CHAPTER-4 THERMAL CONDUCTIVITY OF...
53
62 CHAPTER-4 THERMAL CONDUCTIVITY OF NANOFLUIDS
Transcript of CHAPTER-4 THERMAL CONDUCTIVITY OF...
62
CHAPTER-4
THERMAL CONDUCTIVITY
OF NANOFLUIDS
63
Table of Contents
CHAPTER-4 THERMAL CONDUCTIVITY OF NANOFLUIDS 62-114
4.1 Introduction 64
4.2 Experimental investigation methods 65
4.2.1 Thermal conductivity measurement techniques 65
4.3 Preparation of Graphene nanofluid 67
4.3.1 Preparation of base fluid 67
4.3.2 Preparation of Graphene nanofluid 68
4.3.3 Ultrasonic vibration 71
4.3.4 Chemical surface modifications 72
4.4 Measuring thermal conductivity-Experimental set-up 78
4.5 Mathematical Calculations 83
4.6 Calibration of the instrument 85
4.7 Parameters that show major effect on thermal conductivity of nano
fluids 88
4.8 Conventional models 98
4.9 Thermal conductivity models 98
4.10 Estimating thermal conductivity by using (Hamilton and Crosser
model) 99
4.11 Estimating thermal conductivity by using (Xue-Xu Model) 102
4.12 Estimating thermal conductivity considering temperature as parameter
106
4.13 Summary 114
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CHAPTER - 4
THERMAL CONDUCTIVITY OF NANOFLUIDS
4.1. Introduction
In the previous decade, considerable theoretical and experimental
examinations were made to explore the thermo physical performance of nanofluids. In
those studies, it was observed that a high thermal conductivity enhancement could be
attained with nanofluids, even in the case of very minute particle volume fractions.
Furthermore, most of the experimental work showed that the thermal conductivity
enhancement obtained by using nanoparticle suspensions was to a great extent higher
than that attained by means of traditional suspensions with particles that are
millimetre- or micrometer - sized. Many researchers [11, 18, 20, 27 and 56] proposed
theoretical models to elucidate and expect those inconsistent thermal conductivity
ratios, defined as thermal conductivity of the nanofluid (knf
) divided by the thermal
conductivity of the base fluid (kf) [37].
There are many reviews available in the literature about nanofluid research [8,
38-42]. In all of the nanofluid thermal conductivity reviews, both theoretical models
and experimental results have been discussed. However, a detailed comparison
between theoretical models and experimental results is not provided in most of the
works.
In this section, a comparison between current theoretical models developed for
nanofluids and experimental results is provided. It is thought that such an analysis
provides important information about the assurance of the proposed models and the
related thermal conductivity enhancement mechanisms.
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4.2 Experimental investigation methods
4.2.1 Thermal conductivity measurement techniques
In thermal conductivity calculations of nanofluids, the steady state parallel
plate method is the widely used method [43-46]. A personalized steady-state parallel-
plate method, temperature alternation technique, micro hot strip technique and optical
beam deflection method have also been utilized by some researchers [47-50].
Table: 4.1. Summary of experimental studies of thermal conductivity
Enhancement
Particle
Type
Base Fluid Particle
Volume
Fraction (%)
Particle Size
(nm)
Maximum
Enhancem
ent (%)
Notes
Masuda
et al.[3]
Al2O
3
SiO2
TiO2
water
water
water
1.30–4.30
1.10–2.40
3.10–4.30
13
12
27
32.4
1.1
10.8
31.85ºc -
86.85ºc
Lee et al.
[32]
Al2O
3
CuO
water / EG
water / EG
1.00–4.30 /
1.00–5.00
1.00–3.41 /
1.00–4.00
38.4
23.6
10 / 18
12 / 23
Room
temperature
Wang et al.
[28]
Al2O
3
Al2O
3
CuO
water / EG
EO/PO
water / EG
3.00–5.50 /
5.00–8.00
2.25–7.40 /
5.00–7.10
4.50–9.70 /
6.20–14.80
28
28
23
16 / 41
30 / 20
34 / 54
Room
temperature
Eastman
et al.[7] Cu EG 0.01–0.56 < 10 41 Room
temperature
Xie et al.
[51]
SiC
SiC
water / EG
water / EG
0.78–4.18 /
0.89–3.50
1.00–4.00
26 sphere
600
cylinder
17 / 13
24 / 23
Effect of
particle shape
and size is
examined.
66
Xie et al.
[40] Al
2O
3
Al2O
3
water / EG
PO/glycerol
5.00
5.00
60.4
60.4
23 / 29
38 / 27
Room
temperature
Das et al.
[11] Al
2O
3
CuO
water
water
1.00–4.00
1.00–4.00
38.4
28.6
24
36 21ºC - 51ºC
Murshed
et al.[33] TiO
2
TiO2
water
water
0.50–5.00
0.50–5.00
15 sphere
10x40 rod
30
33 Room
temperature
Hong
et al.[58] Fe EG 0.10–0.55 10 18
Effect of
clustering
was
investigated
Li and
Peter son
[12] Al2O
3
CuO
water
water
2.00–10.00
2.00–6.00
36
29
29
51
27.5ºC –
34.7ºC
28.9ºC –
33.4ºC
Chopkar
et al.[35]
Al2Cu
Ag2Al
water/EG
water/EG
1.00–2.00
1.00–2.00
31/68/101
33/80/120
96/76/61
106/93/75
Effect of
particle size
was
examined.
Beck
et al.
[27]
Al2O
3
Al2O
3
water
EG
1.86–4.00
2.00–3.01
8 – 282
12 – 282
20
19
Effect of
particle size
was
examined.
Minst
et al.[46]
Al2O
3
CuO
water
water
0–18
0–16
36 / 47
29
31/31
24
20ºC – 48ºC
Turgut
et al.[54]
TiO2 water 0.2–3.0 21 7.4 13ºC – 55ºC
Choi
et al., [34] MWCNT PAO 0.04–1.02 25x50000 57 Room
temperature
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Assael
et al., [36] DWCNT
MWCNT
water
water
0.75–1.00
0.60
5 (diameter)
130x10000
8
34
Effect of
sonication
time was
examined.
Liu
et al., [42] MWCNT EG / EO 0.20–1.00 /
1.00–2.00
20~50
(diameter)
12/30 Room
temperature
Ding
et al., [24] MWCNT water 0.05–0.49 40 nm
(diameter)
79 20ºC – 30ºC
a
EG: ethylene glycol, EO: engine oil, PO: pump oil, TO: transformer oil, PAO:
polyalphaolefin
b
The percentage values indicated are according to the expression 100(knf
- kf) / k
4.3 PREPARATION OF GRAPHENE NANOFLUID (WORKING SAMPLE):
In the present study the single step method is used to prepare Graphene
nanofluid sample,
4.3.1 PREPARATION OF BASE FLUID
Water is the heat transfer medium for all heat exchangers in general, because
of its availability and good thermo physical properties. Since water cannot be used
below 4ºc at normal temperatures and pressures another liquid is mixed to lower its
freezing point. Ethyl glycol is the popular anti freezing agent investigated by many
researchers. In the present work 70% water + 30% ethylene glycol by volume fraction
is chosen as base fluid. To prepare one litre of base fluid (700ml water+300ml
ethylene glycol) is stirred well and used.
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4.3.2 PREPARATION OF GRAPHENE NANOFLUID
Fig 4.1: Flow chart shows the preparation of Graphene nanofluid
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The Graphene nanoparticles with two different shapes i.e. cylindrical and
sphere types are chosen with different particle diameters as 10nm, 20nm, 25nm,
50nm, 75nm are selected. The necessary weight for a volume ratio is calculated as per
the relation given below and the required quantity of the Graphene particles is mixed
with the base fluid (70% water + 30% ethylene glycol). One of the major problems
encountered in the preparation of nanofluid is uneven mixing of solid nanoparticles in
the base fluid As such sonification is to be done using surfactants and ultrasonic
vibrator to ensure uniform mixing, surfactants used for sonification are listed in table
4.3 & 4.4,
Volume concentration
/100 n
n
C
C basefluid
w
w w
(4.1)
Ø is the percentage of volume concentration,
ρCn is the density of Graphene nanoparticles (2230 kg/m3), [ Brick Nano technology
centre]
Wbase fluid is the weight of base fluid (100g),
WCn is the weight of Graphene nanoparticles
Table: 4.2: Weight volume ratio of Graphene nanoparticles
S.No. Volume of
Nanoparticles (ml)
Weight of Graphene
Nanoparticles (g)
1 0.2% 1.6110
2 0.4% 2.2551
3 0.6% 3.4364
4 0.8% 4.6210
5 1.0% 5.2210
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Fig: 4.2 A View of Digital Weighing Machine
Table: 4.3: Observations for Graphene (Cn) nanofluids,
Wt% Base fluid pH Observations after 2months
1 WEG Not adjusted Stable
6 WEG Not adjusted Stable
9 WEG Not adjusted Stable
1 WEG Not adjusted Stable
1 WEG Not adjusted Stable for 2 weeks
6 WEG Not adjusted 1mm sediment
9 WEG Not adjusted Very thin sediment
1 WEG 6 Stable
1 WEG Not adjusted Stable for 2 weeks
6 WEG Not adjusted Very thin sediment
9 WEG Not adjusted Very thin sediment
1 WEG 6 Stable
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The ultra sonic vibrator used for sonification is shown in fig 4.3
Fig: 4.3: A View of Ultra sonic vibrator set up
4.3.3 Ultrasonic vibration
All the stated methods try to modify the surface properties of suspended
nanoparticles and to squash forming clusters of particles, with the aim of achieving
uniform and constant suspensions. Ultrasonic bath, homogenizer and processor are
controlling apparatus for breaking down the clusters in comparison with the others
like high shear stirrer and magnetic stirrer as practised by investigators. Still rarely
after departing the optimized period of the progression, it will trigger major crucial
problems in agglomeration and clogging ensuing in quick sedimentation. In addition,
there is a new technique to get constant suspensions projected by Hwang et al. [9]
which contains two micro-channels, separating a liquid stream into two streams. Both
streams are then mixed in a reacting chamber. Violating the clusters of nanoparticles
was analysed using the high-energy of cavitations. This graft was carrying out for
Graphene (Cn) with water + EG nanofluids. When the suspension makes contact with
the interior walls of the contact chamber, it will pass into the micro channel.
