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Improvement of thermal conductivity of paraffin by adding expanded
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Article in Journal of Composite Materials · October 2015
DOI: 10.1177/0021998315612535
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JOURNAL OF
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Article
Improvement of thermal conductivity of
paraffin by adding expanded graphite
Journal of Composite Materials
0(0) 1–13
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DOI: 10.1177/0021998315612535
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Mustapha Karkri1, Mohamed Lachheb2, Didier Gossard1,
Sassi Ben Nasrallah2 and Mariam A AlMaadeed3
Abstract
This paper investigated the use of graphite with different configuration designs to improve the thermal energy storage of
phase change material systems. Two types of graphite have been combined with paraffin in order to improve thermal
conductivity of phase change material: synthetic graphite (Timrex SFG75) and graphite waste obtained from damaged
tubular graphite heat exchangers. Paraffin/graphite phase change material composites have been prepared by the cold
uniaxial compression technique. Their morphologies have been observed and analyzed by scanning electron microscope,
and their thermophysical properties have been estimated using new experimental tools. Results show that the thermal
conductivity and thermal diffusivity can be accurately measured by these new experimental tools. Moreover, results
highlight the fact that the phase change material thermal properties are greatly influenced by the graphite addition.
Keywords
Phase change material, paraffin, graphite, composite morphology, thermal conductivity, specific heat capacity, thermal
diffusivity
Introduction
Currently, thermal energy storage systems are crucial
for reducing dependency on fossil fuels and for minimizing carbon dioxide (CO2) emissions. The Kyoto
Summit secured a commitment from most countries
to establish a global program for CO2 emissions reduction. The buildings are responsible for producing high
levels of CO2 in most countries. According to the
World Business Council for Sustainable Development,
buildings account for up to 40% of global energy use.1
Therefore, the buildings account for a large proportion
of primary energy consumption in most countries.
Consequently, significant reductions in CO2 emissions
from buildings are needed. A portion of this reduction
could be achieved by improving building materials to
reduce energy consumption.
Thermal energy storage can be accomplished either
by using sensible heat storage or latent heat storage
components. Sensible heat storage components have
been used by builders for centuries to store and release
thermal energy passively, but a much larger volume of
material is required to store the same amount of energy
in comparison to latent heat storage systems.2 Latent
heat storage is more attractive than sensible heat
storage because of its high storage density with smaller
temperature fluctuations.3,4
These materials, called phase change materials
(PCMs), can undergo phase changes (usually solid to
liquid transitions) at relatively low temperatures while
absorbing or releasing high amounts of energy.5 During
the last four decades, many PCMs, with different phase
transitions (e.g. solid–liquid, solid–solid) and a wide
range of transition temperatures have been designed
and studied extensively.6,7 A suitable phase change temperature and a large melting enthalpy are two crucial
requirements on PCMs.
Various inorganic and organic substances have been
used in the creation of PCMs, the most common of
which include various inorganic salts (e.g. polyhydric
1
CERTES, Université Paris-Est, Créteil, France
Laboratoire d’Etudes des Systèmes Thermiques et Energétiques,
University of Monastir, Tunisia
3
Center for Advanced Materials, Qatar University, Doha, Qatar
2
Corresponding author:
Mustapha Karkri, CERTES, Université Paris-Est, 61 avenue du Général de
Gaulle, 94010 Créteil, France.
Email: mustapha.karkri@u-pec.fr
2
alcohols) and their eutectics, fatty acids and n-alkanes.
Inorganic salts (salts hydrates) have historically been
used as PCMs, but there are many disadvantages,
such as super-cooling, corrosion, relatively high
volume and chemical instability. Metallic compounds
have limited use as PCMs for commercial purpose
due to their weight and cost.8
The most promising materials used as PCMs for
low-temperature applications (below 100 C) are paraffin waxes due to their high latent heat of fusion, negligible super-cooling, low vapor pressure in the melt and
chemical inertness.9 As for practical applications,
another important issue has to be taken into account,
namely a suppression of flow (leaching). This issue is a
problem for any PCM that undergoes a solid–liquid
transition. There are many strategies to avoid this problem. Firstly, paraffin waxes are kept in tanks of various
shapes and volume that are incorporated into the building according to specific needs. Secondly, porous
materials can be impregnated by paraffin waxes; in
this case capillary forces suppress leaching. Thirdly,
paraffin waxes can be encapsulated within a polymeric
shell to form microcapsules. These microcapsules are
frequently used in the textile industry (an impregnation
of the surface of fabrics or direct incorporation of
microcapsules into fibers during spinning) and in buildings. The most widely known example of such materials
is MICROCONAL from BASF, which is frequently
blended with plaster or concrete for designing of heat
protective blocks. Lastly, paraffin waxes can be directly
blended with polymeric matrices to avoid leaching and
to keep compact shape even after paraffin wax melting.
