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NEW SURFACES FOR THE CONTROL OF BOILING HEAT
TRANSFER: SITE FORMATION AT INCIPIENCE

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NICOLE L. AITCHESON

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NEW SURFACES FOR THE CONTROL OF BOILING HEAT TRANSFER: SITE
FORMATION AT INCIPIENCE

By
Nicole Lea Aitcheson

A THESIS

Submitted to
Michigan State University
In partial fulfullment of the requirements
For the degree of

MASTER OF SCIENCE
Department of Mechanical Engineering

2003

ABSTRACT

NEW SURFACES FOR THE CONTROL OF BOILING HEAT TRANSFER: SITE
FORMATION AT INCIPIENCE

By
Nicole Lea Aitcheson

Mircro-scale structured copper surfaces with periodic surface structure variations
were successfully created using electrochemical deposition on inclined flat surfaces. The
surface inclination angle has previously been shown to produce longitudinal vortices as
the flow transitions from laminar to turbulent. Thus the surface structures created by the
deposition process are a function of the surface inclination angle. The structure of these
specially created surfaces was meticulously characterized using an Environmental
Scanning Electron Microscope andan Atomic Force Microscope. Boiling incipience on
the deposition surfaces of 15° and 30° was investigated and compared to that of a smooth
reference surface. Boiling evaluation of the smooth, 15°, and 30° surfaces suggests that
the more pronounced structure of the 30° surface increases the nucleation site density at
boiling inception as compared to the other surfaces. These preferred nucleation sites at
incipience formed by vapor trapping pockets and basins created by column-like

protrusions on the deposition surface.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my advisor, Dr. John R. Lloyd, for
providing me with a superior education throughout my academic development. His
support and guidance in the completion of this thesis has lead to skills and knowledge
that extends well beyond books and theory. I thank my committee members Dr. D.
Grummon and Dr. I. Wichman for their support of this thesis. To the Department of
Mechanical Engineering, specifically the department support staff, I express my genuine
appreciation for their devoted assistance.

I would like to recognize CRDF Grant # RPI-2337 and NSF Grant # HER-
0090582 for financial support, without which the completion of this thesis would not
have been possible. I sincerely thank Per Askland for the countless hours he spent
helping me with the ESEM. To Ewa Danielewicz I extend the same gratitude for her
assistance with the AF M whenever I needed it. I am grateful for the technical inspiration
of Al Lawrenze whose input was invaluable to the completion of this thesis. I would also
like to thank Lisa N gai for her experimental support.

I am truly grateful to Dan Fickes for his limitless support and understanding
during the completion of this thesis. Finally, I thank my parents, Nancy and Scott

Aitcheson for teaching me how to work hard and never give up.

iii

TABLE OF CONTENTS

LIST OF FIGURES ........................................................................... v
LIST OF TABLES ............................................................................ vii
LIST OF APPENDICES ..................................................................... viii
NOMENCLATURE .......................................................................... ix
CHAPTER
1.0 Introduction ............................................................................... l
1.1. Pool Boiling .......................................................................... 2
1.2. Inception of Boiling ................................................................. 4
1.3. Enhanced Surfaces ................................................................... 6
1.3.1. Machined Surface Enhancements ......................................... 7
1.3.2. Porous Coated Surfaces .................................................... 8
1.3.3. Double Enhancements ...................................................... 15
1.4. Parametric Effects ................................................................... 16
1.4.1. Pressure ....................................................................... 17
1.4.2. Subcooling ................................................................... 17
1.4.3. Electric Field ................................................................. 18
2.0 Experimental Facility and Technique for Surface Creation and Boiling 20
Evaluation
2.1. Electrochemical Deposition Facility .............................................. 20
2.2. Smooth Surface Preparation ....................................................... 23
2.3. Electrochemical Deposition Technique .......................................... 24
2.4. Pool Boiling Facility ................................................................ 26
2.4.1. Boiling Rig ................................................................... 26
2.4.2. Heat Transfer Test Section ................................................ 28
2.5. Pool Boiling Procedure ............................................................. 33
3.0 Results and Discussion of New Surfaces ............................................ 36
3.1. Electrochemical Deposition ........................................................ 36
3.1.1. Smooth Surface .............................................................. 36
3.1.2. Copper Deposition Surfaces ............................................... 38
4.0 Conclusions ............................................................................... 57
5.0 Future Investigations ................................................................... 58
APPENDICES ................................................................................. 59
REFERENCES ................................................................................. 88

iv

LIST OF FIGURES

"Images in this thesis/dissertation are presented in color."

Figure Title Page
1.1.1. Boiling curve for a plain horizontal tube ................................. 3
1.2.1. Magnified cross-section of a plain, smooth metallic surface .......... 5
1.3.1. Conceptual model of boiling in a porous matrix ........................ 10
1.3.2. Theoretical models of (a) micro-porous; (b) porous non-conducting

coated surfaces; (c) porous conducting surfaces ........................ 12
2.1.1. Electrochemical deposition experimental set-up ........................ 20
2.1.2. Cathode and acrylic plate stand at 30 degrees ........................... 22
2.1.3. Electrical circuit diagram for electrochemical deposition ............. 22
2.2.1. Reference smooth surface .................................................. 23
2.3.1. Limiting Current Curve for Cathode at 30° .............................. 25
2.4.1. Nucleate Pool Boiling Rig ................................................. 28
2.4.2. Partially assembled heat transfer test section ............................ 29
2.4.3. Schematic of thermocouple positions and numbering .................. 30
2.4.4. Fully assembled heat transfer test section ................................ 32
3.1.1. Reference smooth surface .................................................. 36
3.1.2. ESEM image of smooth surface at 5000x ............................... 37
3.1.3. RMS surface roughness results for smooth surface .................... 38

3.1.4.

3.1.5.

3.1.6.

3.1.7.

3.1.8.

3.1.9.

3.1.10.

3.1.11.

3.1.12.

3.1.13.

3.1.14.

3.2.1.

3.2.2.

3.2.3.

3.2.4.

3.2.5.

3.2.6.

15° electrochemical deposition surface .................................. 42

30° electrochemical deposition surface .................................. 41
ESEM image of general surface structure EDS at lOOOx .............. 44
ESEM image of light areas on 15° EDS at 5000x ...................... 45
ESEM image of dark streak on 15° EDS at SOOOx ..................... 45
ESEM image of light areas of 30° EDS at 5000x ....................... 46
ESEM image of dark streak on 30° EDS at 5000x ..................... 46
Surface roughness data for dark streak of 15° EDS ..................... 48
3-D surface roughness data for dark streak of 15° EDS ............... 48
Surface roughness data for dark streak of 30° EDS ..................... 49
3-D surface roughness data for dark streak of 30° EDS ............... 49
Pool boiling curves for experimental sufaces ........................... 51
Bubble formation on smooth reference surface ......................... 54
Bubble formation on 30° electrochemical deposition surface. . . . 54
Bubble formation on 15° electrochemical deposition surface. . . . 54

Magnified schematic of possible vapor pockets on deposition
surface ........................................................................ 55

Magnified schematic of possible troughs on deposition surface. . . 58

vi

LIST OF TABLES

Table Title Page
1.3.1. Coating thickness parameters used by Chang and You ................ 12
3.1.1. Values of dimensionless parameters for 15° and 30° surfaces ........ 40
3.1.2. Values of average column-face sizes for 15° and 30° EDS ............ 44

3.1.3. RMS surface roughness values for 15° and 30° EDS .................. 47

vii

LIST OF APPENDICES

Appendices Title Page
A Steady-State Verification ................................................... 60
B Determination of Physical Properties .................................... 63
C Calculation of Physical Properties ........................................ 65
D Pool Boiling Calculations .................................................. 68
E Pool Boiling Data ............................................................ 72
F Uncertainty Analysis ........................................................ 86

viii

Csf

DCU

NOMENCLATURE

concentration of copper ions at the cathode
specific heat (J/kg°C)

experimental boiling constant

average diffusion coefficient of the copper ions
Faraday number, 96,500 (As/g)

acceleration due to gravity (m/sz)

heat transfer coefficient (W/mzK)

enthalpy of vaporization (J/kg)

current density at limiting current conditions
thermal conductivity (W/(mK))

mass transfer coefficient

length (m)

valence of the copper ions

thermal resistance (mzK/W)

heat flux (W/mz)

transference number

temperature (°C)

distance from the leading edge of the cathode

ix

Greek Symbols

(1 thermal diffusivity (mz/s)

B coefficient of thermal expansion (UK)
5 characteristic length of heat transfer surface (m)
u dynamic viscosity (kg/(m*s))

p density (kg/m3)

0 surface tension (N/m)

v kinematic viscosity (mz/s)

Subscripts

i surface of cathode

sub subcooled

w boiling surface

0 location inside OF HC copper block

1 OFHC copper

2 solder

3 surface material

00 bulk condition

CHAPTER 1

INTRODUCTION

Enhanced boiling surfaces are capable of producing heat transfer coefficients up
to 100 times greater than that of plain, smooth surfaces. There are two ways in which a
surface can enhance boiling. To be considered an enhanced boiling surface, the surface
must either increase the number of boiling nucleation sites on the surface or reduce the
required boiling incipient superheat. Enhanced boiling heat transfer is of great
importance to the refrigeration and air conditioning industries, hydrocarbon and chemical
industries, heat pipe industry, and the microelectronics industry. Advances in the
microelectronics industry have produced electronic devices that require increased heat
dissipation to maximize service life and reliability. Thus, interest in immersion cooling
techniques for these devices, involving boiling heat transfer between the device and
coolant, has grown considerably.

Enhanced surfaces are designed to initiate boiling at a lower wall superheat than
that of a plain, smooth surface. The wall superheat refers to the temperature difference
between the heated surface and surrounding liquid. Enhanced surfaces can be divided
into two categories: machined surfaces and porous coatings. Machined enhanced
surfaces contain grooves and cavities specifically designed to promote bubble formation.
Porous surfaces consist of an irregular matrix of cavities produced by such methods as
electrochemical deposition, sputter deposition, and sintering. This matrix provides

preferred sites for bubble generation.

There are many different methods of producing porous enhanced boiling surfaces.

These different production methods result in diverse variations of the sizes, shapes, and
orientation of porous coating particles. Boiling performance enhancements resulting
from specific combinations of these geometric variations for a given fluid are not fully
known. The objective of this work is to create and characterize a new porous surface
with controlled structure variations and relate these variations to nucleate pool boiling
incipience.

In this work, an electrochemical deposition experiment was designed to create
porous surfaces with varying degrees of structure and particle distribution under a
carefully controlled, repeatable process. This method of particle deposition produced a
matrix structure of micron-sized protrusions with pores and cavities that can be preferred
sites. The surfaces were examined using an environmental scanning electron microscope
(ESEM) and atomic force microscope (AF M), which provided a detailed description of
the character of the pores and cavities.

A pool boiling facility was designed to investigate the boiling incipience of water
on the porous surfaces and on a reference smooth surface. Experimental boiling results
were used to evaluate the performance of the new enhanced surfaces. Surface
characterizations and boiling performance results of the porous surface are then

compared to the reference smooth surface as well as other surfaces presented in literature.

1.] POOL BOILING
Pool boiling occurs on a heated surface in a large pool of quiescent liquid. Pool
boiling heat transfer is typically described by plotting the surface heat flux as a function

of the temperature difference between the heated surface and the surrounding bulk liquid

(wall superheat).

Figure 1.1.1 presents the classic boiling curve for boiling on the outside of a plain,
smooth tube in water. The curve is divided into four distinct heat transfer regimes:

single-phase natural convection, nucleate pool boiling, transition boiling, and film

 

   
   
  

 

 

boiling.
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.4
Peak Nucleate Heat Flux
10001 -
: Fully Transition 3
~ Developed Boiling -
500': Nucleate 'j
d Boning at
:K ..
E
3 1001 1
x - .
V 1 Discrete .
g 50- Nucleate a
f; Boiling :
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a
w 1
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5.. [I Boiling _.
j 1’ Minimum
1” Heat Flux
’1 NaturalConvection I
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1 . ......., . ”m-.. -...--
t 10 100 1000

 

Wall Superheat (K)

Figure 1.1.1. Boiling curve for a plain horizontal tube [32]

The natural convection regime exists until the point at which the first vapor

bubbles form on the heated wall (boiling incipience). The temperature of the heated wall

at incipience must reach a value (point A) above the saturation temperature in order for

boiling to initiate. This value is called the nucleation superheat. Once nucleation occurs,
the mechanism of heat transfer changes and the heat flux passing through the heated wall
increases to a higher value (point B). Nucleate pool boiling is initiated at this point. In
this regime, bubbles grow and depart from the heated wall at numerous locations called
nucleation sites. The new surfaces studied in this work are intended to increase the
density of nucleation sites, which will in turn enhance the heat flux and reduce the wall
superheat at incipience.

The wall superheat continues to rise and eventually reaches a maximum called the
peak nucleate heat flux (point C). As the wall superheat is further increased, a vapor film
forms over portions of the heated wall initiating transition boiling. The vapor, which
greatly reduces the amount of heat being transferred from the heated wall to the fluid,

continues to grow until liquid is no longer able to come in contact with the wall.

1.2 INCEPTION OF BOILING

The temperature difference between a heated surface and it’s surrounding liquid
must exceed a particular value in order for the mode of heat exchange to progress from a
single-phase to a two-phase convection process. Once this certain minimum wall
superheat is reached, boiling incipience occurs and is characterized by bubbles that begin
to grow and depart from various sites on the heated wall. These bubbles growing and
departing from the heated surface during boiling originate fi'om preferred nucleation sites
on the surface.

Numerous investigations, including [10], have demonstrated that boiling

nucleation from a smooth surface occurs at microscopic imperfections in the surface.

Thome [32] states that a surface appearing to be smooth is actually covered with small

cavities of various sizes, shapes, and depths (Fig. 1.2.1).

