NAl'l LIBRARY DEC...measured pressure drop was used to calculate the average friction factor, and the measured temperature distribution was used to evaluate single-phase heat transfer

Ul\lIVf=R;-,!TY QI= H,I\\NAl'l LIBRARY

MULTIPHASE MICRO-PIN-FIN HEAT SINK: PRESSURE DROP AND HEAT

TRANSFER

A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI'I IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

December 2007

By Abel Siu Ho

Thesis Committee:

Weilin Qu, Chairperson Beei - Huan Chao Marcelo Kobayashi

We certify that we have read this thesis and that, in our opinion, it is

satisfactory in scope and quality as a dissertation for the degree of Master

of Science in Mechanical Engineering.

THESIS COMMITTEE

ii

© Copyright 2007 by

Abel Siu Ho All Rlghts Reserved

iii

Acknowledgements

There are so many people that I want to thank for giving me support during graduate

schoo!. First, I would like to thank Dr. Weilin Qu for all his help throughout this research

which allowed me to gain an incredible amount of knowledge and experience, his help is

fully appreciated. I am really grateful for the time that Dr. Beei Huan Chao and Dr.

Marcelo Kobayashi have given me as committee members their input have made this thesis

dissertation better. I want to acknowledge Dr. Ronaid Knapp and Dr. Carlos Coimbra for

their advice during my first year of graduate school your guidance is fully appreciated. Dr.

Alex Da Silva, I appreciated your words of advice that made me realized so many things

that I did not thought before.

I want to recognize the help, support and advice of Lance Yoneshige and Lynnette

Ramirez definitely without you guys I would not have successfully gone through all the

years that it took me to accomplish my goal of obtaining my master degree. Some words of

recognition to my lab partner Scott Lee and I think it was quiet a ride that we have at the

Micro-scale Thermal Laboratory and thanks for your help. Also, I would like to thank my

new lab partners Ruey Hwu and Chris Konishi, keep up with the good work! Thanks for all

the support that my ME graduate friends and classmates have given me: Chris Kinoshita,

Jasen Kaya, Kin Wai Leong, Sarah Goorkey, Isaac Victor Bolin, Hugo Pedro, Edwin Lim,

and Karl Santa. Also, I want to thank my friends Dustin Lopes, Cody Aihara, Eddie

Briones and Kristin Uyemura for their support. Finally, I would like to recognized research

funding from the College of Engineering and the support of Graduate Student Organization

iv

for conferences. Last, I really have to thanks my parents for their unconditional support

surely I wouldnt be where I am at without their guidance.

v

Abstract

This paper is a study concerning the thermal and hydrodynamic characteristics of a liquid

single-phase flow and flow boiling in an array of micro-pin-fins. An array of 1950 staggered

square micro-pin-fins with 200 x 200 /Jm2 cross-section by 670 /Jm height were fabricated

into a copper heat sink test section. The ratios of longitudinal pitch (SL) and transverse

pitch (Sr) to pin-fin equivalent diameter (de) are equal to 2. Deionized water was used as the

cooling liquid. Two coolant inlet temperatures of 30·C and 60·C, and six maximum mass

velocities for each inlet temperature, ranging from 183 to 420 kg/m2s, were tested. The

corresponding inlet Reynolds number ranged from 45.9 to 179.6. For single-phase flow, the

measured pressure drop was used to calculate the average friction factor, and the measured

temperature distribution was used to evaluate single-phase heat transfer coefficient and

N usselt number. Predictions of the previous friction factor and heat transfer correlations

that were developed for low Reynolds number (Re < 1000) single-phase flow in pin-fin arrays

were compared to the present micro-pin-fin single-phase pressure drop and Nusselt number

data, respectively. Most predictions of other friction factor and heat transfer correlations

were significantly different from the experimental data collected in this study. Two new heat

transfer correlations were proposed for average heat transfer based on the present data, in

which average Nusselt number is correlated to the average Reynolds number by power law.

Also, there is indication of a strong dependence of Nusselt number on Reynolds number in

micro-pin-fin arrays. A new power-law type of correlation was proposed base on the present

pressure drop data too. Last, micro-pin-fin heat sink was tested at high temperatures in

which pressure drop and temperature were measured and bolling curves were obtained.

vi

Acknowledgements

Abstract ....

List of Tables .

List of Figures

Nomenclature .

Chapter 1: Introduction

1.1 Background..

1.2 Literature Review

1.3 Research Objectives

Chapter 2: Experimental System

2.1 Flow Loop ..

2.2 Test Module.

2.3 Test Procedure

Contents

Chapter 3: Single-Phase Heat Transfer . .

3.1 Temperature Measurements Results

3.2 Average Heat Transfer Characteristics .

3.3 Assessment of Previous Heat Transfer Correlations

3.4 New Heat Transfer Correlations. . .

3.5 Local Heat Transfer Characteristics .

3.6 Summary . . . . . . . . . . . . .

vii

iv

vi

viii

ix

xiii

1

1

2

4

8

8

9

11

24

24

25

29

37

41

46

Chapter 4: Single-Phase Pressure Drop

4.1 Adiabatic Pressure Drop.

4.2 Diabatic Pressure Drop

4.3 Summary . . . . . . . .

Chapter 5: Two-Phase Pressure Drop and Heat Transfer .

5.1 Boiling Curve .....

5.2 Overall Pressure Drop

5.3 Summary . .

5.4 Future Work

Chapter 6: Conclusions

viii

48

49

57

62

65

65

68

68

68

71

List of Tables

3.1 Operating conditions for single phase heat transfer study 24

3.2 Correlations for heat transfer in pin-fin arrays . . . . . . . 33

3.3 Coefficient and exponents of heat transfer correlations for present micro-pin-

fin array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35

4.1 Operating conditions for single phase pressure drop study 48

4.2 Single-phase friction factor correlations. . . . . . . . . . . 54

be

List of Figures

1.1 Typical micro-channel heat sink construction . . . . . . . . . . . . . . 6

1.2 Staggered micro-pin-fin heat sink and aligned micro-pin-fin heat sink . 7

2.1 Schematic of flow loop

2.2 Actual flow loop

2.3 Water reservoir

2.4 Gear pump ..

2.5 Heat exchanger

2.6 Rotameters and digital displays for test module .

2.7 Constant temperature bath

2.8 Test module set up . . . .

2.9 Test module construction

2.10 Test module assembly ..

2.11 Top view of micro-pin-fin array and schematic of unit cell

2.12 Variac ....... .

2.13 Pressure transducers

2.14 Data acquisition system

2.15 Digital power meter ..

3.1 Variation of measured micro-pin-fin base temperature with input heat flux

(a) at Ztcl to Ztc3 for Tin = 30°C and Gm= = 420 kg/m2s, and (b) at Ztcl

for Tin = 30°C and all six G""", .

x

14

15

16

16

17

17

18

18

19

20

21

21

22

22

23

26

3.2 Variation of average micr(}opin-fin base temperature with input heat flux: (a)

11,. = 30°C, (b) Tin = 60°C . . . . . . . . . . . . . . . . . . . . . . . . . .. 28

3.3 Variation of average heat transfer coefficient with input heat flux: (a)

Tin = 30°C, (b) Tin = 60°C ... . . . . . . . . . . . . . . . . . . . . . 30

3.4 Variation of average Nusselt number with average Reynolds number 31

3.5 Comparison of average Nusselt number data with predictions of (a)

correlation 1 , (b) correlation 2, (c) correlation 3, (d) correlation 4, (e)

correlation 5, (f) correlation 6 . .


correlation 7, and (b) correlation 8 . . . . . . . .

36

38

3.7 Linear regression analysis leading to (a) correlation 9, and (b) correlation 10 40


correlation 9, and (b) correlation 10 ...... .

3.9 Variation of local heat transfer coefficient with input heat flux (a) at Ztcl to

Ztc3 for Tin = 30°C and Gma;c = 420 kg/m2s, and (b) at Ztcl for 11n = 30°C

42

and all six Gm= ................................. 44

3.10 Variation of local Nusselt number with local Reynolds number: (a) 11n =

30°C, (b) Tin = 60°C .............................. 45

3.11 Comparison of local Nusselt number data with predictions of (a) correlation

9, and (b) correlation 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47

4.1 Variation of measured pressure drop with maximum mass velocity for

adiabatic tests 50

4.2 Comparison of friction factor data with predictions of correlations for

adiabatic tests .................................. 52

4.3 Variation of measured pressure drop with input heat flux for diabatic tests:

(a) 11,. = 30°C, (b)T;" = 60°C. . . . . . . . . . . . . . . . . . . . . .. 58

xi

4.4 Comparison of measured and predicted values of diabatic pressure drop for

lin = 30D C and G"""" = 264 kg/m2s . . . . . . . . . . . . . . . . . . . . .. 59

4.5 Comparison of measured diabatic pressure drop data with predictions of

correlations of (a) correlation 1, (b) correlation 2, (c) correlation 3, (d)

correlation 4, (e) correlation 5, (f) correlation 6 . . . . . . . . . . . . . . .. 63

4.6 Comparison of measured diabatic pressure drop data with predictions of

correlation 7. . . . . . . . . . . . . . . . . . . . . . .

5.1 Boiling curves at Ztcl to Ztc3 for Gm= = 264 kg/m2s

5.2 Boiling curves at Ztc3 for all six mass velocities .. .

5.3 Variation of measured pressure drop with input heat flux

xii

64

66

67

69

Nomenclature

Ac Cross-sectional area of a micro-pin-fin

Ac.!l Area of unit cell base endwall

A fin Wetted surface area of a micro-pin-fin

Amin Minimum transverse How area

At Total area of micro-pin-fin array base endwall

Awet Total wetted area of micro-pin-fin array

c Coefficient in heat transfer correlation

Cp Specific heat

d Diameter of circular pin-fin

dhe Hydraulic diameter of How passage

d" Volumetric hydraulic diameter

f/in Friction factor in micro-pin-fin array

f/in,i Friction factor in segment i

f/in,l Laminar friction factor component

fJin,t Turbulent friction factor component

xiii

Gm= Maximum mass velocity

h Heat transfer coefficient

ha• e Average heat transfer coefficient for the entire micro-pin-fin array

H fin Height of micro-pin-fin

h; Heat transfer coefficient in segment i

Itt", Local heat transfer coefficient at thermocouple stream-wise location

H", Distance from thermocouple to micro-pin-fin base

k Thermal conductivity

Kcl,Kc2 Contraction loss coefficient

KeJ,Ke2 Expansion recovery coefficient

I Exponent of Prandtl number ratio or viscosity ratio

Lfin Length of micro-pin-fin

Lhs Length of micro-pin-fin array base endwall

m Mass flow rate, kula

m Exponent of Reynolds number

M Number of data points

MAE Mean absolute error

m fin Fin parameter

n Exponent of Prandtl number

N L Total number of rows in micro-pin-fin array

xiv

NT Total number of nUcro-pin-fins in a segment

Nu Nusselt number

Nua •• Average Nusselt number

Nuw. Local Nusselt number at thermocouple stream-wise location

tJ.P Pressure drop across heat sink

tJ.Pcl ,tJ.P c2 Contraction pressure loss

tJ.PeI.tJ.Pe1 Expansion pressure loss

tJ.P/in Cross-section perimeter of a micro-pin-fin

Plin Perimeter of a square nUcro-pin-fin cross-section

Pr Prandtl number

Pr I,a •• Prandtl number at TI,a.e

Prw,ave Prandtl number at Tw, •• e

Pw Power input

" qefl Heat flux based on heat sink top platform area

Q lin Heat transferred to nUcro-pin-fin array

Qlo88 Heat loss

Re Reynolds number based on de

Reave Average Reynolds number

Redhe Reynolds number based on d""