Presently, paraffin waxes blended with appropriate
polymers seem to be the best candidates for preparation
of smart PCMs for different applications, such as thermal storage of solar energy, thermal protection of electronic devices, thermal protection of food and medical
goods, passive storage in bioclimatic buildings, use of
off-peak rates and reduction of installed power and
thermal comfort in vehicles.10,11
Polyethylenes seem to be the most convenient polymer for blending with paraffin waxes due to their chemical and structural similarities with paraffin waxes.
Krupa et al.12 investigated that low-density polyethylene (LDPE) blends with soft and hard paraffin waxes.
The blends were able to absorb large amounts of heat
energy due to the melting of paraffin wax, whereas the
LDPE matrix maintained the material in a compact
shape on the macroscopic level. The importance of
the structural similarity of components was shown in
the other works dealt with PCMs based on isotactic
polypropylene (PP) blended with soft and hard
Fischer–Tropsch paraffin.13 The PP matrix kept the
material in a compact shape during the transition
from solid to liquid. However, a much lower content
Journal of Composite Materials 0(0)
of paraffin wax could be incorporated due to strong
phase separation of components, which is caused by
the different structure of crystallites. The zigzag structure of crystallites in the polyethylene case is much
more favorable for mutual compatibility with paraffin
waxes than the helical crystalline structure of PP, despite the fact that paraffin waxes, polyethylene and PP
are practically chemically identical. Paraffin waxes can
even co-crystallize with polyethylene as discussed in a
prior publication by the authors. The results obtained
from solution crystallization confirmed a strong indication of co-crystallization in the case of LDPE on the
one hand, and practically no miscibility in the crystalline regions of LDPE and oxidized Fischer–Tropsch
paraffin wax on the other.14
On the contrary, the fact that chemical and structural differences lead to strong phase separation of
components was demonstrated in the work focused
on the PCM created from paraffin wax and
polyamide.15
Other polymer matrices, such as styrene–ethylene–
butylene–styrene (SEBS), styrene–isoprene–styrene
(SIS), and styrene–ethylene–propylene–styrene (SEPS),
have been examined.16,17 The mentioned studies
described a shape-stabilized PCM with a melting temperature in the range of 56–58 C. The results show that
the composites can retain their shape even when paraffin
wax is in the liquid state, and no paraffin wax leakage is
observed during thermal performance testing.
However, paraffin suffers from a low thermal conductivity (0.21–0.24 W.m1.K1).17 These drawbacks reduce
the rate of heat storage and extraction during the melting
and solidification cycles and restrict their wide applications. Consequently, more working effort has been
focused to improve the thermal conductivity of PCMs,
by dispersing of highly conducting particles within the
PCM,18,19 impregnation of PCM into high thermal conductivity material with porous structures.20,21 The use of
graphite particles has advantages such as high thermal
conductivity, low density in contrast to metals and high
resistance to corrosion.22,23
Differential scanning calorimetry (DSC) is widely
used for the characterization of the thermal properties
of PCMs as the simplest way to estimate the basic parameters such as melting and crystallization temperatures, the specific heat of melting and crystallization
or the specific heat capacity.24,25 However, DSC gives
information about thermal properties in microsized
samples that can be significantly influenced by local
heterogeneities. For investigation of PCMs in real conditions, it is necessary to design an experimental device
to obtain information about the thermal properties of
sample at large scale.
Very recently, Trigui et al.23 developed a new method
and constructed reliable device for testing PCM
Karkri et al.
materials at long-term performance in large sized samples. They described the first store built with the composite material developed to improve different properties
of PCM such as latent heat storage and released energy,
heat capacity and thermal conductivity. This unique
method for thermal investigation of PCMs was used
for resin epoxy/spherical paraffin wax26 as well as for
LDPE/paraffin wax composites at different concentrations of paraffin wax.27 The objective of these investigations was the thermal conductivity study, and the
amount of energy exchanged during the variation of
thermodynamic state of the samples when the boundary temperatures vary.28 Thermophysical properties
obtained through this method for PCMs are very
important for studying and simulating their behavior.