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Consequently the flow velocity of the suspension through the micro channel should be
enhancing according to Bernoulli’s theorem and all together cavitations take place. In
this fast flow section, particle clusters must be destroyed by the grouping of various
mechanisms, including (i) strong and irregular shock on the wall inside the interaction
chamber, (ii) micro bubbles formed by Cavitation- provoked exploding energy and
(iii) high shear rate of flow. This directs to attain harmonized suspensions with
smaller amount aggregated particles at high-pressure. This method can be replicated
three times to attain the requisite homogeneous nanoparticles dispersal in the base
fluids. An ultrasonic disruptor is more commonly available equipment than the one
used by Hwang et al. [9]. Many investigators used this method to obtain a constant
nano suspension. In some situations, they employed various techniques of
stabilization to fine-tune the results.
4.3.4 Chemical surface modifications
Surface changing of the particle surface chemically is a useful method to build
up the strength of nanoparticles in various liquid media. On adjusting the oxide
nanoparticles surface, silane coupling agent, which has 1~3 alkoxy groups and 3~1
organic functional groups, are utilized since 1960s. Metal-OH group on the particle
surface is treated as a reaction site. The primary objective of the silane coupling
agents was to develop the compatibility of hydrophilic particle surface with
hydrophobic polymer surface by familiarizing various organic functional groups on
particle surface. The surface alteration of nanoparticles by silane coupling agents is
also helpful to develop the diffusion stability in organic media. The basic example is
implanting various polymers on particle surface by using silane coupling agents.
Normally, various reactive groups such as amines, epoxides and vinylsare initially
introduced on the particle surface by silane coupling agents and then polymers or
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implant to the particle surface. Several radical polymers such as poly vinyl
pyrrolidione (PVP) can be embedded on vinyl functionalized particle surface. Radical
polymer brushes such as PMMA can also be grafted from the amino functionalized
shell by reversible addition fragmentation chain transfer polymerization (RAFT) 31.
The kind of solvents, pH and quantity adsorbed water on particles largely
influence to the chemisorbed content of silane coupling agents. Possessing an
imitation from this report, the surface of Graphene (Cn) with small quantity addition
of pH controlled gum Arabic. It was observed that when glyci doxy propyl tri
methoxy silane were customized with small quantity addition of gum Arabic, a
comparatively greater steric repulsive force was computed by colloid probe AFM
method whereas that tailored with small amount addition of ethyl glycol based water
infatuated small steric repulsive force. It was also stated that the scattering of particles
with large calculated steric force had lower viscosity and the silane network on the
particle exterior acts a vital role for recuperating the scattering stability. On
chemically modifying hydrophobic particles such as carbides and carbon associated
materials, it is essential to create the surface by a chemistry that demands the reaction
with the surface functional group on the particle surface. In argument of carbon
related particles, the unsaturated hydrocarbon which mainly connected to the desert of
graphite rings are one of the valuable functional groups. By concerning this
opportunity of radical results at the surface of carbon related particles, various
polymers can be also attached on the particle surface. There are examples of surface
modification methods which slightly respond with the graphite ring on the particle
surface. It is stated that bi radical groups such as nitrene compounds can respond with
double bonds on carbon connected materials. The particle surface can be adjusted by
employing several nitrenes with spontaneous functional groups such as amine,
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carboxyl and bromide groups. The use of 1, 3-dipolar cyclo count of
azomethineylides, which can be produced by reduction of an R-amino acid and an
aldehyde, are also related to fictionalization of carbon connected materials. In the
argument of post-synthesis surface changes, it is achievable to enhance the
distribution stability of nanoparticles in numerous solvents. Still there are large
difficulties in re dispersing them into solvents near to their initial particle size. This is
because nanoparticles sturdily collective when they were gathered as dried powder. In
direct to re scatter this combined dry powder into solvents near to their initial particle
size, as dropping the bead size down to 15-30 m, the clustered size diminished to their
initial particle size as about10 nm where the particles were still clustered when the
bead size was outsized than 100 nm in diameter. This process and other physical
techniques, for example, ultrasonic dispersion, can employ to re disperse several
nanoparticles into liquid media by the instantaneous dispensation of the surface
modification presented above and the bead milling.
Based on above discussed techniques, several nanoparticles comprising of
metals, sulphides, oxides and fluorides that are redispersible into many solvents can
be produced by In-situ surface modification methods. Differing, a large obscurity lies
in stipulations of engineering an in-situ surface modification method to carbon related
nanoparticles, since the particle creation temperature is extremely high. In spite of this
recently, there is several information on synthesis of carbon related materials those
scattered in solvents close to their primary particle size. The primary example is the
making of Carbogenic nanoparticles by thermal decaying of numerous ammonium
citrate salts such as octadecyl ammonium citrate salts and 2-(2-amonoethoxy)-ethanol
salts. It was stated that the citrate groups decays into Carbogenetic nanoparticles
while the organic ammonium salts works as a surface modifier. Hydrophilic and
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hydrophobic Carbogenic nanoparticles about 7 nm were made by using octadecyl
ammonium salts and 2-(2-amonoethoxy)-ethanol salts, correspondingly. Another case
is the treatment of laser irradiation method. Graphite powders were distributed into
PEG and: YAG laser was irradiated to the suspension. After 2 hours of irradiation, the
suspension was centrifuged and the resulted supernatant contained PEG tailored
Graphene nanoparticles whose diameter was about 10 nm.
The surfactant ceilings nanoparticles which were manufactured by in-situ
surface modification process can also further be tailored in instruct to tune their
surface properties. Which exchanges the sealing surfactant, is a normally established
method and has a great benefit in controlling the particle surface by maintaining their
diffusion stability, the outside structure can be controlled by swapping various ceiling
agents which has thermo-sensitivity and that enhances compatibility with aqueous
solution, polymers, or bio molecules. For example, oleic acid soothes ferrite magnetic
nanoparticles were ligand replaced by different silane coupling agents which has
amine, carboxylic acid, or PEG group. After the ligand swapping procedure, ferrite
magnetic nanoparticles were able to redisperse in aqueous media without concentrated
aggregations. This ligand exchange by silane coupling agents can also employed to
various metals and oxides such as Au, Ag and Fe3O4. The exploit of mixed silane
alkoxides are also a helpful tool to harmony the surface properties for their
redispersing in numerous types of solvents. For an example, the surface of Graphene
(Cn) nanoparticles by mixed silane alkoxides with hydrophobic group
(decyltrimethoxysilane: DES) and hydrophilic group (3-aminoproyltrimethoxysilane:
APTMS). When Graphene (Cn) were only tailored by DES, the surface customized
particles were only redispersible into low polar solvents such as toluene whereas these
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turn into redispersible high polar solvents by changing the particles by DES and
APTMS.