Red. Reynolds number based on de

xv

Rete. Local Reynolds number at thennocouple stream-wise location

S D Diagonal pitch

S L Longitudinal pitch

S7' Transverse pitch

T Temperature

T/,ave Average water bulk temperature

T/,tci Water bulk temperature at thermocouple stream-wise location

lin Inlet temperature

Tout Outlet temperature

Ttci Thermocouple reading (i = 1 to 3)

Tw .!"; Micro-pin-fin base temperature at thennocouple location

Tw,ave Average micro-pin-fin base temperature

Tw,i Average micro-pin-fin base temperature in segment i

u Velocity

Uma", Maximum water velocity

W/in Width of micro-pin-fin

Whs Width of heat sink top platform area

z Stream-wise coordinate

Ztci Stream-wise location of thermocouple (i = 1 to 3)

Greek Symbols

xvi

f3 Geometric parameter in the Hwang and Yao correlation (correlation 3)

'l/fin Fin Efficiency

A Geometric parameter in the Hwang and Yao correlation (correlation 3)

'" Viscosity

¢ Weighting factor in the Gaddis and Gnielinski correlation (correlation 2)

11"1, 11"2 Components in the Ko §ar et al. correlation (correlation 5)

p Density

Subscripts

ave Average

c6 Moores and Joshi correlation (correlation 6)

exp Experimental (measured)

Zi A stream-wise segment containing one row of micro-pin-fins

in Inlet

f Liquid (water)

out Outlet

pI Deep plenum

p2 Shallow plenum

pred Predicted

s Solid (Copper)

tci Thermocouple

w Base endwall

xvii

1.1 Background

Chapter 1

Introduction

Breakthrough in many cutting-edge technologies is increasingly dependent upon the

availability of highly efficient cooling techniques that are capable of dissipating a large

amount of heat from small areas. Single-phase liquid-cooled miniature heat sinks, which

incorporate internal heat transfer enhancement structures that are tens to hundreds of

micrometers in size, have emerged as one solution to these cooling challenges. Among a

large variety of possible micro-scale enhancement structures, parallel micro-channels have

received the most attention so far [1-5]. Key technical merits of resulting micro-channel

heat sinks as demonstrated by these previous studies include: low thermal resistance to

dissipative heat flux, high heat transfer area to volume ratio, compact dimensions, and

small coolant inventory requirement (Figure 1.1).

Recent advancement in micro-fabrication techniques, however, allows more complex

micro-scale geometries to be fabricated directly into high-thermal-conductivity solid

substrate at low cost, which makes it possible to explore alternative enhancement structures

that may be more effective than micro-channels. A promising configuration is micro

scale pin-fin arrays [6-11]. Depending on the geometric arrangement of pin-fins, a pin

fin array can be classified as staggered or allgued. Schematics of staggered or allgued

micro-pin-fin heat sinks incorporating square pin-fins are shown in Figure 1.2(a) and 1.2(b),

1

respectively. Important features of micro-pin-fin arrays that are intended for miniature heat

sink applications as discussed in the previous studies [6-11] include: (a) liquid such as water

or refrigerant is the coolant of choice in order to achieve better cooling performance; (b)

heat is transferred to micro-pin-fin array from one endwall only (base endwall); (c) pin

fins span the full distance between the based endwall and cover endwall, and there is no

clearance gap between the cover endwall and pin-fin tips; (d) pin-fin height-to-diameter ratio

H lin/dis in the intermediate range of 0.5 to 8 due to fabrication limitation, and endwalls

have considerable effect on overall array thermal and hydrodynamic characteristics; and (e)

the low coolant flow rate and small characteristic dimension of pin-fins usually yield a low

Reynolds number of less than 1000. The flow is therefore in laminar or transitional regime.

1.2 Literature Review

Effective design and performance assessment of micro-pin-fin heat sinks require a

fundamental understanding and accurate description of virtually all thermal and

hydrodynamic aspects of micro-pin-fin arrays. While interest in micro-scale pin-fins is fairly

recent, arrays of conventional-size pin-fins that are several millimeters or larger in diameter

have been used as heat transfer enhancement structure in a wide variety of engineering

applications, and their heat transfer and pressure drop characteristics have been studies

quite extensively in the past. Both long pin-fins (Hfin/d > 8 ) [12-18] and intermediate

pin-fins ( 0.5 ~ H fin/ d ~ 8) [19-26] were examined in the previous studies. Arrays of long

pin-fins or tube banks are used mostly in heat exchanger applications [12-18]. Most of the

heat transfer and pressure drop occurs at the surface of the tubes and the base endwall

effect is negligible. In addition, available experimental data for low Reynolds number flow,

i.e. Re < 1000, is rather limited. Arrays of intermediate pin-fins are common heat transfer

enhancement structure in turbine cooling applications [19-26]. In these applications, gases

are generally used as the coolant and high flow rate produces a high Reynolds number of

at least several thousands.

2

While fluid flow and heat transfer conditions and/or pin-fin geometry in most previous

conventional-size pin-fin studies differ considerably from those of micro-pin-fins, there are

a few studies that are quite relevant, in which heat transfer and pressure drop associated

with low Reynolds number (Re <1000) single-phase flow in arrays of intermediate pin-fins

were investigated [27-29J. In a two-part paper, Short et al. [27,28J experimentally studied

pressure drop and heat transfer of air flow in 44 different pin-fin configurations of staggered

circular pin-fins having diameter d from 1.57 to 3.18 mm, pin-fin height-to-diameter ratio

H lin/ d from 1.88 to 7.25, longitudinal pitch-to-diameter ratio SLId from 1.83 to 3.21,

and transverse pitch-to-diameter ratio ST / d from 2.0 to 6.41. New empirical correlations

for friction factor and heat transfer were proposed for two flow regimes of low Reynolds

number (175 < Re < 1000) and high Reynolds number (Re > 1000). Moores and Joshi [29J

conducted an experimental study of water pressure drop and heat transfer in three arrays

of staggered circular pin-fins with d from 3.67 to 3.84 mm, H lin/ d from 0.52 to 1.09, SLId

from 1.13 to 1.18, and ST/d from 1.3 to 1.36. They also proposed new friction factor and

heat transfer correlations for the two flow regimes of low Reynolds number (200< Re <

1000) and high Reynolds number (Re > 1000).

A limited number of studies have recently been carried out on liquid single-phase

pressure drop and heat transfer in micro-pin-fin arrays. KO§ar et al. [6J experimentally

studied water pressure drop across four different pin-fin configurations of staggered and

aligned circular and diamond shaped micro-pin-fins having d of 50 and 100 p.m, H lin/ d of 1

and 2, SLId of 1.5 and 5, and ST / d of 1.5 and 5. Reynolds number in the study ranged from

5 to 128. New friction factor correlations were proposed based on the experimental results.

Peles et al. [7J provided a theoretical analysis of heat transfer in micro-pin-fin arrays using

a conventional long pin-fin correlation. KO§ar and Peles [8J experimentally studied water

pressure drop and heat transfer in an array of staggered circular pin-fins with d of 99.5 p.m,

H lin/ d of 2.44, SLId of 1.5, and ST / d of 1.5. Reynolds number ranged from 14 to 112.

KO§ar and Peles [9J experimentally studied refrigerant R-I23 heat transfer in an array of

staggered circular pin-fins having diameter d of 99.5 p.m, Hlin/d of 2.44, SLId of 1.5, and

3

ST/d of 1.5. New heat transfer correlation was proposed based on the R-123 data of as well

as water data from their previous study [8}. KOljar et al. [1O} conducted an experimental

study of water pressure drop and heat transfer in an array of hydrofoil pin-fins with chord

thickness of 100 p.m and height of 243 p.m. Reynolds number ranged from 15 to 720. New

heat transfer correlation was proposed based on the experimental data. Prasher et al. [11]

experimentally studied water pressure drop and heat transfer in five arrays of staggered

circular and square micro-pin-fins having d from 55 to 153 p.m, H fin/ d from 1.3 to 2.8,

SLId from 2.4 to 4, and ST/d from 2 to 3.6. Reynolds number ranged from 15 to 720. New

friction factor and heat transfer correlations were proposed.

1.3 Research Objectives

The present thesis describes experimental study of heat transfer and pressure drop in an

array of staggered square micro-pin-fins with an equivalent diameter of 200 p.m and height

of 670 p.m. The objectives of the study are: (1) to provide new heat transfer and pressure

drop data for liquid single-phase flow in a micro-pin-fin array, (2) to assess the accuracy

of previous correlations at describing the thermal and hydrodynamic characteristics of the

present micro-pin-fin array, (3) to reveal the important parametric trends, and (4) to develop

new correlations for the micro-pin-fin array.

In chapter 2 the experimental system and the procedure in which the single-phase and

two-phase micro-pin-fin heat sink testing was carried out is described. First, the general

characteristics of the single flow regime are described. In chapter 3, the experimental

results are used to compare with predictions of previous heat transfer correlations in order

to assess the feasibility of these existing correlations at describing micro-pin-fin heat transfer

through Nusselt number. New Nusselt number correlations were formulated from this

study. Chapter 4 deals with the single phase pressure drop in which previous friction

factor correlations available in the literature were compared with the experimental data

too. Also, new friction factor correlation was proposed. Chapter 5 describes the two-phase

4

characteristics, Le., the pressure drop and temperature inside the micro-pin-fin heat sink

tested at high temperatures in which boiling was observed. Finally, chapter 6 sumarizes the

findings in the single-phase and two-phase micro-pin-fin heat sink experiments.

5

___ Micro-Channel Heat Sink

'--___ Hlgh-Heat-Flux Device

Figure l.1: Typical micro-channel heat sink construction.

6

DO DO

DOD

Staggered mlcro-pln-fln

heatsink

Flowf ...,.--------, "~-Device

(a)

o 0 0 ~riJlill~ DO OJ, DOD FIOWf

(b)

Aligned micraapin-fin

heat sink

Figure 1.2: (a) staggered micro-pin-fin heat sink, (b) aligned micro-pin-fin heat sink.

7

2.1 Flow Loop

Chapter 2

Experimental System

Figure 2.1 shows a schematic of the flow loop that was constructed to supply deionized

water to the micro-pin-fin heat sink test module at the desired operating conditions. The

flow loop for the micro-pin-fin heat sink is shown in Figure 2.2. Water contained in a

reservoir was circulated through the flow loop using a variable speed gear pump (Figure

2.3 - 2.4). A compact heat exchanger was used to bring the water to a temperature of

approximately 19°C before it entered the pump (Figure 2.5). After leaving the pump, the

water was first filtered to avoid clogging of flow passages in the heat sink with solid particles.

The water then passed through one of two rotameters for flow rate measurement (Figure

2.6). The rotameters were calibrated using the standard weighting method. The accuracy

of flow rate measurement was better than 4 % of the readings in gram per second (9/ s).