Machined Surface

WWW
\ /

Trapped
Vapor

Nuclei

Figure 1.2.1. Magnified cross-section of a plain, smooth metallic surface [32]

These cavities are on the order of 01-10 pm in diameter and act as nucleation sites due to
their ability to trap vapor [30]. As the surface is heated the trapped vapor grows into a
bubble and detaches. Once the bubble departs from the surface, a liquid film again
covers the cavity where some vapor remains trapped. This remaining trapped vapor acts
as an embryo for the next bubble. The criteria for vapor trapping and grth of the vapor
embryo are useful in determining the wall superheat required to initiate boiling.

When boiling on a surface, the number of active nucleation sites per area is
referred to as nucleation site density. Increasing the nucleation site density on a surface
increases the boiling performance. Porous coated surfaces increase the nucleation site
density by increasing the number of preferred bubble sites on the surface. Nucleation site
density is a linear function of heat flux [15] and is also partly dependent on porous
coating geometry. The simplest way to determine the number of active nucleation sites
on a surface is by bubble visualization. Chein and Webb [8] determined bubble

dynamics data by recording the boiling process with a high-speed photography system,

viewing more than 500 frames at 3 different surface locations, and then averaging the
data.

Kim et al. [18] investigated the nucleate pool boiling heat transfer enhancement
mechanism of microporous surfaces immersed in saturated FC-72. The heat transfer
mechanisms associated with pool boiling were stated to be liquid convection and latent
heat transfer. When comparing the plain wire to the microporous wire, it was suggested
that the microporous coating appeared to augment heat transfer through increased latent
heat transfer from the higher active nucleation site density. Due to its lower site density,
the plain surface was said to dissipate more heat through convection heat transfer, which
in turn requires a higher surface temperature to dissipate the same amount of heat as the

microporous coated surface.

1.3 ENHANCED SURFACES

Industrial demand for more efficient heat exchangers has spurred the development
of methods to increase boiling heat transfer coefficients. A smooth plain surface can be
enhanced to increase boiling heat transfer performance. Two important parameters to
consider for enhancing boiling heat transfer, according to Thome [32], are boiling
nucleation and nucleation site density. Boiling nucleation refers to the wall superheat
required for boiling incipience and nucleation site density refers to the number of active
boiling sites per area of the heated surface. In order for a boiling surface to be considered
enhanced, the surface must either require a lower wall superheat for boiling nucleation or

produce a higher number of active nucleation sites compared to boiling on a smooth

surface. Typically the two parameters are coupled and an enhanced surface will satisfy

both conditions.

1.3.1 Machined Surface Structures

Machined enhanced surfaces contain grooves and cavities designed to promote
bubble formation. Examples of commercially available machined enhanced surfaces are
the Turbo-BIITM-LP, GEWA-KTM, and GEWA-TTM. Bubble formation on these types of

surfaces is highly dependent upon the imposed heat flux [1 7].

Surface Characterization

Numerous investigations focus on machined enhanced surfaces consisting of
interconnected tunnels and pores. Two key geometric characteristics of the surfaces are
(1) subsurface tunnels and (2) surface pores or fin gaps [6]. Chien and Webb further
define these key features by the following dimensional parameters: ttmnel pitch, tunnel
height, tunnel width, tunnel base radius, tunnel shape, pore diameter, and pore pitch.

Chien and Webb [6], [7], and [9] identify the effects of the above geometric
parameters on the boiling performance of trmneled enhanced boiling surfaces. These
studies provide boiling data using R-l 1, R-22, R-123, and R-134a as the working fluids
for an extensive variety of parameter combinations. For the fluids and geometries tested
Chien and Webb found that: sharp tunnel comers provide a greater enhancement, the
boiling heat transfer rate decreases as the tunnel height reduces, and the boiling
coefficient is strongly influenced by pore size at a given heat flux.

In a similar study, Ramaswamy et a1 [27] investigated the effect of pore size,

pitch, and tunnel height on the boiling performance of the highly wetting fluid F C-72. A

larger pore size and smaller pore pitch resulted in higher heat dissipation at all heat
fluxes. It was noted that the effect of pore pitch on heat transfer performance was more

significant than pore size.

1.3.2 Porous Coated Surfaces

Porous enhanced surfaces consists of an irregular matrix of potential nucleation
sites produced by such methods as welding, sintering, electrolytic deposition (method
used in present investigation), flame spraying, plating, sputtering, or plasma spraying [3].
These nucleation sites promote high rates of bubble formation such that the required wall
superheat for developed nucleate boiling is significantly lower compared to that required
for boiling from surfaces with natural cavities [1].

A common commercially available porous enhanced surface is the High-FluxTM
surface. The High FluxTM surface contains many irregular cavities similar to those of
coral [17]. The thickness of the porous coating is approximately 0.645 mm and the
porosity of the matrix is 45%. The particles are sintered onto the surface and form
randomly shaped cavity openings that are approximately 0.04 to 0.13 mm in diameter.
The High FluxTM surface provides superior boiling heat transfer performance and is often
used as a benchmark for assessing boiling performance of other porous coated surfaces.

Porous coatings essentially transform heat transfer laws at bulk boiling according
to the heat transfer law q”~0" for n¢1 where 0 is the wall superheat [1]. Andrianov et al.
[1], Kovalev [19], and Chang [4] report that boiling on porous coatings is different from
boiling on plain surfaces and involves two modes. In the first mode the vapor generating

zones inside the porous coating are not connected with each other. In the second mode

the vapor-filled pores are connected over the whole system. The transition from ‘Bubble
Mode 1’ to ‘Bubble Mode 11’, terms used by Andrianov et al. [1], involves a substantial
increase of the wall temperature which indicates that a continuous vapor film is formed in
the vapor layer.

Bergles and Chyu [3] postulate several mechanisms of boiling from porous
coatings. Consider boiling nucleation in the porous matrix shown in Figure 1.3.3. If the
matrix material is poorly wetted, vapor will be retained in the interstitial space when the
temperature is reduced below the saturation temperature. Altemately, with a more
wetting liquid, re-entrant and double re-entrant cavities are required to permit stable
dropwise formation so that the cavities are not filled with subcooled liquid. For either
type of working fluid, the porous matrix increases the probability that nucleation sites are
available which will remain active for repeated cycles of heating and cooling.

Bergles and Chyu postulate a vapor bubble formed in an interparticle space to be
generated primarily by evaporation of the thin film segments separating the bubbles from
the particles. The bubble then grows and squeezes out of a convenient pore. Fresh liquid
is then supplied to vapor production centers through non-bubbling pores and
interconnected channels. The total superheat is then assumed to be the sum of the
conduction temperature drop across the liquid film and the traditional superheat for a

curved liquid-vapor interface.

 

;§<§:‘§& POROUS MATRIX
. RE-ENTRANT CAVITIES
{/{ZéSUBSTWE SERVING As INITIAL
:;:::;:;: LIQUID NUCLEATION SITES

' VAPOR

Figure 1.3.1. Conceptual model of boiling in a porous matrix [3].

Surface Characterization

Porous layers can be characterized by the following four parameters: particle size,
layer thickness, particle material, and porosity [32]. It would be desirable to determine
an optimal combination of these parameters to maximize boiling performance. Within a
specific set of geometries it is possible to determine an optimum layer thickness, particle
diameter, or method for producing a porous layer. The optimal values found in one study
only vaguely correspond to those found in other studies. Thus it is extremely difficult to
identify any particular combination of porous layer parameters to obtain optimal
performance [32]. Extensive research has been dedicated to investigating the boiling

performance of wide varieties of porous layer geometries using different working fluids

[0

with the intent of contributing to the fundamental knowledge of boiling within porous
layers.

Nishikawa, Ito, and Tanaka [26] ran parametric studies of the effect of particle
size, layer thickness, and particle material on boiling R-ll and R-113. Using spherical
copper particles 0.25 mm in diameter, they observed a large maximum in heat transfer
performance with layer thickness. The optimal thickness was found to be 1 mm, which
corresponded to a ratio of layer thickness to particle diameter of 4 for both the copper and
the bronze. At the optimum thickness, the heat transfer coefficient was a strong function
of heat flux, whereas non-optimal values showed less of a dependency.

Chang and You [4] investigated particle size effects on the boiling performances
of micro-porous enhanced surfaces using five different sizes of diamond particles with
FC-72 as the working fluid. The thicknesses of the coatings are compared to the
superheated layer thickness, 699, which is calculated using one-dimensional transient heat
conduction. The coatings are classified into two groups: ‘micro-porous’ and ‘porous’
coatings (Fig. 1.3.4). The micro-porous coatings show different characteristics of boiling
performance compared to porous coatings. Table 1.3.1 gives the values of particular
coating characteristics used Chang and You’s investigation. The micro-porous surfaces
correspond to the coatings with thickness 5 100 um and the porous coatings have a

thickness > 100 um.

11

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.3.2. Theoretical models of (a) micro-porous; (b) porous non-conducting coated

surfaces; (c) porous conducting surfaces [4].

 

 

 

 

 

 

 

Particle Size Coating Thickness Thickness/particle
(pm) (pm) diameter
2 i 1 30 :1: 10 z 15
10 :l: 2 50 i 20 z 5
20 i 3 100 d: 30 z 5
45 i 5 200 d: 50 z 4.4
70i10 250:1:50 z3.6

 

 

 

 

Table 1.3.1. Coating thickness parameters used by Chang and You [4].

For the micro-porous coatings, increasing the coating thickness and particle
diameter resulted in an increase in active nucleation sites and a significant decrease in
incipient superheat. The enhancement of heat transfer coefficient in this regime is
attributed to this increase in active nucleation sites. The micro-porous coating with a
thickness of 100 um and particle size of 20 um resulted in the maximum performance
enhancement for the coatings tested. The thickness of this coating is close to the value of
899. Thus an optimum coating thickness is close to the value of 899, Note that the ratio of
layer thickness to particle diameter for the optimum coating is close to the value
determined by Nishikawa et. a1 [26].

For the porous coated surfaces, increased particle diameter and layer thickness
resulted in higher heat transfer coefficients at lower heat fluxes (S 2.5 W/cmz). For '
higher heat fluxes the trend was reversed. This trend in nucleate boiling performance
was attributed to increased thermal resistance due to an increase in layer thickness as well
increased hydraulic resistance over liquid-vapor exchange channels.

Chang and You [5] also investigated the effect of coating composition (particle
material) on the boiling performance of optimized micro-porous coatings again using F C-
72 as the working fluid. F our different micro—porous coatings were created using the
following particles: aluminum, copper, diamond, and silver. The coatings had a layer
thickness to particle size ratio of between 4 and 5. The experimental boiling data for the
four coatings practically collapsed onto one curve. Thus the boiling performance of the
coatings is independent of particle composition.

The boiling performance of these coatings was compared to a plain uncoated

reference surface. The micro-porous coatings resulted in 80-90% reductions in incipient

superheats and a 30% increase in heat transfer coefficient. Again the performance
enhancement of the micro-porous coatings was attributed to increased nucleation site
density. These coatings were also compared to High Flux commercial porous coating.
The performance of the micro-porous coatings was not as good as the High Flux coating.

Hsieh and Ke [15] investigated boiling on porous Copper and Molybdenum
plasma coated tubes. They introduced a geometric scale factor A = 11/8 where n is the
average pore diameter (related to porosity) and 8 is the coating thickness. These two
parameters were deemed to have the most influence on heat transfer performance, in a
similar investigation by Hsieh and Yang [14], and determine the probability of flooding
of re-entrant cavities and the degree of superheat required for bubble growth. The values
of I. for the Copper and Molybdenum tubes were 0.01 and 0.04 respectively. The Copper
sample resulted in a larger nucleation site density for the fluids tested. Also, for the three
surfaces tested, the nucleation site density was greater for R-134a than for R600. The
two fluids have similar surface tension values, but significantly different values of
enthalpy of vaporization and density. The enthalpy of vaporization of R-134a is nearly
half that of R-600. The density of R-134a is double that of R-600.

Mertz et al. [24] investigated the effect of thickness and porosity on the boiling of
propane on stainless steel tubes with flame-sprayed porous coatings. The thickness of the
porous layers range from 100 to 300 um and the porosities range from 4% to 17%. It was
noted that there is a distinct influence of porous coating thickness and porosity on the
heat transfer coefficient. For thicknesses equal to 100, 150, 200 and 300 pm with the
same porosity (12.7%), the coating with a thickness of 200 um resulted in the highest

heat transfer coefficient. Lower porosities resulted in lower heat transfer coefficients for

the surfaces tested.

Webb [33] explains the differences in performance of porous layers of varying
porosities on the basis that different types of pores produced:

1. Active pores with stable nucleation sites

2. Intermittent pores, which can be filled with either liquid or a vapor meniscus

depending on the type of flow present in the porous matrix.

3. Liquid-filled pores that act to supply superheated liquid to the active and

intermittent pores.

4. Nonfunctional pores, that are closed voids containing neither boiling liquid

nor vapor.

Andrianov et. al. [1] defines the radius of steam evacuation (R1) as a porous
coating characteristic and an integral feature of nucleation site operation. In bubble mode
I, where the greatest increase of heat transfer is achieved compared to a smooth surface,
steam evacuation sites work independently where R; is constant and approximately equal
to the thickness of the coating. With an increase in heat load up to the transition from
bubble mode I to II, R] rapidly increases, then decreases with further increases in heat
load. This decrease of R1 is compensated by the grth of the number of working steam

exit sites.

