use; three dimensional mixing may not be that effective Greatest potential; fabricate complex 3D geometries very difficult Fluid Additives PCMs dominate PCMs possible; fluid additives possi ble Fluid additives; mico and nanoparticles possible

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29 Table 1 4 . Active techniques for heat transfer enhancement Enhanceme nt technique Conventional channel Minichannel microchannel Vibration Surface and fluid vibration util ized currently Possible to implement; can use in compact heat exchangers External power is a problem; integrate piezoelectric actuators Electrostatic Fields Electrohydrodynamic forces currently used; integrated electrodes Could be easier to integrate into compact heat exchanger; external power not as problematic Can integrate electrodes into channel walls; power consumption problematic Flow Pulsation Established work showing enhancement Can implement in compact heat exchangers fluid delivery Possible to i mplement, could make fluid delivery simpler Variable Roughness Structures Difficult to integrate very small variable structures into a conventional channel Difficult to integrate into compact heat exchangers Possible to integrate; piezoelectric actuators change roughness structure Several studies have been done to experimentally investigate the enhancement techniques. Colgan et al. [69] designed a novel microchannel cooler using the optimized offset fins and multiple entrance zones. As a result, the ther mal boundary layer was kept growing and never reached fully developed. On the other hand, since multiple inlets were put in the device, the flows were separated into minor flows . Figure 1 5 shows a three dimensional layout of their design. This device coul d dissipate 300W/cm 2 with the pressure drop less than 35kPa at the design flow rate. Brandner et al. [ 5 ] conducted a series of experiments comparing different geometrical layouts . They tested flat channel, aligned micro column array and staggered micro col umn array. It has to be noted that the arrays were sit on the flat channel. Their data showed that the increase in heat transfer was about 33% for the aligned configuration and 80% for the staggered configuration at the design flow rate. They did not menti on the increase in pressure drop .

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30 Figure 1 5 . Novel mircochannel heat exchanger with offset fins [69]. Lee et al. [ 70 ] designed a novel microchannel heat sink by adding secondary flow to the main flow. This is done by adding oblique fins in the flow passage. Figure 1 6 shows a plain view of their design. Their experimental result showed that the heat transfer property could be as twice as the plat channel while the pressure drop penalty only increased 1.5 times. Figure 1 6 . Oblique fins design of a microchannel heat exchanger [70].

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31 Steinke and Kandlidar [71] used the concept of flow obstruction to enhance the heat transfer in microchannels. They fabricated offset strip fin geometry at the bottom of the channel to interfere the flow. As a result, the boundary could form completely between the fins and thus the growing thermal boundary layer effect strengthen s the heat transfer. From their data, the unit thermal resistance (thermal resistance per un it heat flux applied) in the enhanced channels were two orders of magnitude lower than the plain channel. As a result, the heat dissipated was about two orders of magnitude higher than plain channels. On the other hand, the apparent pressure drop was only 30 40% higher than the plain channels. Using the same concept of developing thermal boundary layer, Xu et al. [ 72 ] kept the thermal boundary layer growing by incorporating repeated flow passage. The Nusselt number for the new geometry was almost 80% higher than the plain channels. The geometry also yields low extra pressure drop penalty at the same thermal resistance. Tang et al . [73] designed a ring shaped microchannel heat exchanger, shown in Fig ure 1 7. By letting the working fluid flow in such a rotatin g path, the flow is continuously being disturbed. In addition, guide vanes were designed to enhance the flow disturbance uniformity among the microchannels. The heat transfer capacity was strengthened. However, since the flow path was actually elongated, additional pressure drop might be induced. No data has been presented in their paper concerning the pressure drop characteristic.

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32 Figure 1 7 . Microchannel heat exchanger based on turning process [73]. Some researches regardin g using the active enhancement techniques have been conducted. Recently, Chandratilleke et al. [ 74 ] used cross flow synthetic jet to enhance the heat transfer in microchannels. By doing this, flow pulsation was realized. At the flow rate lower than 20m/s, the heat transfer was increased 4.3 times while the pressure drop remains reasonable (linear behaviors as conventional channels). Hung et al. [ 75 ] did a numerical study regarding using nanofluids as the working fluid, rather than pure water. They showed th at the performance of the microchannel could be increased by 21% without consuming extra pumping power. Kalteh et al. [ 76 ] conducted both experimental and numerical research on using nanofluid as the cooling fluid in the microchannel heat sink. Their resul t indicates that at low Reynolds number (50 300), the fully developed Nusselt number could reach 8. Recently, much attention are being paid on research coupling nanofluid and microchannels.

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33 In the following chapters, the fundamental theory concerning inte rnal laminar flow will be reviewed. After the overview, the detailed information of the proposed geometry will be provided. The information includes the geometrical dimensions, material parameters and fabrication methodology. Later, an experimental setup w as designed and built. In the experimental loop chapter, a thorough description will be provide. Following the experimental loop chapter is the data reduction section which includes data calculation, comparison of experimental data from two geometries and uncertainty analysis. CFD analysis will be presented thereafter to validate the experimental data from the channel ridge geometry. In light of the CFD code, visualization of the flow field is possible. This could help us further analyze the flow physics. T he last chapter provides the conclusions and recommendations derived from the study.

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34 CHAPTER 2 FUNDAMENTAL THEORIES AND CORRELATIONS FOR LAMINAR FLOW 2.1 Governing Equations While designing any experiment or conducting any analysis, care must be taken to measure the correct quantities. After taking the experimental measurements, performing proper calculation, uncertainty analysis and data interpretation is quite essential. Therefore, before designing an experiment, a rough review of the fundamental phy sical laws involved in the study must be completed. Microchannel study always involves the fundamental knowledge in internal fluid flow and heat transfer. There are a large amount of analytical solutions as well as empirical correlations for internal lami nar flow. In this section, governing equations of internal flow (continuity equation, Navier Stokes equation and energy equation) are briefly reviewed. For circular cross section channels, deviations are made to lead basic conclusions in fluid flow and heat transf er. Then correlations on entry length and developing flow are stated. For rectangular channels, only those related correlations and conclusions are reviewed. For a rectangular cross section duct, the governing equations are as follows: Continuity equatio n (2 1 ) In this equation, it is assumed that the fluid density is not a function of location and time. That is to say, density is a constant value in the flow field and the flow has reac hed steady state. X direction Naiver Stokes equation (momentum equation)

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35 (2 2) Y direction (2 3) Z direction (2 4) In this set of equations, some assumpti ons are made: 1. the fluid is Newtonian, that is the say the viscous shear force is proportional to the strain rate; 2. the fluid is incompressible; 3. Viscosity is constant; 4. No external body force Energy equation (2 5) Several assumptions were made to lead this equation: 1. the fluid thermal conductivity is constant; 2. Incompressible fluid (i.e. no compressibility effect); 3. Zero internal heat generation (i.e. no undergoing chemical reactions); 4. Constant density and specific heat. Strictly speaking, under practical circumstance, all the assumption could not be perfectly met. However, as approximations, the assumptions here are valid and will be able to yield us satisfactory results. For horizontal flows, it is also valid to ignore the effects of gravity on the flow field. In cylindrical coordinates, the governing equations , with the aforementioned assumptions, are listed below. C ontinuity e quation

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36 (2 6) Z direction momentum equa tion (2 7) R direction momentum equation (2 8) direction momentum equation (2 9) Energy equation ( 2 10 ) 2.2 Fully Developed Flow in Circular Tubes Using the governing equations listed above, some important conclusions could be drawn. For internal laminar flow, the circular tube is obviously a perfect representative. The simplest case, fully developed flow, is first reviewed here. Following that, correlations regarding developing flow is presented. Fully developed flow indicate s that on the flow direction, all parameters remain constant. That is to say, in the fully developed region, different locations on the flow direction have the properties. For example, two locations on the flow direction owns the

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37 same velocity profile. Mat hematically, this means that the velocity profile is not a function of x (assume x direction is the flow direction) for hydraulically fully developed flow. Correspondingly, for thermally fully developed flow, at each location on the flow direction, the tem perature profile is the same and not a function of x. Fo r circular tube, assuming symmetry is necessary, that is to say, both the velocity profile and the continuity equation becomes: (2 1 1 ) This indicates that is not a function of r. At the tube wall, since the tube is not porous, . That is to say, u r =0. In order to keep ru r is independent of r, u r has to be directi on is always considered to be symmetrical. Then, onlye the Z direction the momentum equation lefts: (2 12 ) Due to the fully developed condition, the left hand side is essentially zero. Further, we assume that the velocity boundary layer meet at the centerline and the no slip boundary condition. The following two boundary conditions could be applied. at centerline (2 1 3 ) at tube wall (2 1 4 ) Solve and get , this is the hyperbolic velocity profile. Figure 2 1 is an illustration of the development of the velocity profile.

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38 Figure 2 1 . Development of velocity profile in pi pe flow [77]. Next, the average velocity is defined as: (2 15 ) Solve and get (2 16 ) The friction factor is defined as (2 17 ) where is the stress at the wall, defined as (2 18 )

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39 It can be shown that where D h is the hydraulic diameter and Re is the Reynolds number defined as . Here, the number 16 is also called the Poiseuille number (Po). It has to be noted that for different cross section, Po is different. Then, the pressure drop in a circular tube over a distance L could be expressed as (2 19 ) 2.3 Nusselt Number and Heat Transfer Coefficient Two types of boundary condition may be applied, constant surface temperature boundary condition and constant heat flux boundary condition. Applying the fully developed conditions, the energy equation becomes: (2 20) where is the thermal diffusivity Define the following dimensionless numbers: where T e is the fluid entry temperature. The dimensionless energy equation becomes: (2 21)

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40 Noting that in most cases, the effect of axial conduction within the fluid is quite small an d can be neglected. As a result, we could get (2 22) with boundary conditions (2 23 ) (2 24) This partial differential equation could be solved by using separation of variables, and we get (2 25) Next, define the fluid mean temperature as (2 26) The dimensionless mean temperature (2 27) According to the definition of the heat transfer coefficient (2 28) Plug this into the definition of the Nusselt number, (2 29) Recall the energy balance on finite volume, see Figure 2 2 .