Afterwards, the water passed through a second heat exchanger that was connected to a

constant temperature bath (Figure 2.7) which brought the water to the desired test module

inlet temperature. The water then entered the micro-pin-fin heat sink test module (Figure

2.8). The water exiting the test module flowed through a third heat exchanger before it

returned to the reservoir. Several valves were also included in the flow loop for flow control.

Prior to conducting a test, the water in the reservoir was deaerated for one hour through

boiling using the immersion heater to force any dissolved gases to escape to the ambient. The

8

flow loop components were then adjusted to yield the desired test module inlet temperature,

1/ .. , and mass flow rate, m.

2.2 Test Module

Figures 2.9 and 2.10 illustrate the construction and assembly of the micro-pin-fin heat sink

test module. respectively. The test module was composed of a 110 copper micro-pin-fin

heat sink, a G-7 fiberglass plastic housing, a transparent polycarbonate plastic (Lexan)

cover plate, and nine cartridge heaters. The micro-pin-fin heat sink had a platform (top)

area of 1.0 em (width) by 3.38 em (length). An array of 1950 staggered micro-pins with 200

x 200 p,m2 cross-section by 670 p,m height were milled out of the top surface with carbide

micro end mills. A top view of the micro-pin-fin array together with key dimensions is

shown in Fig. 2.11. Below the heat sink top surface, three Type-K thermocouples were

inserted along the center plane to measure the stream-wise temperature distribution in the

heat sink, and are indicated in Figure 2.9 as tel to tc3 from upstream to downstream. The

stream-wise distance of the three thermocouples from the heat sink inlet, zu,b ztc2 and

Ztc3, is 5 mm, 16.6 mm and 28.2 mm, respectively. Further below was a small protruding

platform around the periphery of the heat sink to ensure the top surface of the heat sink

was flush with the top surface of the housing. Three narrow slots were cut from the bottom

surface up through most of the heat sinks height to reduce stream-wise heat conduction

within the heat sink. Nine holes were drilled into the bottom surface of the heat sink to

accommodate the cartridge heaters that were connected in parallel and powered by a 0 -

110 VAC variac (Figure 2.12).

The central portion of the housing was removed where the micro-pln-fin heat sink was

inserted as illustrated in Figure 2.9. RTV silicone rubber was applied along the interface

between the housing and the heat sink to prevent leakage. After the heat sink was inserted

into the housing, visual inspection was performed to ensure that the top surface of the

micro-pin-fins was flush with the top surface of the housing as illustrated in Figure 2.10.

9

The housing contained plenums both upstream and downstream of the micro-pin-fin arrays.

Each plenum had a deep portion leading to a shallow portion to ensure even distribution of

flow. A differential pressure transducer was connected to the inlet and outlet deep plenums

via pressure taps to measure the pressure drop across the heat sink (Figure 2.13). The

uncertainty in the pressure drop measurements was estimated to be less than 0.25 % of

the readings in psi. Also located in the inlet and outlet deep plenums are two Type

K thermocouples to measure the inlet and exit temperatures of the water, respectively.

Errors associated with the thermocouple measurements were smaller than ±0.3°C. The

differential pressure transducer and thermocouple readings were recorded using an HP data

acquisition/control system that was interfaced to a PC (Figure 2.14).

The 12.7 mm (0.5 inch) thick cover plate was bolted atop the housing using eight long

support bolts to hold the heat sink securely in place as shown in Figures 2.9 and 2.10. The

cover plate and the heat sink top surface containing the micro-pin-fin array formed closed

flow passages for the water. A shallow groove was machined into the housing around the

heat sink top surface, and was filled with RTV silicone rubber to create a leak-proof seal.

The bolts-nuts assembly ensured that the bottom surface of the cover plate is in direct

contact with the top surface of the housing and the heat sink, and prevented the cover plate

from deforming due to the higher internal pressure. Upon completion of all the tests and

disassembly of the test module, small shallow dents were observed on cover plate bottom

surface in the area that touched the heat sink, which verifies that no gap existed between

the micro-pin-fin top surface and the cover plate bottom surface.

After the test module was assembled, multiple layers of ceramic fiber were wrapped

around the heat sink for thermal insulation. Heat loss to the ambient was minimized, which

was confirmed by excellent agreement between the electrical power input and the measured

enthalpy change of water flow as shown later in the paper. All heat flux calculations in this

study were therefore based on the electrical power input to the cartridge heaters Pw, which

was measured by a 0.5 % accuracy wattmeter (Yokogawa Digital Power Meter WT21O). The

10

wattmeter was set in such a way that the average AC power input was measured (Figure

2.15).

2.3 Test Procedure

Prior to conducting a test, the water in the reservoir was deaerated for one hour through

boiling using the immersion heater to force any dissolved gases to escape to the ambient. The

flow loop components were first adjusted to yield the desired test module inlet temperature

:lin and total mass flow rate m. Other parameters to describe the flow include G"""" and

Re. G"""" indicates the maximum water mass velocity in the micro-pin-fin array and is

defined as

m Gma%=--'

A",in

where Amin is the minimum transverse flow area of the micro-pin-fin array,

(2.1)

(2.2)

Definition of the inlet Reynolds number in the present study follows that commonly

employed in previous studies of micro-pin-fins [6-111:

Re _ P I,in Umo.zde - ,

""I,in (2.3)

where all water properties are evaluated at :lin. In Eq. (3.3). Umo.z indicates the maximum

water velocity in the micro-pin-fin array,

(2.4)

11

de represents an equivalent diameter of the square micro-pin-fins, corresponding to the

diameter of circular pin-fins d,

4Ac de = --, PI;n

where Ac is the cross-sectional area of a single micro-pin-fin,

and Pfin is the cross-section perimeter of a single micro-pin-fin,

Pli" = 2(Wfin + Llin).

(2.5)

(2.6)

(2.7)

After the flow became stable. the heater power was set to a low level where the highest

thermocouple readings were about 500 e for Tin = 30De and about 70De for Tin = 60De. The

power was then increased in small increments as the flow loop components were constantly

adjusted to maintain the desired operating conditions. At each heater power level, the heat

sink was allowed to reach steady state conditions. Once at steady state, readings from the

pressure transducers and thermocouples were recorded at 0.5 s intervals for 3 min. Readings

from the rotameter and wattmeter were recorded manually. Each test was terminated when

the highest thermocouple reading reached about 1300 e to avoid overheating the test module.

Heat loss from the test module was evaluated from the difference between the total

electrical power input measured by the wattmeter Pw and the measured enthalpy change

of the water flow mep.f (Tout - Tin) during single-phase test.

Q/o •• = Pw - mep,f (Tout - Tin) . (2.8)

Even though effort was made to reduce the heat loss from the test module to the ambient,

it has been found that Q/os. ranged from 3 % to 15% of Pw for Tin = 30De, and from 6% to

12

34% for Tin = 60°C. Higher heat loss occurred at lower water flow rate. In the single-phase

study, the amount of heat that was transferred to the micro-pin-fin array was calculated

from

Q,in = Pw - QZ088' (2.9)

The level of heat flllX that is removed from the micro-pin-fin array by water flow is

represented by an effective heat fllIX q;", defined based on the total area of the micro

pin-fin array base endwall, At = 1.0 x 3.38 cm2

(2.10)

For flow boiling, q;" is evaluated from

II Pw - Q'o8s,ave qe" = At ' (2.11)

where QZos8,ave is the average heat loss obtained from the single-phase teste at the same

mass flow rate.

13

Ge.r Pump

Downstream,, ___ . ____ . ___ -; ~~.~:l~~'rm L-~~~ Control -Valve

Wattmeter

Variac

Test Flow Filter

Figure 2.1: Schematic of flow loop.

14

Rotameter

Figure 2.2: Actual flow loop.

15

Figure 2.3: Water reservoir.

Figure 2.4: Gear pump.

16

Figure 2.5: Heat exchanger.

Figure 2.6: Rotameters and digital displays fo r test module.

17

Figure 2.7: Constant temperature bath.

Figure 2.8: Test module set up.

18

670

Cover Plate (Polycarbonale Plastic)

Hoysing (G-7 Fiberglass Plastic)

Mlcro-Pln-Fln Heat Sink (110 Copper)

Cartridge Heaters

Figure 2.9: Test module construct ion.

19

Figure 2.10: Test module assembly.

20

M'-Pln·FIns

MIcnH"In-FIn Heat SInk (110Copperl

insulating Block (AIumlna '1I1cate)

&apport Plate (AlwnInum)

So=447.2 ).IIT1

SL~).IIT1~

10 0 :, r;j S,.=400 ).IIT1 ". - • "l o '0 :0 ' o : 0 ' ___ 4 Tw,to'

-Flow o 0 10 0 0

T Oll

o D iD 0 0

00 10 0 0 . o ,0 0 IW,In=200).llT1

1 Z, 1\ L,in=200 ~ Segment I

q" .n

Unll cell

H .. =2.505 mm

Figure 2.11: Top view of micro-pin-fin array and schematic of unit cell.

Figure 2.12: Variac.

21

Figure 2.13: Pressure transducers.

Figure 2.14: Data acquisition system.

22

Figure 2.15: Digital power meter.

23

Chapter 3

Single-Phase Heat Transfer

The water single-phase heat transfer in a micro-pin-fin heat sink containing an array of

staggered square micro-size pin-fins were investigated experimentally. In this chapter, the

results are presented and discussed in which an assessment was done to determine the

suitability of existing heat transfer correlations. These correlations were developed for low

Reynolds number (Re < 1000). Table 3.1 summarizes the operating conditions in the heat

transfer study.

3.1 Temperature Measurements Results

Figures 3.1(a) and 3.1(b) plot the measured micro-pin-fin base temperature T."tci versus

the input heat flux q;". Figure 3.1(a) shows the variation of Tw .!'; with q;" at the three

ztci for Tin = 30°C and Gm= = 420 kg/m2s. Assuming one-dimensional heat conduction

between the thermocouple location and the micro-pin-fin base as shown in Figure 2.11,

Table 3.1: Operating conditions for single phase heat transfer study

Maximum mass Inlet Reynolds coolant inlet temperature Mass flow rate velocity number

Tin(OC) m(g/s) Gmo.:JJ(kg/m2s) Rein

Deionized water 30 0.611 - 1.408 183 - 420 45.9 - 105.9 60 0.611 - 1.398 183 - 417 78.6 - 179.6

24

Tw,tct is evaluated from

(3.1)

where Ttci represents the readings from the thermocouples. At each Ztci, Figure 3.1(a}

shows Tw,tct increases with increasing q;". For the same q;", Tw,tci increaJleS along the

flow direction from Ztcl to ztca. Figure 3.1(b} shows T .. ,tci at Ztcl versus q;" for:lin = 30°C

and all six Gm=:. G""", in Eq. (2.1) is the highest mass velocity that the fluid can attain

inside the micro-pin-fin array for a particular flow rate tested and its calculated based on the

smallest area that the fluid passes through a row of pin-fins. Tw,tc! decreases with increasing

Gmoz for a given q;". The overall trend in the measured micro-pin-fin base temperature is

typical for a single-phase heat transfer system.