1.3.3 Double Enhanced Surfaces
Recently, Rainey and You [28] investigated the effects of surface ‘double
enhancements’ on nucleate pool boiling performance. Rainey and You combined a

surface enhancement (microporous coating) and an area enhancement (square pin-fins)

15

on 1 cm2 flush mounted copper surfaces. Porous coated pin-fins with lengths of l, 2, 4,
and 8 mm were tested and compared to surfaces with plain fins of the same lengths and a
flat microporous surface. All tests were performed in saturated FC-72 at atmospheric
pressure under increasing heat flux conditions. The microporous coated finned surfaces
provided significantly higher heat transfer coefficients over the plain finned surfaces and
resulted in slightly lower incipient superheats. Interestingly, the nucleate boiling data for
the coated finned surfaces collapse to one curve when plotted relative to the flat micro-
porous surface regardless of fin length (up to 8 mm). This shows that the nucleate
boiling heat transfer coefficient (based upon a given base area) can be increased with the
application of a micro-porous coating, however, no further improvement is gained by
increasing the fin length. It is also interesting to note that for the tests with the plain
finned surfaces, increasing the fin length significantly changes the results in the natural
convection regime.

Honda et al. [1 1] compared the boiling performance of F 072 on a square silicon
chip with micro-pin-fins and a chip of the same base size with submicron scale
roughness. The flat chip with the submicron-scale roughness showed a higher heat
transfer performance than the micro-pin-finned chip in the low-heat-flux region. This

trend was reversed in the high-heat-flux region.

1.4 PARAMETRIC EFFECTS
For pool boiling heat transfer investigations, the experimental setup and
methodology directly influence heat transfer measurements. Particular attention must be

given to parametric effects for accurate boiling measurements and comparisons.

l6

1.4.1 Pressure

Boiling curves for plain surfaces move to the left with increasing pressure [32].
Thus conventional boiling performance increases with rising pressure. Rainey et al. [29]
report that the incipient superheat increases with decreasing pressure. They also found
that the difference in the nucleate boiling performance between the plain and

microporous surfaces appears to decrease with increased pressure.

1.4.2 Subcooling

When boiling occurs on a heated surface and the bulk liquid is at a temperature
lower than its saturation temperature, subcooled boiling occurs. Generally, the boiling
curve moves to the right as subcooling increases [32]. For boiling on plain surfaces, the
boiling heat transfer coefficient drops off rapidly with increased subcooling [32].
Bajorek [2] investigated the effect of subcooling on boiling on a low-finned copper tube.
He obtained data for water, ethanol, and several mixtures at atmospheric pressure for
subcooling ranging from 0 —- 40 K. He found that the largest drop in the heat transfer
coefficient occurred in the first 10 K of subcooling. In this range, boiling performance
was reduced by 40% to 50%.

Rainey et al. [29] investigated the effect of subcooling on boiling on plain and
microporous flat copper blocks immersed in F C-72. They felt the most prominent effect
of subcooling on boiling was that the fully developed nucleate boiling curves collapsed
onto a single line regardless of the degree of subcooling. The insensitivity of the nucleate
pool curve to increased subcooling is attributed to the combined effects of (1) reduced

bubble departure diameters and frequencies leading to reduced amounts of heat

17

transferred through latent heat and microconvection and (2) decreased superheated liquid

layer thickness leading to increased natural and Marongoni convection heat transfers.

1.4.3 Electric Field

Leontiev et. al. [20] investigated the effect of an electric field on the boiling of
liquid nitrogen. An electrode with a 30 kV potential was placed 3 mm above the test
surface. Both uniform and non-uniform electric fields were tested on horizontal smooth
and corrugated surfaces. The uniform electric field, with an intensity of up to 107 V/m,
had little or no effect on the initial part of the boiling curve of the smooth surface. The
non-uniform electric field was created by welding a metallic pin near the test surface.
With the presence of the non-uniform electric field, both the smooth and corrugated
surfaces showed a reduction on incipience superheat as compared to the results with the
uniform electric field.

Snyder et al. [31] performed an experiment to produce a dielectrophoretic (DEP)
force (up to 23 kV) over the length of a horizontal platinum wire heater (1.91 cm by
0.025 cm diameter). It was concluded that the overall boiling heat transfer coefficient in
the presence of an electric field can be modeled as the summation of a heat transfer
coefficient due to bubble dynamics and a heat transfer coefficient due to
electroconvection. The heat transfer in the presence of an electric field will be enhanced
if the effective gravity acts to hold the vapor bubbles near the heated surface, while at the
same time permitting access of the liquid to the surface in order to prevent dryout. The
work done by Leontiev et. al. [20], as discussed above, reported that a non-uniform

electric produced areas, called “field traps”, where the dielectrophoretic forces trap

18

growing bubbles on the heated surface. Maximum local heat transfer coefficients were

observed for the areas with the presence of field traps.

l9

CHAPTER 2
EXPERIMENTAL FACILITY AND TECHNIQUE FOR SURFACE CREATION
AND BOILING EVALUATION

2.1 ELECTROCHEMICAL DEPOSITION FACILITY

The test environment for the electrochemical deposition consisted of an
electrolyte solution in a 204 liter polyethylene tank as shown in Figure 2.1.1. The anode,
cathode, and reference electrode were immersed in the electrolyte solution and connected
to a series of potentiometers, digital multimeters (DMM) and a DC power supply. The
cathode was the test surface for deposition.

./~
. 'e’
.”

v
. \

.1

. r— V

.'~_¢ -

 

Figure 2.1.1. Electrochemical deposition experimental set-up.
The tank was a 81 by 50 by 50 cm Rubbermaid container. The bottom of the tank
was made horizontal as measured with a precision level. The tank was filled with an

electrolyte solution consisting of aqueous solutions of 1.5 molar reagent grade sulfuric

20

acid (112804) and 0.05 molar copper ll sulfate (CuSO4). The copper ions of the CuSO4
served as the transferred species of ions and the H2804 was the supporting electrolyte.

The anode and cathode were constructed from 0.32 cm thick copper sheets with
dimensions 54.3 by 30.5 cm and 6.0 by 7.5 cm respectively. The anode surface area was
34 times larger than the surface area of the cathode to insure that the electrode reaction
would be controlled by the cathode. The reference electrode was made by inserting 14
gauge copper wire into a polyethylene test tube with a capillary hole drilled in the
bottom.

The cathode was held approximately 1.3 cm off the bottom of the tank, facing the
anode by an acrylic stand. The stand, Figure 3.1.2, was made of two 7.5 by 7.5 by 0.64
cm thick pieces of acrylic sheet stock. The plate holder was designed such that the
sidewalls would eliminate any edge effects and the flow of ions would be parallel to the
sidewalls. A protractor was secured to one side of the plate stand to measure the angle of
the cathode relative to vertical. The cathode was held in place facing up between acrylic
plates by 8.9 cm long, 0.64 cm diameter brass bolts. The anode and cathode were
connected to the electrical circuit with 14 gauge copper lead wire.

The electrical circuit is shown in Figure 2.1.3. The DC power supply was a deep
cycle 12 Volt battery connected, in series, to a 1000-Ohm resistor, plus 0200, and 0-
1000 Ohm potentiometers, respectively. The electrode voltage and current were

monitored and recorded with the DMMS.

21

‘— Lead Wires

Cathode

/,

Protractor

(.9

Acrylic Plate
Stand

 

Figure 2.1.2. Cathode and acrylic plate stand at 30 degrees.

 

\lki U "m

 

 

 

 

 

I Reference
I Electrode
0-2000
thode m
TankBottom 10000
ll 1
I I
tsz

Figure 2.1.3. Electrical circuit diagram for electrochemical deposition.

22

2.2 SMOOTH SURFACE PREPARATION

The smooth surface was prepared according to the methods outlined by Hong [12]
and Shakir [30] and adhered to the following procedure. The surface was rinsed with
distilled water, wiped clean with a soft cloth, rinsed with Acetone, and wiped dry again.
Using the 600-grit sandpaper, the surface was sanded 20 times in the vertical direction,
bottom to top, pressing with the same force for each pass. The surface was then wiped
with a soft cloth and turned 90 degrees. The surface was sanded an additional 20 times,
bottom to top, pressing with the same force for each pass. The surface was wiped again
and turned 270 degrees, back to its original position. This sanding technique was
repeated 4 times for the 600-grit paper. The surface was then rinsed with distilled water,
wiped clean, rinsed with acetone, and wiped dry again. Then 1000 grit and then 1500 grit
sandpapers were used, respectively, repeating the technique above, thus producing a

smooth, mirror finish as shown in Figure 2.1.4.

 

Figure 2.2.1. Reference smooth surface.

23

2.3 ELECTROCHEMICAL TECHNIQUE

The electrochemical deposition procedure is consistent with that of Lloyd [20].
To eliminate concentration gradients, the electrolyte solution was stirred for
approximately 30 minutes prior to placing the test surface in the tank. A Type-T
thermocouple was used to measure and verify the uniformity of the solution temperature.
The temperature was measured along the bottom of the tank, two-thirds from the top,
one-third fiom the top, and near the surface totaling 20 different locations throughout the
solution. The solution temperature was considered uniform if the measurements did not
vary by more than 0.5 degrees Celsius as stated by Moran [25].

Before each run, a cathode surface was prepared for deposition by completing the
sanding regiment presented in Section 3.2 to produce a smooth surface. Once a smooth,
mirror surface was obtained, the back of the cathode was insulated with duct tape. The
cathode was then secured to the acrylic plate stand and the lead wires were attached.

The anode was sanded with coarse sandpaper on the front and back surfaces to
insure that the surface was free from an insulating film. After the surface was sanded it
was rinsed with distilled water, wiped clean, rinsed with Acetone, and then wiped dry
again.

The potentiometers were set at maximum resistance and the anode and reference
electrode were suspended into the solution. The cathode was carefully placed on the
level portion of the tank bottom, facing the anode, and allowed to set for 20 minutes. The
lead wires were connected, completing the electrical circuit, and the voltage and current
were allowed to reach steady state. The voltage was increased by incrementally reducing

the 0-1000 Ohm potentiometer resistance. Once the resistance was reduced, the solution

24

was allowed to reach steady state and the voltage and current readings were recorded.

The voltage was increased until the characteristic limiting current curve was achieved

 

 

 

 

 

(Fig. 2.3.1).
Limiting Current @ 30 Degrees
0.180 .. fi #fi as male a s .I -
. a I
I I . I I I I I I W
I . I , i I I 1
-0.170.+—;st # .4 _ mmmmfifi _ _f___ _L__ +— —..;
N I f I | I I I I I
E I I I I I I . I
‘2’ 0.160 I L 7 L, 7 I I i I .
E I I ‘ . ; 5 e
T 0150 I ~ r I , ' , - i if i a s It i
E I I I . I O ': I
a I I I
I '. I I I I
5 0140; 7 I , W e, s. - 1-- I , a J a I_ .,I
a I I I I .
c I . I
g 0.130 -~I————+9~—--—I—- ———«,— I ;
I . i I I I I
O 0.120 I. I I I i I 7 I *1: i , a In L‘ L
I. I I I II I II I
0.110 I” _ I . A-” _.L__._I_ _._ _._m I. I + .
45 95 145 195 245 295 345 395 445 495 545
Voltage (mV)

Figure 2.3.1. Limiting Current Curve for Cathode at 30°.

The plateau region of the limiting current curve is the condition where diffusion
of the copper ions controlled the mass transfer of the copper deposition process. Once
the nominal current value of the plateau of the limiting current curve was determined, the
electrode voltage was set to produce this current. The cathode was then allowed to set at

this current for 2 hours to be consistent with the procedure used by Moran [25].

25

2.4 POOL BOILING EXPERIMENTAL FACILITY
2.4.1 Boiling Rig

A steel pressure vessel, built and developed at Michigan State, was used for the
experimental studies of nucleate pool boiling. This apparatus, shown in Figure 2.4.1, was
used to obtain boiling incipience superheats and heat transfer coefficients.

The pressure vessel, shown schematically in Figure 2.4.2, is a 2.54 cm thick
stainless steel chamber with flanged ends. The diameter of each of the flanged ends is
10.16 cm. The volumetric capacity of the vessel is 4 Liters. The top and bottom
openings were bolted with 2.54 cm thick stainless steel cover plates. Each of these cover
plates had a series of openings to install the necessary attachments. A third opening was
a side-flange used for mounting the test section. The fourth opening was a side-flange
equipped with a viewing port made of high-quality glass (Fig. 2.4.1(6)). The vessel
assembly was mounted on a rugged tripod assembly capable of rotating and tilting the rig
to any desired position. To minimize heat loss through the chamber walls, the vessel was
covered with 0.635 cm thick polyethylene foam insulation.

A 1350—watt immersion heater (Fig. 2.4.1 (5)), mounted at the bottom of the
chamber was used to heat the liquid pool to saturation conditions. The heater was coiled
from a 0.635 cm O.D. straight length of a Chromalox incoloy sheath heater and powered
by a Variac variable AC power supply. Two 30-gage Type-T stainless steel sheathed
thermocouples (Fig. 2.4.1 (3,4)) were mounted through the bottom cover plate of the
chamber to measure the temperature of the bulk liquid. An Omega HHP-102F pressure
transducer read the chamber pressure via the pressure tap mounted on the top cover plate

of the chamber (Fig. 2.4.1 (11)).

26

P‘S‘PP‘P!‘

 

 

 

 

 

\XX‘

 

 

 

Tl/f/j

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Y ‘ Y L

 

 

 

 

Boiling Vessel

Boiling Test Surface

Bulk Liquid Thermocouple
Bulk Liquid Thermocouple
Immersion Heater

Site Glass Window

 

 

 

 

 

 

 

 

 

7. Liquid Feed Line
8. Condenser

9. Degassing Line

10. Safety Relief Valve
11. Pressure Tap

Figure 2.4.1. Nucleate Pool Boiling Rig.

27

A submersible pump was used to pump liquid through the liquid feed line and into
the chamber (Fig. 2.4.1 (7)). A valve, located along the liquid feed line, was closed once
the liquid had reached the desired level in the vessel. The condenser (Fig. 2.4.1 (8)) was
mounted to the top cover plate of the chamber and consisted of 0.635 cm O.D. stainless
steel tubing. Cold tap water was run through the coiled condenser tube during boiling. A
pressure safety valve (Fig. 2.4.1 (10)) was mounted to the top of the chamber to relieve
any accidental overshoot of pressure inside the vessel. A second valve (Fig 2.4.1 (9))

was mounted to the top of the chamber for degassing purposes.