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41 Figure 2 2 . Energy balance in a finite volume of pipe flow . We could simply write (2 30) Then substitute the dimensionless groups defined above, we ge t (2 31) And noting that, when x goes to infinity, the surface temperature is actually the mean fluid temperature. Integrate and get (2 32) (2 33) Expand this and we find that for x + greater than 0.1, only the first term in the series is important. As a result, we have Nu=3.657 for circular tube with the constant surface temperature boundary condition.

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42 For the constant heat flux boundary con dition, the thermal behavior of both the fluid and the walls are very different from the constant surface temperature boundary condition. As a result, we need to define a new dimensionless temperature as (2 34) Plug into the energy equation and we get (2 35) With boundary conditions: (2 36) (2 37) Solve the above equation and we could get (2 38) As we expand this, only the first term in the bracket is important. In the end, we end up with the Nusselt number for circular tube under constant heat flux boundary condition to be a constant 4.364. 2.4 Entry Length Eff ects Almost every mic ro channel study cited here involves the entry length effec ts. The flow within microchannel s could be hydraulically developing, thermally developing or the combination of hydraulically and thermally developing. T he entry lengths (hydra ulic and thermal) are a function of the average fluid velocity. When conducting experimental studies, researchers need to run experiments at various fluid velocity. However, most

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43 designed testing geometries could not make sure that the entry length effect to be trivial when running the working fluid at a high average velocity. When the flow path within microchannels involves large part of developing region, the measured value of friction factor and heat transfer properties would be higher than the fully dev eloped value. Therefore, it is important to consider the entry length effects before designing the testing geometry. The hydrodynamic entry length is defined as the distance from the channel entrance to the location where the boundary layers meet at the c enterline [77]. In common engineering practice, this is practically defined as the distance from the entrance to the location where the wall shear stress reaches within 2% of the fully developed value. From the viewpoint of the velocity profile, in the hyd rodynamic entry length the velocity profile is developing. Therefore, the velocity is a function of the flow direction. The entry length is defined as [77] (2 39) Noting that this correlation holds only when the i nlet velocity is uniform. Practically, the uniform inlet velocity is almost impossible to be achieved. For microchannles experiments, manifolds were designed to serve as the fluid inlet and outlet. In many cases, the entrance velocity is not uniform. It is proposed by some engineers that an abrupt entrance from a manifold to a microchannel significantly decreases the hydrodynamic entrance length [79] . Thermal entrance length is defined as the distance it takes the flow along the channel to reach where the relative shape of the temperature profile becomes constant.

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44 Another way to define the thermal entry length is the length along the channel at which the local heat transfer coefficient, h x , becomes constant. For a circular tube in laminar regime , the therma l entry length could be expressed as [77] (2 40) It has to be noted that in the developing regions, both the friction factor and heat transfer coefficient are higher than that of the fully developed region. Various c orrelations were developed to account for the developing region properties for circular tube. However, since this study deals with rectangular channels, those correlations are not reviewed here. 2.5 Conclusion and Correlations for Rectangular Channels Eve n if the circular cross section yields the most common a pplication, in most microchannel s studies, only rectangular channels were used due to the easiness in manufacturing. Unlike circular channels, the characteristic length used is the hydraulic diameter, rather than diameter. It has been shown that some of the correlations for circular tube could yield reliable conclusion when replacing the tube diameter with the hydraulic diameter. The hydraulic diameter for the rectangular duct with height b and width a is defined as ( 2 41) Another very important geometrical characteristic property for rectangular ducts mathematically,

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45 (2 42) For rectangular channels with different aspect ratios, the constant heat flux Nusselt number, constant surface temperature Nusselt number and Poiseuille number is different from circular tubes. These dimensionless numbe rs derived by Kakac et al. [78]. The conclusions are listed in Table 2 1 . Table 2 1 . Fully developed Nu and Po for rectangular channels . Aspect ratio a/b Nu H Nu T Po= f Re 1 3.61 2.98 14.23 0.5 4.13 3.39 15.55 1/3 4.79 3.9 6 17.09 0.25 5.33 4.44 18.23 1/6 6.05 5.14 19.70 0.125 6.49 5.60 20.58 0 8.24 7.54 24.00 It has to be noted that the NuH is for the boundary condition that the four sides of the rectangular channel are all heated equally. In most cases of the mic rochannel heat transfer experiments, the top side of a rectangular channel is always not heated. Therefore, directly plug the four side heating Nusselt number is not accurate. The three sides heating boundary condition Nusselt number has been complied by W ibulswas [79] and Phillips [80]. Table 2 2 shows the fully developed laminar flow Nusselt number for the three sides heating boundary condition. Noting that, in aspect ratio here a is defined as the length of the unheated wall. Table 2 2 . Fully developed Nu for three sides heating rectangular channel Nu fd,3 0 8.235 0.1 6.939 0.2 6.072 0.3 5.393 0.4 4.885

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46 Table 2 2. Continued Nu fd,3 0.7 3.991 1.0 3.556 1.43 3.196 2.0 3.146 2.5 3.169 3.33 3.306 5.0 3.636 10.0 4.252 >10.0 5.385 2.6 Entry Length Effect for Rectangular Ducts Not ing that the Poiseuille number is for the hydrodynamic fully developed region. In the developing region, the pressure drop is not a function of the friction factor. It is associated with the apparent friction factor. The pressure drop is expressed by (2 43) The difference between the apparent friction factor over a length x and fully developed friction factor f is expressed in terms of an incremental pressure defect K(x) (2 4 4) Combining E quation 2 42, the pressure drop can be expressed in terms of the incremental pressure drop (2 45) It has to be noted that since the velocity inlet of any microchannel testing device is not uniform, the hydro dynamic length is shorter than the theoretical value and in most cases, the effect of the hydrodynamic length on the pressure could be ignored. Several

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47 correlations and formula calculating the entrance region friction factor has been summarized by Steinke and Kandlikar [35]. Different from the thermally entrance length of the circular tube, the thermally entrance length for rectangular duct expressed by: (2 46) For rectangular channels with four sides heating, the dev eloping Nusselt number is tabulated in Table 2 3. Table 2 3 . Developing Nu for rectangular channels with four sides heating x* 0.0001 31.4 26.7 27.0 23.7 25.2 31.6 0.0025 11.9 10.4 9.9 9.2 8.9 11.2 0.005 10 8.44 8.02 7.46 7.1 9.0 0.00556 9.8 8.18 7.76 7.23 6.86 8.8 0.00625 9.5 7.92 7.5 6.96 6.6 8.5 0.00714 9.3 7.63 7.22 6.68 6.32 8.2 0. 00833 9.1 7.32 6.72 6.37 6.02 7.9 0.01 8.8 7 6.57 6.05 5.69 7.49 0.0125 8.6 6.63 6.21 5.7 5.33 7.2 0.0167 8.5 6.26 5.82 5.28 4.91 6.7 0.025 8.4 5.87 5.39 4.84 4.45 6.2 0.033 8.3 5.77 5.17 4.621 4.18 5.9 0.05 8.25 5.62 5.00 4.38 3.91 5.55 0.1 8.24 5. 45 4.85 4.22 3.71 5.4 1 8.23 5.35 4.77 4.11 3.6 5.38 It has to be noted that the dimensionless distance X* is defined as (2 47) For the three side heating case, a c orrection formula is given as b low [78] : (2 48)

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48 All the conventional theory and correlation reviewed here will be served as the theoretical value and be compared with the experimental data obtained from the flat channel geometry. It has to be noted that effects such as surface roughness is not reviewed here. However, as one of the most common practical condition, these factors will be analyzed in the data reduction section.

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49 CHAPTER 3 STAGGERED HERRINGBONE STRUCTURE 3.1 Geometry and Dimensions Due to the rapid developm ent of metal based manufacturing technology, making smaller and more complicated geometries has become possible. New geometries, which is more complicated than flat channel, began to emerge. The purpose of adding secondary structure is to enhancing the hea t transfer capability while paying less for the pressure drop penalty. As reviewed earlier in the introduction section, researchers spend much attention on geometrical optimization design. These include increasing the surface roughness, adding flow disrup tions, creating channel curvature, utilizing re entrant obstructions, and generating secondary flow. In this thesis, two geometry configuration, flat channel and channel with staggered herringbone structure (channel ridge for short), are experimentally inv estigated and compared here. Figure 3 1 shows the plain channel geometry. The channel length is 15.2cm (6 inches), width 1mm and the depth is 500 µ m. In the testing section, 60 channels were aligned in parallel with 200 µ m space. Figure 3 1 . Flat channel geometry and dimensions .

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50 The proposed new structure, channel with ridges, is shown Figure 3 2. In this configuration, two types of ridges were fabricated at the bottom of channels along the flow direction. Figure 3 3 shows the geometrical parameters of the ridge type 1 and Figure 3 4 show the details about ridge type 2. Both ridges are 300um de ep from the bottom of channels. As demonstrated by Bigham et al. [32], this structure could generate vortices, thus enhance the mixing of the warmer and cooler fluid. The streamlines of the flow field could also be stretched and folded. Another way to view this design is the greater surface area to volume ratio, compared to the flat channel case. It is obviously that the surface area to vol ume ratio has been increased significantly. In addition, as the fluid flows through the ridges, swirls and vortices might be created such that the enhancement of cross flow will be achieved. Specifically for microchannels heating on three sides, the enhan ced cross flow would help the warmer bottom fluid come up and mix with the cooler top fluid. Consequently, additional mixing would help increase the hat transfer coefficient. On the other hand, since there are more surface area that the wall is in contact with water, more shear force will present. As a result, the pressure drop penalty will increase. Figure 3 2 . The proposed channel ridge structure

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51 Figure 3 3 . Geometry and dimensions of type 1 r idge . Figure 3 4 . Geometry and dimensions of type 2 ridge. All the testing geometries are separately fabricated on brass pieces, one piece for flat channel and one piece for channel ridge. The testing piece is made in brass ( Alloy 260). The material property is shown in Table 3 1. The pieces were fabricated using a Desktop Computer Numerical Controlled (CNC) milling machine ( Figure 3 5 ). The CNC machine was provided by MiniTech.