3.2 Average Heat 'fransfer Characteristics

Average heat transfer coeflicient for entire micro-pin-fin arrays indicates their performance

as heat transfer enhancement structure and has been of the focus of most previous micro

pin-fin heat transfer studies [7-11J. In the present study, the average heat transfer coeflicient

for the micro-pin-fin array have is evaluated from

(3.2)

Eq. (3.2) is derived from a sinIple energy balance: the left-hand side represents the heat

input to the micro-pin-fin array, and the right-hand side the heat removal from the pin-fin

array by water flow. In Eq. (3.2), Nt indicates the total number of pin-fins in the array

(Nt = 1950 ) and A/in is the wetted surface area of a single pin-fin,

(3.3)

25

100 WaID.

90 Tin = 30°C • G_ = 420 kg/ma• • • z", • 80 • z", • • z.., •

~ • • U 70 • • L.. • ~

• • • • 60 • l- • • • • • • • • • • • 50 • • • • • • • • • • 40 • • •

30 20 40 60 80 100

q· ... lW/cm') (a)

Figure 3.1: Variation of measured micro-pin-fin base temperature with input heat flux (a) at Ztcl to Ztc3 for 1in = 30°C and Om=: = 420 kg/m2s, and (b) at Ztcl for Tin = 30°C and all six Om.,,'

26

The term At - NtAc in Eq. (3.2) therefore represents the wetted area of the micro-pin-fin

array base endwaU, and NtAc the total wetted surface area of micro-pin-fins. l1/in represents

the fin efficiency,

(3.4)

where mli" represents the fin parameter,

(3.5)

The fin efficiency concept is introduced in order to account for the effect of the decreasing

temperature difference on heat transfer from the base of the pin-fin to the tip of pin-fin [30J.

Tw •• v• and TI.ave represent the average micro-pin-fin base temperature and the average water

bulk temperature. respectively. Tw •• ve is obtained by averaging the measured micro-pin-fin

base temperature at the three thermocouple locations Tw.tci:

(3.6)

TI •• ve is taken as the average of the measured water inlet and outlet temperature

T _ Iln+ Tout I.ave - 2 (3.7)

Figures 3.2(a) and 3.2(b) show Tw ••• e as a function of q;ff for Iln = 30·C and 1l" = 60·C,

respectively. The figures include data for aU Gm= that were tested. The general trend of

Tw•av• versus q;ff is similar to that of Tw.tcl versus q;/f as shown in Figure 3.1(b).

Once Tw •av• and TI.ave are determined from Eqs. (3.6) and (3.7), respectively, the value

of h.ve for the entire micro-pln-fin array can be readily calculated from Eq. (3.2).

Figures 3.3(a) and 3.3(b) show the variation of h.ve with q;" for Iln = 30·C and

Tin = 60·C. respectively. The data for aU G"""" that were tested were included in Figs.

27

Figure 3.2: Variation of average micro-pin-fin base temperature with input heat flux: (a) 1in = 30°C. (b) 1in = 60°C.

28

3.3(a) and 3.3(b). Figures 3.3(a) and 3.3(b) show that h~ve increases appreciably with

increasing Gmaa: for a given q;". For a constant Gmaa:, have remains fairly constant or

increases only slightly with increasing q;". The observed trend is consistent with that

reported in previous micro-pin-fin studies [8-10]. The slight increase in have value with

increasing q;" may be attributed to the increase in the average Reynolds number Reave,

defined as

Re _ PJ,ave'lLtruu,4vede - , (3.8)

JL/,4ve

where water properties are evaluated at TI,ave' This is because a high Tw,ave corresponding

to a high q;" led to a reduced water density and viscosity.

Figure 3.4 plots the variation of the average Nusselt number NUave with the average

Reynolds number Reave on a log-log scale. N Uave is evaluated from

have N Uave = -k--'

l,4ve (3.9)

Despite the scatter of the data, Figure 3.4 shows that N Uave increases with increasing Reave

in a fairly linear fashion for both inlet temperatures. The observed trend indicates that the

reletionship between N U ave and Reave may be described by power law (N Uave oc Re:::'e ).

3.3 Assessment of Previous Heat Transfer Correlations

Eight previous correlations for low Reynolds number (Re < 1000) single-phase heat transfer

in pin-fin arrays are selected and summarized in Table 3.2. Among the eight correlations, the

first four (correletions 1 - 4) were based on heat transfer experimental data for conventional

long pin-fin arrays (Hli" > 8), the next two (correletions 5 and 6) for conventional

intermediate pin-fin arrays ( 0.5 $ H lin/ d ~ 8), and the last two (correlations 7 and

8) for micro-pin-fin arrays. It should be noted that most correlations were developed for

circular pin-fins.

29

30 • G_Q183 kg/m's

• G..."228 kg/m's 25 • G_Q284 kg/m's

• GIQU=330 kgIm2s • G_Q389 kg/m's

~ 20 • G_c420 kg/m's f • i • • • * *t : • 4' •

15 •• • • • • • • • • • ! • • • • .. ,. ... ,. • • • • .c 10 • • • •• • • • •• • • •

5 Waler TIn =30°C

0 20 40 60 80 100

q" .. LW/cm'l (a)

30 • G_Q183 kg/m's

• G_Q228 kg/m's 25 • G_=260 kglm2s

• G_Cl328 kg/mas

• GmuCl388 kg/mas

~ 20 • G_c417 kg/m's

• • • • • • • ...

I 15 • • • • I • • •• • • • • .c 10

• • • • 5 • • • Wsler

TInClBDoC

0 0 10 20 30 40 50

q" ... LW/cm1 (b)

Figure 3.3: Variation of average heat transfer coefficient with input heat flux: (a) T;n = 30°C, (b) Tin = 60°C.

30

10

6 .. •

6

4

':J! Z

2

50

Water

..

T .. =30 ·C T .. =60·C

."~ ""'III ... t!:-. ... " •

....

.. ....... • • ... ~ ........ • .... "'. .. .. ......

.. .... •

•

• •

100

Reave

• r1" •

150 200 250 300

Figure 3.4: Variation of average Nusselt number with average Reynolds number.

31

A close examination of the correlations listed in Table 3.2 reveals that most previous

pin-fin heat transfer correlations adopted either one of the following two functional forms

to correlate the experimental data:

and

N Uav• = cRe'.::,.Prj,av. ("'pp,...r I""a=v::.. ) I Tw,ave

(3.10)

(3.11)

Prl,ave in Eqs. (3.10) and (3.11) is the water Prandtl number at TI,av., and Pr .. ,a •• in Eq.

(3.11) is the water Prandtl number at T .. , •••. The term (PrJ,a •• IPr .. ,.v.)' in Eq. (3.11)

represents a property correction factor to account for the effect of fluid property variation

on heat transfer. (JLI,a.ellLw,a •• i was used instead of (Prl,aveIPr .. ,ave)' in the correlations

by Whitaker (correlation 2) and Hwang and Yao (correlation 3). While the exponents m,

n, and I are usually constants in the correlations, the coefficient c is often correlated as a

function of geometric parameters of pin-fin arrays, such as d, H fin, SL, and ST, to account

for the effect of geometric parameters on heat transfer.

The values of the coefficient c and exponents m, n, and I for the eight correlations

when they are applied to the present micro-pin-fin array are calculated and summarized in

Table 3.3. Table 3.3 shows that the exponent m of Reave in the conventional long pin-fin

correlations (correlations 1 - 4) has lower values between 1/3 and 0.5, while m in the two

micro-pin-fins correlations (correlations 7 and 8) has higher values of 0.99 and 0.84, which

indicates a stronger dependence of N Uav• on Reav• in micro-pin-fin arrays as compared

to that in conventional long pin-fin arrays. No clear trend could be identified in the m

values for the two conventionBl intermediate pin-fin correlations (correlations 5 and 6): a

m value of 0.33 for the short et al. correlation (correlation 5) is at the low end of those for

the conventional long pin-fin correlations, and a m value of 0.64 for the Moores and Joshi

correlation (correlation 6) is higher than those for the conventional long pin-fin correlations.

32

Table 3.2: Correlations for heat transfer in pin-fin arrays.

Correlation Reference Average Nusselt number, NUlLve MAE %

( f25 1 Zukauskas [12] _ 0.4 0.36 Pr f,Clt71! 168.5 N UlLve - 0.9Re"vePr i ave P, I tIl,cave

( f14 2 Whitaker [14] _ 1/3 1/3 1'1,0" 314.3 N U._e - 2Re:.vePr i ave p.", , tll",e

&;

( f14 NUave = 0.83>..1/3~Prl/3 I'f, ••• i,ave 1'ut,Q,tle

3 Hwang and Yao [16] >.. = (l+il') ln~t+(1 il') 107.2

( t2 (3 = _1_ e = BTSL-~.nL"n l-e I ST L

4 Khan et al. [17,18] _ O.61(BT{<t.)o .•• t(SLl<t.)"·0l!3 1/2 1/3 NUa_e - [(BT/<t.) 1]"·d{I-2exp[-I.09(SL/<t.))} Re;,l,ePr i,ave 453.2

For RelLve <1000, 5 Short et al. [28] 71.1

( f16 ( f2 ( ro.ll

Nuao• = 0.76 ~ ~ H£n Re~a:Pr}::.e'

Table 3.2: (Continued) Correlations for heat transfer in pin-fin arrays.

Correlation Reference Average Nusselt number, Nuave MAE %

For Reave < 1000,

NUave=~ /.o.1Je

6 Moores and ~ - h h - NUcijkl.o. ve fJ/in - c6, c6 - de 497.0

Joshi [29] ( f36 NUc6=O.64 H£. Re~:Pr~;,~

s:: ( fao 7 KOljal' and Peles [9] Nu = O.0423Re0.99 PrO.21 Prf. ••• 77.7 atle ave !.ave Prw,u.ve

For Reave < 100,

8 Prasher et aI. [11] ( rO.256 NUave = 0.132 ¥ Re~: 104.2

9 Present study NUave = O.0285Re~;,1I,;l2 Pry: .. 11.7

10 Present study ( fao Nu.,ve = O.024IRe~:a Pr~:~ J:;" LO.7

Table 3.3: Coefficient and exponents of heat transfer correlations for present micro-pin-fin array.

Correlation Reference c m n I 1 Zukauskas [12[ 0.9 0.4 0.36 0.25 2 Whitaker [14] 2 1/3 1/3 0.14 3 Hwang and Yao [16] 1 1/3 1/3 0.14 4 Khan et aI. [17,18] 1.23 0.5 1/3 -5 Short et aI. [28] 0.854 0.33 1/3 -6 Moores and Joshi [29] 0.989 0.64 0.36 -7 KO¥X and Peles [9] 0.0423 0.99 0.21 0.25 8 Prasher et aI. [11] 0.132 0.84 - -9 Present study 0.0285 0.932 1/3 -10 Present study 0.0241 0.953 0.36 0.25

The coefficient c, on the other hand, shows an opposite trend as compared to the

exponent m: values between 0.9 and 2 for the conventional long pin-fin correlations, values

of 0.854 and 0.989 for the conventional intermediate pin-fin correlations, and values of 0.0423

and 0.132 for the micro-pin-fin correlations.

The exponent n of PrJ,ave in the previous correlations has values of either 1/3 or 0.36,

except that in the Ko§8J' and Peles correlation (correlation 7) a value of 0.21 is used. The

exponent I has a value of 0.25 when Pr"ave/Prw,ave is used and a value of 0.14 when

PI,ave/ /l-w,ave is used.