Table: 4.4: The study of surfactants
Surfactant Amount (Wt% of
nanoparticle) Base fluid
Sonification.
time(hr) Result
Hydropalat 5040
1
0.5
0.1
0.5
WEG
WEG
WEG
WPG
4
4
4
4
2mm sediment
Thin sediment
1mm sediment
1mm sediment
Anti-Terra 250 0.5
0.5
PG-EG
WEG
4
4
Not soluble
Sedimentation,
foamy
Disperbyk-190
0
0.1
0.05
All
WEG
WEG
0
0.5
0.5
Very foamy in all
base fluids
Phases separated
Phases separated
Gum Arabic 0.1
0.05
WEG
WEG
0.5
0.5
Phases separated
Phases separated
Disponil A 1580
0.1
0.01
0.5
0.05
WEG
WEG
WEG
WEG
4
4
4
4
Foamy
Thin sediment
Thin sediment
Thin sediment
Hypermer LP1 0.1 WEG 4 Phases Separated
Aerosol TR-70 0.1
0.5
WEG
WEG
4
4
Foamy
Stable
Aerosol TR-
70HG
0.1
0.5
WEG
WEG
4
4
Foamy
Stable, Foamy
AerosolOT-70PG 0.1
0.5
WEG
WEG
4
4
Thin sediment
Stable, Foamy
By employing these methods, several reactive groups can be initiated on the
particle surface without formation of strong clusters. Since the particles are guarded to
be not clustered throughout the entire process, from the particle making to surface
modification process, it is a practical process to engineer the particle surface for
nanotechnology applications.
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Now the Graphene nanofluid is checked for its alkaline nature through a pH
meter as shown in fig 4.4, The prepared Graphene nanofluid has a range of
8.5<pH<10.5, The prepared Graphene nanofluid is stored in air tight container as
shown in fig 4.5.
Fig: 4.4: A View of Digital pH Meter Set Up
And the Graphene nanofluid with a mixture of 70% water + 30% EG is shown
in fig 4.5 after sonification,
Fig: 4.5: Samples of Graphene nanofluids after sonication
78
4.4 MEASURING THERMAL CONDUCTIVITY - EXPERIMENTAL
SET UP
In order to calculate the convective heat transfer characteristics of Graphene
nanofluid, first of all it is customary to calculate the thermal conductivity of Graphene
nanofluid, the experimental procedure adopted to measure the thermal conductivity of
fluid is by parallel plate method. The experimental set up, Experimental procedure
and the calibration of apparatus is as follows,
4.4.1 Experimental set-up
PARALLEL PLATE THERMAL CONDUCTIVITY APPARATUS
Fig:4.6: Thermal conductivity measuring apparatus
NOMENCLATURE SPECIFICATIONS
Guarded heater 400 Watts
Central heater 400Watts
Centre plate Copper 100mm dia
Guarded ring plate Copper inner dia 106mmOuter dia108mm
Temp sensor Cr-Al/PT 100 type
Temp indicator 0-300ºc,Multi channel digital display
Ammeter 0-5A,2no.s
Volt meter 0-230v,2no.s
Press wood 180mm
79
Fig: 4.7: Schematic of Thermal conductivity measuring apparatus
Description:
4.4.2 PARALLEL-PLATE APPARATUS DESIGN
The schematic of the PPTC apparatus with all components labelled and
relevant nomenclature is presented in Fig.4.7. The objective was to provide controlled
one-dimensional heating by conduction through a stationary test fluid specimen and
accurate measurements of relevant temperatures in order to ascertain accurate
measure of the fluid thermal conductivity. The main components are described one
after the other,
4.4.2.1 Test Fluid Specimen Cavity:
The test fluid specimen cavity (highlighted black on Fig.4.7) is a critical
component of the PPTC apparatus that houses the test fluid sample for measurement
80
of thermal conductivity. The top and bottom of the test fluid cavity are formed by the
parallel plates described. The faces of the parallel plates in contact with the test fluid
specimen have a high level of planarity and mirror-polished finish to minimize
measurement errors due to surface geometry imperfections of the parallel plates. The
side edge of the test fluid specimen cavity is centred by the upper and lower lips
located on both the upper and lower Teflon shells, In order to accurately measure the
thermal conductivity of the test fluid specimen, a well-defined heat transfer
mechanism consisting conduction only must be provided. This is accomplished by
two major design parameters. First, the Heater is above and the Chiller is below the
test fluid (the heat transfer is in the gravity direction) thus suppressing the convection
effects due to buoyancy. The second major design parameter is a very small thickness
of the test fluid specimen cavity, LF =1.21 mm. This prevents the convection from
developing within the test fluid specimen. Once the test fluid specimen is allowed to
the test fluid specimen cavity, any addition of extra heat flow in the vicinity is
arrested.
4.4.2.2 Parallel (Thermometry) Plates:
The parallel (thermometry) plates provide the plane surfaces that comprise the
top and bottom of the test fluid specimen cavity described above. These plates also
house the thermocouples used to measure a number of temperatures at different
locations, used to determine the temperature difference across the test fluid specimen,
as well as temperature uniformity in the other two directions, see Fig.4.7. One parallel
plate is press fit into the bottom of the upper assembly and one parallel plate is press
fit into the top of the lower assembly, resulting in one parallel plate on either side of
the test fluid specimen. The parallel plates are made from copper of thickness of 1/4th
inch. (6.35mm).Copper was the material for the parallel plates. One surface of each of
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the parallel plates facing the test specimen has a mirror finish. Each face of the
parallel plates facing away from the test fluid specimen has radial thermocouple
grooves, see Fig. 4.7. These grooves provide locations needed to place thermocouples
and clearance for thermocouple wires. There are three radial thermocouple grooves
evenly spaced around the circumference of each parallel plate. These grooves extend
from the centre to the outside edge of the parallel plates and are 0.2 inch (5.08mm)
wide and 0.02 inch (0.0508mm) deep. There are fifteen, 30-gauge T-type
thermocouples mounted on each parallel plate, with each thermocouple groove
containing five thermocouples. The thermocouple grooves are then filled with a high
thermal conductivity epoxy that isolates and holds the thermocouples in place.
Having a large number of evenly spaced thermocouples provides means to verify the
radial and circumferential temperature uniformity, needed for evaluation of heat
looses, if any and validation of one-dimensional heat transfer through the thickness of
the test specimen, as modelled by the working equation used for evaluation of the
thermal conductivity. In Fig. 4.7, the Teflon (Insulation) thermometry plate for
evaluation of heat losses from the top of the apparatus is also presented. The Teflon
thermometry plate is located above the Heater assembly; the purpose of the Teflon
thermometry plate is two-fold. First, the low thermal conductivity of the Teflon (0.35
W/m-K) provides extra insulation to the top of the Heater assembly. Second, the
thermocouples provide a means to calculate the heat loss through the top of the Heater
assembly. The Teflon thermometry plate is made of virgin electrical grade Teflon. It
is 4.50 inch (114.3mm) in diameter and has a thickness of 0.75 inch (19.05mm).
Thermocouples are attached on both sides of the Teflon thermometry plate and are
located in thermocouple grooves that are machined into each face of the Teflon
thermometry plate.
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4.4.2.3 Heater Design:
The Heater generates the heat flux and thus the temperature difference across
the test fluid specimen. The Heater is made of a resistance wire that is formed into a
spiral and sandwiched between two copper plates to equalize radial and
circumferential temperature distribution. The resistance wire of 55% copper and 45%
nickel with a diameter of 0.036 inch has Teflon insulation. The resistance is
approximately 0.227 ohms per foot, resulting in the total of the Heater wire resistance
of 4.21 ohms. The plates made from 145 tellurium copper alloy of (400 W/m-K
thermal conductivity) are chosen to ensure that the heat generated by the Heater wire
will be evenly distributed across the entire surface of the test fluid specimen. The top
copper plate is a 0.375inch (9.525mm) thick circular disc with 100mm diameter. The
Heater wire is wrapped spirally around the post in the bottom copper plate, providing
an evenly distributed heating and the two plates are screwed together creating a single
Heater assembly. The Heater assembly and the Teflon thermometry plate are press fit
into a Teflon shell, creating the upper assembly of the apparatus. Teflon is used for
the Heater assembly housing for three reasons. First, the Teflon provides sufficient
rigidity for the press fitting of the Heater assembly. Second, the low thermal
conductivity of Teflon provides insulation, reducing the amount of heat lost to the
surroundings. Finally, the Teflon provides for easy cleaning of the apparatus. The
upper Teflon shell has an outer diameter of 6.00 inch (152.4mm) and an overall height
of 2.58 inch (65.532mm). It also has a raised lip (0.25 inch (6.35mm) deep and 0.25
inch (6.35mm) thick) at the bottom surface. This lip helps to centre the upper
assembly when it is placed on the lower assembly. It also forms the outer side of the
test fluid specimen cavity. Finally, the upper assembly is covered with a polystyrene
shell. This shell provides a 0.75 inch (19.05mm) thick layer of insulation around the
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entire upper assembly. The polystyrene shell has an extremely low thermal
conductivity of approximately 0.027 W/m-K and further minimizes the heat loss to the
surrounding.