2.4.2 Heat Transfer Test Section

Kedzierski and Worthington [16] presented a technique specifically designed for
building an accurate, uniform temperature boiling heat transfer apparatus. A flat plate
was used as the heat transfer specimen as opposed to round tubes, as was done by
Bajorek [2] because more thermocouples could be spaced parallel to the heat flow in a
thick plate than in a thin-walled tube. This arrangement of thermocouples allows for
simultaneous measurement of wall superheat and surface heat flux values. Copper was
the suggested heat transfer material since it has a very high thermal conductivity, and the
temperature profile within the block could be assumed to be linear for the calculations of
both the heat flux and surface temperature. The use of 0.053 cm diameter thermocouple
holes was recommended to minimize hole position uncertainty. The heat transfer test
section used in this work was designed based on the Kedzierski and Worthington [16]

and Kedzierski [17] studies.

28

The, heat transfer test section used in this work consisted of the boiling test
surface, a thick copper block with a series of fourteen embedded thermocouples, and
another thick copper block containing three cartridge heaters. The test surface was
soldered on top of the copper block housing the thermocouples, which was soldered to
the top of the copper block with the heater cartridges. The heater cartridges were used to
heat the test surface while the thermocouples were used to simultaneously measure the
surface temperature of the boiling surface as well as the heat flux. The sides and bottom
soldered copper blocks and test block were insulated with a Teflon sleeve. Figure 2.4.2
shows the stacked copper blocks (without the test surface) and Teflon sleeve with the

front cover removed.

 

Figure 2.4.2. Partially assembled heat transfer test section.

29

Two 4.45 x 4.45 x 2.54 cm thick oxygen free high conductivity (OFHC) copper
blocks, stacked and soldered one on top of the other with 60/40 tin/lead solder, were used
to transfer heat from the heat source to the test surface. The bottom OFHC copper block
housed three 0.635 cm diameter by 3.81 cm long 125-Watt Chromalox model CIR-1015
heater cartridges. The heaters, used to heat the test section, were first coated with
Chromalox Boron Nitride Lubricoat and then inserted into pre-drilled tight-fitting holes
in the OFHC copper. The holes were drilled 0.635 cm from the edge of the copper and
0.635 cm apart centering the heaters with respect to the test section. Fourteen 30-gage
0.075 cm diameter Type-T thermocouples were used to measure the surface temperature
of the test section and heat flux. The temperature sensing ends of thermocouples were
inserted into 0.08 cm diameter holes in the top OFHC copper block. The thermocouples,
represented by black dots in Figure 2.4.3, were arranged into 3 rows of four in the
vertical direction and one row of 5 in the horizontal direction each 0.635 cm apart. The
numbers to the left of the thermocouple positions in Figure 2.4.3 depict the sequence in

which temperature readings were taken.

——>0. 635 cm Thermocouple

I (.__ / Positions

In—> 4i—13+ 8 e 2‘s 12s
0.635 cm

 

 

 

7’ 110
I 20 6’ 10’
1' 6’ 9’

 

 

 

Figure 2.4.3. Schematic of thermocouple positions and numbering.

30

Once the thermocouples and heater cartridges were in place, the copper blocks
were inserted into a partially assembled Teflon sleeve (as shown in Fig. 2.4.2). The fully
assembled Teflon sleeve consisted of 6 cut and milled pieces of 1.27 cm thick Teflon
bolted together to fit tightly around the copper blocks. Two front cover pieces were
drilled and tapped to be able to connect to a threaded brass male-female adaptor. The
brass adaptor connected to a 2.7 cm CD. by 20 cm long threaded stainless steel tube.
The two fi'ont cover pieces were bolted to the assembled side pieces of the sleeve. The
thermocouple and heater cartridge lead wires exiting the sleeve through the tapped hole.
The lead wires were held in place and insulated with General Electric RTV 106 high
temperature silicone rubber adhesive sealant. Sealant was applied to the area on copper
block directly surrounding the wires and was approximately 2 cm thick. The unsealed
length of the lead wires was strung through the brass adaptor and stainless steel tube. The
brass adaptor was then screwed into the tapped hole of the insulating sleeve as shown in
Figure 2.4.4. Special care was taken not to twist the lead wires while attaching the brass
adaptor to the insulating sleeve.

The stainless steel tube was used to support the heat transfer test section in the
boiling rig and allowed the lead wires from the thermocouples and heater cartridges to
exit the rig without coming into contact with the water. The diameter of the end of the
stainless steel tube (not attached to the test section) was reduced using a lathe to be able

to fit through the existing 2.5 cm hole in the side cover plate of the boiling rig.

31

 

Figure 2.4.4. Fully assembled heat transfer test section.

Once the test section was assembled as shown in Figure 2.4.4, the test surface, cut
to 4.45 cm x 4.45 cm, was soldered to the exposed copper. When the solder had cooled
sufficiently, the entire assembly was then sealed with Perfecto 100% clear silicone rubber
aquarium sealant. The lathed end of the stainless steel tube extending from the heat
transfer test section was placed through the hole in the boiling rig side cover and sealed
with the aquarium sealant. The steel tube fit very tightly through the hole in the cover
plate providing ample support to the test section. More aquarium sealant was used to seal

the steel tube to the cover plate.

32

2.5 POOL BOILING PROCEDURE

You et al. [34] found that tests with large step changes in heat flux, using a thin-
film cylindrical heater, indicated increases in incipience superheat of as much as 20%
over tests with a series of incremental steps in heat flux up to the same level. Thus
increases in heater setting, for this work, were completed with a series of incremental
steps.

To initiate a pool boiling run, the inside of the boiling rig and the surface of the
test section were thoroughly cleaned with acetone then distilled water and allowed to dry.
The side cover plate with the attached, extending test section was tightly bolted to the
boiling rig with the test surface horizontally upward-facing. Ambient temperature values
of the 16 thermocouples (l4 embedded in the OF HC copper block and 2 secured to the
chamber) were then recorded. All of the thermocouples displayed the same temperature
and ensured the accuracy of the temperature readings. Distilled water was then pumped
into the rig via the liquid feed line with only the degassing valve open. Once the water
was sufficiently above the condenser, the valve to the liquid feed line closed and the
pump was turned off.

The immersion heater was turned on and the liquid was heated t0100 “C. The
cartridge heaters were then turned on to a moderate setting of 40, corresponding to a heat
flux of approximately 15000 W/mz, and the surface was allowed to boil for
approximately 30 minutes. The degassing valve was then closed and the immersion
heater was turned off. The foam insulation was removed from the outside of the chamber
and the condenser was turned on. The liquid was allowed to cool to 45 °C as

recommended by Bergles [3]. Extra care was taken during cool-down to maintain the

33

pressure at its saturation value of 1.01 bar by controlling the flow through the condenser.
Once the liquid had cooled, the foam insulation was returned to the boiling chamber. The
immersion heater was turned back on and again the pressure maintained at 1.0] bar by
controlling the water flow through the condenser. The water flowing through the
condenser was chilled with an ice bath. Once the liquid was heated to 90 °C (10 degree
subcooling), the heater cartridges were turned on to a low setting. A subcooling of 10°
was determined as the boiling condition due to immersion heater difficulties. The system
was then allowed to reach steady-state.

The temperatures from the embedded thermocouples were then recorded by
dialing through the values displayed on the Omega Trendicator to the tenth of a degree.
If the temperature displayed bounced back and forth between tenths of degrees, the
recorded temperature was the average of the varying values. If there was no temperature
variation, the displayed temperature was recorded. Power to the heater cartridges was
then increased in increments of 5 on the Variac and the process was repeated until
nucleate boiling was achieved. The time delay between temperature readings was 15
minutes. This amount of time was determined sufficient for steady-state conditions by
experimental verification (see Appendix A).

Bubble growth was recorded during the pool boiling experiments by positioning a
IV C digital video camera on a tripod in front of the glass-viewing window of the
chamber. A SOC-Watt lamp was positioned on a tripod next to the digital video camera to
illuminate the test surface. Once the test section was secured to the chamber and a run
was initialized, the lamp and video camera were positioned to provide the best image

possible. Once very small bubbles began to form on the surface the lamp and video

34

camera were turned on and bubble growth was recorded. The lamp and camera were
periodically turned off to avoid any heating of the liquid by the heat of the lamp. Thus
bubble growth was watched diligently. Special care was taken to record initial bubble

growth and departure.

35

CHAPTER 3

RESULTS AND DISCUSSION

3.1 ELECTROCHEMICAL DEPOSITION
3.1.1. Smooth Surface
The smooth surface, as prepared according to Section 2.2 has a shiny, mirror-like

finish (Fig. 3.1.1.).

 

Figure 3.1.1. Reference smooth surface.

The smooth surface was examined with an ElectroScan Environmental Scanning Electron
Microscope (ESEM) model 2020. Figure 3.1.2 shows the surface magnified at 5000x.
Very fine scratches are present on the surface as a result of the surface preparation. The
spans of the fine scratches were measured using the length scale provided on the ESEM

image and vary from 0.85 to 2.55 pm.

36

 

Figure 3.1.2. ESEM image of smooth surface at 5000x.

The RMS surface roughness was measured using a Digital Instruments Atomic
Force Microscope (AF M). The RMS surface roughness is the standard deviation of the 2
values, Z referring to the vertical direction, within a given area. The RMS surface
roughness values were measured at three different locations using a scan size of 70 pm.
The averaged RMS surface roughness of the smooth surface was 76 nm. Figure 3.1.3

displays the 3 dimensional results from the AF M.

37

NanoScope Contact AFN

Scan size 70.00 mi
Setpoint 0 U
Scan rate 4.069 Hz
Nuuber of samples 512

X 20.000 Int/div
2 2.000 Int/div

 

Figure 3.1.3. RMS surface roughness results for smooth surface.

3.1.2 Copper Deposition Surfaces

The principle mechanisms for the transfer of copper ions to the cathode surface
are migration, diffusion and convection. Using the known values of temperature of the
solution, copper ion concentration, sulfuric acid concentration, limiting current, and
characteristic length of the test surface, dimensionless numbers to describe the flow over
the plate during deposition can be determined. The following discussion of
dimensionless parameters is consistent with that used by Lloyd [20].

Under limiting current conditions, the concentration of copper ions at the surface

is negligible. Thus, the expression for the mass transfer coefficient is

38

(l-t)-i
k =———— 3.1.1
m n-F-cw ( )

where t is the transference number for the copper ions at the average copper sulfate and
sulfuric acid concentrations, 1' is the current density at limiting current conditions, n is the
valence of the copper ions, F is the Faraday number, and cm is the bulk concentration of

copper ions at the cathode. The evaluation of the transference number is outlined in
Appendix B.

The dimensionless mass transfer module, analogous to the Nusselt number for
heat transfer, is the Sherwood number. The Sherwood number represents the
effectiveness of mass convection at the surfaces and is defined as

Sh, = kmx (3.1.2)
DCU

 

where x is the distance from the leading edge of the cathode to the point of interest and

Dcu is the average diffusion coefficient of the copper ions in the sulfilric acid. The

diffusion coefficient is evaluated at the specific deposition temperatures (Appendix B).
The Rayleigh number is the product of the Grashof and Schmidt numbers as

shown in Equation 2.4.3.

 

Raw = Gr”, -Sc (3.1.3)
The Grashof number is defined as
er = g'°059'(p°°2“ pry/"f (3.1.4)
,u

where g is the acceleration due to gravity, cost) is the cosine of the angle of the cathode

measured from vertical, and u is the average dynamic viscosity of the electrolyte solution.

39

The values of P... , ,0, and p are the densities of the solution in the bulk, at the surface,

and at average conditions respectively.

The Schmidt number, analogous to the Prandtl number, is defined as

 

Sc = ” (3.1.5)
P ' Dc'u

and represents the relative magnitudes of molecular momentum and mass difiusion in the
velocity and concentration boundary layers respectively. Again, property evaluations are
outlined in Appendix B.

According to Lloyd et. al. [22], for 8032000, the Sherwood number can be

calculated based on the Rayleigh number as a function of inclination angle as follows

Sh“, = 0.499Raw'” (3.1.6)
This equation is for laminar flow over the plate. The transition from laminar to turbulent

flow is based on the Rayleigh number. Laminar flow exists for Ra < 1011 where turbulent
flow exists for greater values of Ra The flow in this work was considered laminar.
Calculated values of the dimensionless parameters for the electrochemical
deposition surfaces can be found in Table 3.1.1. The Schmidt numbers correlate well to
the work done by Lloyd et. al. [22] and Moran [25] and are approximately 2000. The
Rayleigh number is on the order of 106 thus the flow can be considered laminar. The
Sherwood numbers based on the transference of copper ions and the Rayleigh number,
calculated using Equations 3.1.5 and 3.1.6 respectively, agreed within 1% for both
deposition surfaces. This validates the experimental set-up and procedure discussed in
Sections 2.1 and 2.3. Detailed information regarding values used to calculate these

parameters can be found in Appendix C.

40

 

 

Dimensionless 15° 30°
Parameter
Sc 1894 1773
er 1.09 x 107 1.02 x 107
Ra... 2.07 x 10” 1.86 x 10‘0
Sh 224 217
Shae (Ra...) 189 184

 

 

 

Table 3.1.1. Values of dimensionless parameters for 15° and 30° surfaces.