In this paper, a new device and dynamic measurement
method were used to determine the thermophysical
properties of paraffin/graphite composites. Two kinds
of graphite were used to enhance thermal conductivity
of the paraffin: synthetic graphite (Timrex SFG75) and
graphite waste obtained from damaged tubular graphite
heat exchangers. Paraffin/graphite phase change composites with the mass fraction of 5%, 10%, 15%,
20%, 30% and 40% were prepared by cold uniaxial
compression method. The results indicate a noticeable
improvement in the effective thermal conductivity of
composites compared to the PCM.
Experimental investigation
Investigated materials
PCM and graphite selection. The PCM tested in the present
work is paraffin with melting temperature of 56–58 C
and with specific density of 900 kg m3. The thermal
conductivity enhancement is obtained by addition of
conductive graphite particles. Two different kinds of
graphite were used. One type is an industrial graphite
‘‘graphite waste’’. It was obtained from damaged tubular
graphite heat exchangers. It is a form of carbon with
crystalline structure; it has good thermal and mass transfer characteristics. The measured bulk density is
1936 kg m3 with an average size of 85 lm. Moreover,
graphite has strong resistance to corrosion and chemical
attacks, which makes it compatible with most PCM. The
recycling of graphite has a lot of benefits, it can save
natural resources of graphite for future generations, i.e.
recycling graphite reduces the need for raw materials and
embodied energy and has economic benefits. The second
kind that has been tested is the Timrex (SFG75) powder
supplied by Timcal Graphite & Carbon at a bulk density
of 2240 kg m3. It is synthetic graphite with spherical
shape and an average size of 75 lm, characterized by a
well-aligned crystal structure and by a high thermal conductivity in plane.29
3
Samples elaboration. The elaboration method developed
in the present study is based on the cold uniaxial compression. In this method paraffin powders and graphite
particles are mixed together, and then the obtained
mixture is poured into a stainless steel mould followed
by a uniaxial compression (80 bars) at ambient temperature (Figure 1). This technique leads to an anisotropic composite structure whose porosity is partially
occupied by paraffin grains. Cylindrical paraffin/graphite samples were prepared under the same manufacturing conditions with mass fraction of 5%, 10%, 15%,
20%, 30% and 40%. The thickness and the diameter of
all these specimens were 10 mm and 60 mm, respectively
(Figure 2). Then, they are neatly cut of the cylindrical
samples (Figure 2(b)) to obtain a parallelepiped-shape
specimen (Figure 2(c)) with dimensions (42 mm
42 mm5 mm) for heat capacity measurements.
This technique leads to an anisotropic composite
structure whose porosity is partially occupied by paraffin grains. Cylindrical paraffin/graphite samples were
prepared under the same manufacturing conditions
with mass fraction of 5%, 10%, 15%, 20%, 30% and
40%. The thickness and the diameter of all this specimens were 10 mm and 60 mm, respectively (Figure 2).
Characterization
In this section, different experimental tools and characterization methods will be exposed. They will be used to
determine the morphology of microstructure of the paraffin/graphite composites, the specific density and
volume fraction, the specific heat capacity and the thermal conductivity.
Scanning electron microscopy (SEM). The fracture surfaces
of the samples have been investigated using a Nova
Nano SEM 450 Scanning Electron Microscope.
Brittle fracture of the samples was achieved in liquid
nitrogen.
Specific density, volume fraction. The determination of the
composite density is important not only for the specific
thermal capacity estimation but also for checking the
quality of the samples. It is clear that if composite samples are well processed, i.e. good homogeneity is
reached without air bubbles in the sample as well as
without unfilled pores at the paraffin/graphite interface,
the specific density of the composites should have a
linear dependence on the volume fraction, according
to the simple rule of mixtures given by
eff ¼ f f þ m m
ð1Þ
where m and f are the densities of the paraffin matrix
and the graphite filler, respectively.
4
Journal of Composite Materials 0(0)
Pressure
Embossing
metal plate
Mobil platen
Metal cavity
Paraffin/graphite
Fixed platen
Figure 1. Cold uniaxial compression technique.
Figure 2. Example of paraffin/graphite composite samples: (a) paraffin, (b) paraffin/graphite.