4.4.2.4 Chiller Design:
The Chiller forms the lower assembly of the apparatus and utilizes cold water
as its cooling medium, see Fig.4.7 a channel made from aluminium is designed to
guide the cooling water around the lower assembly and provide even removal of the
heat generated by the Heater. The basic shape of the fluid channel is spiral-like, with
the water entering the Chiller close to the centre and leaving at the outer edge, thus
enabling more uniform circumferential temperature. The fluid channel has an outer
circumference of 4.50 inch (114.3mm) and a depth of 0.50 inch (12.7mm). The
channel walls are 0.08 inch (2.032mm) thick, providing sufficient rigidity. The Chiller
is also comprised of a copper plate that forms the top of the Chiller assembly and
provides even heat transfer to the Chiller fluid. The material and dimensions of the
Chiller copper plate are identical to those of the upper Heater copper plate. The
Chiller fluid channel and Chiller copper plate are press fit into a Teflon shell, creating
the lower assembly of the apparatus, nearly identical to the upper Teflon shell.
4.5 MATHEMATICAL CALCULATION
The schematic of the PPTC apparatus with all components labelled and
relevant nomenclatures is presented in Fig 4.7. The objective was to provide
controlled one-dimensional heating by conduction through a stationary test fluid
specimen. The assembly ensures a simple one dimensional heat conduction through
parallel sections. With the assumption of one dimensional flow the following can be
utilised to calculate the fluid thermal conductivity.
84
2
FF
H C CC
X CC
LK
T T LA
Q K A
(4.2)
A = Surface area (sq-m) (in this case same as cross sectional area)
LF = Test fluid specimen thickness between two plates (mm)
LCC= Thickness of copper plates (mm)
KCC= Thermal conductivity of copper plates (W/m-K)
X EH lossQ Q Q (4.3)
Typically in PPTC apparatus the QEH is calculated by
2
heaterEH
heater
VQ
R (4.4)
where Qlosses comprises of two components loss through convection from top surface
of Teflon shell and radiation from top surface. Since the temperature on the Teflon
shell surface is very nearly the surrounding temperature, the loss is estimated to be
less than 1%. The Vheater and Rheater are measured voltage across and the calibrated
resistance of the Heater wire. The TH and TC are representative temperatures at upper
and lower parallel thermometry plates.
85
4.6 CALIBRATION OF THE INSTRUMENT (THERMAL CONDUCTIVITY
APPARATUS)
To check the validity of the instrument calibration test is done upon the set up,
considering the normal conventional base fluid (DI water) de-ionized distilled water
as a test fluid, calibration test is performed.
Table: 4.5: THERMAL CONDUCTIVITY OF WATER MEASURED USING
THE APPARATUS
S.No TEST
FLUID
TEMPERATURE
(ºC)
THERMAL
CONDUCTIVITY (K)
W/mK
THERMAL
CONDUCTIVITY (K) W/mK
FROM DATA BOOK(Heat and
Mass Transfer Data Book, New
Age International Publisher)
1 WATER 40 0.6199 0.6280
2 WATER 50 0.6354 0.63965
3 WATER 60 0.6498 0.6513
4 WATER 70 0.6576 0.6600
5 WATER 80 0.6623 0.6687
6 WATER 90 0.6685 0.67455
MODEL CALCULATION:
From Eq (4.2) KF is calculated as follows
4
1.21
40 28 2 0.06358824.7
5.4243 10 386 8824.7
FKX
X X
0.6199W/ mk,
86
Fig: 4.8: Graph shows the Experimental Values vs Data book values of water
The calibration chart shows that the experimental values are very close to the
exact values taken from data hand book with a minor deviation of 0.8%.
Table: 4.6: THERMAL CONDUCTIVITY FOR BASE FLUID (70%WATER
+30% EG) USING THE APPARATUS
S.No Test Fluid Voltage
(V)
volts
TC ºC TH ºC Thermal
Conductivity(K)
W/mK
1 Base Fluid 70 28 30 0.43265
2 Base Fluid 70 28 40 0.44195
3 Base Fluid 70 28 50 0.448575
4 Base Fluid 70 28 60 0.45535
5 Base Fluid 70 28 70 0.460275
6 Base Fluid 70 28 80 0.5466
7 Base Fluid 70 28 90 0.55086
MODEL CALCULATIONS:
From Eq 4.2 KF is calculated as follows
1.210.43265
30 28 2 0.06358824.7
6310.0102 386 8824.7
FK
W/mK,
0.5
0.6
0.7
0.8
0 20 40 60 80 100
The
rmal
Co
nd
uct
ivit
y (K
) W
/mk
Temperature(ºc)
Data book value
Experimental value
87
Table: 4.7: THERMAL CONDUCTIVITY OF NANOFLUID (70%WATER
+30% EG+GRAPHENE 20nm) (1% VOL) USING THE APPARATUS
S.No Nanofluid Voltage
(V) volts
Volume
added
(ml)
THºC TCºC Thermal
conductivity(K)
W/mK
1 Graphene 70 1% 30 28 0.45428
2 Graphene 70 1% 40 28 0.46846
3 Graphene 70 1% 50 28 0.47997
4 Graphene 70 1% 60 28 0.49633
5 Graphene 70 1% 70 28 0.51090
MODEL CALCULATIONS:
From (Eq 4.2) Knf is calculated as follows
,
1.210.4542825
30 28 2 0.06358824.7
6625.47 386 8824.7
nfK
W/mK,
Table: 4.8: THERMAL CONDUCTIVITY OF NANOFLUID (70%WATER
+30% EG+GRAPHENE 20nm) (2%VOL) USING THE APPARATUS
S.No Nanofluid Voltage
(V)
Volts
Volume
added
(ml)
THºC TCºC Thermal
conductivity(
K) W/mK
1 Graphene 70 2% 30 28 0.47158
2 Graphene 70 2% 40 28 0.49056
3 Graphene 70 2% 50 28 0.50240
4 Graphene 70 2% 60 28 0.51909
5 Graphene 70 2% 70 28 0.52931
88
Table: 4.9: THERMAL CONDUCTIVITY OF NANOFLUID (70%WATER
+30% EG+GRAPHENE 20nm) (3%VOL) USING THE APPARATUS
S.No Nanofluid Voltage
(V)
Volts
Volume
added
(ml)
TH ºC TC ºC Thermal
conductivity(K)
W/mK
1 Graphene 70 3% 30 28 0.48889
2 Graphene 70 3% 40 28 0.50824
3 Graphene 70 3% 50 28 0.52034
4 Graphene 70 3% 60 28 0.53731
5 Graphene 70 3% 70 28 0.55233
Table: 4.10: THERMAL CONDUCTIVITY OF NANOFLUID (70%WATER
+30% EG+GRAPHENE 20nm) (4%VOL) USING THE APPARATUS
S.No Nanofluid Voltage
(V)
Volts
Volume
added
(ml)
TH ºC TC ºC Thermal
conductivity(K)
W/mK
1 Graphene 70 4% 30 28 0.50187
2 Graphene 70 4% 40 28 0.52150
3 Graphene 70 4% 50 28 0.53829
4 Graphene 70 4% 60 28 0.55552
5 Graphene 70 4% 70 28 0.57074
As the volume fractions of Graphene nanoparticles increases from 1% to 4%
consecutively thermal conductivity is also increases even though the input electrical
energy is same.
4.7 Parameters that show major effect on thermal conductivity of nanofluids
Experimental studies show that thermal conductivity of nanofluids depends on
many factors such as particle volume fraction, particle material, particle size, particle
shape, base fluid material and temperature. Amount and types of additives and the
acidity of the nanofluid were also shown to be effective in the thermal conductivity
89
enhancement [37]. In the following sections, experimental studies about the thermal
conductivity of nanofluids are summarized. In each case, a specific parameter that is
effective on thermal conductivity is discussed.
1. Nanoparticles volume fraction
2. Nanoparticle Material
3. Conventional Base fluid
4. Nanoparticle size
5. Nanoparticles shape
6. Temperature
7. Nanofluid Clustering
8. pH value
4.7.1 Nanoparticles volume fraction
There are numerous studies in the literature about the effect of nanoparticles
volume fraction, which is the volumetric strength of the nanoparticles in the
nanofluid, upon the thermal conductivity of nanofluids. A linear correlation exists
between thermal conductivity and particle volume fraction (thermal conductivity
increases with particle volume fraction). Thermal conductivity enhancement is found
in nanofluids with Al2O
3 (28 nm) and CuO (23 nm) nanoparticles. For the case of 8%
Vol. Al2O
3/water nanofluid, thermal conductivity improvement as high as 30% was
achieved [37, 47, 3] for water and ethylene glycol-based nanofluids, thermal
conductivity ratio showed a linear relationship with particle volume fraction. Particle
volume fraction is a parameter that is investigated in almost all of the experimental
studies and the results are usually in agreement qualitatively. Most of the researchers
report increasing thermal conductivity with increasing particle volume fraction and
the relation found is usually linear,[51,52]
90
However, there are also some studies which indicate nonlinear behaviour. An
example is the study made by Murshed et al. [52]. They measured the thermal
conductivity of TiO2/deionised water nanofluid at room temperature by using
transient hot-wire method. Volume fraction of nanoparticles was varied between 1%
and 5%. A nonlinear relationship was observed between thermal conductivity ratio
and particle volume fraction, in particularly at low volume fractions.