The appearance of the electrochemically deposited surfaces (EDS) is very
different from that of the smooth surface shown in Figure 2.4.1. The deposited surfaces,
shown in Figures 3.1.4 and 3.1.5, appear matte-like as opposed to shiny and are
accompanied by the presence of dark colored streaks near the top. These streaks are
approximately 1 mm wide and 1 mm apart, corresponding to the spanwise dimensions
determined by Lloyd [23], and result from longitudinal vortices that develop along the
surface during deposition. These vortices are characteristic of natural convection on
upward facing surfaces at angles of 14 - 45° [21]. At inclination angles less than 14°
from vertical, wave instabilities dominate flow along the plate. As the inclination angle
increases from 14°, the outward normal force on the plate increases and longitudinal
vortices begin to dominate the flow. At 15°, the flow is governed by both wave
instabilities and longitudinal vortices. As the plate angle is increased from 15 to 30°, the
longitudinal vortices dominate the flow. Hence the streaks are more pronounced on the
30° plate than the 15° plate. The streaks present on the electrochemical deposition

surfaces result in spanwise mass transfer variations.

41

Streaks

 

Figure 3.1.4. 15° electrochemical deposition surface.

/
/

Streaks

 

Figure 3.1.5. 30° electrochemical deposition surface.

42

For the 15° EDS the dark streaks are vague and begin to form approximately two-
thirds of the way up the plate. The dark streaks on the 30° EDS, however, are very
distinct and begin to form approximately halfway up the plate. The difference in
appearance of the two surfaces translates into differences in periodic surface structure.

The surface structures of the deposition surfaces were meticulously examined
with the ESEM (Figs. 3.1.7 — 3.1.10) and AFM (Figs. 3111-3114). The surface
structures are assumed to be closely packed columns formed fi'om the stacking of copper
ions. The particle-like surface formations are the visible top faces of the columnar
protrusions.

It was found that the variations in mass transfer distribution during deposition
resulted in periodic surface structure variations. The dark streaks represent areas in
which the surface roughness is slightly greater and the column-faces are slightly larger
than that of the lighter colored areas of the surfaces. Also, the range of column-face sizes
is greater in the dark streak than in the lighter colored areas.

The general surface structure of both the 15° and 30° EDS resemble that shown in
Figure 3.1.6. The columns vary in size and shape, yet appear uniformly distributed. The
variations in column-face size and shape are assumed to be the result of “clustering” of
copper ions during deposition.

The average column-face sizes were determined using the reference scale
provided on the ESEM images (see Fig. 3.1.7 — 3.1.10). Column-face sizes were
measured at twenty different locations and were then averaged. The average column-face
sizes of the lighter colored areas and dark streaks for the 15° and 30° EDS are given in

Table 3.1.2.

43

 

Figure 3.1.6. ESEM image of general surface structure EDS at lOOOx.

The column-faces in the dark streaks are slightly larger that those of the lighter colored
area for both deposition surfaces. This appears to be due to larger clusters of copper ions
in the dark streaks. The column-faces in the dark streaks are approximately 57% and
50% larger than the column-faces in the lighter colored area for the 15° and 30° surfaces
respectively. The average column-face size of the light areas of the 30° surface was 32%
larger than that of the 15° surface and the average column-face size of the dark streaks of

the 30° surface was 36% larger than that of the 15° surface.

Area on EDS

1.1 1.5

 

Table 3.1.2. Values of average column-face sizes for 15° and 30° EDS.

 

Figure 3.1.8. ESEM image of dark streak on 15° EDS at 5000x.

45

 

Figure 3.1.9. ESEM image of light areas of 30° EDS at 5000x.

 

Figure 3.1.10. ESEM image of dark streak on 30° EDS at 5000x.

46

The values of RMS surface roughness, measured with the AF M, were determined
for the dark streaks and lighter colored areas of the deposition surfaces. Values are given
in nanometers and are given in Table 3.1.3. Again, for a given area, the surface
roughness was measured three times and then averaged. Images of the roughness data for
both the 15° and 30° surfaces are shown in Figures 3.1.10 — 3.1.13.

The surface roughness of the dark streaks of the 15° and 30° surfaces is
approximately 287 nm and is 278% greater than that of the smooth reference surface. For
the 15° EDS, the RMS surfaces roughness of the dark streaks is 21% greater than that of
the lighter colored areas. For the 30° EDS, The surfaces roughness of the dark streaks is
30% greater than the lighter colored areas. The surface roughness of the lighter areas of
the 15° EDS is 8% larger than that of the 30° EDS. Thus the difference in surface

roughness between the dark and light areas of the 30° sample is 40% larger than that of

 

 

 

 

the 15° sample.
Area on EDS R??? Surface Roughnessggzn)
Light 237 219
Dark Streaks 286 287

 

 

 

 

 

Table 3.1.3. RMS surface roughness values for 15° and 30° EDS

47

Image Statistics

 

 

 

lms.2 nune 2.€fllum
lms.fleur 0.UN!nm
lms.lunmeur -63Js7ru
lms. nms (R!) 293.28 nm
lmg. la 234.11 nm
1mg. Imam 2.488 um
lmg.$rr.arma scars mf
1mg. Srf. area arrr 32.417 x
Box Statistics
2 numn 2JH2|m
lent 2.$fiinm
lhslmq) 1.40ru
leanrmwmhnass duo ZflLOB nm
lax height (Imam) 2.080 um
&uTun uma imwuiuf
Surface area diff 31.335 a
Box m dimension 27.871 um
lam y dimension 29.178 um

 

 

 

 

 

lianoSoope Contact AFN
Scan size 70.
SatPOInt 0.5000 0
Scan rate 3.052 H2
mber of samples 512

X 20.000 ins/div
2 3.000 rim/div

    

Figure 3.1.12. 3-D surface roughness data for dark streak of 15° EDS.

48

Roughness Anahsh

 

     

 

 

 

 

 

mm . m
.ammm rune...
Mm...Jmah. MA..W.W.M S
mammmmsmuumLMmmnmumm m mm
u an I e /d
am a. m m w
a m) ass em amm 0 mo
mm a as ram a am
i m .. an. m mam
. um mm” . emu an
an» a ss m m mmmxs k
........ m m ffmm .w X2 Xm.
mmmmmmmm “mmmmmwmu m ,
f
m um
" 22
m. mmm m
m t 5a
a .... .
t
a a .
3 M
n. a
as“ S
n nutufl
m mama“
F whens.“
mmamm

 

49

Figure 3.1.14. 3-D surface rouglmess data for dark streak of 30° EDS.

The AF M also provided maximum height (Rm) data for both deposition surfaces.
The values of Rm, indicate the difference in height between the highest and lowest points
on the surface relative to the mean plane. Image data has a minimum variance about the
mean plane of the surface. In other words, the mean plane results from a first-order least-
squares fit on the Z data. For the 15° AFM data, the dark streaks and light areas had
average Rmam values of 2.9 and 1.9 pm respectively. The 30° EDS had average Rm
values of 2.9 and 1.8 um for the dark streaks and light areas respectively. For both
surfaces, the maximum height difference for the dark streaks and light areas differs by

approximately 1 pm.

3.2 POOL BOILING

The experimental pool boiling curves for the smooth, 15°, and 30° surfaces are
shown in Figure 3.2.1. Initially, the heat flux increases linearly with increasing wall
superheat and is characteristic of natmal convection. Once boiling incipience is
achieved, the boiling curve is no longer linear. The significant increases in heat flux with
increasing wall superheat after boiling incipience verifies that that the mode of heat
transfer progressed from natural convection to nucleate boiling. The methods used to
calculate the surface temperature and heat flux values for the surfaces tested can be found
in Appendix D. Experimental boiling data can be found in Appendix E.

The linear portion of the boiling curves indicates that the mode of heat transfer is
natural convection. Both the laminar and turbulent natural convection curves for a

horizontal upward facing place are included on Figure 3.2.1. Laminar natural convection

50

dominates up to a wall superheat of approximately 10 degrees after which turbulent

natural convection takes over.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Heat Flux vs Wall Superheat
100000 I — I
I
s I I
x I I
2 I I
i 1000 I I
z I T
I I
I I
100 L . 4'
1 10 100
Wall Superheat (Degrees C)
'— - laminar net. 6031}. __._ 30 deg. 0 $0001 I
a 15 deg. _. __ I turbulent nat.conv.__;_~_ __ epr._lam. nat. conv. I

 

 

 

 

Figure 3.2.1. Pool boiling curves for experimental sufaces.

The transition from laminar to turbulent natural convection was determined by the
intersection of the two curves. A power-law relationship exists between the non-
dimensional Nusselt and Rayleigh numbers resulting in a power-law relationship between
heat flux and wall superheat. A power-law curve fit was applied to both the theoretical
laminar natural convection curve as well as to the linear portion of the experimental data
resulting in curve fit equations of q” = 896"'(AT)"25 and q” = 601“'(AT)"2 respectively.
The exponents on the wall superheat, AT, differ by a mere 4% thus the theoretical and

experimental laminar convection curves are nearly parallel. The experimental laminar

51

natural convection curve results in heat flux values approximately 20% less than that of
the theoretical curve at the same wall superheat. Detailed information for the laminar
natural convection calculations can be found in Appendix D.

Thome [32] reported measured the saturated nucleation superheat of water on a
plain copper disk at atmospheric pressure to be between 6—8 °C. Boiling incipience,
indicated in this work by an initial layer of growing bubbles on the heated surface,
occurred at 12-13 °C for the reference smooth surface. This higher value of incipient
superheats was anticipated because as the bubbles depart from the heated surface during
subcooled boiling, subcooled liquid fills the voids left by the departing bubbles. Thus the
filling liquid would take some amount of time to return to saturation conditions.

Boiling incipience on the electrochemical deposition surfaces occurred at 11-12
°C and is only 8% less than that of the reference smooth surface. Microporous enhanced
surfaces produced by Chang and You [4] resulted in 80-90°/o lower superheats compared
to a smooth reference surface using F C-72 as the working fluid. Although both of the
electrochemical deposition surfaces resulted in a decrease in incipient superheat, this
reduction is minimal within the uncertainty of this work. This reduction in incipient
superheat will not be used to indicate whether or not the electrochemical deposition
surfaces can be considered enhanced boiling surfaces.

The portion of the boiling curves after boiling incipience for the smooth, 15° EDS
and 30° EDS are very similar (see Fig. 3.2.1). The data for the 30° porous
electrochemical deposition surface virtually collapses onto the smooth surface data. For
the boiling on the 15° EDS, the heat flux for a given wall superheat is slightly less than

that of the 30° EDS and smooth surface data.

52

Bubble visualization was also used to evaluate boiling on the different surfaces
tested. Still images of bubble growth on each surface were captured fi'om digital video
recordings of boiling incipience. Figures 3.3.2 - 3.3.4 represent bubble growth on the
surfaces tested at boiling incipience and are shown at equal length scales.

As discussed previously, a surface can enhance boiling by either reducing the
incipient superheat (increasing the effective heat transfer coefficient) or increasing the
nucleation site density at incipience as compared to a smooth surface. From Figures
3.2.2 and 3.2.3, it is obvious that the 30° EDS promotes bubble growth and increases the
nucleation site density compared to the smooth reference surface. This increase in
nucleation site density implies that the 30° surface can be considered and enhanced
boiling heat transfer surface. Bubbles on the 30° surface, as shown in Figm‘e 3.2.3,
appear to form uniformly in periodic clusters across the boiling surface. This suggests
that the periodic surface structure variations on this surface promote preferred nucleation
sites. Bubble formation on the 15° EDS (Fig. 3.2.4) also depicts periodic clusters,
however, there is not an increase the nucleation site density at boiling inception as
compared to the smooth surface. This lack of bubble formation on the 15° surface is
responsible for the lower heat flux for a given wall superheat as compared to the smooth
and 30° surfaces. Boiling inception on the 30° surface produced a significantly greater
nucleation site density than that on the 15' surface. This suggests that the more
pronounce surface structure of the 30° surface, compared to the less distinct structure of

the 15' surface, increases nucleation site density at boiling inception.

53

 

 

Figure 3.2.2. Bubble formation on smooth reference surface.

 

 

Figure 3.2.3. Bubble formation on 30' electrochemical deposition surface.

 

 

Figure 3.2.4. Bubble formation on 15° electrochemical deposition surface.

54

The 30 ° electrochemical deposition surface increases the nucleation site density
at boiling inception, compared to that of the reference smooth surface, and hence is
considered an enhanced boiling surface. The mechanisms responsible for the promotion
of preferred nucleation sites, as shown in Figure 3.2.3, lie in the unique structure of the
30° deposition surface. The packing distribution of the column-like protrusions on the
surface appears to create vapor-trapping pockets. These pockets can then act as steam
evacuation channels and become preferred sites for the formation of smaller bubbles.
The height distribution of the columns also creates a mechanism for preferred sites of
bubble growth. Taller columns surrounding a group of smaller columns form basin-like
areas in which larger vapor bubbles could grow. Also, on a slightly larger scale, the

streaks can act as vapor trapping mechanisms.

 
 
  

Column-like
Protrusions

 

Figure 3.2.5. Magnified schematic of possible vapor pockets on deposition surface.

55

The streaks, as previously stated, consist of periodic spanwise surface variations that
extend longitudinally along the plate. These unique variations can be thought of as
troughs (Fig. 3.2.6) which trap vapor in the same manner as basins. The troughs simply

are basins on a larger scale that extend into the page.

Troughs

 

 

Figure 3.2.6. Magnified schematic of possible troughs on deposition surface.

56

CHAPTER4

CONCLUSIONS

The following summary and resulting conclusions are supported by the
experimental work performed in this investigation. Mircro-scale structured copper
surfaces with periodic surface structure variations were successfully created using
electrochemical deposition on an inclined flat surfaces of 15° and 30°. The surface
structure of the 30° surface is visibly more pronounced than that of the 15° surface. The
structures of these deposition surfaces were meticulously documented in this work. The
ESEM and AF M were used to characterize the micron and sub-micron sized structural
features of the surfaces. Boiling incipience on the deposition surfaces was investigated
and compared to that of a smooth reference surfaces. Boiling evaluation of the smooth,
15' and 30° surfaces suggests that the more distinct structure of the 30’ surface increases
the nucleation site density at boiling inception. These preferred nucleation sites are
formed by: vapor-trapping pockets between column-like protrusions present on the
surface; basins created by height differences in clusters of columns; and troughs

characterized by spanwise periodic column variations.