Then, by using the values of m and f , it is possible
to compute the volume fraction of each compound
knowing the graphite mass fraction m and using the
classical relationship
h
i
mÞ
v ¼ 1= 1 þ mf : ð1
;
m
m ¼ 1 v
measurement is obtained from the following
equation
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 m 2 V
þ 2
c ¼ c
m2
V
ð3Þ
ð2Þ
The density measurements were achieved using
square-plate samples. A Mettler-ToledoTM AT61
delta range balance was used to measure the mass
of the samples (m) and the sample sizes were
measured using a caliper square. Then, the density of
samples c is defined as mass divided by volume of
the composites (V). The uncertainty on the density
Transient guarded hot plate technique (TGHPT). Transient
guarded hot plate technique (TGHPT) method for
measurement of heat capacity has been described previously.23,28 In brief, determination of the overall thermophysical properties of PCMs over several cycles
requires the design of a genuine experimental device
(Figure 3).
Karkri et al.
5
Figure 3. Experimental set-up of transient guarded hot plate technique.
The proposed test bench for the parallelepipedshaped/circular composite provides temperature and
heat flux measurements at the material borders. The
sample is located between two horizontal aluminum
heat exchangers. Thermo-regulated baths, supplying
the exchangers, allow a fine regulation of the injected
fluid temperature with a precision of approximately
0.1 C. Heat flux sensors and thermocouples (type T)
are placed on each side of the composite. The whole
thing is maintained in place by the use of a slightly
tightened pneumatic jack. The thickness of flux
meters is approximately 0.2 mm, and their sensitivity
is approximately 13.7 mV/W/m2 for a sensor having a
circular active surface area of 28.27 cm2. The various
sensors are connected to a Labviewß program adapted
to measure heat flux and temperature fluctuations.
Experimental data are recorded with regular and
adjustable time steps (6 s). The lateral side faces are
insulated by polyethylene expanded foam (PE) which
reduces multidimensional heat transfer to a 1D problem. In this work, the temperature varied between 0 C
and 50 C.
Thermophysical characterization of PCMs. A second experimental device has been developed in order to measure
thermal properties of PCM composites. Figure 4 shows
an overview of the experimental device. Figure 4(a)
shows the device when the piston is lowered and
closes the cavity: this is the normal operating position
when a measurement is launched. Figure 4(b) shows the
device when the piston is raised and the cavity is
opened: in this configuration, the sample can be positioned in the cavity before starting measurements. The
experimental device was designed in aluminium in
order to conduct the heat flux upward and produce a
significant temperature gradient around the PCM
sample. The piston support (the ‘‘head’’, Figure 4(a))
of the device may be considered as a thermal fin which
evacuates the heat. The whole cylindrical part of the
measurement device has been isolated with mineral
wool in order to reduce drastically thermal losses (cf.
Figure 4(c) and (d)). The cavity bottom is maintained at
a fixed temperature by a heating element and a coil heat
exchanger in which an isothermal fluid is circulated by
a thermo-regulated bath. The temperature and the heat
flow below and above the PCM samples are, respectively, measured by thermocouples and heat flux meter
and recorded by a LabViewß application specially
developed for the PCM thermal measurements. The
thermocouples have been calibrated by using the comparative method process, and the heat flux meters have
been calibrated by the manufacturer (the sensibility are
6
Journal of Composite Materials 0(0)
Figure 4. The experimental device: (a) simplified drawing, (b) closed, (c) open (empty cavity) and (d) insulated part.
74,074 W.m2.V1 and 129,366 W.m2.V1 for the
bottom and the upper heat flux sensors, respectively).
The thermo-regulated bath thermostat and the power
source of the heating element are controlled by the
same LabViewß application. A temperature difference
was imposed between the upper and the down sides of
the composites until heat steady-state and the apparent
thermal conductivities are calculated by the following
expression
eff ¼ e:’=2:T
ð4Þ
where e is the thickness of the specimen and ’ is the
sum of the measured heat fluxes.
Results and discussion
Microstructure of the paraffin/graphite composites
SEM has been used to observe the morphology of paraffin/graphite composites and also pure paraffin and
graphite (SFG75 and graphite waste), as shown in
Figure 5 (a) to (h).