4.7.2 Nanoparticle Material
Majority of the studies illustrate that particle material is a significant
constraint that affects the thermal conductivity of nanofluids. At first glimpse, it might
be deliberation that the discrepancy in the thermal conductivities of nanoparticle
materials is the key basis of this effect. However, studies show that nanoparticle type
may influence the thermal conductivity of nanofluids in many ways. The thermal
conductivity of nanofluids with CuO and Al2O
3 nanoparticles as indicated in the
previous section and they bring up that nanofluid with CuO nanoparticles showed
improved augmentation when compared to the nanofluids prepared by Al2O
3
nanoparticles. It should be distinguished that Al2O
3 has elevated thermal conductivity
than CuO. Therefore, thermal conductivity of nanoparticle material may not be the
governing parameter that determines the thermal conductivity of the nanofluid.
According to the authors, the basis feature is the fact that Al2O
3 nanoparticles shaped
moderately outsized clusters. When compared to CuO nanoparticles. [54] That may
be a clarification if the key mechanism of thermal conductivity enhancement is
acknowledged to be the Brownian motion of nanoparticles, since the effect of
Brownian motion diminishes with increasing particle size. However, it must also be
noted that there are some studies that consider the clustering of nanoparticles as a
thermal conductivity augmentation mechanism.
91
The appearance of nanoparticle type was made dispersed Ag2 Al and Al2 Cu
nanoparticles into water and ethylene glycol. 1 vol. % oleic acid was used as the
surfactant. Observations were made at room temperature. It was noticed that Ag2 Al
nanoparticles enhanced thermal conductivity considerably more when compared to
Al2 Cu nanoparticles. According to the authors, this is due to the fact that the thermal
conductivity of Ag2 Al is higher when compared to Al2 Cu Effect of particle material
is much more distinct when carbon nanotubes are used for the making of nanofluids
[54, 53, 55],
4.7.3 Conventional Base fluid
According to the conventional thermal conductivity models as the base fluid
thermal conductivity of blend decreases, the thermal conductivity ratio (thermal
conductivity of nanofluid (knf
) divided by the thermal conductivity of base fluid (kf)
increases. When it comes to nanofluids, the situation is more difficult due to the fact
that the viscosity of the base fluid influences the Brownian motion of nanoparticles
and that sequentially affects the thermal conductivity of the nanofluid, the
consequence of electric dual layer forming around nanoparticles on the thermal
conductivity of nanofluids and showed that the thermal conductivity and width of the
layer depends on the conventional base fluid.
Nanoparticles were used to make nanofluids with several conventional base
fluids; ethylene glycol, water, engine oil and vacuum pump fluid. With Al2O
3
nanoparticles, the maximum thermal conductivity ratio was experienced when
ethylene glycol was used as the conventional base fluid. With CuO nanoparticles [59,
56, 54]. Engine oil showed somewhat poor thermal conductivity ratios than ethylene
glycol. Only ethylene glycol and water based nanofluids were prepared and, they
showed precisely the same thermal conductivity ratios for the same particle volume
92
fraction. The effect of the base fluid on the thermal conductivity of nanofluids was
also analyzed. Nanofluids with Al2O
3 nanoparticles were primed by using different
conventional base fluids i.e. glycerol, deionised water, pump oil and ethylene glycol.
In addition glycerol-water and ethylene glycol-water mixtures with different volume
fractions were also used as conventional base fluids and the discrepancy of the
thermal conductivity ratio with thermal conductivity of the conventional base fluid
mixture was studied. It was concluded that, thermal conductivity ratio decreased with
increasing thermal conductivity of the base fluid. Thermal conductivity of nanofluids
were calculated by a transient hot-wire method. 1% vol MWCNT/ethylene glycol
nanofluid gives 12.4% thermal conductivity improvement, whereas for 2% vol
MWCNT/synthetic engine oil nanofluid, improvement was 30%. It was observed that
higher improvements were achieved with a combination of composite fluid like 70%
water + 30% ethylene glycol as the conventional base fluid, in common several types
of conventional base fluids are available, some of the experimental studies used a
mixture of water and ethylene glycol was used for more efficient calculations of
thermal conductivity and thermal convection [58, 57, 47].
4.7.4 Nanoparticle size
Particle size is another important constraint on thermal conductivity of
nanofluids. It is possible to prepare nanoparticles of various sizes, commonly ranging
between 5nm to 100 nm. By using one-step production technique, suspensions with
Cu nanoparticles smaller than 10 nm were obtained. Thioglycolic acid less than 1 vol.
% was mixed to some of the samples for stabilizing purposes and those samples gave
much better improvement when compared to samples without Thioglycolic acid. A
40% enhancement in thermal conductivity was experienced at a particle volume
fraction of 0.3% (with Thioglycolic acid). The investigators obtained 22%
93
improvement with 4 vol. % CuO (23.6 nm)/ethylene glycol nanofluid. As a result of
the uncharacteristic improvement obtained, it is understood that the size of the
nanoparticles is a significant feature in thermal conductivity improvement this is
different to the conclusions of conventional models [22, 37],
Hamilton and Crosser model [18], which does not take the influence of
particle size on thermal conductivity into account. They changed the nanoparticle size
between 10 and 80 nm and they intimated that thermal conductivity improvement
decreases with increasing nanoparticle size. For 0.5 vol. % nanofluid, thermal
conductivity enhancement decreased from 36 to 3% by increasing the particle size
from 10 to 80 nm. It was concluded that thermal conductivity enhancement increases
with decreasing particle size. [63, 14, 62, 46, 54]
This effect is more prominent for nanofluids with particles smaller than 50
nm. As a result of the experimental conclusions, it was declared that nanoparticle
thermal conductivity decrease with decreasing particle size is liable for the observed
size dependence of the thermal conductivity of nanofluids. It should be observed that
these results are not in consistency with afore mentioned investigations. The results
also disagree with the effect of Brownian motion, since the effect of Brownian motion
decreases with increasing particle size, which reduces the associated thermal
conductivity improvement. The common drift in the tentative data is that the thermal
conductivity of nanofluids enhances with decreasing particle size. This result is
theoretically supported by two mechanisms of thermal conductivity improvement;
liquid layering around nanoparticles and Brownian motion of nanoparticles [37].
However, there is also a considerable amount of conflicting data in the literature that
specify decreasing thermal conductivity with decreasing particle size. In fact, for the
94
case of nanofluids with Graphene (Cn)
the results showing increasing thermal
conductivity with decreasing particle size are more common [61, 18, 60 and 51].
4.7.5 Nanoparticles shape
There are mostly two particle shapes used in nanofluid research; cylindrical
particles and spherical particles. Cylindrical particles generally have a large length-to-
diameter ratio. It was found that 4.5 vol. % water-based nanofluids with spherical
particles had a thermal conductivity enhancement of 35.8%, where as 4 vol. %
nanofluids with cylindrical particles had a thermal conductivity enhancement of
37.9%. Stability and dispersion of nanoparticles were improved by using oleic acid
and CTAB surfactants. For nanofluids with spherical particles, a maximum
enhancement of 29.7% was obtained at 5 vol. %. At the same volume fraction, rod-
shaped nanoparticles showed a development of 32.8%.
In addition to these experimental results, the fact that nanofluids with carbon
nanotubes (which are cylindrical in shape) generally show greater thermal
conductivity enhancement than nanofluids with spherical particles should also be
considered. As a result, one can conclude that cylindrical nanoparticles provide higher
thermal conductivity enhancement than spherical particles. One of the promising
reasons of this is the rapid heat transfer along relatively larger distances in cylindrical
particles since cylindrical particles usually have lengths of the order of micrometers
[37]. However, it should be noted that nanofluids with cylindrical particles usually
have much high viscosities than those with spherical nanoparticles [64]. As a result,
the increase in pumping power is large and this reduces the possibility of usage of
nanofluids with cylindrical particles and spherical particles.
95
4.7.6 Temperature
In conventional suspensions of solid particles (with sizes of the order of
millimetres or micrometers) in liquids, thermal conductivity of the mixture depends
on temperature only due to the dependence of thermal conductivity of base liquid and
solid particles on temperature [26]. However, in case of nanofluids, change of
temperature affects the Brownian motion of nanoparticles and clustering of
nanoparticles, which results in dramatic changes of thermal conductivity of nanofluids
with temperature. Masuda et al. [3] measured the thermal conductivity of water-based
nanofluids containing Al2O3, SiO2 and TiO2 nanoparticles at different temperatures.