S7

CHAPTER 5

RECOMMENDATIONS

Suggestions for future work in the area of nucleate pool boiling on microscale

structured electrochemical deposition surfaces are as follows:

1. Use low surface tension working fluid

2. Measure the contact angles on both the light areas and dark streaks of the
electrochemical deposition surfaces. This could help quantify the effects of the

differences in surface structure of the EDS.

3. Design an experimental set-up for top-view bubble visualization. If a visual
recording device was used to document bubble growth on the entire
electrochemical deposition surface, preferred nucleation sites could be directly

related to particle composition and surface structure.

4. Include the presence of an electric field in the experimental set-up. The results of

the electric field boiling data could help further characterize the electrochemical

deposition surfaces.

58

APPENDICES

59

APPENDIX A

STEADY-STATE VERIFICATION

PURPOSE: This experiment was designed for testing the assumption that, after raising
the supplying energy level to the test section, 15 minutes is enough for time for the

temperature to reach the steady state.

PROCEDURE: Once the liquid was heated to 90 degree Celsius (10 degree
subcooling), the power to the heater cartridges was increased in increments of 5 on the
Vatic every 30 minutes. Special care is taken to keep the liquid temperature at 90 degree

Celsius. Temperature data for Channel 8 shown on the Omega Trendicator is taken every

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 minutes.

DATA:

Voltage(V) Time (min) Temp. for Ch. 8 Voltage(V) Time (min) Temp. for Ch. 8

20V 1 89.8 25V 31 90.7

3 89.8 33 90.9
5 90 35 91.2
7 90.4 37 91.5
9 90.5 39 91.8
11 90.4 4] 92.2
13 90.6 43 92.1
15 90.6 45 92.2
17 90.6 47 92.2
19 90.4 49 92.2
2] 90.5 51 91.2
23 90.5 53 92.2
25 90.4 55 92.2
27 90.7 57 92.2
29 90.5 59 92.2

 

 

 

 

 

 

 

 

 

 

60

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Voltagem Time (min) Temp. for Ch. 8 Voltage(V) Time (min) Temp. for Ch. 8

30V 61 93.3 35V 91 95.3
63 93.9 93 96.5
65 94.3 95 96.9
67 94.2 97 96.8
69 94.2 99 96.9
71 94.3 101 96.9
73 94.3 103 97
75 94.3 105 97
77 94.4 107 97
79 94.2 109 96.9
81 94.3 11 1 96.5
83 94.5 1 13 96.8
85 94.3 1 15 97
87 94.3 117 97.1
89 94.2 1 19 97.2

 

 

 

 

 

 

 

Voltage(V) Time (min) Temp. for Ch. 8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40V 120 97.9
122 98.3
124 98.5
126 98.5
128 98.6
130 98.7
132 98.9
134 98.7
136 98.6
138 98.6
140 98.7
142 98.8
144 98.8
146 98.9
148 98.8

 

61

Temperature ( C )

Time V.S. Temperature for Channel 8

 

 

 

 

 

 

 

 

 

 

1oo.fi , ~ .. “#“flmw __.fl ______.m A
!
2
98 fi+— # ifiwiiw': __
E xwng“
961‘"— " —"* #** _._,,_ -—-~—- [726v
! x guzsv
94 i z t f g , g .130v
1 ‘x35v
! (MW
92 T— — --_ _
l I
1.3””
90
88 I ' "‘ "' r ‘—Y_ ——‘ ——'— #—".— . 1 g
0 20 40 60 00 100 120 140 160

Time ( mine. )

Figure A1. Time V.S. temperature for Channel 8 while changing Variac setting.

62

 

APPENDIX B

DETERMINATION OF PHYSICAL PROPERTIES

The determination of the physical properties of the electrolyte solution was
accomplished by the following method used by Lloyd [28].
May of Electrolyte Solution

The equation for the density of the copper ion-sulfuric acid solution, as shown
below, was a least squares curve fitted to through a plot of density as a fimction of copper

ion and sulfuric acid concentration and of temperature.
p = AH(T)+ BH(T)-HS+CH(T)oHS2 + DH(T)-CU + EH(T)-CU2
In the above equation, HS and CU are the molar sulfuric acid and copper ion

concentrations respectively and

AH(T) = 1.0060 - (0.000006 . T) — (0.0000052 - T2 )
BH(T) = 0.06735 — (0.00033 - T) + (0.00000317 - T2)
CH(T) = —0.00341 + (0.000041 - T) — (000000043 . T2 )
DH(T) = 0.12717 + (0.000307 -T) - (0.0000177 . T2)
EH(T) = 0.03225 - (0.00144 . T) + (0.00004053 - T2)

where T is the solution temperature in degrees Centigrade.
Viscosity of Electrolyte Solution

The equation for the viscosity of the copper ion-sulfuric acid solution, as shown
below, was a least squares curve fitted to through a plot of viscosity as a function of

copper ion and sulfuric acid concentration and of temperature.

p = A V(T) + BV(T) . HS + CV(T) . H82 + DV(T) . CU + EV(T) . CU2

63

In the above equation, the coefficients of sulfuric and copper ion concentrations are

A V(T) = 1.69713 — (0.045652 - T) + (0.000535 . T2)

BV(T) = 0.330104 — (0.008309 - T) + (0.000072 - T2)
CV(T) = 0.01317133 — (0.00037356 - T) + (0.00000763 . T2)
DV(T) = 2.3982 — (0.13872 . T) + (0.002267 - T2)

EV(T) = 0.99679 + (0.14558 - T) — (0.0032494 - T2)

Diffu_sion Coefficients
The least squares best-fit equation for the diffusion coefficient for the sulfuric
acid is
D”, = (AK(T) + BK(T) . HS + CK(T)-1'IS°")-10‘S
where

AK(T) = 0.92452 + (0.042135 . T) + 0.00005207 . T2)
BK(T) = 0.061912 — (0.001293 . T) — (000024615 . T2)
CK(T) = 0.6688 — (0.004727 - T) + (0.0004895 . T2)

At 22°C the copper ion concentration is

(0.7363 + (00051 1 . HS) + (0.02044 - CU ) . 10 .5
p

 

DC‘U =

Transference Numbers
The expression used in this work for the transference numbers of copper ions and
hydrogen ions are as follows

I...” = (0.2633 — (0.102 - HS)) - CU
1,, = 0.8156 — (0.2599 - CU) - (0.1089 . CUZ)

APPENDIX C

CALCULATION OF PHYSICAL PROPERTIES

15 Degrees

Density of Electrolyte Solution

Temperaure (degrees C)
CH (molar cone. H2804)
CU (molar conc. CuSO4)
AH

BH

DH

PH

RH

Total Density (glcm‘3)

Density wlout CuSO4 (glcm‘3)

Density Change (glcm‘3)

Viscosity of Electrolyte Solution

AV

BV

CV

DV

EV

Total Viscosity

Correct Viscosity (gl(cm*s))

Diffusion Coefficients

AK
BK
DK
Diff. Coeff. H2304 (cm‘2ls)
Diff. Coeff. CuSO4 (cm‘ZIs)

Transference Numbers

t-CuSO4
t-HZSO4

65

22.6000
1.5000
0.03
1.0032
0.0615
-0.0027
0.1276
0.0308
1 .093
1 .089
0.004

0.9386514
0.17909532
0.0086
0.4210
2.6272
1.2417
0.0124

1 .9034
0.4642
0.81 1987
0.0000359
0.0000060

0.0033
0.8077

Miscellaneous Values

theta (degrees) 15.0000
theta (rad) 0.2617
gravity (mls‘2) 981.0000
cos theta 0.9660
x-location (cm) 7.5000000
Mass Transfer Coefficient

current density (Nem‘2) 0.1660000
CU conc. (g/cm"3) 0.00478860
n 2

F ((A‘syg) 96500
Km (cmls) 0.00017902
Schmidt # 1894.1983
Grashof # 109283580695
Rayleigh # 207004772020999
Sherwood # 223.9080
Sh(Ra)# 189.2760
30 Degrees

Density of Electrolyte Solution

Temperaure (degrees C) 24.0000
CH (molar oonc. H2804) 1.5000
CU (molar conc. 00804) 003

AH 1.0029
BH 0.0613
DH 00027
PH 0.1276
RH 0.0308
Total Density (glem‘3) 1.093
Denslty wlout CuSO4 (glcm‘3) 1.089
Denslty Change (glcm‘3) 0.004

Viscosity of Electrolyte Solution

AV 0.909642
BV 0.17216
CV 0.0086

66

DV

EV

Total Viscosity

Correct Viscosity (gl(cm's))

Diffusion Coefficients

AK
BK
DK
Diff. Coeff. H2804 (cm‘2ls)
Diff. Coeff. CuSO4 (cm‘ZIs)

Transference Numbers

t-CuS04
t-H2S04

Miscellaneous Values

theta (degrees)
theta (rad)
gravity (m/s"2)
cos theta
x-location (cm)

Mass Transfer Coefficient
current density (Alcm‘2)
CU conc. (glcm"3)

n

F ((A‘S)/9)

Km (cmls)

Schmidt #
Grashof #
Rayleigh #
Sherwood 1!

3mm):

67

0.3747
2.6191
1.2008
0.0120

1 .9658
0.4463
0.837304
0.0000366
0.0000062

0.0033
0.8077

30.0000
0.5233
981.0000
0.8662
7.5000000

0. 1 660000
0.00478860
2
96500
0.00017902

1 772.6587

104711220308
185617258843779

216.5390

184.1854

APPENDIX D

POOL BOILING CALCULATIONS

C.l HEAT FLUX
The heat flux through the boiling surface was determined using Fourier’s Law:

q"=—kd—T C.l.l
dx

where k is the known thermal conductivity of the boiling surface and dT/dx is the average
temperature gradient through the OFHC copper block. The average temperature gradient
through the OF HC copper block is determined by averaging three measured x-location
temperature gradients. An x-location temperature gradient profile is determined by
plotting the known y-location of a thermocouple versus its temperature display for four
consecutive thermocouples. Plots are generated for three sets of thermocouples: #1-4,

#5—8, and #9-12 for each variac setting for each surface (see Appendix E).

C.2 SURFACE TEMPERATURE
For conduction through a series of materials, the thermal resistance model for the

heat flux through a wall is equal to

7,-7)
'E———— C21
q R

where q” is the heat flux through the surface, To is a known temperature in the material
and Tw is the surface temperature of the material. Rm. is the total thermal resistance

through the material. Solving the thermal resistance model for equation for TW gives:

u=n—¢mm C22

68

where, for this work, q” is the measured value of the heat flux through the boiling
surface, To is the average of five thermocouple readings at a known location in the OF HC
copper block, and TW is the unknown temperature of the boiling surface. Run is equal to
the sum of the resistances for each material as shown below.

R

o, = R1 + R2 + R, C23

f

where R1 is the thermal resistance of the OF HC copper block, R2 is the thermal resistance

of the solder layer, and R3 is the thermal resistance of the boiling surface as defined

below.
R1 = 5 C24
k1
R2 = 5 C25
k2
R, = 5 C26
It

For the resistances defined above, L is equal to the known thickness of the material and k
is the known thermal conductivity of the material. Note that L1 is the distance from the

known temperature of the OF HC copper, To, to the solder layer. The table shown below

gives the length and thermal conductivity values used to calculate the total thermal

 

 

 

 

 

 

 

 

 

 

resistance.
1 2 3
OFHC Solder 110 Alloy
k (WImKL 391 50 388
L (m) 0.002 0.0005 0.001
R (m’KM) 5.12 E-06 0.00001 2.58 E-06
R-tot (m’KM) 1.77 E—05

 

Table C.2.l Values used for thermal resistance model.

69

 

C.3 HEAT TRANSFER COEFFICIENT

The boiling heat transfer coefficient was calculated using the following equation:

h=_1"—— 0.3.1
(TV _T3ub)

where q” is the heat flux through the boiling surface, Tw is the temperature of the boiling

surface, and Tsub is the temperature of the subcooled liquid.

C.4 NATURAL CONVECTION CURVES
The heat flux versus temperature values for the natural convection curves were
calculated using the following series of equations. Heat flux can be defined as
q"= h - (T... - T...) C.4.1
where h is the convective heat transfer coefficient and is calculated by

h = £0 Nu C42

6
In the above equation, k is the thermal conductivity of the liquid, 8 is the characteristic
length of the heat transfer surface equal to its area divided by perimeter, and Nu is the

Nusselt number. The Nusselt number for laminar flow and turbulent flow are defined as
Laminar: Nu = 0.54 - Ray“ (104 s Ra s 107) C43

Turbulent: Nu = 0.15 - RM (107 s Ra 510“) 04.4
where Ra is the Rayleigh number. The Rayleigh number can be calculated using known

properties of the liquid with the following equation:

= g.fl.(Tw _Trub).63 'PI'

02

 

Ra C.4.5

70

For this work, the Rayleigh numbers were less than 107 thus the laminar equation for the

Nusselt could be used. Table C.4.1 defines and give the values for the variables in the

above equation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Symbol Units Value
Specific Heat (liq) CL J/Qg'C) 4217
Thermal Diffusivity (qu) a mzls 1.68 E-07
Thermal Conductivity (liq) k W/(m'KL 0.679
Surface Area A m2 0.0019
Surface Perimeter P m 0.178
Characteristic Length (NP) 6 01 0.0111
Prandtl Number Pr none 1.75
Acceleration due gravity 9 m/s2 9.81
Beta 6 1/K 0.002
Dynamic Viscosity (liq) u. kgl(m"s) 0.00028
Density (liq. ) pl lglms 957
Kinematic Viscos'fl (ulp) v mzls 2.95 E-07
Density (vapor) pv kg/m3 0.6
Surface Tension 0 Wm 0.0589
Enthalpy of Vaporization hm Jlkg 2257000
Experimentall BoilinlConstant 0; none 0.013

 

Table C.4.1 Property values for variables used in boiling data calculations.