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52 Table 3 1 . Propert ies of Brass alloy 260 Property Value Density (kg/m 3 ) 8530 Thermal Conductivity k (W/m·K) 120 Specific heat c p (kJ/kJ·K) 0.375 Figure 3 5 . MiniTech Mill 4 CNC machine . (Photo courtesy of Wei Xing) The two structures, flat channel and channel ridge , are made on two brass pieces respectively. The two piece will be subjected to testing the heat transfer properties and pressure drop. The testing pieces are 5 inches wide, 9 inches long and

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53 ¼ inch thick. It has to be noted that other than the ridge struc tures, the two pieces are exactly the same in dimensions and material. Figure 3 6 shows all the two testing pieces. Figure 3 7 and 3 8 show the two testing pieces in greater details, respectively. Figure 3 6 . Testing pieces, l eft is channel ridge structure, right flat channel . (Photo courtesy of Wei Xing)

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54 Figure 3 7 . Detailed photo of flat channel testing piece . (Photo courtesy of Wei Xing) Figure 3 8 . Detailed photo of the channel ridge testing piece. (Photo courtesy of Wei Xing)

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55 3.8 Fabrication of the Microchannel Heat Ex c hangers In the following part, a brief description on the testing piece fabrication is presented. Since the geometrical features need to be fabricated on both sides, determining the top side (manifolds, microchannels, ridges) and b ottom side (thermocouple trenches) is important. It is obviously that the top side requires greater manufacturing attention and accuracy. In turn, the smoother side of the raw brass piece will be used as the top side and the less smooth side will serve as the bottom side. The trenches on the bottom side are for thermocouples to be inserted inside the material. The trenches are 5 inches long, 0.1 inch wide and 0.1 inch deep. To cut these trenches, a 0.0938 inch diameter flat end mill was used. Figure 3 9 sho ws the location of the trenches. Figure 3 9 . Locations of trenches on the back side of testing pieces. (Photo courtesy of Wei Xing)

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56 Before fabricating the features on the top piece, care must be taken on the alignment of the raw material . W hen cutting t he material from the channel bottom, tool must travel between channels. If the channels do not have the same height, tool might be in touch with the higher channel walls. This may break the tool, especially for the small tool (200um diameter) using here. A s a result, it is necessary to keep the piece lie horizontal. To do this, a dial indicator was used to determine the relative position of the raw material and the vice. However, it has to be noted that the brass piece is not perfectly flat, tens or even hu ndreds of micron difference in height might exist. The next step is to perform a 2 ½ D rectangular pocketing on the surface. This is done by a 1/8 flat mill. After pocketing the surface, two manifolds were milled using the 0.0938 inch flat mill. A 0.04 inc h tool was used to fabricate the microchannels. The above three steps are the same for both pieces. For the channel with ridges piece, additional steps for cutting the ridges are needed. It has to be noted that since the number of the ridges are so great ( 7200 ridges in total), it is important to find out the best fabrication strategy which could minimize the manufacturing time and meanwhile provide the required geometry. After some practice on sample pieces, the following manufacturing parameters are deter mined to ensure the tool life, manufacturing accuracy and manufacturing time. The 200 um diameter end mill , 60% step over, 52.5 mm/min feed rate and 100um depth per cut were set to be the cutting parameters. This ensured maximum tool life and reasonable t ime spent.

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57 Figure 3 10 . Flat mills used in fabricating the testing pieces . (Photo courtesy of Wei Xing) However, since the cross section of any end mill is circular, the fabricated geometry is not exactly identical with the design geometry. As a result, all the corners cannot be the same as designed. They are actually round corners and the radius for the coroners are the tool radius. Figure 3 11 illustrates this phenomena and Fig ure 3 12 shows the actual shape of the manifolds and ridges. It has to be no ted that this phenomena can never be avoid. As long as a tool has a diameter, the proposed geometry can never be perfectly manufactured. If continue using a cutting strategy to fabricate the structure, tools with smaller diameter could help make the actual structure closer to the proposed one. However, the time required to manufacture the structure could be huge.

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58 Figure 3 11 . Illustration of the off design structure. Figure 3 12 . Actual structur e made by CNC fabrication. (Photo courtesy of Wei Xing) Because the ridges are not exactly the same as the designed geometry, there must be some effects of the off design geometry on the numerical model. The effects of the off designed geometries will be discussed later.

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59 CHAPTER 4 EXPERIMENTAL SETUP 4.1 Theory In order to test the heat transfer properties, such as heat transfer coefficient and Nusselt number, the following parameters should be measured: fluid flow rate, fluid temperatures and wall temperatures. In addition, there ar e two types of boundary conditions to be applied: the constant surface temperature boundary condition and the constant heat flux boundary condition. Most researcher chose to apply the constant heat flux boundary condition since this boundary condition is e asier to be achieved experimentally. Some researchers have applied the constant surface temperature boundary condition by immersing the whole testing section into a constant temperature bath. In this study, we chose to apply the constant heat flux boundar y condition. This is done by attaching a piece flexible heater on the back of the testing pieces. Although the heating provided by the heater is not perfectly uniform, this approach could be approximated as uniform heating. Measuring the total heat flux gi ven by an external source can be easily achieved by measuring the temperature difference of the working fluid from the inlet to the outlet and the mass flow rate. Since the specific heat of the working fluid is known, the total heat flux could be calculate d below . (4 1) Based on the definition of local heat transfer coefficient, the temperature difference between the wall temperature and mean fluid temperature at that location is required. However, the fundamental dif ficulty in conducting such an experiment is the adequate temperature measurement. It is almost impossible to directly put

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60 thermocouples or any other temperature measurement at channel walls without influencing the flow passage . As a result, the interface w all temperature can never be measured directly. Some researchers measure the near wall temperature, then interpolate the interface wall temperature by (4 2) In this study, we take this approach of measuring the n ear wall temperature using thermocouples. The heat flux applied was about 60W and the distance between the measuring point and the wall fluid interface was about 2mm. According to Equation 4 2 , it could be shown that the interface temperature would be 0.00 1 degree or lower, which is to say, the near field temperature measurement could represent the wall interface temperature at each location. Further, we assume that at each location, the wall temperature is uniform. That is to say, at each location, the tem perature difference in the walls is negligible. Another difficulty is the fluid temperature measurement. Similarly, inserting physical temperature measurement into the fluid passage could have influence on the flow field. Some researchers utilized infrare d thermal camera to measure the fluid temperature profile . However, the infrared thermal measurement requires careful calibration of the instrumentation and meticulous manipulation . Based on the derivation of the thermally fully developed Nusselt number, a local mean fluid temperature is required. However, it is impossible to measure the temperature field at any specific location in the flow passage and then calculate the local mean fluid temperature. That is to say, it is almost impossible to measure the precise local Nussult number. Alternatively, some researchers [81] have measured the fluid temperature at the inlet

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61 and outlet of the whole microchannel testing section, then taken the average. Th u s mean fluid temperature was regarded as the averaged fluid temperature across the whole micorocha n nel heat exchanger. Accordingly, the mean wall temperature came into use to calculate the fluid wall temperature difference. As a result, the Nusselt number and heat transfer coefficient calculated from these tempera tures were actually the average Nusselt number and average heat transfer coefficient of the entire testing section. It has been shown that this approach could yield satisfactory experimental result. In this study, we will follow this approach. More informa tion and details regarding the temperature measurement will be presented in the testing section and experimental apparatus part. It is much easier to test the pressure drop along to two locations. Simply, a pressure transducer could complete the mission. However, for the pressure drop testing, attention must be paid to the pressure drop in the manifold and inlet/outlet tube section . It has been proved that for some specific applications, the pressure drop in the manifolds inlet/outlet tube could take accou nt up to 70% of the total pressure drop across the testing section. 4.2 Test Loop Based on the discussion in the previous section, an experimental loop was designed to quantitatively measure all the desired parameters. Figure 4 1 shows the schematic diagr am of the experimental loop. The loop consists of a recirculating chiller, a positive displacement flow meter, the testing section, data acquisition system, insulation, AC power supplier connecting tubes and valves. DI water was selected to be the working fluid (properties shown in Table 4 1) and a flexible thin film heater was

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62 attached on the back side of the test piece to provide the constant heat flux boundary condition. Figure 4 1 . Schematic diagram of the experimental lo op . Table 4 1 . Properties of water at 20°C Property Value Density (kg/m 3 ) 998.3 Specific heat c p (kJ/kgK) 4.183 Kinematic viscosity (m 2 /s) 1.004E 06 Expansion coefficient (1/K) 0.207E 03 7.01 The whole test rig works in the following order: 1. DI water is pumped from the recirculating chiller with the outlet temperature of 20°C; 2. then it flow s through a valve so that the flow rate could be adjusted; 3. It then flow s through the flow meter and the flow rate is measured; 4. Afterwards, water flows across the test section and being heated up an d 5. Finally it goes back to the chiller . Two thermocouples are inserted at both the inlet and outlet of the testing section, so that the temperature difference of the flow across the testing section could be recorded. At the same time, a pressure transduc er is also mounted to measure the change in pressure across the testing

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63 section. The testing loop is also shown in Fig ure 4 2, noted that the recirculating chiller is not shown in the photo. Figure 4 2 . A photograph of the ex perimental loop. (Photo courtesy of Wei Xing) 4.3 Testing Section In the testing section, microchannel heat exchanger, Plexiglas cap, temperature and pressure measurement and insulation were assembled together. As discussed earlier, 14 thermocouples were attached in the trenches made on the back side of the brass microchannel heat exchanger. The thermocouples were put into the trenches and secured with conductive epoxy ( Figure 4 3). Figure 4 4 (blue circles) shows t he location of these thermocouples with respect to the testing piece . It can be seen from the figure that the thermocouples were aligned in two rows. Row one lies exactly at the centerline, while row two lies half an inch away from row one. In each row, two adjacent

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64 thermocouples have a distance of 1 inch. This design could achieve the following purposes: 1. for each row, the thermocouples are equally distributed, so that the temperature variation in the flow direction could be monitored; 2. since the testing piece is symmetrical at the centerline, row one could measure the t emperature at the centerline while row two could measure the temperature on one side of the centerline. If great temperature difference would be observed in row one and row two, it indicates that the flow is not uniform. The average value of the 14 thermoc ouples will be calculated as the mean wall temperature and used to calculate the mean Nussult number. Figure 4 3 . Conductive Epoxy . (Photo courtesy of Wei Xing)

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65 Figure 4 4 . Locations of thermocouples in the testing piece ( blue circles) . (Photo courtesy of Wei Xing) Since the testing brass piece was not closed on the top, a piece of Plexiglas were cut into the same size as the brass piece to serve as the cap. An O ring grove was also cut in the Plexiglas to provide space for the O ring sealing the whole assemble. In addition, 3 holes were drilled and will be serving as the inlet, outlet and drain (Figure 4 5 ). The inlet and outlet were locat ed on the diagonal such that every single stream of flow could experience the same length of flow passage a nd, in turn, the pressure drop for each stream could be the same . By doing this, we could help the flow stream to be uniform. However, since the Plexiglas is not perfectly flat, not all the channels could be perfectly closed. As a result, some channels wo uld be perfectly closed and form a perfect rectangular flow passage, while others might not be closed and flow could travel from one channel to another. The drain is a special design in this experiment. Having such a drain could yield two benefits: 1. whe n the system was first

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66 charged with water, air bubbles might be trapped and it would take a long time to eliminate them. However, a drain could help remove all the bubbles. W hile charging the testing section with DI water from the recirculating chiller, th e drain was firstly opened . When we see water coming up continuously, close the drain. At this time, air bubbles should be completely removed from the testing rig. 2. Since the drain lies at the other side of a manifold, it would be possible to measure the pressure drop along the manifold and tubes by install the pressure transducer at the drain port. Figure 4 5 . Plexiglas cap with inlet, outlet and drain . (Photo courtesy of Wei Xing) The whole testing section was wrapped with insulation. This is to min imize the heat loss to the ambient . Moreover, since the problem is actually three dimensional, heat travels in all directions and will finally be lost not only from the top side but also from the vertical sides. This would let the wall temperature measurem ent be lower than the actual value. Figur e 4 6 shows the complete testing section.