The morphology of graphite SFG75 is illustrated in
Figure 5(a) and (b). From these figures, the structure of
SFG75 can be observed; it is characterized by a wellaligned crystal structure and by many inter-lamellar
pores (especially in Figure 5(b)). The characteristic graphene layers are clearly shown. The characteristics of
the microstructure of a material are determined by its
nature. Figure 5(c) and (d) shows the SEM photographs of the used graphite waste and the paraffin
respectively. Figure 5(e) and (f) illustrated composite
with 10 wt% and 20 wt% of SFG75, respectively.
Also, the morphology of the paraffin/graphite waste
composite with 10 wt% and 20 wt% of graphite
waste is shown in Figure 5(g) and (h), respectively.
These figures exhibit different types of morphology
and show the presence of two different regions that
represent two different materials, namely paraffin and
graphite (SFG75 or graphite waste). It can be observed
that the graphite (SFG75 and graphite waste) is dispersed into the paraffin used as matrix material. We
can easily recognize the graphite scattered in the paraffin by the darker region and by its uniform shape, this
dispersion enhances the thermal properties of the
Karkri et al.
7
Figure 5. Scanning electron microscopy images: (a) graphite SFG 75 2000 50 mm, (b) SFG 75 120,000 1 mm, (c) graphite waste
2000 50 mm, (d) paraffin 60,000 3 mm, (e) composite 10 wt% of graphite SFG75 with paraffin 2000 50 mm, (f) composite 20 wt%
of SFG75 with paraffin 2000 50 mm, (g) composite with 10 wt% of graphite waste with paraffin 2000 50 mm, (h) composite with 20
wt.% of graphite waste with paraffin 2000 50 mm (c) open (empty cavity), (d) insulated part.
8
Journal of Composite Materials 0(0)
12
1,5
Paraffin/SFG75
additive rule
Paraffin/graphie waste
additive rule
Paraffin/SFG75
Paraffin/graphite waste
10
1,3
8
λeff / λm
ρc (g .cm-3 )
1,4
1,2
6
1,1
4
1,0
2
0,9
0
5
10
15
20
25
Graphite volume fraction (%)
0
0
5
10
15
20
25
30
35
40
Mass fraction φm
Figure 6. Specific density of the composite versus volume
fraction.
matrix. Observed phase separation in composites was
caused by unlike chemical nature of paraffin and
graphite.
Specific density
The experimental density of the paraffin/graphite composites is also compared to a theoretical curve computed
according to the rule of mixture (equation (1)) using
density values of paraffin (m ¼ 900 kg m3) and the
graphite (SFG75 ¼ 2240 kg m3) or the graphite waste
density: gw ¼ 1936 kg m3. The measured values and
the theoretically calculated density versus volume fraction of graphite are plotted in Figure 6 for paraffin/
graphite waste and paraffin/SFG75 composites. It can
be seen from Figure 6 a linear dependence of the density
on the graphite volume fraction and as the mass fraction
of graphite increased, the density of the composite
increased and a good agreement between experimental
and theoretical values can be observed.
Thermal conductivity of composites
Thermal conductivity (eff ) of the PCMs composite
with different graphite mass fraction has been measured
at room temperature, using the previously mentioned
method. The results obtained for the two types of composites (paraffin/SFG75 and paraffin/graphite waste)
and their associated uncertainties are, respectively,
plotted in Figure 7.
Figure 7 shows that the measured thermal conductivity of paraffin/graphite composite is greatly influenced
by the graphite addition and increased with increasing
the mass fraction of graphite. This rise is due to the
higher thermal conductivity of the graphite. In the
case of paraffin/SFG75, we observe a non-linear
increase of the thermal conductivity with increasing
synthetic graphite (SFG75) mass fraction. We can
Figure 7. Thermal conductivity of paraffin/graphite composite
versus graphite mass fraction.
observe that the thermal conductivity of paraffin/
SFG75 composite abruptly changes when the mass
fraction of graphite changes from 15% to 20% and
from 30% to 40%. The results of the thermal conductivities of paraffin/graphite composites and their
intensifications are shown in Table 1.
In Table 1, we can observe that the thermal conductivity intensification Ieff of paraffin/SFG75 samples
increase from 35.6% to 675.1%, with increasing of
mass fraction (5% to 40%). A smaller increase was
observed for paraffin/graphite waste with a maximum
Ieff ¼ 193:6%. For the same graphite amount, thermal
conductivity intensification in the case of paraffin/
SFG75 composites is more important than in the case
of the paraffin/graphite waste; this can be explained by
the fact that thermal conductivity of the SFG75 is
higher than graphite waste.