71

 

APPENDIX E

 

 

 

POOL BOILING DATA
Heat .
Surface Wall Superheat Heat Flux Transfer Variac
(deg C) (WIM‘Zi Coefficient Setting
(WIm‘2K)
Smooth 3.67 2173.96 592.11 15
5.31 4700.21 885.69 20
7.61 6732.24 884.55 25
8.53 8682.16 1018.27 30
10.06 10139.41 1007.83 35
1244 14039.25 1128.41 40
13.64‘ 19888.61 1458.31 45
14.57 23049.45 1581.74 50
14.87 31464.55 2115.50 55
15.44 38853.67 2516.01 60
15 Degree 2.24 1573.38 701.73 15
4.22 3879.23 918.95 20
6.45 6793.63 1053.31 25
8.39 9030.93 1076.36 30
9.44 7224.90 765.17 35
11.18“ 9852.03 881.56 40
13.32 15701.39 1178.59 45
14.12 22947.01 1624.68 50
14.64 27729.33 1894.16 55
15.65 32819.37 2097.17 60
30 Degree 4.43 4002.28 903.61 20
6.45 4371 .77 677.52 25
8.90 8209.83 921.96 30
9.43 8271.61 876.82 35
11.75* 9913.41 843.36 40
13.70 14490.46 1057.42 45
14.79 18513.46 1251.55 50
15.89 23829.50 1499.80 55
16.93 29556.08 1746.08 60

* indicates boiling incipience

72

Smooth

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

THERMOCOUPLE LOCATIONS
#4 #13 #8 #14 #12
#3 #7 #11
#2 #6 #10
#1 #5 #9
E 15 X-Direction (m)
3 0.009525 0.015875 0.022225 0.028575 0.034925 Averggg
.2 0.022225 93.45 93.6 93.45 93.45 93.6 93.51
3 0.015875 93.5 93.5 93.6 93.53
5, 0.009525 93.5 93.55 93.65 93.57
" 0.003175 93.55 93.6 93.7 93.62
dT/dx [slqge] .472 -9.45 -5.51 -5.58
dT/dx ave. -5.56
q" ave. (w/m‘2) 2173.96
To ave. (degree 0) 93.51
Tw (degree C) 93.472
Tbulk (degree 0) I 89.900 I I 89.700 I
T bulk ave. (deg C) 89.800
11 exp. (W/mAzK) 592.112
20 0.009525 0.015875 0.022225 0.028575 0.034925 Ave e
0.022225 95.95 96 96 95.9 96.1 95.99
0.015875 96 96.05 96.1 96.05
0.009525 96.05 96.15 96.2 96.13
0.003175 96.15 96.2 96.3 96.22
dT/dx [slope] -7.87 -15.75 -11.81 42.021
dT/dx ave. -12.021
q" ave. (w/mAZKL 4700.21 1
To ave. (dgqree C) 95.99
Tw (degree 0) 95.907
Tbulk (degree C) I 90.400 I | 90.800 I
T bulk ave. (dgg C) 90.600
h exp. (W/mAZK) 885.689
25 I0.009525 0.015875 0.022225 0.028575 0.034925I Averagi
0.022225 I 98.25 98.35 98.25 98.15 98.4 I 98.28
0.015875 I 98.3 98.35 98.55 I 98.40

 

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0.009525 98.45 98.45 98.55 98.48 I
0.003175 98.5 98.6 98.75 98.62 I
dT/dx Elopel 45.748 -20.472 -19.67 472181
dT/dx ave. -17.218
q" ave. (w/m‘ZK) 6732.238
To ave. (degree C) 98.28
Tw (dggree 0) 98.161
Tbulk (degree C) I 90.300 I I 90.800 I
T bulk ave. (deg C) 90.550
11 exp. (W/m‘2K) 884.553
30 0.009525 0.015875 0.022225 0.028575 0.034925 Avegg_e_
0.022225 99.4 99.45 99.35 99.25 99.45 99.38
0.015875 99.45 99.45 99.55 99.48
0.009525 99.55 99.55 99.65 99.58
0.003175 99.75 99.8 99.9 99.82
dT/dx[slope1 -20.472 -26.772 22.047 -22.205
dT/dx ave. .2205
q" ave. (w/m‘2K) 8682.155
To ave. (dggree C) 99.38
Tw (degee C) 99.226
Tbulk (degree C) I 90.600 I I 90.800 I
T bulk ave. (deg 0) 90.700
h exp. (W/m‘2K) 1018.268
35 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 100.95 101.1 100.85 101 101.05 100.99
0.015875 101.05 101.05 101.05 101.05
0.009525 101.25 101.2 101.35 101.27
0.003175 101.4 101.4 101.6 101.47
dT/dx [slope] 45.75 .20472 -26.77 45.932
dT/dx ave. 25.932
(1" ave. (wlm‘2K) 10139.412
To ave. (degee C) 100.99
Tw (degree 0) 100.811
Tbulk (degree C) I 90.600 I I 90.900 I
T bulk ave. Egg C) 90.750
11 exp. (WIm‘2K) 1007.833
I 40 [0.009525 0.015875 0.022225 0.028575 0.034925IAverage_]
I 0.022225 | 103.4 103.6 103.3 103.3 103.6 I 103.44
I 0.015875 I 103.45 103.6 103.65 I 103.57J

 

 

 

 

 

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0.009525 103.75 103.8 104.05 103.87 I
0.003175 103.95 104.1 104.25 104.10 I
dT/dx [slope] 22.05 -33.071 -29.92 55.906]
dT/dx ave. ~35.906
q" ave. (w/m‘ZK) 14039.246
To ave. (dggree C) 103.44
Tw (degree C) 103.192
Tbulk (degree C) I 90.600 I I90.900 I
T bulk ave. (deg 0) 90.750
h exp. (Wlm"2K) 1128.411
45 0.009525 0.015875 0.022225 0.028575 0.034925 Avegge
0.022225 104.75 104.75 104.65 104.5 104.8 104.69
0.015875 104.85 105.05 104.9 104.93
0.009525 105.25 105.25 105.35 105.28
0.003175 105.55 105.65 105.75 105.65
dT/dx [slope] -32.28 44.09 44.09 50.866
dT/dx ave. -50.866
q" ave. (wlmAZK) 19888.606
To ave. (d_egree C) 104.69
Tw (degree C) 104.338
Tbulk(deggee C) I 90.600 I I 90.800 I
T bulk ave. (dgg 0) 90.700
11 exp. (W/m"2K) 1458.310
50 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 105.6 105.75 105.5 105.6 105.7 105.63
0.015875 105.75 105.95 105.85 105.85
0.009525 106.15 106.25 106.45 106.28
0.003175 106.65 106.7 106.85 106.73
dT/dx [slope] 42.52 -66.142 -64.567 58.95
dT/dx ave. -58.95
q" ave. (wImAZK) 23049.45
To ave. (degree C) 105.63
Tw (degree C) 105.222
Tbulk (degree C) I 90.500 | I 90.800 I
T bulk ave. (deg C) 90.650
h exp. (WIm‘2K) 1581.741
I 55 I0.009525 0.015875 0.022225 0.028575 0.034925I Ave e
[ 0.022225 | 106.4 106.5 106.3 106.3 106.4 I 106.38
| 0.015875 I 106.6 106.7 106.7 I 106.67 I

 

 

 

 

 

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0.009525 107.2 107.25 107.5 107.32
0.003175 107.7 107.9 108 107.87
dT/dx [slope] -57.48 -66.142 -72.441 -80.472
dT/dx ave. -80.472
q" ave. (w/m‘2K) 31464.552
TO ave. Mme C) 106.38
Tw (degree C) 105.823
T bulk (degree C) I 90.900 I I 91.000 I
T bulk ave. (deg C) 90.950
h exp. (W/m"2K) 2115.503
50 0.009525 0.015875 0.022225 0.028575 0.034925 Avera e
0.022225 107.1 107.2 106.9 106.9 107.3 107.08
0.015875 107.45 107.7 107.5 107.55
0.009525 108.05 108.25 108.45 108.25
0.003175 108.8 108.95 109.1 108.95
dT/dx (slope) 63.78 -91.34 -83.465 -99.37
dT/dx ave. -99.37
q" ave. (wlm"2K) 38853.67
To ave. (degree 0) 107.08
Tw (degree C) 106.393
T bulk (degree C) I 90.800 I I 91.100 I
T bulk ave. (deg C) 90.950
h exp. (W/mAZK) 2516.008
15 Degrees
THERMOCOUPLE LOCATIONS
#4 #13 #8 #14 #12
#3 #7 #11
#2 #6 #10
#1 #5 #9
E 15 X-Direction (m)
= 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
3 0.022225 93.4 93.6 93.5 93.5 93.6 93.52
§ 0.015875 93.4 93.5 93.6 93.50
'5 0.009525 93.4 93.5 93.6 93.50
" 0.003175 93.45 93.5 93.7 93.55
dT/dx Islope] 472 -945 -5.51 -1 .417
dT/dx ave. -1.417

 

 

 

 

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q" ave. (w/m’gL

 

554.047

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To ave. (d_egree C) 93.52
Tw (degree CL 93.510
T bulk (degree C) I 89.900 I I 89.700 I
T bulk ave. (dgg 0) 89.800
h exp. (\NIm"2K) 149.331
20 0.009525 0.015875 0.022225 0.028575 0.034925 Averagefl
0.022225 95 95.2 95.1 95 95.2 95.10
0.015875 95 95.1 95.2 95.10
0.009525 95.1 95.1 95.4 95.20
0.003175 95.2 95.2 95.45 95.28
dTldx [slope] -7.87 -15.75 -11.81 40.238
dT/dx ave. -10.236
q” ave. (w/mAZK) 4002.276
To ave. (degree 0) 95.1
Tw (degree CL 95.029
T bulk (dggree C) I 90.400 I I 90.800 I
T bulk ave. (deg C) 90.600
h exp. MWZK) 903.614
25 0.009525 0.015875 0.022225 0.028575 0.034925 Averagg.
0.022225 96.9 97.2 97.1 97 97.2 97.08
0.015875 96.9 97.1 97.2 97.07
0.009525 97 97.1 97.4 97.17
0.003175 97.15 97.2 97.5 97.28
dT/dx [slope] -15.748 -20.472 -19.67 41.181
dT/dx ave. -11.181
q" ave. (wlm‘2K) 4371.771
To ave. flee C) 97.08
Tw (degree 0) 97.003
T bulk (degree C) I 90.300 l I 90.800 I
T bulk ave. (deg 0 90.550
h em. (WIm‘2K) 677.515
30 0.009525 0.015875 0.022225 0.028575 0.034925 Averag_e__
0.022225 99.6 99.85 99.75 99.55 100 99.75
0.015875 99.6 99.8 100 99.80
0.009525 99.8 99.85 100.15 99.93
0.003175 100 100.1 100.35 100.15
dT/dx [slope] -20.472 -26.772 -22.047 -20.997
dT/dx ave. -20.997

 

 

 

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q" ave. (w/m‘2K)

 

8209.827

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To ave. (degree C) 99.75
Tw (degree 0) 99.605
T bulk (degee C) I 90.600 I I 90.800 I
T bulk ave. (deg 0) 90.700
h exp. MImAZK) 921.961
35 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 100.2 100.45 100.3 100.15 100.55 100.33
0.015875 100.2 100.45 100.55 100.40
0.009525 100.35 100.5 100.75 100.53
0.003175 100.6 100.7 100.9 100.73
dT/dx [slope] -15.75 -20.472 -26.77 -21.155
dT/dx ave. -21.155
q" ave. (w/m"2K) 8271.605
To ave. (degree C) 100.33
Tw (degge 0) 100.184
T bulk (degree C) I 90.600 I I 90.900 I
T bulk ave. (deg 0) 90.750
h exp. (WIrn‘2K) 876.819
40 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 102.65 102.85 102.55 102.45 102.9 102.68
0.015875 102.65 102.85 102.9 102.80
0.009525 102.8 102.9 103.15 102.95
0.003175 103.05 103.1 103.35 103.17
dT/dx [slope] -22.05 -33.071 -29.92 -25.354
dT/dx ave. -25.354
q" ave. (w/m42K) 9913.414
To ave. (degree C) 102.68
Tw (dggree C) 102.505
T bulk (dggree C) I 90.600 I I 90.900 I
T bulk ave. @g C) 90.750
h exp. (W/m"2K) 843.364
45 0.009525 0.015875 0.022225 0.028575 0.034925 Ave
0.022225 104.75 104.8 104.5 104.35 104.9 104.66
0.015875 104.75 105 105.45 105.07
0.009525 104.95 105.15 105.35 105.15
0.003175 105.35 105.35 105.55 105.42
dTldx [slope] -32.28 -44.09 44.09 417.08
dT/dx ave. -37.06

 

 

 

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q" ave. (w/m"2K) 14490.46
To ave. (dggge C) 104.66
Tw (degree 0) 104.404
T bulk (degree C) I 90.600 I I 90.800 I
T bulk ave. (degg) 90.700
h exp. (ern‘2K) 1057.418
50 0.009525 0.015875 0.022225 0.028575 0.034925 Aveggi
0.022225 105.85 105.95 105.55 105.45 106.05 105.77
0.015875 105.85 106.1 106.1 106.02
0.009525 106.15 106.3 106.55 106.33
0.003175 106.55 106.6 106.85 106.67
dT/dx [slope] -42.52 66.142 64.567 47.349
dT/dx ave. 47.349
q" ave. (w/mAZK) 18513.459
To ave. (degree C) 105.77
Tw (degree 0) 105.442
T bulk (degree C) I 90.500 I I 90.800 I
T bulk ave. (deg C) 90.650
h exp. (WIm’QK) 1251.548
55 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 107.45 107.45 107 106.85 107.55 107.26
0.015875 107.45 107.65 107.75 107.62
0.009525 107.75 107.95 108.2 107.97
0.003175 108.3 108.35 108.65 108.43
dTIdx [slope] -57.48 66.142 -72.441 60.945
dTIdx ave. 60.945
(fl ave. (wim‘2K) 23829.495
To ave. (degge C) 107.26
Tw (degree 0) 106.838
T bulk (degree C) I 90.900 I I 91.000 I
T bulk ave. (deg C) 90.950
h exp. (W/m"2K) 1499.805
50 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 108.6 108.65 108.05 108 108.7 108.40
0.015875 108.6 108.85 108.9 108.78
0.009525 109.1 109.25 109.5 109.28
0.003175 109.7 109.8 110 109.83
dTIdx [slope] -63.78 -91.34 -83.465 -75.591
dTIdx ave. -75.591