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67 Figure 4 6 . Complete picture of the testing section . (Photo courtesy of Wei Xing) 4.4 Experimental Apparatus The testing apparatus used here in this experiment are T type thermocouples, pressure transducers, volumetric flow meters, recirculating chillers, voltage regulator thin film heater and data acquisition system. In this section, brief overview on these apparatus is provided and their technical specifications are liste d. 4.4.1 Thermocouples Thermocouples are the most widely used temperature measurement in various applications. Their structures are simple and rugged and they could be used over a wide range, typically from 200°C to 1600°C, with great precision. As its n ame indicates, a thermocouple is actually a pair of different metals or alloys, where they joined together as a junction and form a loop. One of the junctions is at the reference temperature (for example 0°C) and the other junction at the temperature to be measured. When the temperature of one of the junctions differs from the reference temperature at other parts

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68 of the circuit , a temperature dependent voltage was produced. This is the Seebeck effect. Based on this, the voltage could be converted into the c orresponding temperature value. A thermocouple is available in different combinations of metals or calibrations. The four most common calibrations are type J, K, T and E. There are also high temperature calibrations R, S, C and GB. Each calibration has a d ifferent temperature range and application environment, although the maximum temperature varies with the diameter of the wire used in the thermocouple. According to the nature of this study, T type thermocouples were selected as the temperature measuremen t. The working temperature range is from 250°C to 350 °C and the accuracy was plus or minus 0.3°C. It has to be noted that the thermocouples were used to measure the fluid inlet, outlet and wall temperature. To measure the fluid temperature, the junction has to be inserted into the inlet and outlet tubes. As a result, the transient joint probe thermocouples were selected to measure the fluid temperature. Care must be taken that when inserting the probe into the tubes, the head of the probe might touch the wall and the temperature readout yields the wall temperature, rather than the fluid temperature. To avoid this situation, Teflon type was wrapped near the tip of the probe thermocouple to prevent the junction from touching the tube wall . Figure 4 7 shows the thermocouple with Teflon type at the tip .

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69 Figure 4 7 . T Type thermocouple (probe) with Teflon type on the tip . (Photo courtesy of Wei Xing) Thermocouples were also used to measure the wall temperature of the microchannel heat exchanger. As discussed earlier, 14 thermocouples were attached in the trenches made on the back side of the brass microchannel heat exchanger. The thermocouples were put into the trenches and secured with conductive epoxy. The thermocouples used here were type T thermocouples a s well. However, rather than the probe shape, the conventional wired thermocouples came into use (Shown in Figure 4 8). Different from the probe type, the wire thermocouples need to be welded first before measuring. A small scale desktop argon welding mac hine (Fig ure 4 9) was used to connect the junctions. Care must be taken that when joining the conjunctions, in insulation wrap of the wire tip might influence the quality of welding and make the thermocouple yield wrong temperature reading. It is necessar y to check the accuracy of all welded thermocouples to make sure that they are ready to use. All the checked wire

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70 thermocouples were attached in the trenches by the conductive epoxy. Moreover, to make sure that the bottom surface is flat, careful polish wa s executed by using sandpaper of different surface roughnesses. With a flattened surface, the thin film heater could be in well contact with the testing piece. Figure 4 8 . T Type wired thermocouples. (Photo courtesy of Wei Xing) Figure 4 9 . Thermocouple welding machine . (Photo courtesy of Wei Xing)

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71 4.4.2 Flowmeter Flow measurement is the quantification of bulk fluid movement . Flow can be measured in a variety of ways. The most common flow meters are variable area flowmeters, turbine flowmeters, magneti c flowmeters, coriolis mass flowmeters and positive displacement flowmeters. Variable area flowmeter is the most common and simplest flow meter. Variable area flowmeters measure flow by allowing the flow stream to change the opening within the flowmeter by moving an internal part. When the flow increases, the fluid generates more force and moves the internal part farther. One variable area flowmeter measures flow in a vertical metering tube by balancing the downward weight of a float with the upward force o f the flowing fluid. (rotor) in the flow stream. Blades on the rotor are angled to transform energy from the flow stream into rotational energy. The rotor shaft spins on bear ings. When the fluid moves faster, the rotor spins proportionally faster. Shaft rotation can be sensed mechanically or by detecting the movement of the blades. Blade movement is often detected magnetically, with each blade or embedded piece of metal genera ting a pulse . A sensor, always located external to the flowmeter convert the pulse signal into the corresponding volumetric flow rate. Similarly, Coriolis flowmeter measures the mass flow rate by measuring the force resulting from the acceleration caused by mass moving toward (or away from) a center of rotation. The physics of Coriolis flowmeter is rather complicated and will not be reviewed here. It has to be noted that, for experiments concerning microscale transport phenomena, Coriolis flowmeter is the

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72 most accurate flow measurement. However, due to the high cost of Coriolis flowmeter, it was not selected for this experiment. Since the total heat flux is directly calculated from flow rate and temperature difference of the working fluid, the heat transfe r coefficient is directly calculated from the heat flux and wall fluid temperature difference. Flow measurement is the key to calculate the heat transfer coefficient and its accuracy largely influence the final data reliability. Appropriate flow measuremen t, as a result, is essential for obtaining precise and reliable result. Among the listed flowmeters in this section, positive displacement flowmeter was selected as the flow measurement apparatus for this experimental study due to its uniqueness in flow qu alification. Positive displacement flowmeter technology is the only flow measurement technology that directly measures the volume of the fluid passing through the flowmeter. T his is acheived by repeatedly entrapping fluid in order to measure its flow. This process can be thought of as repeatedly filling a bucket with fluid before dumping the contents downstream. The number of times that the bucket is filled and emptied is indicative of the flow through the flowmeter. Many positive displacement flowmeter geo metries are available. The process of e ntrapment is usually accomplished using rotating parts that form moving seals between each other and/or the flowmeter body. In most designs, the rotating parts have tight tolerances so these seals can prevent fluid fr om going through the flowmeter without being measured (slippage). In some positive displacement flowmeter designs, bearings are used to support the rotating parts. Rotation can be sensed mechanically or by detecting the movement of a rotating part. When mo re fluid is flowing, the rotating parts turn

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73 proportionally faster. The transmitter processes the signal generated by the rotation to determine the flow of the fluid. The flowmeter used here is the AW JV 12KG positive displacement flowmeter (shown in Figu re 4 10). The range for this meter is 0.003 to 0.8 gpm (12 to 3000 ml/min), with accuracy of plus or minus 1%. Before using this equipment in the experimental loop, a re calibration was done by comparing the readout from the flowmeter with the flow measu rement from a graduated cylinder. The detailed technical specifications of this flow meter is listed in Table 4 2. Figure 4 10 . AW JV 12KG positive displacement flowmeter . (Photo courtesy of Wei Xing) Table 4 2 . AW JV 12KG flow meter specifications. Specification Value Flow range (gpm) 0.003 to 0.8 Accuracy (%) ±1 Max working temperature (°C) 200 Working pressure (psi) Up to 5,000 psi

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74 4.4.3 Pressure Measurement In order to evaluate the pressure drop of the microchannel heat exchangers, both flat channel and channel ridge geometry, appropriate pressure measurement is needed. The most common pressure measurement is the pressure transducer. A pressure transducer consists of two main parts, an elastic material which will deform when exposed to a pressurized medium and a n electrical device which detects the deformation. The elastic material can be formed into many different shapes and sizes depending on the sensing principle and range of pressures to be measured. The most common m ethod of utilizing the elastic material is to form it into a thin flexible membrane called a diaphragm. The electrical device , which is combined with the diaphragm to create a pressure transducer , can be based on a resistive, capacitive or inductive princi ple of operation . This electrical device has the ability to sense the deformation and convert it to the corresponding pressure reading. In this study, the only thing that is concerned is the pressure drop, rather than the gauge pressure at the inlet or out let. In turn, a differential pressure transducer (shown in Figure 4 11) was selected to measure the inlet and outlet pressure difference. The differential pressure drop transducer is the omega PX409 005DWUI differential pressure transducer with specificati ons listed in Table 4 3.