Specific heat capacity
The method used to measure sensible and specific heat of
the composites consists of simultaneously measuring the
heat flux ’1 and ’2 and temperatures T1 and T2 on the
two faces of the sample (T1 and T2 are the two thermocouples integrated in the flux meters). At the beginning, the two exchangers are maintained at a constant
temperature until a constant density flux on the two
faces of the sample is obtained, and then the temperature
of the exchangers is increased. Between these two isothermal states, the sample stores an amount of
energy Qsens which represents the internal variation of
the system energy. Stored sensible heat is given by equation (5)
Qsens ¼
Z tf
1
’:dt ¼ cp eff :ðTf Ti Þ
c :e ti
ð5Þ
Karkri et al.
9
where cpeff is specific heat (J.kg1.K1), ’ is the difference of heat flows measured at each step of acquisition time dt (s), c (kg m3) is the density of the sample,
and e (m) is the thickness of the sample.
Figure 8 shows an example of heat storage in the
samples for solid state. The temperatures measured by
Table 1. Thermal conductivity intensification values of paraffin/
graphite composite.
Samples
eff ðW:m1 :K1 Þ
Ieff (%)
Paraffin
Paraffin/SFG75 composite
Mass fraction ’m (%)
5
10
15
20
30
40
0.233 0.007
–
0.316 0.005
0.409 0.01
0.569 0.023
0.906 0.026
0.979 0.095
1.806 0.092
35.6
75.5
144.2
288.8
320.2
675.1
Paraffin/graphite waste composite
Mass fraction ’m (%)
5
0.289 0.012
10
0.342 0.012
15
0.383 0.008
20
0.428 0.021
30
0.536 0.008
40
0.684 0.117
24.0
46.7
64.4
83.7
130.0
193.6
the heat flux meters on the lower (T1 ) and the upper
(T2 ) faces of the sample evolve in an asymptotic way to
the set point. The measured heat flux on both sides of
the sample also evolves very quickly at the beginning of
recording and then goes to zero, which corresponds to a
new equilibrium state obtained at the end of the test.
This confirms that lateral thermal losses are negligible.
Figure 9 plots the variation of the heat storage of
selected PCMs in the solid phase for a temperature
range varying from 25 C to 34 C.
Figure 10 represents the evolution of the specific
heat capacity of the two kinds of composite paraffin/
graphite waste and paraffin/SFG75 as a function of
graphite mass fraction. It can be seen that the specific
heat of the test materials is influenced by the graphite
addition. There is a non-linear decrease in the specific
heat capacity with increasing the graphite mass fraction
for the two kinds of composites. This is due to the low
heat capacity of the graphite and a mixture problem.
After that, we can observe that the heat capacity values
of the paraffin/SFG75 are superior to those of the composite paraffin/graphite waste in the 5%, 10% and 30%
mass fraction (expect in the case of 20% and 40%), this
unexpected variation may be due to the non-homogeneity of the composite sample which directly affects
heat capacity.
Thermal diffusivity and thermal effusivity
The thermal diffusivity of the samples has been calculated using the previously measurements. The behavior
38
80
T1
φ1
T2
60
40
34
20
32
2
0
Heat flux (W/m )
Temperature ( °C)
36
φ2
30
-20
28
-40
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
Time (h)
Figure 8. Heat flux and temperature evolution of PCMs at solid state (from 28.8 to 37 C) based on paraffin/EG waste 60/40 w/w/.
10
Journal of Composite Materials 0(0)
38
120
T1
φ1
100
T2
80
60
34
40
32
20
0
30
28
φ2
2
-20
Heat flux (W/m )
Temperature ( °C)
36
-40
-60
26
-80
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
Time (h)
Figure 9. Heat flux and temperature evolution of PCMs at solid state (from 28 to 37 C) based on paraffin/SFG75 60/40 w/w/.
2000
-1
-1
Cp eff (J. kg .K )
paraffin/graphite waste
paraffin/SFG 75
1500
1000
0
5
10
15
20
25
30
35
40
φm (%)
Figure 10. The specific heat capacity of paraffin/graphite composites.
of thermal diffusivity (aeff ) of paraffin/graphite composite is depicted in Figure 11 as function of the graphite
mass fraction.