Thermal conductivity ratio decreased with increasing temperature, which is contradictory
to many other findings in the literature. The temperature dependence of the thermal
conductivity of Al2O3 (38.4 nm)/water and CuO (28.6 nm)/water nanofluids was studied
by Das et al. [15]. Thermal diffusivity was measured by using a temperature oscillation
technique and then thermal conductivity was calculated. Several measurements were
made at different temperatures varying between 21°C and 51°C. It was seen that for 1%
vol Al2O3/water nanofluid, thermal conductivity enhancement increased from 2% at
21°C to 10.8% at 51°C. While the Temperature dependence of 4% vol Al2O3 nanofluid
was much more significant i.e., from 21°C to 51°C, enhancement increased from 9.4 to
24.3%. A linear relationship between thermal conductivity ratio and temperature was
observed for both 1% and 4% vol cases.
Li and Peterson [20] also investigated the effect of temperature on thermal
conductivity of CuO (29 nm)/water and Al2O
3 (36 nm)/water nanofluids. For both
nanofluid types, it was observed that at a constant particle volume fraction thermal
conductivity ratio increased with temperature. In addition, it was noted that for
Al2O
3/water nanofluid, the dependence of thermal conductivity ratio on particle volume
96
fraction became more pronounced with increasing temperature. For the Al2O
3/water
nanofluid and CuO/water nanofluid, two correlations were proposed for the determination
of the thermal conductivity. Nanofluids used in the experiment were prepared by a two-
step method and ultrasonic vibration was applied to the samples. 3ω method was used in
the measurements. Measurements were made at different temperatures; 13, 23, 40 and
55°C. Particle volume fraction of the sample nanofluids were varied between 0.2 and
3%vol. It was noted that the results of the analysis can be well predicted by conventional
theoretical models such as Hamilton and Crosser model [18]. It was also observed that
thermal conductivity ratio does not vary with temperature significantly. This observation
is contradictory with the aforementioned studies. The results can be considered as an
indication of the importance of the usage of surfactants in nanofluids, because no
surfactant was used in this study.
Temperature dependence of thermal conductivity of nanofluids was also
investigated for the case of nanofluids with carbon nanotubes. Ding et al. [43] measured
the thermal conductivity of MWCNT/water nanofluid. Ultrasonic vibration was applied to
samples. First Gum Arabic was added to the samples in order to obtain better dispersion
and to adjust the pH value; the nanofluid was homogenized with a high shear
homogenizer. Transient hot-wire method was applied for thermal conductivity
measurements. No information was given about the size of MWCNT but from the
provided scanning electron microscopy images, a very rough estimation of nanotube
diameter could be made as 40 nm. Measurements were made at three different
temperatures; 20, 25 and 30°C. Particle weight fraction was varied between 0.1 and 1%. It
was found that thermal conductivity ratio increases with both particle volume fraction and
temperature. However, at 20 and 25°C, increase of thermal conductivity ratio with
particle volume fraction stopped after 0.5 wt%. On the other hand, at 30°C, thermal
conductivity ratio continued to increase after 0.5 wt%. A maximum enhancement of 80%
97
was achieved at 30°C for 1 wt% of MWCNT/water nanofluid. At 20°C, the associated
enhancement decreased to 10%.
4.7.7 Nanofluid Clustering
Clustering is the development of larger particles due to aggregation of
nanoparticles. Clustering effect always exists in nanofluids and it is a significant
parameter in thermal conductivity. The thermal conductivity of nanofluids was
affected by the period of time of application of ultrasonic vibration, which was varied
between 0 min, that is, no ultrasonic vibration applied and 80 min. It was observed
that thermal conductivity ratio enhanced with increasing vibration time and the rate of
this growth became smaller for longer vibration time. Furthermore, the variation of
thermal conductivity of nanofluid with time after the treatment of vibration was
investigated and it was identify that thermal conductivity decreased as time increased.
Deviation of average size of clusters was also determined as a function of time after
the treatment of vibration and it was identified that cluster size increases with time.
As a result of these observations, it was concluded that the size of the clusters
generated by the nanoparticles had a key control on the thermal conductivity. It was
assured that this nature is due to the fact that nanoparticles in the nanofluids with high
volume fractions formed clusters at a higher rate.
4.7.8 pH value
More number of studies about the pH value of nanofluids is limited when
compared to the studies concerning the other parameters. The measured thermal
conductivity of nanofluids, which are prepared by scattering Graphene(Cn)
nanoparticles into water, pump oil and ethylene glycol; they reported considerable
decrease in thermal conductivity ratio with increasing pH values. It was observed that
the rate of change of thermal conductivity with particle volume fraction was
98
dependent on pH value. The effect of pH on the thermal conductivity of nanofluids
was considered in Al2O3/water and Cu/water nanofluid, with sodium dodecylbenzene
sulphonate, added as the dispersant. They obtained optimum values of pH
(approximately 8.0 for Al2O3/water and 9.5 for Cu/water nanofluids) for high thermal
conductivity enhancement. It should also be remembered that the thermal
conductivity of conventional base fluid does not change considerably with pH. The
authors related the observed phenomenon to the fact that at the optimum value of pH,
surface charge of nanoparticles increases, which generates repulsive forces between
nanoparticles. As a result of this effect, severe clustering of nanoparticles is
prevented,
4.8 Conventional Models
The conventional models are listed that measure the thermal conductivity of
different types of nanofluids
1. Max Well model
2. Hamilton & Crosser model
3. Xue & Xu model
4. Koo & Kelniester model
5. Jang & Choi model
4.9. Thermal Conductivity Models
4.9.1. Nanoparticle Volume Fraction
conclusions of some of the afore mentioned thermal conductivity models are
compared with the tentative data of four research groups [51,15,69,70] Graphene
(Cn)/water+ ethylene glycol nanofluid is chosen; all of the experimental data were
obtained in the region of 50ºc temperature. Standard particle diameter is taken as 20
nm in the models since the particle sizes in the experiments are close to that value, as
99
shown in the figures. Therefore, it may be predicted that those samples are closer to
the legality range of the Hamilton and Crosser model.
4.10 ESTIMATING THERMAL CONDUCTIVITY BY USING
(HAMILTON&CROSSER MODEL)
Belief upon the theoretical models on particle size is analysized with
experimental data Figs. 4.9-4.10, for Graphene (Cn)/water+EG nanofluids. In the
figures, lines shown are experimental data. Experimental data are around 50ºc
temperature and 50ºc temperatures is substituted for model calculations. Linear
interpolation was practical to some of the experimental data for formative thermal
conductivity ratio at integer values of particle volume fraction. Since a virtually linear
relationship exists between thermal conductivity ratio and particle volume fraction,
coupled errors are not usual to be large.
As seen from the figures, there is considerable inconsistency in tentative data.
However, the common trend is raising thermal conductivity with growing particle
size. While this inclination is the case for nanofluids with Graphene (Cn)
nanoparticles, when generally trend is considered for several types of nanofluids, it is
observed that thermal conductivity usually increases with reducing particle size. At
this point, it should be noted that thermal conductivity rises with reducing particle size
when Brownian motion is taken into account as the main mechanism of thermal
conductivity improvement, because the drift of Brownian motion elevated with
reduction in particle size, which enhances micro-convection throughout nanoparticles.
Similar is true for the development of liquid layers around nanoparticles as an
augmentation mechanism, because the enrichment effect of nanolayers rises with
increasing particular exterior area of nanoparticles. Because specific surface region of
nanoparticles is superior in case of slighter particles, reducing particle size increases
100
the thermal conductivity enrichment according to the models, which are based on
inter facial liquid layering. It is considered that the conflicting style in the marks of
nanofluids with Graphene (Cn) nanoparticles may be due to the irregular clustering of
nanoparticles,
The Hamilton and Crosser model do not take the consequence of particle size
on thermal conductivity into consideration, but it becomes somewhat charge on
particle size due to the statement that nanoparticle thermal conductivity raises with
increasing particle size according to Eq. (4.10). However, the method still is unable to
predict experimental data for particle sizes larger than 80 nm since particle size
craving diminishes with growing particle size.
MODEL CALCULATION:
The thermal conductivity of the specimen fluid is calculated by the following equation
( 1) ( 1) ( )
( 1) ( )
p f f p
nf f
p f f p
k n k n k kk k
k n k k k
(4.5)
Where3
n
, being Ψ is the sphericity. Sphericity is the ratio of the surface area of a
sphere with a volume equal to that of the nanoparticles, therefore Ψ=1 and n=3
kp is the thermal conductivity of particle and it is calculated by using the
Expression [18]
3 / 4,
3 / 4 1p b
rk k
r
(4.6)
Ø = Nanoparticles volume fraction = 3% (0.03)
kb is the thermal conductivity of bulk material,
r*= rp/λ where rp is the particle radius and λ is the mean free-path of phonons
λ = 35 [Brick Nano technology Centre, Purdue University]
For present case r* = 20nm/35nm =0.571,
101
3(0.571) / 438.5 48.126,
3(0.571) / 4 1pk
48.126 2(0.45865) 2(0.03)(0.45865 48.126)0.45865 0.504515 / ,
48.126 2(0.45865) (0.03)(0.45865 48.126)nfk W mk
Associated thermal conductivity ratio is
0.5045151.1 / ,
0.45865
nf
f
kW mk
k
Table: 4.11: Calculated results by using Hamilton & Crosser model.