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75 Figure 4 11 . Omega PX409 005DWUI differential pressure transducer . (Photo courtesy of Wei Xing) Table 4 3 . Specifications of Omega PX409 005DWUI differential pressure transducer. Specifications Value O perating temperature (°C) 45 to 115 Accuracy (%) 2 Range (psi) 0 to 5 4.4.4 Thin Film Heater Other than the measuring equipment, other apparatus are needed to provide the testing environment. To apply the constant heat flux boundary condition, heat ne ed to be applied at the bottom of the testing piece. To do this, researchers used different types of heaters. Lee et al. [47 ] used four cartridge heaters and inserted them deep into their testing section. It has to be pointed out that it is because the siz e of their testing section is small (2mm by 25mm), cartridge heater was the most suitable heating device, considering its size and capacity. However, in this study, the testing section has a dimension of 76mm by 152mm. obviously, cartridge heaters are not suitable and capable for this application. Instead, a flat thin flexible heater is the first option. The

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76 heater used in this study is an Omega SRMU100306 which has the size of 76.2mm by 15.24mm and a heating capacity of 180W. Figure 4 12 is a photo of the flexible heater. This heater could endure the highest temperature of 232°C and it is chemical and moisture resistant. By using a voltage regulator, the heating capacity could be adjusted. The voltage could adjust the incoming voltage from 0V to 240V so tha t the heating capacity could be from 0 180W. The voltage regulator is shown in Figure 4 13. Figure 4 12 . Omega SRMU100306 flexible heater. (Photo courtesy of Wei Xing) Figure 4 13 . TDGC 0.5KM voltage regulator. (Photo courtesy of Wei Xing)

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77 4.4.5 Recirc ulating Chiller Another important part of the experimental setup is the DI water supply. Since the experimental setup forms a closed loop, the incoming DI water has to be in the same condition in each run. That is to say, the inlet water temperature has to be the same so that the steady state condition could be reached and measured. In order to achieve this goal, a recirculating chiller, which has the ability of providing a constant flow at a fixed temperature, came into our eyes. With a chiller, the DI wat er could be pump into the testing section with a steady flow rate and a constant temperature. The recirculating chiller used here in this study is the Thermoflex NES lab 900 recirculating chiller (shown in Figure 4 14) . It has the cooling capacity of 3500W and working temperature range of 5 to 40°C. Even more, it could precisely control the fluid temperature within 0.1°C. The full specifications of this chiller is listed below (Table 4 4) . Figure 4 14 . Thermoflex NES lab 900 r ecirculating chiller .

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78 Table 4 4 . Technical specifications of Thermoflex NES lab 900 recirculating chiller. Specifications Value Temperature range (°C) 5 to 40 Cooling capacity (W) 900 Volume reservoir (L) 7.2 Hertz (Hz) 50 T emperature stability +/ 0.1°C Ambient temperature (°C) 10 to 40 4.4.6 Data Acquisition System In this study, all the measurements were connected to the data acquisition system (Figure 4 15). The flowmeter and pressure transducer were connected to their corresponding readout. Since 16 thermocouples were used to measure the fluid and testing piece wall temperature, they were all connected to the Agilent 34970A Data acquisition/switch unit. The Agilent 34970A Data Acquisition / Data Logger Switch Unit c onsists of a three slot mainframe with a built in 6 1/2 digit digital multimeter. Each channel can be configured independently to measure one of 11 different functions without the added cost or hassles of signal conditioning accessories. With the correspon ding data recording and monitoring software, all the temperature data from the 16 thermocouples could be recorded and monitored. In this process, the data curve could be us see the variation of the temperature data and determine whether the system has reac hed steady state condition.

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79 Figure 4 15 . Data acquisition system . (Photo courtesy of Wei Xing) 4.5 E xperimental Procedure After connecting every single part of the experimental loop, it is necessary to determine what the operating steps are. In order t o keep the test accurate and safe, the order of operations must be carefully determined. Generally, the first step to start such an experimental study is to charge the experimental loop with the working fluid, namely, DI water. However, at the first run of the test, we found that air bubbles were entrapped within the testing piece (Figure 4 16 ). Even if we increase the flow rate and shake the testing section, air bubbles could be eliminated completely. Have such air bubbles could lead to the following conse quences: 1. Air bubbles could be considered insulated comparing the air conductivity with the water conductivity. As a result, the working fluid could not be heated uniformly; and the wall temperature could be higher as the air

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80 insulated the heat. 2. Since the space inside the channels were occupied by air bubbles, the working fluid has to bypass the air bubble in order to flow. Because of this, the flow inside the channels is no longer uniform. Based on the above analysis, it is essential to eliminate the air bubbles before recording any data. Figure 4 16 . Air bubbles trapped in testing section . (Photo courtesy of Wei Xing) From the experience of several trial and error, eliminating the air bubbles need to make the brass piece be easier to be wet, so that the water could be able to wet the whole surface and push the bubbles away. This is done by using applying the AN10717 surface modifier (Figure 4 17) and using the drain to eliminate the air bubbles.

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81 Figure 4 17 . Aculon HB AN10717 surface modifier . (Photo courtesy of Wei Xing) Having the whole test setup charged with water and no air bubble existing, the experiment is good to get started. First, the heat flux is adjusted by the power supply. Flow rate could also be changed via the valve located at the exit of the recirculating chiller and monitored by the flow meter. T esting loop is run at the fixed flow rate and heating power until all the reading value has reached steady state. After r ecord ing the data , the test is run at another flow rate. It has to be noted that since the kinematic viscosity is strongly a function of temperature, the pressure test obeys the same procedure as describe before but with the heater off. All the tests concerning heat transfer and pressure are the same for both testing pie ces.

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82 CHAPTER 5 EXPERIMENTAL DATA DEDUCTION, ANAYLYSIS AND UNCERTAINTY ANALYSIS 5.1 Experimental Data Reduction With all the experimental data in hand, it is important to perform the data reduction and analysis. In this process, several points have to be clarified. First, all the data here was collected in a steady state condition. However, as the variation of the desired qualities with respect to time was impossible to eliminate, the values collected were actually average value. Second, since data were col lected in a practical condition, some analytical solution or empirical correlations might not exactly match . Third, it is hard to quantify the effects of some factors such as uneven heating given by the heater. In the following section of this chapter, the selection of appropriate analytical solution and empirical correlations are discussed. Also, the comparison between the experimental data and theory is presented. Last, possible reasons that lead to the disagreement are analyzed and quantified to make up the difference. 5.2 Heat Transfer Data Reduction and Analysis In the heat transfer side of this study, the most important quantities are the Nusselt number (a dimensionless number which indicates the effects of convective heat transfer to the effects of conductive heat transfer within the fluid and solid interface) and heat transfer coefficient. Their mathematical expressions are given below (5 1) where is the temperature difference between the wall and fluid, if the fluid is being heated by the wall, which is the case in this study. (5 2)

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83 It has to be note here, D is the diameter r of circular cross section and hydraulic diameter for a rectang ular cross section. The heat flux that has applied to the testing section could be calculated by the difference of the inlet and out fluid temperature (5 3) where Q is the total heat applied to the testing piece and is the mass flow rate. Noting that this quantity can only be derived from the volumetric flow rate as (5 4) where is volumetric flow rate that directly reads f rom the flow meter. It has to be mentioned that the heat flux used to calculate the heat transfer coefficient is the heat flux per channel. ( 5 5) where A is the heating wall area of a single channel, basical ly the sum of the bottom wall and two side walls for the flat channel and 60 is the number of channels . For the channel ridge geometry, the increased area must be taken into account. Although the calculation of the heated area is more difficult for the cha nnel ridge geometry than the case of flat channel, this value can be obtained by adding addition side wall area to the flat channel heating area. As discussed earlier, at each location along the flow direction, the wall fluid temperature difference varies and it is impossible to measure those temperatures and calculate the difference at all locations. Alternatively, mean temperatures are used here

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84 instead of the local values. The wall fluid mean temperature difference could then be expressed as (5 6) where the is the average temperature of the wall and calculated by the average of all the 14 thermocouples inserted into the testing piece. is the mean fluid temper ature. With all the above formulas, the heat transfer coefficient could be expressed as (5 7) Some researchers also calculated the heat transfer coefficient from a heat exchanger point of view by using the concept of UA value and log mean temperature. The heat transfer coefficient could also be expressed as (5 8) where and indicate the wall fluid temperature at the inlet a nd outlet respectively. This expression is extremely convenient for calculating the heat transfer coefficient if the wall boundary condition is constant temperature, rather than constant heat flux. This is could be considered as a counter flow heat exchan ger where one side is heated by condensation heat transfer (constant temperature heat source). However, in the current study where the constant heat flux boundary condition is applied, we will use the former way to calculate the heat transfer coefficient. Having the heat transfer coefficient calculated, it is quite easier to determine the Nusselt number.

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85 The experimental Nusselt number of the flat channel case geometry is plotted in Figure 5 1. The heat transfer coefficient, which is not dimensionless, i s not plotted here. However, due to the fundamental difficulty in calculating the Nusselt number for the channel ridge geometry, the heat transfer coefficient will be used to compare the heat transfer capacity of the two structures. Figure 5 1 . Experimental Nu vs Re in the flat channel testing geometry . 5.2.1 Entry Length Effects As reviewed in the earlier chapters, the thermal entry length is proportional to the flow rate, the higher the flow rate, the longer the entry length . And in the entry length, the Nusselt number is greater than the thermally fully developed. The thermal entry length is (5 9) 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 0 50 100 150 200 250 300 350 400 Nu R e Experimental Nu vs Re (flat channel)

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86 Ta ke the case of Reynolds number 3 08 for example, plug in every value, we found tha t t he thermal entry length is 6 cm which is about 40% of the channel length . That is to say, part of flow is thermally developing in this case and the effects of the thermal entry length needs to be evaluated. To do so, we need to evaluate the mean Nusselt num ber within the whole entry length or some portion of the entry length. As reviewed in Table 2 3, the local Nusselt number at different locations inside the thermal entry length has been tabulated. Seen from the values, the Nusselt approaches infinity at th e very beginning of the channel, then suddenly decrease and reach a constant value. This is the characteristic of an exponential curve. In other words, a proper curve fitting could be utilized and analyzed to describe the Nusselt number inside the thermal entry length. Having such a curve enables us to find the average Nusselt number of any location inside the entry length by performing an integration and divided by the length. Moreover, the average Nusselt number of the whole entry length can be readily ca lculated by using the same method. Equation 5 10 is the fitted equation for the local Nusselt number in the developing region . The fitted curve is shown in Figure 5 2. (5 10)

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87 Figure 5 2 . Curve fitting of the developing Nu for 3 sides heating flat channel. It could be observed that the curve shows very good agreement with the local points. With the fitted curve, the average Nusselt number within the thermally developing region could be determined . Fig ure 5 3 plots the experimental Nu vs. the corrected Nusselt number.