Figures 3.5(a) to 3.5(f) compare the predictions of the six previous conventional pin-fin

correlations (correlations 1 - 6) with the present data. Similarly, Figures 3.6(a) and 3.6(b)

compare the predictions of the two previous micro-pin-fin correlations (correlations 7 and

8) with the data. Also included in these figures as well as in Table 3.2 for each correlation

is the mean absolute error (MAE), defined as

MAE = ~ L INuave,e%p-Nuave,predl100%, M NUave.e%p

(3.12)

where M is the number of data point.

35

10

J z

an.--------.....,,..............,,.....,. 2D

10

J z

Correlatlon1 MAE~166,5%

10 2D an (0'

+40~'

-.... / .. :::::~.~. ~#'. Tml:r30 °C

.' ",#. TIII=60 °C

"",,# "" Correlation 2 "#,,, MAEI:I314.3%

10 20 an (b)

an,.--------........,,......,-.,. an..-------.....,,..............,,....,. 20

10

t ,.1 z

30

20

10

J z

• •

• •

Water TIn=30 aC T1n1l80°C

Water Tlna30 aC TlllerSO °C

2D

10

J z

Conelatlon 3 MAEa107.2%

10 2D an (e)

10 20 an (d)

an..---_--=:-.....,~-...,,....,.

2D ~..".

CorrelationS MAEt;l71.1%

10 2D 30

10

J z

(e)

...... +40'7-'

#-4i~# ..-"""

", Water ,,'. TrnCl30 ClC

",,'. TlncaD (Ie

,1'" CorrelationS ",,# MAEsz497.0%

10 NU .......

2D an (I)

Figure 3,5: Comparison of average Nusselt number data with predictions of (a) correlation 1, (b) correlation 2, (c) correlation 3, (d) correlation 4, (e) correlation 5, (f) correlation 6,

36

Figures 3.5(a) to 3.5(f) show that the previous conventional long and intermediate pin-fin

correlations overpredict the present N U"ve data. The deviation is larger at low N uave,ezp and

decreases with increasing NU"ve,ezp. Figures 3.6(a) and 3.6(b) show the previous micro-pin

fin correlations also overpredict the present N Uave data by fairly large margins. However,

the deviation is fairly constant throughout the entire N uave,ezp range.

The comparisons suggest that the previous heat transfer correlations may not be able

to describe heat transfer in the present micro-pin-fin array with sufficient accuracy. It is

important to emphasize that the discrepancy between the previous correlation predictions

and present data is not necessarily related to weaknesses in the correlations themselves,

but more to the geometric parameters and operating conditions of the present micro-pin-fin

arrays falling outside the reco=ended application range for these previous correlations.

Extrapolating a correlation to geometrical parameters and operating conditions beyond

those for which the correlation was originally developed can lead to appreciable errors.

3.4 New Heat Transfer Correlations

Deviations in the predictions of previous correlations from the present data point to the need

to develop new correlations that can yield more accurate predictions. Two new heat transfer

correlations are proposed based on the two co=on functional forms given by Eqs. (3.10)

and (3.ll). It should be noted that a correlation based on Eq. (3.10) without accounting

for the property variation effect may lead to less accurate predictions when there exists a

high temperature difference between micro-pin-fin base and liquid coolant. The functional

form is nevertheless adopted as the resulting correlation is much easier to use and no prior

knowledge of Tw,a.e is needed in order to calculate NUa.e.

Since only water was tested as cooling liquid, the range of Prandtl number is not wide

enough to allow the exponents n and I in Eqs. (3.10) and (3.1l) to be correlated from the

present data. The values that were used in the previous correlations are therefore adopted

in the new correlations: the exponent n of PrJ,ave in Eq. (3.10) is assumed to be 1/3, and

37

20 Water +40% /

15 T~=30·C ; • ;

• T~=80·C ;

.... ::it;; ; ; 10 " ;

, -40% ;

I ·Ji("t; " 5

;

t ;

~. .",. (; " " Z i..; ; ; " ; ;

" ; ; ;

" ; ; ; COlTGlaUon 7

; ;

MAE=n.7°A ;

5 10 15 20

Nu ........ (a)

20 Water +40% /

15 T~=30·C ;

• ;

• T.=80·C ~; " ; 10 ~.. / " . ; ;

.J ".I''Jij'' , -40%

" I ... t l ;" ;

5 " ,. ; ;

• i.. ; ; ::J ; ; Z ; ;

; ;

" " "

;

" ;

; ; ; ; COmllatlon 8

" MAE=104.Z% ; ;

5 10 15 20

Nu ........ (b)

Figure 3.6: Comparison of average Nusselt number data with predictions of (a) correlation 7. and (b) correlation 8.

38

the exponent n of and exponent I of Pr'.avel Prw •ave in Eq. (3.11) are assumed to be 0.36

and 0.25, respectively. The two correlations can then be expressed as

and

N cRem P 1/3 'Uave = ave T /,ave

Tn 0.36 r'.o,ve (P )0.25

N U ave = eRe.voPr I.avo ';'p"'-!-!= Tw,ave

(3.13)

(3.14)

A linear regression analysis is performed to determine the values of the coefficient c and

exponent m for the above two correlations, and it is illustrated in Figures 3.7(a) and 3.7(b),

respectively. The final correlations are

and

N Re0.953p 1/3 Ua•e = 0.0285 avo r I.a.e

_ 0.953 0.36 r l,a.e (P )0.25

N Ua.e - 0.0241Rea•o Pr I.a.o -=p,.-L!'=:' Tw,Gve

(3.15)

(3.16)

The two correlations are listed in tables 3.2 and 3.3 as correlation 9 and 10, respectively.

Figures 3.8(a) and 3.8(b) compare the predictions of correlations 9 and 10 with the

present data, respectively. The overall MAE values of 11.7 % and 10.7 % for the two new

heat transfer correlations demonstrate their excellent predictive capability. The exponent

m in correlations 9 and 10 has values of 0.932 and 0.953, respectively. The values are fairly

close to those for the two previous micro-pin-fin correlations (0.99 for correlation 7 and 0.84

for correlation 8) and substantially higher than those for the previous conventional long and

intermediate pin-fin correlations (form 0.33 to 0.64), which confirms a stronger dependence

of N Uavo on Reave in micro-pin-fin arrays. The stronger N Ua•e dependence on Rea•e in

micro-pin-fin arrays leads to the different trend in deviations in the predictions from the

39

6 Water

5 • T~~30 ·c

4 • T~~80 ·c ~"" £! 3 ~ Ii

$

..:' • )2 Z

•• 0.0286Re":.B32 •

50 100 150 200 250 300

Rea .. (a)

6

5 Water

r • Tb~30 'c "I ~4 • Tb~80 'c

Ii ~

"" 9:1i 3

.;, ."" a. • ;;-2 ., "'Ii .. :> I!:. i •• 0.0241 Re.,:· ... $

::::0 • Z

50 100 150 200 250 300

Rea .. (b)

Figure 3.7: Linear regression analysis leading to (a) correlation 9, and (b) correlation 10.

40

data between the previous conventional pin-fin correlations and the previous micr<>-pin-fin

correlations as illustrated in Figures. 3.5(a)-(f) and 3.6(a)-(b).

The coefficient c in correlations 9 and 10 is assumed as constants and has values of 0.0285

and 0.0241, respectively. Most previous studies on heat transfer in pin-fin arrays indicated

that the c value is affected by pin-fin geometric parameters, such as d, Hjin, SL, and

ST. A common approach to account for the effect, which has been adopted in developing

correlations 3 - 6 and 8, is to correlate c as a function of these geometric parameters.

However, as the interest in using micro-pin-fin arrays as heat transfer enhancement structure

is fairly recent, only limited number of micr<>-pin-fin geometries have been tested so far,

which makes it difficult to develop such a general correlation for c.

3.5 Local Heat Transfer Characteristics

The present test section design allows the local heat transfer coefficient averaged over the

four surfaces (upstream, downstream, and sides) of a single micr<>-pin-fin htc; at the three

ztci to be evaluated. Taking advantage of symmetry, a unit cell containing a single micr<>-

pin-fin is examined at each ztci as shown in Figure 2.11. Tw,tci is evaluated from Eq. (3.1).

Assuming a linear increase in water temperature along the flow direction, the water bulk

temperature at ztci, T"tci, can be determined from

(3.17)

The following energy balance can be written for the unit cell:

(3.18)

where Ace/I is the area of the unit cell base endwall,

(3.19)

41

J z

J z

10~----------------.---~--~

• 5

,

Water +40% ;, ,

, ,

T .. =30'C T .. =80'C

, , ' • .1 ,

.')' , ,tA ,

, , , "," , '_.-. , ....

, , , ,

, , , ,

, , -40% ,

,

, , , , ,

Nu ..... ."

COlTBlatlon 9 MAE=11.7%

5 10 (a)

10r-------------------.----,--~ Water

• T rnCl30GC • T .. =60'C

5

Nu ..... ."

, , , , -40% ,

COITBiatlon 10 MAE=10.7%

5 10 (b)

Figure 3.8: Comparison of average Nusselt number data with predictions of (a) correlation 9, and (b) correlation 10.

42

Once Tw,tci and TI,td are determined from Eqs. (3.1) and (3.17), respectively, the value of

htci can be calculated from Eq. (3.18).

Figure 3.9( a) shows the variation of htci with q;" for 1i" = 30D e and G"""" = 420

kgJm2s. At each Ztci, htci increases slightly with increasing q;ff' For a given q;", htci

increases appreciably along the flow direction. The higher value of htci downstream of the

micro-pin-fin array may be caused by the increase in Reynolds number along the stream

wise direction. This is because the higher downstream water temperature led to a reduced

water density and viscosity. Figure 3.9(b) shows htci at %tel versus q;/f for 1i" = 30DC

and all six Gm=. ht<:! increases appreciably with increasing Gmaz for a given q;". For a

constant Gm=, htc! remains fairly constant or increases only slightly with increasing q;/f'

The observed trend is consistent with that found in have as shown in Figure 3.3(a) and

3.3(b).

Figures 3.1O(a) and 3.1O(b) plot the local Nusselt number Nutd versus the local Reynolds

number Retci on a log-log scale for Tin = 30DC and T,n = 60DC ,respectively. N Utci is

evaluated from

Re = PI,tciUmaz,tcid• iLI,tci

(3.20)

(3.21)

where water properties are evaluated at TI,tci' Figures 3.1O(a) and 3.1O(b) show that Nutd

increases with increasing Retci in a fairly linear fasWon for both inlet temperatures. The

observed trend indicates that the relationsWp between N utd and Retci may also be described

by power law (Nutd ex: R~ ).

Figures 3.11(a) and 3.11(b) compare the predictions of correlations 9 and 10 with

the N utd data, respectively. The overall MAE values of 13.7% and 13.0% for the two

43

WatDr Tin cs 30 aC

G_ " 420 kg/m'. .. z,." • z.., • z..,

• • • • • • • • • • •

• • • • • • • • • • • • • • .. .. .. .. .. .. .. • .. .. .. .. .. 15

..