S.No Particle
size
% volume
added Kf Knf Knf/Kf
1 4
1 0.45865 0.4815825 1.05
2 0.45865 0.486169 1.06
3 0.45865 0.495342 1.08
4 0.45865 0.504515 1.1
2 20
1 0.45865 0.4907555 1.07
2 0.45865 0.4999285 1.09
3 0.45865 0.504515 1.1
4 0.45865 0.513688 1.12
3 40
1 0.45865 0.4916728 1.072
2 0.45865 0.504515 1.1
3 0.45865 0.513688 1.12
4 0.45865 0.5274475 1.15
4 60
1 0.45865 0.4925901 1.074
2 0.45865 0.5091015 1.11
3 0.45865 0.522861 1.14
4 0.45865 0.532034 1.16
5 80
1 0.45865 0.4925901 1.074
2 0.45865 0.5091015 1.11
3 0.45865 0.522861 1.14
4 0.45865 0.532034 1.16
102
Fig.4.9: Calculated results of the thermal conductivity ratio for Graphene
(Cn)/water+EG nanofluid with Hamilton and Crosser model [18] as a function of
the particle size at various values of the particle volume fraction.1%, 2%, 3%,
4%,
From the above graph it is observed that as the particle size increases with
same volume fraction the thermal conductivity ratio increases upto some extent and
after trend the Thermal conductivity maintains constant trend. The graph indicates
trends for different particle sizes i.e. 4, 20, 40, 60,80nm for different volumetric
fractions i.e. 1%, 2%, 3%, 4%. As the particle size increases thermal conductivity
ratio increases.
4.11 ESTIMATING THERMAL CONDUCTIVITY USING XUE-XU MODEL
Xue and Xu [68] suggested another hypothetical study for the effective
thermal conductivity of nanofluids. Earlier days nanoparticles were supposed to have
a liquid layer around them with a specific thermal conductivity. First, an equation for
the effective thermal conductivity of the complex particle, which was clear as the
mixture of the nanoparticle and nanolayer, was determined”. Then, by using
Bruggeman’s effective media theory [67], the effective thermal conductivity of the
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
0 10 20 30 40 50 60 70 80 90
The
rmal
Co
nd
uct
ivit
y R
atio
, Kn
f/K
f
Particle Size,dp(nm)
1% vol
2%vol
3%vol
4%vol
103
nanofluid was determined. The resulting inherent expression for thermal conductivity
of nanofluids is
( )(2 ) ( )(2 )1 0,
2 (2 )(2 ) 2 ( )( )
nf f nf l l p p l l nf
nf f nf l l p p l l nf
k k k k k k k k k k
k k k k k k k k k k
(4.7)
Where subscript l refers to nano layer, α is defined as
3
,p
p
r
r t
(4.8)
Where t is the thickness of the nanolayer.
Nanoparticle thermal conductivity is calculated by using the following expression:
*
*
3 / 4k ,
3 / 4 1p b
rk
r
(4.9)
Here, kb
is thermal conductivity of the bulk material and r*
= rp/ λ, where λ is
the mean-free path of phonons. Mean-free path of phonons can be calculated
according to the following illustration:
10,maT
T
(4.10)
Here, a is crystal lattice constant of the solid, γ Gruneisen constant, T
temperature and Tmthe melting point (in K). Thickness of nanolayer around
nanoparticles is calculated according to Eq. (4.11).
1/3
41t ,
3
f
f A
M
N
(4.11)
Where Mf and ρ
fare the molecular weight and density of base liquid, respectively and
NA
the Avogadro constant (6.023x1023
/mol).”
104
MODEL CALCULATIONS:
1/3
41t ,
3
f
f A
M
N
1
3
23
31.22030.5773 4
1042 6.023 10t
0.3333
250.5773 1.989832 10
93.4348 10
*
*
3 / 4k ,
3 / 4 1p b
rk
r
3 0.07142 / 438.5
3 0.07142 / 5
48.125
3
,p
p
r
r t
3
9
2.5
2.5 3.4348 10
0.9999
( )(2 ) ( )(2 )1 0,
2 (2 )(2 ) 2 ( )( )
nf f nf l l p p l l nf
nf f nf l l p p l l nf
k k k k k k k k k k
k k k k k k k k k k
140.45 2 140.45 48.125 0.9999 48.125 140.45 2 140.450.458650.04 0.041 0
0.9999 2 0.45865 0.9999 2 140.45 2 140.45 48.125 2 0.9999 48.125 140.45 140.45
nf nfnf
nf nf nf
k kk
k k k
0.66504nfk
0.66504251.45 / ,
0.45865
nf
f
kW mk
k
105
Table: 4.12: Results of Calculation by using Xue & Xu model.
S.No Particle
size
%Volume
added Kf Knf Knf /Kf
1 5
1 0.45865 0.5274475 1.15
2 0.45865 0.596245 1.3
3 0.45865 0.64211 1.4
4 0.45865 0.6650425 1.45
2 7
1 0.45865 0.5182745 1.13
2 0.45865 0.5733125 1.25
3 0.45865 0.632937 1.38
4 0.45865 0.651283 1.42
3 10
1 0.45865 0.5091015 1.11
2 0.45865 0.5641395 1.23
3 0.45865 0.6191775 1.35
4 0.45865 0.64211 1.4
4 18
1 0.45865 0.4907555 1.07
2 0.45865 0.541207 1.18
3 0.45865 0.596245 1.3
4 0.45865 0.623764 1.36
5 25
1 0.45865 0.486169 1.06
2 0.45865 0.522861 1.14
3 0.45865 0.5733125 1.25
4 0.45865 0.614591 1.34
6 35
1 0.45865 0.4815825 1.05
2 0.45865 0.513688 1.12
3 0.45865 0.5641395 1.23
4 0.45865 0.596245 1.3
7 65
1 0.45865 0.476996 1.04
2 0.45865 0.504515 1.1
3 0.45865 0.5457935 1.19
4 0.45865 0.577899 1.26
8 75
1 0.45865 0.476996 1.04
2 0.45865 0.504515 1.1
3 0.45865 0.5457935 1.19
4 0.45865 0.577899 1.26
9 85
1 0.45865 0.476996 1.04
2 0.45865 0.504515 1.1
3 0.45865 0.5457935 1.19
4 0.45865 0.5733125 1.25
106
Fig: 4.10: Calculated results of the thermal conductivity ratio for Graphene
(Cn)/water+EG nanofluid with Xue and Xu model [68] as a function of the
particle size at various values of the particle volume fraction.1%, 2%, 3%, 4%,
4.12 ESTIMATING THERMAL CONDUCTIVITY CONSIDERING
TEMPERATURE AS PARAMETER
The thermal conductivity is the ratio of thermal conductivity of the nanofluid
to the thermal conductivity of water at that temperature. In the model, particle size is
considered as 20 nm since most of the experimental data is nearer to that value, as
discussed in the previous sections. Even though there is no quantitative agreement
among researchers experimental results usually propose that thermal conductivity
ratio rises with temperature. This may be explained by the reality that the standard
size of nanoparticles in that study is outsized when compared to others, since growing
particle size diminishes the effect of both Brownian motion and nanolayer
development. It might also be observed that dependence on particle volume fraction
becomes more distinct with rising temperature in all of the experimental studies When
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
0 20 40 60 80 100
The
rml c
on
du
ctiv
ity
Rat
io,K
nf/
Kf
particle size,dp(nm)
blue 1%
red 2%
green 3%
voilet 4%
107
it comes to speculative models, predictions of Yu and Choi model [30], Hamilton and
Crosser model [18], Xie et al. [31] and Xue and Xu model [68], do not depend on
temperature apart for a very small reduction in thermal conductivity ratio with
temperature due to the enrichment in the thermal conductivity of water with
temperature. Therefore, these models are not success to forecast the above mentioned
trends of experimental data.
4.12.1 KOO AND KLEINSTREUER MODEL FOR MEASURING THERMAL
CONDUCTIVITY CONSIDERING TEMPERATURE
The model suggested by Koo and Kleinstreuer [66] taken into account the
influence of Brownian motion on the thermal conductivity and the limitations of this
model are presented in Fig. 4.11: In this model, temperature dependency of thermal
conductivity is considered into account by an empirical factor f, which is a function of
temperature and particle volume fraction. The investigators did not offer the linked
function for nanofluids with Graphene nanoparticles. Because of this, the purpose
provided for Graphene nanoparticles is used in the calculations (Eq. 4.15). A
multiplicative constant is introduced into the coupled expression in order to match
experimental data. As seen from Fig.4.10: model of Koo and Kleinstreuer commonly
predicts the drift in the experimental data accurately. Since f is a function of both
particle volume fraction and temperature, one can formulate auxiliary adjustments in
the related parameters to predict a precise data place with high accuracy. It is
appealing to note that the relation between particle volume fraction and thermal
conductivity ratio is not linear at high temperatures: This is mostly due to the second
term on the right-hand side of Eq. (4.15), which offers a decrement in the effect of
particle volume fraction with rising temperature. By using a different function for f
and concluding the linked constants, it is achievable to eliminate such effects.