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88 Figure 5 3 . Nu vs Re with adjusted theoretical Nu . 5.2.2 Experimental Uncertainty For any experimental study, uncertainty is always an important factor to be considered. In this study, a standard uncertainty analysis was conducted for each measurement and the error propagation was evaluated. The uncertainty of the temperature measurement was found to be 0.3 °C. The uncertainty of the flow rate measurement was found to be 1%. According to the data given by the CNC machine manufacturer, the uncertainty of the channel dimensions were less than 10 um. Using these uncertainties, an uncertainty analysis for the heat transfer coefficient and Nuseelt number based on the error propagation criteria was conducted. These uncertainties were calculated by the following equation: 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 0 50 100 150 200 250 300 350 400 Nu Re Nu vs Re (flat channel) Theorotical Nu Experimental Nu

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89 (5 11) Where is the uncertainty of the secondary value R (heat transfer coeffic ient/Nu in this case) and is the uncertainty of a given quantity upon which R is based. For heat transfer coefficient, these quantities include Q (total heat applied to the fluid), b (the channel width) , a (the channel height), L (the channel length), V (volumetric flow rate of the DI water), (the temperature difference between the water inlet and outlet) and (the temperature difference of the mean fl uid temperature and mean wall temperature). This method of determination of uncertainties allowed for the errors in each measurement to be compounded together to estimate the total error for heat transfer coefficient and Nusselt number. Figure 5 4 shows t he experimental data with corresponding error bars and the corrected value based on laminar flow theory.

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90 Figure 5 4 . Nu vs Re with adjusted Nu and error bars . 5.2.3 Surface R oughness Surface roughness plays an important role in both heat transfer and pressure drop. It has been proved that surface roughness could increase both the heat transfer and pressure drop of a micro channel heat exchanger. Wu and Cheng [57] performed a detailed study on the effects of surface roughness on convective heat transfer in mircochannles. They tested silicon microchannles of 13 different geometries at a range of Reynolds number of 0 to 1600. Their experimental data showed that at low Reynolds number(less than 100), the Nusselt number increase a lmost linearly with the Reynolds number under the effect of surface roughness. For Reynolds number greater than 100, 0 0.5 1 1.5 2 2.5 3 3.5 4 0 50 100 150 200 250 300 350 400 Nu Re Nu vs Re (flat channel) Theorotical Nu Experimental Nu

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91 Nusselt number increases very slowly with the Reynolds number. It could be concluded from their study that, for Reynolds number greater tha n 100, the role of surface roughness on Nusselt number is negligible. The same relationship between the Reynolds and Nusselt number could also be observed here in Figure 5 4. For the region where Reynolds number is less than 100, Nusselt number increases a s Reynolds number grows. After the Reynolds number reaches 100, the Nusselt number could be considered constant. It is valid to ignore the surface roughness effect at high Reynolds numbers. 5.2.4 System Error The last reason analyzed here that leads to th e difference between experimental data and laminar theory is the design of experiment. Even if the experimental loop was carefully designed, it has to be noted that all the theoretical condition cannot be perfectly met. The flexible heater could provide a constant heat flux boundary condition, however, no one could ensure that heat flux is uniform everywhere. Considering that fact that the heating power comes from the electric wires inside the heater and the wires could not spread uniformly. As a result, th e constant heat flux boundary condition is actually off. Another possible reason is that the Plexiglas top is not perfectly flat. This leads to the consequence that the flow passage could not be perfectly enclosed and the flow is not uniform. The uneven fl ow and heat flux together lead obscures the precise of the wall temperature measurement. The heat could not dissipate into the fluid uniformly and cause irregular behavior of the wall. As a result, the wall temperature measurement is not the same as the pr ediction brought by theory. The same data reduction and uncertainty analysis procedure could be readily applied to the channel ridge geometry. The only difficulty associated with the channel -

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92 ridge geometry is the determination of the hydraulic diameter. T he cross section is not only irregular but also changes with the flow direction. In order to calculate the Reynolds number and Nusselt number, an equivalent hydraulic diameter is need. Since the width and length of the channel ridge geometry is the same as the flat channel, the only different dimension is the depth. The equivalent depth could be determined by calculating the equivalent cross section area. This can be easily done by dividing the volume by the channel length. Having the equivalent cross secti on area, the equivalent depth could be calculated by dividing the area by the width. With the width and equivalent depth, the equivalent hydraulic diameter could be calculated. (5 12) With the equivalent depth, the equivalent hydraulic diameter is as follows: (5 13) Using the channel ridge equivalent hydraulic diameter, the Nusselt and Reynolds number could be readily calculated. Figure 5 5. shows the comparison of heat transfe r coefficient of both flat channel and channel ridge geometry. The increase of heat transfer coef ficient would be about 10% to 32 % at Reynolds number from 48.6 to 358 . This is due to the generation of vortices brought by the additional micro structure at t he bottom of the channels. With the vortices, the warmer bottom fluid could come to the top and better mix with the top cooler fluid. The detailed temperature profile and fluid field could be obtained by using CFD software. The flow field visualization wil l be presented in the CFD analysis chapter. Another way to view the heat transfer augmentation is to calculate the surface area to

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93 volume ratio. By having such additional structures, the area to volume ratio was increased by 10%. Figure 5 5 . Heat transfer coefficient comparison between two geometries . 5.2.5 Flow Illustration It has been shown that the ridge geometry could effectively increase the heat transfer coefficient. This is due to the vortices given by the ridge struct ure. In this section, flow visualization will be presented to illustrate the presence and effects of vortices. The best way to illustrate the presence of vortices is to show the streamlines of the flow passage. It can be seen from Figure 5 6, the streaml ines were folded and stretched and vortices were formed in the ridge area. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 100 200 300 400 500 600 700 800 Heat Transfer Coefficient (W/m 2 K) Volumetric Flow Rate (ml/min) Experimental heat transfer coefficient comparison Flat h C-R h

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94 Figure 5 6 . Streamlines in the flow passage.

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95 Figure 5 7 . Velocity vectors and temperature profile of a random cross se ction Figure 5 7 shows a random cross section inside the flow passage and the velocity vectors and temperature field are plotted. It is obviously that the vortices induced by the ridges help mix the fluid. 5.3 Pressure Drop and Friction Factor By measuring the pressure drop from the inlet to the outlet of the testing section, the apparent Darcy Friction Factor ( f app ) could be easily determined. The uncorrected apparent Darcy Friction Factor is defined as

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96 (5 14) where is the pressure difference directly measured from the inlet and outlet of the testing section, u is the line velocity inside of each channel and could be calculated as follows: (5 15) where is the cross section area of each channel. It has to be noted that, even if the channel ridge geometry has a variable cross section, its inlet is rectangular. So the geometrical irregularity does not affect the calculation of line velocity. Since the differential pressure transducer was mounted at the inlet and outlet of the testing section, the measure pressure drop is not pressure drop across the channels, but include the pressure drop of the manifold. It is important to be awar e of the fact the confused with the fully developed Darcy friction factor f (commonly refer to friction factor for short), which is defined by (5 16) where is the shear stress at the fluid wall interface. When the flow reaches hydrodynamically fully developed, the apparent friction factor the same as the fully developed friction factor. In order to accoun t for the pressure drop induced by the manifolds, inlet and outlet, an adjusted pressure drop is needed to calculate the apparent friction factor

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97 (5 17) w here is the adjusted pressure drop w hich has taken the inlet and outlet energy loss into consideration. It could be determined by the following equation (5 18) w here the factor is the loss coefficient for the abrupt inlet and is the loss coefficient for the abrupt outlet [82]. The values of the loss coefficients were determined by experimental results on circular tubes. Of the two loss coefficients, is the most readily identi fied and is equal to 1. For any abrupt exit to a large reservoir (i.e. an exit from a series of microchannels to a large manifold), the geometry of the exit has no effect on the loss coefficient. That is to say, in most cases, the exit loss coefficient is geometry independent. However, the loss coefficient for the inlet, , is highly dependent on the geometry of the inlet area. For different inlet geometries, the inlet loss coefficient has different values. For a sharp edged inlet ( i.e. 90° corners), = 0.5. For a well rounded inlet (defined as / >0.2), = 0.03. For a slightly rounded inlet (defined as / > 0.1 ), = 0.12 [82]. The ratio of / is unknown for the microchannels tested, and the ratio certainly varies for each individual channel. Therefore, an in termediate loss coefficient of = 0.25 is used as an estimate. To compare the experimental data with the theoretical values, the following analytical solution for laminar pressure drop was used [78] . (5 19)

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98 In this study, the aspect ratio . As a result, the friction factor could be expressed as (5 20) Figure 5 8 plots the comparison of pressure drop between the theoretical value and the experimental value for the case of flat channel. It could be easily seen that the experimental pressure drop is actually higher than the theoretical calculation. The following reasons may account for this. Figure 5 8 . P ressure drop for flat channel geometry . The first reason might be the surface roughness effects. The high relative wall roughness coupled with its nonuniformity could generate a large hydraulic diameter, as mentioned by Pfahler [66]. The same authors also suggested that the excessive 0 1000 2000 3000 4000 5000 6000 7000 0 100 200 300 400 500 600 700 Pressure Drop(Pa) Volumetric Flow Rate (ml/min) Pressure drop (Flat channel) dp exp dp cal

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99 pressure drop could be induced by the reduction in the apparent viscosity of the fluid with the reduction in hydraulic diameter. Another hypothesis in the literature suggests that the momentum transfer augmentation could be due to the roughness in the wall boundary layers. Mala and Li [ 59 ] showed the influence of roughness by introducing a viscosity model th at depends on channel roughness. This model originates in the work of Merkle et al. [83, 84] who showed that the presence o f roughness affects the flow velocity profile and the transitional Reynolds number. However, as reviewed in chapter 1, the pressure drop deviation is not notable for relative smooth channels. The second reason might be the difference for wall materials. The bottom and side walls are made by brass while the top cap is made by Plexiglas. It is obviously that surface roughness for these two materials might be different and lead to the deviation in pressure drop. Thirdly, as described earlier, the experiment al uncertainty might cause the discrepancy between experimental and theoretical values. This effect has been plotted in Figure 5 6 as the error bars. The last reason might be the imperfect closure of the Plexiglas cap. The calculated friction fact or is plo tted in Figure 5 9 . It could be seen that at low Reynolds rate the friction factor is much higher than that of high Reynolds number. As predicted before, the experimental friction factor is higher than the experimental friction factor due to the excessive pressure droop caused by the roughness effects , entry length effects and experimental uncertainty . The uncertainty analysis of the friction factor obeys the same rule as described in for the heat transfer coefficient.