20 40 60 80 100

q"", [W/cm2]

Ca)

30 .. G_"183 kg/m's • G_=228 kglm2s

25 • G_"284 kg/m's • G_"330 kg/m's • G_"389 kg/m's

~ 20 • G_=420 kg/m's U iii E

! 15 ••• •• • :: • • ~ .. • • • • • • • • • • • • .J 10 • : • ,.,. .... ! .. • • • • • •• •••

5 .. .. .. .. .. .. Water TIn =30 aC

z,." 0

20 40 60 80 100

q':'" [W/cm2)

Cb)

Figure 3.9: Variation of local heat transfer coefficient with input heat flux (a) at Ztcl to ztca for T;n = 30°C and G"""" = 420 kg/m2s, and (b) at Ztcl for T;n = 30°C and all six G"""".

44

.J z

.J z

10

8

6

4

2

Wala. Tb "30 'c A z,.,

• • z.,. ••• "I1fI'pIp" • z.,. ~~

-...A C·· . . ..... • Vi" "'.tit: .. ... ~ • ,. ... .......

"\ A •

~

50 100 150

Relcl

200 250 300 (a)

10r--r--------~--~--_.--~~ Wala.

8 Tb "60'C

6

4

2

50

A z,., • z.,. • z.,.

....... A

100 150

Relcl

200 250 300 (b)

Figure 3.10: Variation of local Nusselt number with local Reynolds number: (a) 1in = 30°C, (b) Tin = 60°C.

45

correlations demonstrate that the correlations developed for average Nusse1t number can

adequately describe the local heat transfer characteristics.

3.6 Summary

General characteristics of average and local heat transfer were described. Six previous

conventional long and intermediate pin-fin correlations and two micro-pin-fin correlations

were examined and were found overpredicting the average Nusselt number data. Two new

heat transfer correlations were proposed for average heat transfer based on the present data,

in which average Nusselt number is correlated to the average Reynolds number by power law.

Values of the exponent m of Reynolds number for the two new correlations are fairly close

to those for the two previous micro-pin-fin correlations but substantially higher than those

for the previous conventional pin-fin correlations, which indicates a stronger dependence of

Nusselt number on Reynolds number in micro-pin-fin arrays. The correlations developed

for average Nusselt number can adequately predict the local Nusselt number data.

46

10 WalBr

• T.=30·C • T.=80·C

5 /

/ / -40%

I /

/

l! / /

::I / Z / /

/ /

/ /

/ COlT8lation 9 / MAE=13.7%

/ /

5 10

Nu..,. .... (a)

10 WalBr

• Tb=30'C

• T.=80·C

5 /

/ ~ -40%

I /

/

l! /

::I • /

Z / /

• ~/ • /

/ /

'" . /

/ /

/ /

/ / / COlT8lation 10

/ MAE=13.0% /

/

5 10

Nu..,. .... (b)

Figure 3.11: Comparison of local Nusselt number data with predictions of (a) correlation 9, and (b) correlation 10.

47

Chapter 4

Single-Phase Pressure Drop

For study of the single-phase pressure drop, two sets of tests were conducted: adiabatic

tests without heat transfer and diabatic tests with heat transfer. Operating conditions for

both sets of tests are summarized in Table 4.1. Grrw.:z: and Re;n in Table 4.1 represent the

maximum water mass velocity and inlet Reynolds number, respectively

The procedure for diabatic (heat transfer) tests was described in details in chapter 2.

Procedure for adiabatic tests is the same as that for diabatic tests, except no heat was

supplied to the micro-pin-fin array and the testing water was at a constant temperature of

around Tin = 21 DC.

Table 4.1: Operating conditions for single phase pressure drop study

Inlet Temperature Mass flow rate Maximum mass velocity, Inlet Reynolds number, 1i,,(DC) m(gjs) Gmo.z(kgjm2s) Re;n

Adiabatic test 21 0.611 - 1.398 183-417 I 37.9 - 85.8

Diabatic tests 30 0.611 - 1.408 183 - 420 45.9 - 105.9 60 0.611 - 1.398 183 - 417 78.9 - 179.6

48

4.1 Adiabatic Pressure Drop

Pressure drop data obtained during adiabatic tests are presented in Figure 4.1. Figure 4.1

plots the variation of the mea8ured heat sink pressure drop f:1P with maximum mass velocity

Gmaz. f:1P increa8es with increasing G"""", which is typical for a single-phase system. Since

the diiferential pressure transducer was connected to the inlet and outlet deep plenums of

the housing, the mea8ured heat sink pressure drop f:1P is the sum of pressure drops across

the inlet deep and shallow plenums, micro-pin-fin array, outlet shallow and deep plenums,

as well as pressure losses and recoveries associated with the consecutive sections. Neglecting

pressure drop in the plenums, pressure drop across the micro-pin-fin array f:1P/in can be

evaluated from

f:1Ppin = f:1P - (f:1Pcl + f:1Pc2 + f:1Pe2 + f:1Pe1). (4.1)

f:1Pc1 and f:1P c2 are the contraction pressure losses from the deep plenum to the shallow

plenum, and from the shallow plenum to the micro-pin-fin array, respectively [32[.

(4.2)

and

(4.3)

where subscripts pi and p2 denote the deep plenum and shallow plenum, respectively, and

Kcl and Kc2 are the loss coeflicients for the corresponding abrupt contractions. Sinrllarly,

f:1P e2 and f:1Pel are the expansion pressure recoveries from the micro-pin-fin array to the

shallow plenum, and from the shallow plenum to the deep plenum, respectively, which are

expressed as

(4.4)

49

0.15 Water

Adiabatic .. T,=21 'c ..

0.10

~ as .e. a.. <I

.. ..

0.05 ..

0.00 L......._--'-__ '--_-'-__ '--_--'-_......J 150 200 250 300 350 400 450

Gmax [kglm2s]

Figure 4.1: Variation of measured pressure drop with maximum mass velocity for adiabatic tests.

50

and

(4.5)

where Kel and Ke2 are the recovery coefficients associated with the corresponding abrupt

expansion. Values of KcI. Kc2, K.l and Ke2 for the present heat sink geometry are evaluated

in accordance with reference [32J. Once l!.Plin is determined from Eq. (4.1), friction factor

in the micro-pin-fin array "in can be evaluated from

flin = (s...)' NL PI 2

(4.6)

where N L is the total number of rows in the stream-wise direction, and is equal to 85 for the

present micro-pin-fin geometry. The variation of flin with Reynolds number Re is plotted in

Figure 4.2 on a log-log scale. Figure 4.2 shows flin decreases with increasing Re in a fairly

linear fashion, which indicates that the relationship between f lin and Re may be described

by power law (f fin ex Re ). Six previous friction factor correlations for low Reynolds

number (Re < 1000) single-phase flow in pin-fin arrays are selected and summarized in

Table 4.2. Among the six correlations, the first two (correlations 1 and 2) were developed

for conventional long pin-fin arrays (Hfin/d> 8 ), the next two (correlations 3 and 4) for

conventional intermediate pin-fin arrays (0.5 ~ H lin/ d ~ 8 ), and the last two (correlations

5 and 6) for micro-pin-fin arrays. It should be noted that most correlations were developed

for circular pin-iins. Table 4.2 shows that four of the six correlations (correlations 1, 3, 4,

and 6) used a power-law functional form:

(4.7)

Reynolds number in the Gunter and Shaw correlation (correlation 1) is defined based on

a volumetric hydraulic diameter d", while for other three correlations Re based on pin-fin

diameter d. The exponent m is constants in these correlations, and the coefficient c is

51

6....-~--.--~~~-.-~~....,..~~ ...... ~ ........ ~......, 5

4

3

2

1

Water Adiabatic T,=21 ·C

• Exp. data

............. Cor3

· .. · .. · .. · .. · ... · .. · .. · .. ··· ...... L , .............. .. ..... . .................... .. ........ ............

........ CorS Cor1 .......... \. Cor7

~ ....... '. - .... t....,. ...... ,

'""'".;0:.'':-'_'_ ............ Cor4 -- .......... ~-. -.................. ~

\ -- ...... .-.-:, ..... _.... .......-. ".... ........ . .... Cor2 -.. .. .. .. .. "" ..

CorS

40 50 60 70 80

Re 90

Figure 4.2: Comparison of friction data with predictions of correlations for adiabatic tests.

52

correlated as a function of geometric parameters of pin-fin arrays, such as d, Hfin, SL,

and ST, to account for the effect of pin-fin geometry on friction factor. Among the four

correlations, the exponent m has an intermediate value of -1 for the conventional long pin-fin

correlation (correlation 1), high values of -0.65 and -0.502 for the conventional intermediate

pin-fin correlations (correlation 3 and 4), and a low value of -1.35 for the micro-pin-fin

correlation (correlation 6).

The Gaddis and Gnielinski correlation (correlation 2) for transitional flow (1 ~ Re ~

3 x 105) in conventional long pin-fin arrays adopted a superimposition form: addition of

a laminar friction factor component Ifin,! and a turbulent friction factor component Ifin,t

with a weighting factor ¢ that is a function of Re. Both I fin,l and Ifin,! used the power-law

functional form given by Eq. (4.7), and values of exponent m are -1 and -0.25, respectively.

The Ko§8J' et al. correlation (correlation 5) for micro-pin-fin arrays also adopted a

superimposition form by adding two components, 11'1 and 11'2 , together, where 11'1 accounts

for friction effects of pin-fins and 11'2 that of top and bottom endwa1ls. The Reynolds number

in 11'2 is defined based on hydraulic diameter of the flow passage dhe' Both 11'1 and 11'2 used

power-law functional form given by Eq. (4.7), and values of exponent m are -1.7 and -1,

respectively.

Predictions of the above six previous correlations are plotted in Figure 4.2 along witb

the Ifin data for comparison. The mean absolute error (MAE) for each correlation, defined

as

MAE = ..!:.. I: Ilfin,exp - iJin,predl lOO%, M Ifin,exp

(4.8)

where M is total number of data points, is presented in Table 4.2. Figure 4.2 shows

the two conventional long pin-fin correlations (correlations 1 and 2) underpredict the data

by a large margin. The deviation may be explained by the fact that pressure drop in

long pin-fin arrays is dominated only by pin-fins, while the effect of the top and bottom

endwalls is substantial in the present micro-pin-fin array, which may lead to a higher friction

53

Table 4.2: Single-phase friction factor correlations

Correlation Reference Friction Factor, lpin MAE % Adiabatic Diabatic

( f4( f6 Gunter and lIin = 180 t ~ !;,'NL Red~ 1 Shaw [13]

d" - 4(STSL-W,.nL,.n) Re _ prUm=d" 60.6 70.4

- 2(1 .)' dv-2 W/in+L/in #J./

Ilin = lIin,l + ¢lIin,t

2: 2 Gaddis and . _ 280 .. { [(SL/d"jO.6_0.6]" +0.751 -1 = _ _ &+200

IIm,l - [4(Sr/d.)(SL/d.j-,,](ST/d.r Re , ¢ 1 exp ( 1000) 65.2 63.7

Gnielinski [15] . - { 1.2 [& - t - [8 - n -0.25 I/m,t - 2.5 + [(ST/d.j O.85]I.!RI + 0.4 SL 1 0.01 F,; 1 Re

For Re <1000 3 Short et aI.