We note a non-linear raise in the composite thermal
diffusivity by increasing the graphite mass fraction for
the two kinds of composites paraffin/SFG75 and paraffin/graphite waste. A comparison with the thermal
diffusivity of pure paraffin (1:303 107 m2.s1) indicates that the thermal diffusivity of the paraffin/graphite composite increases from 47.1% to 382.5%, with
increasing of the mass fraction of graphite Timrex
(SFG75), and a smaller increase can be seen for graphite waste composite with an increasing rate from 51.3%
to 157.4%. On the other hand, a similar behavior can
Karkri et al.
11
12
paraffin/SFG75
paraffin/graphite waste
11
10
8
2
-1
aeff x 10 (m .s )
9
-7
7
6
5
4
3
2
1
0
5
10
15
20
25
30
35
40
Mass fraction φm (%)
Figure 11. Thermal diffusivity of paraffin/graphite composites versus graphite mass fraction.
Table 2. Thermal properties of paraffin/graphite composite.
aeff (m2.s1).107
beff (W.s1/2.m2.K1)
1.303 0.086
645.256 20.737
5
10
15
20
30
40
1.878 0.06
2.390 0.107
4.253 0.307
6.127 0.508
6.37 0.085
10.945 0.508
729.085 11.742
836.447 20.927
872.405 37.356
1157.388 36.398
1225.89 37.356
1726.21 36.398
5
10
15
20
30
40
1.969 0.11
2.185 0.148
2.741 0.26
3.36 0.383
3.43 0.124
4.77 0.383
651.130 27.962
731.628 27.127
731.450 18.344
738.273 40.936
914.98 18.344
989.931 17.344
Parameters
Samples
Paraffin
Paraffin/SFG75 composite
Mass fraction ’m (%)
Paraffin/graphite waste composite
Mass fraction ’m (%)
be seen for the two curves for low mass fraction (0% to
10%). The third parameter is the thermal effusivity of
the composites samples. It can be calculated using the
thermal conductivity and diffusivity values as follows
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2 ðÞ 1 u2 ðaÞ
þ : 2
uðbÞ ¼ b:
2
2 a
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
eff
beff ¼ ð::CP Þeff ¼ pffiffiffiffiffiffiffi
aeff
where uðÞ and uðaÞ are the uncertainty of the sample
thermal conductivity and diffusivity, respectively. This
is an important thermophysical property that can be
defined as a ‘‘contact sensation’’; this property
ð6Þ
ð7Þ
12
determines the interfacial temperature when two
objects at different temperatures come into contact
with each other. Thermal effusivity and diffusivity are
summarized in Table 2.
We can note that the thermal effusivity varies from a
paraffin/graphite composite to another due to their differing ability to transfer heat. This is due to differences
in heat transfer through and between particles, and is
therefore a function of density and morphology.
Conclusion
In this work, composites based on a PCM and graphite
have been manufactured using uniaxial cold compression method. In such a composite, the paraffin serves as
a latent heat material and the graphite as an effective
heat transfer promoter. Two types of graphite have
been compared: graphite waste and graphite synthetic
Timrex (SFG75). The thermophysical properties of
composites are characterized using new experimental
tools. Results show that increasing the mass fraction
of graphite from 0% to 40% gradually increases the
thermal conductivity and diffusivity of paraffin/graphite composite. A non-linear increase of the thermal conductivity and diffusivity with increasing graphite
synthetic (SFG75) and a linear increase for the case
of graphite waste were observed for ’m 20%. Two
experimental methods were adopted for measuring the
thermal properties of composites. A good agreement
between experimental densities of paraffin/graphite
composites and theoretical values according to the
rule mixture is obtained.
Declaration of Conflicting Interests
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this
article: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The statements made herein are solely the
responsibility of the authors.
Funding
This publication was made possible by NPRP grant # 4-4652-173 from the Qatar National Research Fund (a member of
Qatar Foundation).
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Appendix
Notation
a
b
cp
e
I
m
t
T
V
thermal diffusivity, (m2.s1)
thermal effusivity, (W.s1/2.m2.K1)
specific heat capacity, (J. kg1.K1)
thickness, (m)
thermal conductivity intensification ()
mass, (kg)
time, (s)
temperature, (K)
volume of composite, (m3)
’
’
thermal conductivity, (W.m1.K1)
filler fraction
heat flux density, (W.m2)
density, (kg m3)
Subscripts
c
eff
exp
f
m
v
th
composite
effective (composite)
experimental
filler
matrix
volume fraction
theoretical