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100 Figure 5 9 . Friction factor for flat channel geometry . The pressure drop across the channel ridge geometry was experimentally investigated as well. Figure 5 10 plots the pressure drop comparison between the flat channel and channel ridge geometry. Noting that t he comparison is between experimental data to experimental data, uncertainty analysis is not made here. Instead of having Reynolds number as the horizontal axis, volumetric flow rate is used here. This is due to the fundamental difficulty of calculating t he exact hydraulic diameter of the channel ridge geometry. It could be readily seen from the figure that at low volumetric flow rate, the pressure drop remains almost the same. As the flow rate grows higher, the pressure drop of the channel ridge geometry gradually outweighs the pressure drop of the flat channel geometry. A 10% maximum raise in pressure drop is observed. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 100 200 300 400 500 600 700 f Re Friction factor(flat channel) f exp f theory

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101 Figure 5 10 . Pressure drop comparison of two testing geometries . The friction factor for the channel ridge geometry was calculated in the similar manner, noting that the laminar theory might not be a good theoretical expectation. The comparison of friction factor of the two geometries are plotted in Figure 5 9. Noting that due to the hardness calculating the Reynolds number, the horizontal axis is plotted with the volumetric flow rate. Seen from the graph, the friction factor of the channel ridge structure is firstly lower than the flat channel geometry, then grows higher than the flat channel geometry. This i s also observed in the pressure drop data that at low Reynolds number, the pressure drop in the channel ridge geometry is actually lower. However, considering the experimental uncertainty at low flow rate, this phenomena could be regarded as reasonable. 0 1000 2000 3000 4000 5000 6000 7000 8000 0 100 200 300 400 500 600 700 Pressure Drop (Pa) Volumetric Flow Rate(ml/min) Pressure drop comparison C-R Pa Flat Pa

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102 Figure 5 11 . Comparison of friction factor. F rom the above experimental data, it has been observed that a 30% maximum increase in heat transfer coefficient has been reached in the proposed channel ridge geometry, comparing to the flat channel geometry. On the other hand, only 10% of excessive pressure drop has been found in the flow rates from 115 to 630 ml/min. Due to the complexity of the channel ridge geometry, the theoretical prediction of the performance of the channel rid ge structure has to been completed by advanced computation technologies. In the next chapter, CFD analysis was made to perform the theoretical calculation of the channel ridge geometry. After the CFD analysis, variable comparison between the experimental a nd theoretical data will be made. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 100 200 300 400 500 600 700 f Flow Rate(ml/min) Comparison of friction factor C-R f Flat f

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103 CHAPTER 6 COMPUTATIONAL FL U ID DYNAMICS ANALYSIS 6.1 CFD Model Establishment 6.1.1 Governing Equation s The new proposed channel ridge geometry is complicated and could be considered to be irregular. One of the fundamental difficulties to evaluate this geometry is that cross section is continuously changing on the flow direction. Even if the equivalent depth could be calculated using the method described earlier, it is better the check the experimental result with more reli able calculation. As the rapid development of computational science and technology, large scale computation is possible. Computational Fluid Dynamics (CFD) has been used in more and more heat transfer studies as a reliable approach. In this chapter, CFD is used as a powerful tool to theoretically evaluate the performance of the channel ridge geometry. The first step to launch a CFD analysis is to set up appropriate governing equations. In this case, the governing equations include continuity equation, mome ntum equation s and energy equation for Newtonian and incompressible fluid. The momentum and energy equations are: (6 1) (6 2) where is the body force vector , is the specific enthalpy.

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104 In this specific case, some assumptions could be made. The flow could be considered as steady flow, so that the time derivative term is crossed out (zero) . Another assumption made here is constant pro per ties, which means the density, viscosity and thermal conductivity are considered as constants. The density and thermal conductivity can be factored out. Other assumptions include no body forces, only axial pressure variation, no viscous dissipation and negligible axial heat conduction. With the above assumptions, the governing equations could be simplified as follows: Continuity (6 3) X momentum (6 4) Y momentum (6 5) Z momentum ( 6 6) Energy (6 7) Considering the complexity of solving these partial differential equations in such a complicated geometry, large scale co mputational resources are required. For this case, the commercial CFD code Fluent 14.5 is used. The calculation was done on a super computer which has 84 CPUs and 16 0 GB of memory. 6.1.2 Geometrical model The first step for setting up a CFD task is to cre ate the geometrical model. However, the geometry could be created in Fluent. GAMBIT, a supporting software of Fluent, serves as the model creator for this study. The model was created in the unit of

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105 millimeter. It would not be an easy job to create such a complicated model with many sub structures. However, since most of the structures are repetitive, this model built process could be simplified. The complete geometrical model is shown in Figure 6 1. Figure 6 1 . Channel ridge structure in GAMIBT . 6.1.3 Meshing Generating the mesh is the step after building the geometrical model. The quality implies both the accuracy and easiness of the simu lation. Fine mesh could yield accurate result which may either be close to theoretical value or experimental value. make the calculation not converge. An accurate simulati on could be achieved by building bazillion cells within the geometrical structure. However, that would take infinite long computational time. As a result, the principle of a fine mesh is that the mesh could lead to accurate result while

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106 taking as less comp utational time as possible. The steps for generating mesh is similar to that of creating a structure , following the order of line, face and volume . Three measurements of quality are used to judge whether a mesh is good. They are skewness, smoothness and a spect ratio. The determination of skewness varies since the shape of the cells are different from case to case. Generally, it reflects the quality of cell size. Its value is between 0 and 1. The finer the mesh, the lower the skewness . Table 6 1 lists the value of skewness and their mesh quality [85]. Table 6 1 . Skewness and mesh quality Value of Skewness 0 0.25 0.25 0.50 0.50 0.80 0.80 0.95 0.95 0.99 0.99 1.00 Cell Quality excellent good acceptable poor sliver degenerate For hexahedron and quadrilateral cells, skewness should not exceed 0.85. This is also the same for triangular. Tetrahedron yields a higher limit for skewness at a value of 0.9. Smoothness measures the change in cell size. The change in size of adjacent cell s hould be gradual. In other words, sudden change in size on adjacent cells should be avoided. Aspect ratio directly reflects the shape of cell. Good cell should have the aspect ratio around 1. With the discussion above, the optimized mesh was generated via trial and error. In order to maintain the accuracy of the simulation, it has to be guaranteed that in the ridge depth direction, at least 30 nodes were created. That is to say, the interval size for nodes on edge is 0.01mm. After creating the nodes, face meshes were generated. To ensure the mesh quality, face mesh was generated using Triangular shape cells and pave type. The spacing was also set to be 0.01mm. The volume mesh was generated using Tet/Hybrid elements mode and TGrid type. Nothing that this mes hing

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107 configuration has shown good accuracy and reasonable computation time. This has been proved by Bigham et al [32]. The meshed model is shown in Figure 6 2. Figure 6 2 . Meshed channel ridge structure in GAMBIT . 6.1.4 Boun dary Conditions The last thing that has to be done in GAMBIT is to specify the boundary conditions. GAMBIT only allows the user to define the type of boundary conditions. By the boundary condition types are wall, velocity inlet and outlet. The details of the boundary conditions will be specified in Fluent. Care must be taken that after reading the mesh, it is important to specify and scale the units used when creating the mes h. In this study, millimeter was the unit when building the mesh. For the velocity inlet boundary, the input parameters average line velocity and temperature at the inlet. The temperature is obtained directly from the experimental data. The average line ve locity at the inlet is calculated by:

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108 (6 8) Two walls are actually serving as boundaries. The top wall, which corresponds to the Plexiglas cap, and the heating channel bottom and side walls. For the top wall, the bo undary condition could be considered to be insulated. This could be achieved by setting the heat flux to be zero. Similarly, the bottom and side walls could be considered together as a wall boundary condition. This needs to set the heat flux to be: (6 9) where A heated is the area of all the heated surface. The material used here is liquid water and the properties were considered to be constant. Using the Fluent database, the material could be readily input into the model. 6.1.4 Solver and Solution Controls Having set up the boundary condition and material property, it is important to choose the models, solver configuration and solution controls. The models here are laminar flow model and energy model. The solution m ethods were set as the following. The scheme (algorithm) is set to be SIMPLE. SIMPLES stands for Semi Implicit Method for Pressure Linked Equations. In this study, the steady state problem is to be solved iteratively. The SIMPLE algorithm could be descri bed as follows [ 86 ] . 1. An approximation of the velocity field is obtained by solving the momentum equation. The pressure gradient term is calculated using the pressure distribution from the previous iteration or an initial guess. 2. The pressure equation is formulated and solved in order to obtain the new pressure distribution. 3. Velocities are corrected and a new set of conservative fluxes is calculated.

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109 The pressure velocity coupling scheme was set to be PRESTO!. This is because in the PRESTO! method, pressure was calculated based on faces of a cell, rather than the center (this is used in STANDARD scheme). This could yield better result in three dimensional case. The momentum and energy scheme were set to be 2 nd order upwind. The determination of the momentum and energy scheme was largely influenced by the type of mesh. 1 st order upwind is more suitable for regular mesh such as laminar flow in a rectangular duct modeled with a quadrilateral or hexahedral grid. When the fluid field is not aligned with the grid, 2 nd order upwind scheme has to be launched to yield reasonable result. The solution monitors are to be set the criteria for convergence. The absolute criteria for continuity, x velocity, y velocity, z velocity and energy were set to be 0.001, 10 E 5, 10E 5, 10E 5 and 10E 6 respectively. This is to ensure the calculation could lead to accurate results. The solution was initialized by the hybrid initialization and the iteration was set to be at least 3000 to ensure the residual curves reach flat. 6. 2 Simulation Results and Analysis 6.2.1 Heat Transfer Coefficient As an important comparison, the experimental and the CFD heat transfer coefficient of the channel ridge structure is compared and plotted in Figure 6 3. The simulated heat transfer coefficie nt varies quite linearly with the volumetric flow rate. It could be readily seen that the experimental heat transfer coefficient is lower than the simulated result at volumetric rates greater than200 ml/min. The maximum discrepancy between the simulated an d experimental heat transfer coefficient was 35% at the volumetric flow rate of 670 ml/min.