108
Koo and Kleinstreuer [66] considered the thermal conductivity of nanofluids to be
composed of two parts:
,knf static Browniank k (4.12)
Where kstatic
indicates the thermal conductivity enrichment due to the higher thermal
conductivity of the nanoparticles and kBrownian
takes the effect of Brownian motion into
consideration. For the static part, the classical Maxwell model [56] was proposed:
2 2( ),
2 ( )
nf p f p f
f p f p f
k k k k k
k k k k k
(4.13)
For kBrownian
, Brownian motion of particles was measured together with the effect of
fluid particles moving with nanoparticles around them. As a result, the following
expression was proposed:
4k 5 10 ,BBrownian f pf
p p
k Tc f
d
(4.14)
Where ρp
and ρf
are the density of nanoparticles and conventional base fluid
respectively and T the temperature in k. cp,f
is specific heat capacity of conventional
base fluid. In the study, the exchanges between nanoparticles and fluid volumes
moving around them were not measured and an additional term, β, was introduced in
order to take that effect into account. Koo and Kleinstreuer concluded that this term
becomes more useful with increasing volume fraction. Another parameter, f, was
introduced to the model in order to increase the temperature dependency of the model.
Both f and β were determined by utilizing available experimental data”:
( 134.63 1722.3 ) (0.4705 6.04 ) ,f T (4.15)
Which is obtained by using the results of the study of Das et al. [15] for CuO
nanofluids for other nanofluids, f can be taken as “1” due to lack of experimental data.
109
MODEL CALCULATION:
,knf static Browniank k
For the static part, the classical Maxwell model [56] was proposed
2 2( ),
2 ( )
nf p f p f
f p f p f
k k k k k
k k k k k
120 2 0.43265 2(120 0.43265)0.04
0.43265 120 2 0.43265 (120 0.43265)0.04
nfk X
X
0.48613,statick
4k 5 10 ,BBrownian f pf
p p
k Tc f
d
Where cp,f ,
ρf ,
β are got from standard data book’s (Data hand book New age
international publishers)
234 1.3806488 10 303
5 10 3.184 0.04 1021 3349.25400.248 20
brownian
X Xk X X X X X
X
=0.015744,
0.48613 0.015744
0.501874
nf static brownian
nf
nf
k k k
k
k
0.5018741.16 / ,
0.43265
nf
f
kW mk
k
110
Table: 4.13: Results Calculated by using Koo and Kleinstreuer model
S.No Temperature(ºc) %Volume
added Kf Knf Knf/Kf
1 30
1 0.43265 0.4542825 1.05
2 0.43265 0.4715885 1.09
3 0.43265 0.4888945 1.13
4 0.43265 0.501874 1.16
2 40
1 0.44195 0.468467 1.06
2 0.44195 0.4905645 1.11
3 0.44195 0.5082425 1.15
4 0.44195 0.521501 1.18
3 50
1 0.448575 0.4799752 1.07
2 0.448575 0.502404 1.12
3 0.448575 0.520347 1.16
4 0.448575 0.53829 1.2
4 60
1 0.45535 0.4963315 1.09
2 0.45535 0.519099 1.14
3 0.45535 0.537313 1.18
4 0.45535 0.555527 1.22
5 70
1 0.460275 0.5109052 1.11
2 0.460275 0.5293162 1.15
3 0.460275 0.55233 1.2
4 0.460275 0.570741 1.24
Fig.4.11: Calculated results of the thermal conductivity ratio for Graphene (Cn)
20 nm/water+EG nanofluid with Koo and Kleinstreuer model [66] as a function
of temperature at various values of particle volume fraction 1%, 2%, 3% and
4%.
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
10 20 30 40 50 60 70 80
The
rmal
co
nd
uct
ivit
y ra
tio
(K
nf/
Kf)
Temperature (ºC)
1%vol
2%vol
3%v0l
4%vol
111
4.12.2 THERMAL CONDUCTIVITY BY USING JANG AND CHOI MODEL
CONSIDERING TEMPERATURE
Jang and Choi [65] studied the thermal conductivity of nanofluids by
considering the effect of Brownian motion of nanoparticles. The projected model is
thermal conductivities of the conventional base fluid and nanoparticles, but it also
includes on the temperature and dimension of the nanoparticles. Energy transfer in
nanofluids was measured by considering four modes i.e. heat conduction in the
conventional base fluid, heat conduction in nanoparticles, effect of collisions between
nanoparticles (due to Brownian motion) and micro-convection caused by the Un-
systematic motion of the nanoparticles. In all of these, the collisions between
nanoparticles were found to be negligible when compared to other modes. As a result
of the consequence of the three outstanding modes, the following expression was
presented:
* 2(1 ) 3 Re Pr ,f
nf f p l f d f
p
dk k k c k
d (4.16)
Where Cl is a proportionality constant, d
f the diameter of the base fluid molecules, d
p
the diameter of the nanoparticles, Prf
is Prandtl number of base fluid and kp
*
is defined
so that it also includes the effect of the Kapitza resistance,
* ,p pk k (4.17)
Where β is a constant, Reynolds number is defined as:
.Re ,
RM p
d
f
C d
v (4.18)
the arbitrary motion velocity of the nanoparticles and νf can be determined by using
the kinematic viscosity of the base fluid.
112
. ,o
RM
f
DC
(4.19)
Where λf
is the mean-free path of the base fluid molecules. Do
is nanoparticle
dispersion coefficient and it can be calculated by using the following expression:
D ,3
Bo
f p
k T
d (4.20)
kB
is the Boltzmann constant, T the temperature in K and μf the dynamic viscosity of
base fluid. When the model’s dependency on nanoparticle size is measured, it is seen
that nanofluid thermal conductivity rises with decreasing particle size, since
decreasing particle size raises the effect of Brownian motion. In the derivation of this
model, thickness of the thermal boundary layer around the nanoparticles was taken to
be equal to 3df / Pr, where d
f is the diameter of the conventional base fluid molecule.
Furthermore, the volume fraction of the liquid layer around nanoparticles was
assumed to be equal to the nanoparticles volume fraction.
MODEL CALCULATIONS:
* 2(1 ) 3 Re Pr ,f
nf f p l f d f
p
dk k k c k
d
12 20.43265(1 0.04) 2.5959 0.04 3/ 20X0.43265X(3.773X10 ) 29.338 0.04nfk X X X
= 0.51918 W/mK,
0.519181.2 / ,
0.43265
nf
f
kW mk
k
113
Table: 4.14 Results Calculated by Using Jang and Choi model
S.No Temperature(ºc) %Volume
added Kf Knf Knf/Kf
1 30
1 0.43265 0.458609 1.06
2 0.43265 0.48240475 1.115
3 0.43265 0.4975475 1.15
4 0.43265 0.51918 1.2
2 40
1 0.44195 0.4728865 1.07
2 0.44195 0.494984 1.12
3 0.44195 0.5170815 1.17
4 0.44195 0.5435985 1.23
3 50
1 0.448575 0.484461 1.08
2 0.448575 0.5091326 1.135
3 0.448575 0.53604712 1.195
4 0.448575 0.56071875 1.25
4 60
1 0.45535 0.4963315 1.09
2 0.45535 0.52137575 1.145
3 0.45535 0.55780375 1.225
4 0.45535 0.582848 1.28
5 70
1 0.460275 0.5063025 1.1
2 0.460275 0.53852175 1.17
3 0.460275 0.57534375 1.25
4 0.460275 0.607563 1.32
Fig: 4.12: Calculated results of the thermal conductivity ratio for Graphene (Cn)
20nm/water+EG nanofluid with Jang and Choi model [65] as a function of
temperature at various values of particle volume fraction.1%, 2%, 3%, 4%,
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
10 20 30 40 50 60 70 80
Ther
mal
co
nd
uct
ivit
y ra
tio
(K
nf/
Kf)
Temperature (ºC)
1%vol
2%vol
3%vol
4%vol
114
4.13: SUMMARY
Experiments were carried out to collect data and to calculate thermal
conductivity. Hamilton and crosser, Xue-Xu model are based on variation of particle
size while Jang and Choi, Koo and Kleinstreuer give for variation of temperature.
Thermal conductivity is measured by using the parallel plate apparatus. The results
show that as the particle size increases the thermal conductivity ratio also increases
with temperature as well as increase thermal conductivity enhancement ratio also
increases. This is in line with the trends for Al2O3 based nanofluids with variation of
particle size and temperature.