[27] ( r1.3 ( r

O.7S ( r

O.55 ( ) lpin = 14Q.4 ~ t- H JOn /:'IIL Re-0.66

10.9 9.3

For Re <1000 4 Moores ( rO.742 53.6 52.2

and Joshi [29] lpin = 19.04 HJt Re-O.602

-- --

en en

Correlation

5

6

7

Reference

KO§llX et al. [6]

Prasher et al. [11]

Present study

Table 4.2: (Continued) Single-phase friction factor correlations

Friction Factor, fpin MAE % Adiabatic Diabatic

/jin = 11"1 + 11"2

11"1 = 1739 Hl'n/d.. f!LJJx. Re-1.7 ( y-1( ro.a H,'nld..+l Ac

( f( ro.a 11"2 = 345 H"Jd..+1 ¥- Redi., 52.5 75.3

Re - er"",,,,,d,,,, dhe - 1'""

dhe = ~!!,h" Awet = NtAlin + 2 (At - NtAe)

For Re < 100,

( rO.54 ( rO.

258 ( r283

fpin = 679.28 Hs;n ¥ Sxi.d.. Re-1.35 39.7 64.4

flin = 20.09Re-O.547 0.9 6.9

factor. For the two conventional intermediate pin-fin correlations (correlations 3 and 4),

the Short et al. correlation (correlation 3) overpredicts the data, and the Moores and Joshi

correlation (correlation 4) underpredicts the data. The Short et al. correlation provides

the best agreement with the data among the six correlations (MAE = 10.9%). Despite

the appreciable discrepancy in magnitude between their predictions and the data, the two

intermediate pin-fin correlations can fairly accurately predict the slope of the data as shown

in Figure 4.2. The two micro-pin-fin correlations (correlations 5 and 6), despite they were

developed based on the experimental data for micro-pin-fin arrays, underpredict the present

data by a fairly large margin. Furthermore, the two correlations cannot predict the slope

of the data well. Both correlations predict a more rapid decrease of fjin with increase Re

as compared to that indicated by the data. The power-law functional form given by Eq.

(4.7) is adopted to develop a new friction factor correlation for the present micro-pin-fin

array. Values of the coefficient c and exponent m are determined through a linear regression

analysis of the data as shown in Figure 4.2. The final correlation is

(4.9)

The correlation is listed in Table 4.2 as correlation 7. The MAE value of the new correlation

is 0.9% for the adiabatic fjin data. Slope of a power-function represented by Eq. (4.7) in

a log-log coordinate is dictated by the exponent m. The exponent m in correlation 7

has a value of -0.547. The value is fairy close to those for the two previous conventional

intermediate pin-fin correlations (-0.65 for correlation 3 and -0.502 for correlation 4) and

substantially higher than those for the previous micro-pin-fin correlations (between -0.17 and

-1 for correlation 5 and -1.35 for correlation 6), which explains the steeper slope predicted by

the two micro-pin-fin correlations. The coefficient c in correlation 7 is assumed a constant

value of 20.29. When correlation 7 is applied to a micro-pin-fin array that has a different

geometry, it is expected that the coefficient c will take a different value due to the effect of

pin-fin geometry on f/in. Ideally, the coefficient c should be correlated as a function of the

56

pin-fin geometric parameters, such as d, Hltn, SL, and ST. Unfortunately, as the interest

in using micro-pin-fin arrays as heat transfer enhancement structure is fairly recent, only

limited number of micro-pin-fin geometries have been tested so far, which makes it difficult

to develop such a general correlation for c.

4.2 Diabatic Pressure Drop

In this section, the six previous friction factor correlations and the new correlation are

applied to predict pressure drop of diabatic water flow in the micro-pin-fin array, and the

predictions are compared with the data. Pressure drop data obtained during diabatic tests

are presented in Figures 4.3(a} and 4.3(b}. Figures 4.3(a} and 4.3(b} plot the variation of

the measured heat sink pressure drop AP with input heat flux q;f/ for 1/n = 30°C and

Tin = 60°C , respectively. The data for all Grr=: that are tested were included in Figs.

4.3(a} and 4.3(b}. q;f/ represents the effective heat flux that is removed from the micro

pin-fin array by water flow, defined based on the platform (top) area of the heat sink, At

= 3.38 x 1.0 =<2.

" _ "'Cp,1 (Tout - Tin) q.1f - At . (4.1O)

Figures 4.3(a} and 4.3(b} show AP increases with increasing G"""" as expected. AP

decreases slightly with increasing q;If' This is because high water temperature at high

heat flux led to a reduced water viscosity. Fig. 4.4 compares the predictions of the seven

correlations listed in Table 4.2 with the present data for 1/" = 30°C and G"""" = 264

kg/m2s. When applying the correlations to calculate the pressure drop, AP is calculated

from

AP = Pel + APc2 + Pit" + APe2 + APe!. (4.11)

Equations (4.2) to (4.5) are used to evaluate the inlet contraction pressure losses APel

57

• G_"183 kg/m'B ~ G_"228 kg/m'B

0.15 • G_"2B4 kg/m'B • G .... "330 kg/m'B • G .... "388 kg/m'B

• G .... =420 kg/m'e 'i:' ! 0.10 ..... ... .. ... ~

....... • • • • • • • • • •

0.05 .... ... .. ... Y.,. 9' .,. .,. • • • • ~ ~

.10. ........... WaID •

Dlabatfc Tb "30·C

0.00 0 20 40 60 80 100

q"e1I [W/cm'l (a)

• G_"183 kg/m'B ~ G"",,=228 kg/m'e

0.15 • G .... =280 kg/m'B • G"",=328 kg/m'B • G"",=386 kg/m'B

• G_=417 kg/m'B 'i:' ! 0.10 • • • • • • ~

• • • • • • • • • • • •

0.05 • • • ~ ~ ~ ~

• • • WaID • Dlabatfc Tb"80 ·C

0.00 0 20 40 60

q"e1I [W/cm'] (b)

Figure 4.3: Variation of measured pressure drop with input heat flux for diabatic tests: (a) 7in = 30°C, (b) Tin = 60°C.

58

'i:' III .e. ~

0.12 ,........~ .... ~~"T""---.r-'~'"T"~~T"""~......,

0.10

0.08

0.06

0.04

0.02

Water Dlabatlc T .. =30·C

G.,.. = 264 kg/m'B

.. Exp. data - - - - - - _. Correlation 1 - - - - Correlation 2 _._._._._._._.. Correlation 3 _._._.- Correlation 4 --- Correlation 5 _ .. _ .. _ .. _. Correlation 6

Correlation 7

:: ................................................... . .... .. .. ... .................. . .. .. .. ).

-... -.\=.~-.-.-.-. - -··_·._u_ .. =·_·_·-._ .. = =- "'= .... 1::1'" .. a-:~":"':":"'': .. - ........... ..

0.00 ':--~-""""":':--~-""""":':--~-~ 10 20 30 40 50 60 70

q"otr [W/cm2]

Figure 4.4: Comparison of measured and predicted values of diabatic pressure drop for lin = 30°C and Gmax = 264 kgjm2s.

59

and APc2 and outlet expansion pressure recovery APe2 and APe1 • Water properties at

the inlet and outlet are evaluated based on the measured inlet temperature Tin and outlet

temperature Tout. respectively. The following equation is emplayed to evaluate pressure

drop across the micro-pin-fin array AP,in in order to better resolve the water property

variation along the stream-wise direction during diabatic tests.

NL NL ()0.58 2 J.I /,i P 1,;11."""",; AP,in = L: AP,;n,i = L: [flin,; -. 2 1,

i=l i=l Jl.w,t (4.12)

where i indicates a segment in the stream-wise direction that contains a row of micro

pin-fins as well as the corresponding portion of the top and bottom endwaJla as shown in

Figure 2.11, and AP,in,i represents pressure drop acrosa the segment i. ff;n,. in Eq. (4.12)

represents friction factor in the segment i. and is evaluated using the seven correlations. All

water properties in Eq. (4.12) except J.Iw,i are evaluated based on the average water bulk

temperature Tf,i in the segment. Assuming a linear increase in water temperature along

the stream-wise direction. Tf,i is determined from

Z; Tf,i = T;n + (Tout - T;n) Lha' (4.13)

where z; indicates the stream-wise location of the center of the segment i as shown in

Figure 2.11. The term {J.II,iiJ.lw,;)O.58 in Eq. (4.8) represents a property correction factor to

account for the effect of fluid property variation within the segment due to heat transfer.

and is introduced following the recommendation of reference [33J. J.Iw,; is evaluated based

on the average micro-pin-fin base temperature in the aeguIent Tw,;. Tw ,; can be calculated

from the following energy balance equation for the segment:

(4.14)

60

where Ai is the area of the segment base endwall,

(4.15)

In Eq. (4.14), NT indicates the total number of pin-fins in the segment and A,in is the

wetted surface area of a single pin-fin,

(4.16)

The term A; - NTAc in Eq. (4.14) represents the wetted ares of the micro-pin-fin array

base endwall in the segment, and NTA,in the total wetted surface area of micro-pin-fins in

the segment. 1/lin fin represents the fin efficiency,

(4.17)

where m lin represents the fin parameter,

(4.18)

II; in Eq. (4.14) represents the hest transfer coefficient in the segment, which is evaluated

using the following hest transfer correlation developed in Chapter 3 of this work.

(4.19)

Comparisons of all the t!.P data obtained in the present study with the predictions of

the six previous correlations are shown in Figure 4.5, and with the predictions of the new

correlation (correlation 7) in Fig. 4.6. Figures 4.4 to 4.6 show that the best agreement

is achieved using the new correlation. The mean absolute error (MAE) for correlation 7,

61

defined 88

(4.20)

is 6.9 %. The Short et al. correlation (correlation 3) for conventional intermediate pin

fin arrays also provides fairly accurate predictions with a MAE value of 9.3%. All other

correlations underpredict the present tlP data by fairly large margins.

4.3 Summary

Two sets of tests were conducted: adiabatic tests without heat transfer and diabatic

tests with heat transfer. For adiabatic tests, a water temperature of around 21ee, and six maximum mass velocities, ranging from 183 to 417 kg/m2s, were tested. The

corresponding Reynolds number ranged from 37.9 to 85.8. For diabatic tests, two coolant

inlet temperatures of 30ee and 60e e, and six maximum mass velocities for each inlet

temperature, ranging from 183 to 420 kg/m2s, were tested. The corresponding inlet

Reynolds number ranged from 45.9 to 179.6. Six previous friction factor correlations for

low Reynolds number (Re <1000) single-ph88e flow in conventional-size and micro-size

pin-fin arrays were examined and found underpredicting the data except the Short et al.

correlation [27], which overpredlcts the data. Two previous conventional intermediate pin

fin correlations were able to predict the slope of the present data. Two previous micro

pin-fin correlations predicted a steeper slope. A new power-law type of correlation W88

proposed b88e on the present data. Value of the exponent m of Reynolds number for the

new correlation is fairly close to those for the previous conventional intermediate pin-fin

correlations but substantially higher than those for the previous micro-pin-fin correlations.

Predictions of the previous and new correlations were compared with the diabatic pressure

drop data. The new correlation yielded the best agreement with the data. The Short et

al. correlation [27] for conventional Intermediate pin-fin arrays also produced an acceptable

agreement with the data.