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110 Figure 6 3 . Heat transfer coefficient comparison for C R structure. One of the reasons accounting for this, of course, is the experi mental uncertainty. With the error bars plotted in the figure, some data points are still not in agreement with the experimental data. The difference in geometrical model between experimental testing piece and simulation structure should account for this. As discussed earlier in Chapter 3, the fabricated structure is not exactly the same as the simulated structure. Figure 6 4 illustrates the difference. It could be easily discovered that as the shape corners turned into round corners, part of the ridge do es not exist. This is even more obviously ridge shown in the upper part of the figure. The herringbone structure simply order of thousands in the testing piece), the d eviation of the heat transfer coefficient is an inevitable result. Based on the current fabrication capacity , making better ridges could cost too much time and effort. Considering the off design condition of the 0 1000 2000 3000 4000 5000 6000 0 100 200 300 400 500 600 700 800 Heat Transfer Coefficient (W/m 2 K) Volumetric Flow Rate (ml/min) H eat transfer coefficient comparison for C R structure h simu h exp

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111 experimental testing piece, this discrepancy could be regarded as acceptable. It has to be noted that simulating the experimental could be difficult due to the complicated geometry. The computation time brought by the complicated geometry could be more as well. Moreover, simulating the off design ge ometry deviates the purpose of the study. Figure 6 4 . Illustration of the off design structure. Another important comparison is the comparison between the calculated flat channel and channel ridge structure. To purpose of do ing this is to confirm difference in perform theoretically. The comparison of calculated heat transfer coefficient of flat channel and channel ridge geometry is plotted in Figure 6 5. It could be seen from the figure that the new geometry has an advanceme nt in heat transfer coefficient. This increase could be as high as 80%. Due to the continuously growing heat transfer coefficient, it could be hypothesized that the flow does not reach fully developed. In fact, due to the presence of ridges, the flow insid e is being continuously disrupted and will

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112 never be fully developed, considering the constant heat flux boundary condition. This guarantees the continuously growing heat transfer coefficient. Figure 6 5 . Comparison of calcul ated heat transfer coefficients . 6.2.2 Pressure Drop and Friction Factor The pressure drop comparison between the simulated and experimental data is plotted in Figure 6 6. It could be observed in the figure that the experimental pressure drop is generally greater than the simulation result. The difference in both data could be as high as 30%. As before, experimental uncertainty is one of the reasons. Other reasons for the excessive pressure drop could be surface roughness effects and inlet and outlet pressu re drop induced by the manifolds. 0 1000 2000 3000 4000 5000 6000 0 100 200 300 400 500 600 700 800 Heat Tansfer Coefficient (W/m 2 K) Volumetric Flow Rate(ml/min) Comparison of calculated heat transfer coefficients flat h cal C-R h cal

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113 Figure 6 6 . Comparison of simulated and experimental pressure drop . The comparison of calculated pressure drops of flat channel and channel ridge structures is plotted in Figure 6 7. It coul d be seem from the plot that the calculated pressure drops of the two structure do not show great difference. This means that the channel ridge structure does not lead to much pressure drop penalty while greatly enhances the heat transfer capacity. 0 1000 2000 3000 4000 5000 6000 7000 8000 0 100 200 300 400 500 600 700 Pressure Drop(Pa) Volumetric Flow Rate(ml/min) Comparison of simulated and experimental pressure drop (C R) dp simu dp exp

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114 Figu re 6 7 . Comparison of calculated pressure drop . The comparison of simulated and experimental friction factor is plotted in Figure 6 8. No great deviation has been detected between the simulated and experimental friction factor. This is because the pressure drop data was actually close. The comparison of calculated friction factors for flat channel and channel ridge structures is plotted in Figure 6 9. Noting that the difference of friction factor at low rate is due to the lower p ressure drop given by the channel ridge simulation. 0 1000 2000 3000 4000 5000 6000 0 100 200 300 400 500 600 700 Pressure Drop (Pa) Volumetric Flow Rate (ml/min) C omparison of calculated pressure drop dp simu CR dp flat cal

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115 Figure 6 8 . Comparison of simulated and experimental friction factor . Figure 6 9 . Comparison of calculated friction factors . 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 100 200 300 400 500 600 700 f Volumetric Flow Rate(ml/min) Comparison of simulated and experimental friction fator (C R) f simu f exp 0 0.1 0.2 0.3 0.4 0.5 0.6 0 100 200 300 400 500 600 700 800 f Volumetric Flow Rate (ml/min) Comparison of calculated friction factors f C-R sim f flat cal

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116 CHAPTER 7 CONCLU SIONS AND RECOMMENDATIONS An experimental investigation of a new geometry, the staggered herringbone structure, was conducted. The motivation of this study was described in details. A literature review on studies concerning the heat transfer and pressure drop of microchannels was completed. Some of the major heat transfer enhancement techniques and their applications in microchannels were briefly reviewed. Accompany with the experimental study, a CFD analysis was also conducted to verify and compare with the experimental results. It was found that the new geometry could enhance the heat transfer properties with reasonable pressure drop penalty. Experiments were conducted on two different testing pieces, flat channel and staggered herringbone (channel ridge ) structure. The only difference between these two pieces is the presence of secondary ridge structure on the bottom of every single channel. The experimental results of the flat channel geometry showed good agreement with the laminar flow theory on both N usselt number and pressure drop. This agreement further confirmed the reliability of the designed experimental setup. The reasonable deviations should be induced by experimental uncertainty, surface roughness effects and system error. The thermohydraulic properties, namely the heat transfer coefficient and pressure drop, were tested using the same experimental setup. For the heat transfer coefficient, the experimental heat transfer coefficient of the channel ridge geometry grows as the flow rate increases. A 30% increase in heat transfer coefficient was observed in the testing flow rates. On the other hand, a 10% increase in the pressure was observed. It could be concluded from the experimental results that the

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117 channel ridge structure enhanced heat transfer while paying reasonable pressure drop penalty. A CFD analysis on the channel ridge followed the experimental study. Interestingly, the simulated heat transfer coefficient showed 35% of maximum increase than the experimental result. Comparing the simulated with the flat channel heat transfer coefficient, a maximum increase of 80% was found. The deviation between the simulated and experimental heat transfer coefficient was largely induced by the difference in geometrical structures that are being experimenta lly tested and simulated. Because of the limits of the fabrication technology, it would take too much time and effort to fabricate the geometry in great detail. Considering the tested geometry, this deviation could be considered reasonable. The simulated p ressure drop showed great agreement with the experimental data. In conclusion, the channel ridge geometry could yield a maximum increase of 80% in heat transfer coefficient and 10% increase in pressure drop theoretically. Even the experimental result unde restimates the heat transfer coefficient, the deviation was acceptable considering the off design geometry. Some improvements could be made to this study. The first retrofit that can be done is to make smaller testing pieces and fabricate the ridges clos e to the design geometry. Making smaller testing piece could shorten the time for fabrication and have more precise structure. A smaller testing piece could also make it possible to investigate a greater flow range, so that the data can be taken in turbule nt regime. Another recommendation is to replace the thin film heater by cartridge heater with greater heating capacity. Low heating capacity leads to lower temperature rise of the working

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118 fluid and cause s greater experimental uncertainty. Moreover, since the heat from the film heat is not uniform, the constant heat flux boundary condition could be perfectly met. More works could be done to further investigate the thermohydraulic property of the structure. PIV or other visualization technologies could be used to further study the flow field. More investigations could also be done in the turbulence regime.

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119 LIST OF REFERENCES [1] D.B. Tuckerman, R.F.W. Pease, High performance heat sinking for VLSI, IEEE Electron Device Lett. 2 (1981 ). [2] B. Palm, Microscale Thermophysical Engineering HEAT TRANSFER IN MICROCHANNELS, (2010) 37 41. [3] G. Hetsroni, a. Mosyak, E. Pogrebnyak, L.P. Yarin, Heat transfer in micro channels: Comparison of experiments with theory and numerical results, Int. J. Heat Mass Transf. 48 (2005) 5580 5601. [4] M.E. Steinke, S.G. Kandlikar, Single phase heat transfer enchancement techniques in microchannel and microchannels flows , in: Proceeding of ASME 2nd International Conference on Microchannels and Minichannels , R ochester, New York, USA, 2004, pp.141 148. [5] J.J. Brandner, E. Anurjew, L. Bohn, E. Hansjosten, T. Henning, U. Schygulla, et al., Concepts and realization of microstructure heat exchangers for enhanced heat transfer, Exp. Therm. Fluid Sci. 30 (2006) 801 809. [6] H.A. Mohammeda, , G. Bhaskarana, N.H. Shuaiba, R. Saidurb, Heat transfer and fluid flow characteristics in microchannels heat exchanger using nanofluids: A review, Renewable and Sustainable Energy Reviews 15 (2011) 1502 1512. [7] R. Nasr Isfahani , S. Moghaddam, Absorption characteristics of lithium bromide (LiBr) solution constrained by superhydrophobic nanofibrous structures, Int. J. Heat Mass Transf. 63 (2013) 82 90. [8] P. Srikhirin, S. Aphornratana, S. Chungpaibulpatana, A review of absorption refrigeration technologies, Renew. Sustain. Energy Rev. 5 (2000) 343 372. [9] D. Yu, J. Chung, S. Moghaddam, Parametric study of water vapor absorption into a constrained thin film of lithium bromide solution, Int. J. Heat Mass Transf. 55 (2012) 5687 5695 . [10] R. Nasr Isfahani, A. Fazeli, S. Bigham, S. Moghaddam, Physics of lithium bromide (LiBr) solution dewatering through vapor venting membranes, Int. J. Multiph. Flow. 58 (2014) 27 38. [11] R. Nasr Isfahani, K. Sampath, S. Moghaddam, Nanofibrous membran e based absorption refrigeration system, Int. J. Refrig. 36 (2013) 2297 2307. [12] Y. Li, L. Fu, S. Zhang, X. Zhao, A new type of district heating system based on distributed absorption heat pumps, Energy. 36 (2011) 4570 4576.

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126 BIOGRAPHICAL SKETCH Wei Xing was born in Tianjin, China, in1991. He received his Bachelor of Engineering in Process Equipment and Controlling Engineering from Nanjing University of Technology in June of 2 012. During his undergrad study, he participated in various research concerning solar and hydrogen energy. He owns two patents of industrial solar equipment. Wei conducted research on microscale heat transfer during his graduate study. Wei plans to contin ue his stud ies as a Ph.D. student at Rensselaer Polytechnic Institute.