 

 

 

79

 

q" ave. (w/m"2 K)

29556.081

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To ave. (degree C) 108.4
Tw (degree 0) 107.877
T bulk (dggree C) I 90.800 J I 91.100 I
T bulk ave. ((139 C) 90.950
h exp. (W/m"2K) 1746.082
30 Degrees
THERMOCOUPLE LOCATIONS
4 13 8 14 12
3 7 11
2 6 10
1 5 9
’5" 15 X-Dlrection (ml
; 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
3 0.022225 91.6 91.8 91.6 91.8 91.8 91.72
3 0.015875 91.6 91.7 91.8 91.70
5 0.009525 91.6 91.7 91.85 91.72
" 0.003175 91.7 91.8 91.9 91.80
dTIdx [slope] .472 -9.45 -5.51 4.024
dTIdx ave. 4.024
q” ave. (w/m"2) 1573.384
To ave. (degree C) 91.72
Tw (degree 0) 91.692
T bulk gegree C) 7 89.200 I I 89.700 l
T bulk ave. (deg C) 89.450
h exp. (\NlmAZK) 701.726
20 0.009525 0.015875 0.022225 0.028575 0.034925 Averagg
0.022225 94.8 94.95 94.8 94.95 94.95 94.89
0.015875 94.8 94.85 94.95 94.87
0.009525 94.85 94.95 95.1 94.97
0.003175 94.95 95.1 95.15 95.07
dTIdx (slope) -7.87 -1575 -11.81 -9.9213
dTIdx ave. -9.9213
q" ave. (w/m‘2K) 3879.2283
To ave. (degree C) 94.89
Tw (d_egree C) 94.821

 

 

 

 

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I Tbulk (degree C) L I 90.400 I I 90.800 I
I T bulk ave. (deLC) I 90.600
I hexg (W/m"2K) I 918.951
25 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 97 97.2 97 97.2 97.2 97.12
0.015875 97 97.1 97.2 97.10
0.009525 97.1 97.2 97.4 97.23
0.003175 97.4 97.5 97.55 97.48
dTIdx (slope) -15.748 20.472 -19.67 47.375
dTIdx ave. -17.375
q" ave. (wlm"2K) 6793.625
To ave. (degree C) 97.12
Tw (d_egree 0) 97.000
Tbulk (degree C) I 90.300 I I 90.800 I
T bulk ave. (dgg C) 90.550
11 exp. (W/m"2K) 1053.307
30 0.009525 0.015875 0.022225 0.028575 0.034925 AveEge_
0.022225 99.2 99.3 99.15 99.2 99.4 99.25
0.015875 99.2 99.2 99.4 99.27
0.009525 99.3 99.4 99.6 99.43
0.003175 99.6 99.65 99.8 99.68
dTIdx (slope) -20.472 -26.772 -22.047 23.097
dTIdx ave. -23.097
q" ave. (w/m"2K) 9030.927
To ave. (degree 0) 99.25
Tw (degree 0) 99.090
Tbulk (degree C) I 90.600 I I 90.800 I
T bulk ave. (dgq 0) 90.700
l1 exp. (VV/m"2K) 1076.363
35 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 100.2 100.4 100.2 100.4 100.4 100.32
0.015875 100.2 100.3 100.4 100.30
0.009525 100.3 100.4 100.6 100.43
0.003175 100.5 100.6 100.9 100.67
dTIdx (slope) 45.75 -20.472 -26.77 48.478
dTIdx ave. -18.478
q" ave. (w/mAzK) 7224.898
TO ave. (degree C) 100.32
Tw (degree C) 100.192

 

 

 

 

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I T bulk (degree C) I I 90.600 I I 90.900 I
I T bulk ave. @gg C) I 90.750
I h exp. MIm‘ZK) I 765.173
40 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 102 102.2 101.9 102.2 102.2 102.10
0.015875 102.05 102.2 102.2 102.15
0.009525 102.1 102.2 102.6 102.30
0.003175 102.45 102.6 102.7 102.58
dTIdx [slope] -22.05 -33.071 -29.92 45.197
dTIdx ave. -25.197
q" ave. (w/mAZK) 9852.027
To ave. (degree C) 102.1
Tw (degree C) 101.926
T bulk (degree C) I 90.600 I I 90.900 I
T bulk ave. (dgg C) 90.750
h exp. (WIm‘2K) 881.558
45 0.009525 0.015875 0.022225 0.028575 0.034925 AveragL
0.022225 104.3 104.5 104.1 104.1 104.5 104.30
0.015875 104.35 104.5 104.6 104.48
0.009525 104.6 104.6 105 104.73
0.003175 104.9 105.1 105.3 105.10
dTIdx (slope) -32.28 44.09 .4409 40.157
dTIdx ave. 40.157
1" ave. (wlm‘2K) 15701.387
TO ave. (degree C) 104.3
Tw (degree C) 104.022
T bulk (degree C) I 90.600 I I 90.800 I
T bulk ave. (deg C) 90.700
h exp. M/m‘2K) 1178.588
50 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 105.3 105.3 105 105 105.3 105.18
0.015875 105.4 105.5 105.5 105.47
0.009525 105.7 105.8 106 105.83
0.003175 106.1 106.3 106.5 106.30
dTIdesIOpe] 42.52 66.142 -64.567 68.888
dTIdx ave. -58.688
q" ave. (w/m‘2K) 22947.008
TO ave. (degree 0) 105.18
Tw (degree C) 104.774

 

 

 

 

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T bulk (degree C) I 90.500 I I 90.800 I
T bulk ave. (degC) 90.650
h exp. (W/m"2K) 1624.681
55 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 106.2 106.2 105.9 105.8 106.3 106.08
0.015875 106.35 106.5 106.5 106.45
0.009525 106.7 106.9 107.2 106.93
0.003175 107.2 107.4 107.6 107.40
dTIdx [slope] -57.48 -66.142 -72.441 -70.919
dTIdx ave. -70.919
q" ave. (w/mAZK) 27729.329
To ave. (degree C) 106.08
Tw (degge C) 105.589
T bulk (degree C) I 90.900 I l 91.000 I
T bulk ave. (dgg 0) 90.950
h exp. (Wlm‘2K) 1894.157
60 0.009525 0.015875 0.022225 0.028575 0.034925 Average_
0.022225 107.2 107.3 106.9 107 107.5 107.18
0.015875 107.35 107.6 107.6 107.52
0.009525 107.8 108 108.4 108.07
0.003175 108.4 108.7 109 108.70
dTIdx [slope] -63.78 -91.34 -83.465 -83.937
dTIdx ave. -83.937
q" ave. (w/m‘2K) 32819.36?
To ave. (degree 0) 107.18
Tw (degree 0) 106.599
T bulk (degree C) I 90.800 I I 91.100 I
T bulk ave. (degfl 90.950
h exp. (WImAZK) 2097.172

 

 

 

83

TEMPERATURE GRADIENT PLOTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Smooth Surface:
110.00 #44 22-- 2-- - —— L. e 7 —~ — A ,_
E I e 15 1
108.00 =_ _ , _ I 20 I
=-80.472x+108. ‘; ‘ 23: I
106.00 'I_' _ _ “I‘- x I
4— - F5_8.95x+ 106.87 . . x 35 g
= -50.866x + 105.79 ' a
6 104.00 4— y fig:— . 40 I
:- y=-35.906x+ 104.2 4 + 45 1'
._, 102.00 - -, ' 55:
8 X 4— 1|! . ..
g 1 y = -25.932x + 101.52 4‘ 60
& ‘°°'°° i 7“ as... ‘ a... 2.. final; “15>
‘ =- . x+ .
IE 9300 I r y ¢ 4 "20)
' ' ‘ y = -17.218x + 98.664 —-Linear (25)
—-Linear (30)
96.00 gr_._-_.--Eg:|,E1x + 96.25 F _. —Unear (35)
—Linear (40)
94.00 '4 _.
: | : Linear (45)
y = 6.56431: + 93.627 —Linear (50)
92.00 1 1 1 4 . —Linear(55)
0 0.005 0.01 0.015 0.02 0.025 —-Linear (60)
anxls Location (m)

84

15 Degree Surface:

112.004————e~e+e-eiefffe
I
1100014 a: A fl—A flew—I .._ -—w 7 , e
I y = -75.591x + nor
108.00 3T2
I y = 60.945x + 108.59 *
, _
,. 105-0° I .2, y = 479W; ————
E10400) y=-'37.06x+105.54 7?
.. l E W .
E 102 00 I v 2. v #Y_= ' £354X: 12 ,:m__ 2
: y= ~21.155x+100.77
1 x— 111
E I y = -20.997x + 100.18
98.00 , _ -m r—~ m— - ——— 4—4 ~—
1 " y=T11.181x+97.291 ' ‘
96.00 T . fl
F J I
94 00 I y = -10.236x + 95.301 _
‘ e f c t
L y = -1.4173x + 93.535
92.m r T I ' I j
0 0.005 0.01 0.015 0.02 0.025
Y-axis Location (m)
30 Degree Surface:
110.00 1 ~ _ - aw 22--
1 .00 i
08 I ~ v = 60.47am
10600 Is __2 y=69.9_74x+ . ., _ ¥
1 +_ = -5g.688x + 106.44
104.00 1 ' __,-
3 I $ y=-41.732x+105.18
' I if C--. —.—_- _ ,,__
5 102-0° I y=25397x +1026 4
V X— y = - 8.478x + 100.66
§ 100.00 L— - — -- ~~»———- T4
8 9800 y=-2'3.097x+99.702 " "
E 96 00 y = - .265x + 97.479—" A
I
94 00 y = 3.92m + 95.073 ' '
92.m "‘ I
4 v
y = 4.04211 + 91.786
m.m T T I l ‘1
0 0.005 0.01 0.015 0.02 0.025
Y-axls Location (m)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

85

 

{67111:} ‘.
8888888888

I —Linear (15)
—Linear (20)
-—Linear (25)
—Linear (30)
—Linear (35)

—Linear (45)
—Linear (50)
—Linear (55)
—Linear (60)

 

—Linear (40) 1

 

I
l
I
I

 

l
I

I

+DXX>IOI
8888888883

I
I
I
I
|
I
I

—Lineer (1 5) I
—Linear (20)
—Lineer (25)
—Linear (30)
—Linear (35)
—Linear (40)
—Linear (45)
—Linear (50)
—Unear (55)
—Linear (60)

 

 

APPENDIX F

UNCERTAINTY ANALYSIS

F.l Temperature Measurement Uncertainty

Temperature was measured to the tenth of a degree, thus the uncertainty in each

temperature measurement was 0.05° C. This leads to an uncertainty of 02° C for the

measured wall superheat values.

F.2 Heat Flux Uncertainty

Given a 0.05° C uncertainty in each temperature measurement, the calculated heat

flux values could vary by as much as 86% at low heat fluxes and only 6% at high heat

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fluxes.
15 X-Directlon (m)
0.009525 0.015875 0.022225 0.028575 0.034925
0.022225 91.6 91.8 91.6 91.8 91.8 91.75
0.015875 91.6 91.7 91.8 91.80
0.009525 91.6 91.7 91.85 91.85
0.003175 91.7 91.8 91.9 91.95
dTIdx [slope] -4.72 -9.45 -5.51 -10.236
dTIdx ave. -10.236 4002.28 q” uneart
q" ave. (w/m"2) 4002.276 2154.41 1" exp
To ave. (degree C) 91 .72 1847.87 diff
Tw (degree C) 91.649 85.7715 % diff
T bulk (degree 0 I 89.200 I I 89.700 I
T bulk ave. (039 C) 89.450
h exp. (WIm‘ZK) 1819.886

 

 

 

 

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F.3 Solder Layer Thickness Uncertainty

60 0.009525 0.015875 0.022225 0.028575 0.034925
0.022225 107.2 107.3 106.9 107 107.5 107.45
0.015875 107.35 107.6 107.6 107.60
0.009525 107.8 108 108.4 108.40
0.003175 108.4 108.7 109 109.05
dTIdx [slope] -63.78 -91.34 -83.465 -88.189
dTIdx ave. -88.189 34481.90 (1" uncert
q" ave. (w/m‘2K) 34481.899 32634.82 q" exp
To ave. (degree C) 107.18 1847.08 diff
Tw (degLee C) 106.570 5.68 % diff
T bulk (d_egge C) I 90.800 l I 91.100 I
T bulk ave. (dgg C) 90.950
11 exp. (WImAZK) 207.558

The uncertainty in solder thickness between the OFHC copper blocks and test surface is

assumed to be 500 microns. Variations of up to 06° C exist in the x-direction measured

temperature of the OF HC block. A simple thermal resistance model was created to

calculate these x-direction temperature values using different solder thickness values

(within the uncertainty of the measurement). X-direction temperature variations of up to

02° C for low heat fluxes and up to 06° C for high heat flux were calculated. Thus

variations in solder layer thickness are attributed to x—direction temperature variations.

87

REFERENCES

88

 

[1]

[2]

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[4]

[5]

[6]

[7]

[3]

[9]

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91

 

     

 

1293 02504

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