62

Corrolatlon 1 MAEIIII70.4%

............................ ~~ ·"l4ldt·~ ....... 6 ... •

+40%

...............•••.••....... ~~ ..I!I'Mohofd ....... ~6. At~.·

o o 20 40 60 8Q

q" .. lW/cm'l

100 0 OL...~ .... 20 ...... ~-'40~-eo.J.....-~80 ...... -.,..,00

(a) q" .. lW/cm'l (b)

3r-~r-~r---.---r---' atar Cone 3

Dlabatlc MAE-S.3% • Tln1ll30 DC • T ... cr60 ClC

!2 t2

~ ................••••.••.... ~~. ~ +4O"A>

~ 1 H .. !.FIw..,H-~;..;.:;t+t.+"':_!____l ~ 1 1----------1 ... ............................ ~%

OL---~-~--~---~--.... O~ __ .J....._-L __ ~ ___ ~ __ -' o 20 40 60 80 100 0 20 40 eo so 100

q" .. lW/cm'I (e) q" .. lW/cm'I (d)

3r---.-~~---,--~r---, Water

Dlabatlc • T",Cl30 DC

Correlation 5 MAE-78.3%

• T",a80 DC f2 t 2

~ ........................... ~ ~ •.....•........•........•... ~J:

~,r---------------~~,r_------------~

o

----1-·······--··------·--····--)i.rUaAu~u ... ~~

o 20 40 60 SO 100 20 40 60 80 100 q" .. lW/cm'I (0) q" .. lW/cm'I (I)

Figure 4.5: Comparison of measured diabatic pressure drop data with predictions of correlations of (a) correlation 1, (b) correlation 2, (cl correlation 3, (d) correlation 4, (e) correlation 5, (fl correlation 6.

63

2

Water Olabatlc

.. T .. =30·C • T .. =60·C

Correlation 7 MAE=6.9%

+40%

.. ..

-40%

oL-~~~~~--~~~--~~~~

o 20 40 60 80 100

q"oll [W/cm2]

Figure 4.6: Comparison of measured diabatic pressure drop data with predictions of correlation 7.

64

Chapter 5

Two-Phase Pressure Drop and Heat Transfer

Hydrodynamics and thermal characteristics of a two-phase boiling micro-pin-fin heat sinks

were observed during a set of experiments. The water inlet temperature 7jn W"" set to

30°C. Six mass flow rates were tested: 0.611, 0.762, 0.883, 1.104, 1.302, and 1.408 g/s.

These flow rates correspond to inlet Reynolds numbers Rein of 45.9, 57.3, 66.3, 83.3, 98.3,

and 105.9, and maximum m""s velocity G"""" of 183, 228, 264, 330, 389, and 420 kg/m2s.

5.1 Boiling Curve

Fig. 5.1 shows boiling curves obtained at the three thermocouple locations for G"""" = 264

kg/m2s. In these curves, q;" is plotted versus the difference between micro-pin-fin b""e

temperature Tw,tci and 7j". At low heat fluxes, the slopes of aJJ boiling curves are fairly

constant, indicative of single-phase heat transfer. As the heat flux increases, the slope of

the boiling curve at ztc3 begins to increase first, indicating flow boiling had commenced

at that location. With further increases in heat flux, the increase in slope is detected at

the upstream thermocouple location ztc3 as well, indicating the boiling front propagated

upstream of the heat sink. Fig. 5.2 shows boiling curves at ztc3 for aJJ six water mass

velocities. While general trend remains the same, the boiling curves shift upward with

increasing mass velocity.

65

.... N

E u

~ 11=

" .. "0'

250

200

150

100

50

.. ..

, , Water

T = 30·e bt

G.,.. = 264 kg/mas

;/', ~

.. z,., ~ z,.. • z,..

.. .. .. .. .. y

~ y •

~" .} .... .~: t , .... ~~ I .. ~. .. ~. .. ~. .. ~. .. ~.

~ • ~ •

~ • ~ •

• •

15~--______ ~~~ ____ ~ __ ~ __ ~~ 8

, , .. 20 40 60 80 100

T w,tGl" T In rC]

Figure 5.1: Boiling curves at Ztcl to Ztc3 for Gm= = 264 kU/m2s.

66

300 250 • G .... =183 kg/m2s

200 .. G .... =228 kg/m2s

• G""",=264 kg/m2s 150 • G .... =330 kg/m2s

• G .... =389 kg/m2s 100 • G .... =420 kg/m2s t .... ..

E .1' .. u ...... <III ..... .,

~ 50 .. oil! ... ., .. 4

41 • • .. .. .. . • .. • " " " • • .. • "C" # • • .. •

• • ... • • • • .. Watsr .. • To. =30·C z...

10 15 20 40 60 80 100

T .,103" T In rC]

Figure 5.2: Boiling curves at Ztc3 for all six mass velocities.

67

5.2 Overall Pressure Drop

Fig. 5.3 shows the measured heat sink pressure drop t:..P as a function of input heat flux

q;" for all six mass velocities. At small heat flux values where flow is single-phase, t:..P

decreases slightly with increasing q;". This is because the higher water temperature at

higher heat flux led to a reduced water viscosity. Once boiling is initiated, AP begins to

rise appreciably with increasing q;". For single-phase flow, t:..P increases with increasing

G= for a fixed input heat flux q;". In the flow boiling regime, however, AP increases

with decreasing Gma:c for a fixed q;" as more vapor was generated inside the heat sink at

lower mass velocity.

5.3 Summary

Flow boiling in a micro-pin-fin heat sink containing an array of staggered square micro

size pin-fins were investigated experimentally. The measurements indicates that the boiling

started at the outlet of the heat sink and the boiling propagated upstream of the heat sink.

5.4 Future Work

First, flow boiling heat transfer and pressure drop correlations will be examine to compare

predictions available In the literature with the experimental data just described above.

Second, flow visualization of water flow boiling in a micro-pin-fin heat sink would be

performed with a high-speed video camera. Closed flow passage will be formed by using

a transparent polycarbonate cover piate that also facilitates direct visua1 access to boiling

and two-phase in the micro-pin-fin array. The heat sink will be mounted horizontally with

the transparent cover plate facing upwards. The high-speed video camera that is fitted

with a microscope lens is placed above the heat sink to record two-phase flow activity

in micro-pin-fin array. The high-speed video camera has a maximum recording speed of

36,778 partial frames per second (£Psl. Video images from the high-speed video camera

68

0.7 ,.....---r--..---r--..---r--....,

0.6

0.5

'i:' 0.4

l 11. <I 0.3

0.2

0.1

.. .. • • • •

G .... =183 kg/m's G .... =228 kg/m's G.,..=264 kglm's .. ".

.. G .... =330 kglm's .. .... G.,..=389 kg/m's ........ . G.,..=420 kg/m's ..... 4·. .... .

...... III- .. <4." .. ... .. "' ... . &. <II •• .. ..... :. .............. ....... .... .... . ..... ..... .

..... 4 .. . ............ ~ .. y,.. • .... .. Water •• 4 .... 4. T =30·C

0.0 ~~~ ............................. ~ ............... ~In:=..:J o 50 100 150 200 250 300

q"o"LW/cm2]

Figure 5.3: Variation of measured pressure drop with input heat flux.

69

are processed frame by frame to obtain a series of still photos, from which flow pattern in

the micro-pin-fin array under a range of two-phase flow and heat transfer conditions are

identified. A flow pattern map would be then constructed. Features unique to the water

flow boiling in micro-pin-fin arrays are identified and discussed.

70

Chapter 6

Conclusions

First, the new average and local heat single-phase transfer data were presented,

complemented by identification of unique parametric trends and assessment of the suitability

of previous correlations to predicting the present experimental results. Two new single

phase heat transfer correlations were developed based on the average heat transfer data.

Key findings from the single-phase heat transfer study are as follows:

1. Average heat transfer coefficient increases with increasing maximum mass velocity.

Values of heat transfer coefficient are at the high end of those typically attainable

by liquid single-phase forced convection despite low average Reynolds number of less

than 250.

2. Average Nusselt number increases with increasing average Reynolds number. The

relationship can be described by power law.

3. Six previous heat transfer correlations for low Reynolds number (Re < 1000) single

phase flow in conventional long and intermediate pin-fin arrays were examined in

predicting the average Nusselt number data. All previous correlations overpredict the

data. Deviation in the predictions from the data is larger at low Nusselt number and

decreases with increasing Nusselt number.

4. Two previous micro-pin-fin correlations, the KOIjar and Peles correlation [91 and the

Prasher et al. correlation [111, were also examined and were found overpredicting the

71

data. Deviation in the predictions from the data is fairly constant throughout the

entire N usselt number range.

5. Two new correlations were proposed for average Nusselt number base on the present

data, in which average Nusselt number is correlated to the average Reynolds number

by power law. Values of the exponent m of Reynolds number in the two new

correlations are fairly close to those for the previous mlcro-pin-fin correlations (the

correlations of K~ and Peles [9] and Prasher et al. [11]) but substantially higher

than those for the previous conventional long and intermediate pin-fin correlations.

The result indicates a stronger Nusselt number dependence of on Reynolds number

in mlcro-pin-fin arrays.

6. The correlations developed for average N usselt number can adequately predict the

local N usselt number data.

Second, new single-phase pressure drop data for both adiabatic and diabatic water flow

were presented. The suitability of previous friction factor correlations at predicting the

present experimental results was assessed. A new single-phase friction factor correlation

was developed based on the new data. Key findings from the single-phase pressure drop

study are as follows:

1. Adiabatic friction factor decreases with increasing Reynolds number. The relationship

can be described by power law.

2. Six previous friction correlations for low Reynolds number (Re < 1000) single-phase

flow in pin-fin arrays were examined in predicting the adiabatic friction factor data.

All previous correlations underpredicted the data except the Short et al. correlation

[27], which overpredicted the data.

3. Two previous conventional intermediate pin-fin correlations, the Short et al.

correlation [27] and the Moores and Joshi correlation [29], were able to predict the

72

slope of the present data. Two previous micro-pin-fin correlations, the KOllar et al.

correlation [6J and the Prasher et al. correlation [llJ, predicted a steeper slope.

4. A new friction factor correlation was proposed base on the present data, in which

friction factor is correlated to Reynolds number by power law. Value of the exponent

m of Reynolds number for the new correlation is fairly close to those for the previous

conventional intermediate pin-fin correlations (the correlations of Short et al. [27J and

Moores and Joshi [29]) but substantially higher than those for the previous micro-pin

fin correlations (the correlations of Kosar et al. [6J and Prasher et al. [ll]).

5. The previous friction factor correlations and the new correlation were applied to

predict the diabatic pressure drop data. The new correlation yielded the best

agreement with the data. The Short et al. correlation [27J for conventional

intermediate pin-fin arrays also produced an acceptable agreement with the data.

Third, flow boiling in the micro-pin-fin array was measured and described in which:

1. Boiling was first initiated near the heat sink outlet and propagated upstream with

increase in input heat flux.

2. Pressure drop across the heat sink decreased slightly with increasing heat flux for

single-phase liqnid flow, but increase appreciably when boiling commenced inside the

micro-pin-fin array. In the flow boiling regime, pressure drop increased with decreasing

mass velocity for a fixed input heat flux.

73

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Documents

NAl'l LIBRARY DEC...measured pressure drop was used to calculate the average friction factor, and the measured temperature distribution was used to evaluate single-phase heat transfer