refrigeration and air conditioning

1. Heat transfer study of submicro-encapsulated PCM
plate for food packaging application
H.M. Hoang a,*
, D. Leducq a
, R. Perez-Masia b
, J.M. Lagaron b
, E. Gogou c
,
P. Taoukis c
, G. Alvarez a
a
Irstea, UR GPAN, 1 rue Pierre-Gilles de Gennes, CS 10030, 92761 Antony, France
b
Novel Materials and Nanotechnology Group, Institute of Agrochemistry and Food Technology (IATA-CSIC), Avda,
Agustin Escardino 7, 46980 Paterna Valencia, Spain
c
National Technical University of Athens, School of Chemical Engineering, Athens, Greece
a r t i c l e i n f o
Article history:
Available online 11 July 2014
Keywords:
Heat transfer
Thermal properties
Encapsulation
Phase change material (PCM)
a b s t r a c t
In recent studies, encapsulated phase change materials (PCM) were developed as novel
materials for food packaging because of their improved thermal insulation capacity. The
PCMs (often liquid in room temperature) are encapsulated in a shell material so as they can
be practically handled. In this work, the thermal behaviour of an encapsulated PCM ma-
terial (Rubitherm RT5 encapsulated in polycaprolactone PCL) with two different PCM mass
fractions was studied. The model was validated by experimental cooling and heating
processes, under controlled air temperature conditions. The numerical result demon-
strated a better thermal buffering capacity of the encapsulated PCM material compared to
a standard one (cardboard).
© 2014 Elsevier Ltd and IIR. All rights reserved.
Etude du transfert de chaleur d'une plaque en PCM encapsules
a l'echelle sub-microscopique
Mots cles : Transfert de chaleur ; Proprietes thermiques ; Encapsulation ; Materiau a changement de phase (PCM)
1. Introduction
Temperature abuse in perishable product cold chain can lead
to deterioration in food quality and safety. The quality
changes can be microbiological (growth of microorganisms),
physiological (e.g. ripening, senescence and respiration),
biochemical (e.g. browning reactions, lipid oxidation and
pigment degradation), organoleptic and/or physical (e.g.
moisture loss) (Likar and Jevsnik, 2006; Laguerre et al., 2013;
Krı´zek et al., 2014). Packaging can play an active role in tem-
perature controlling of perishable products. However, stan-
dard materials for product packaging (plastic, cardboard or
wood) usually have limited thermal buffering capacity. One
possible approach to enhance this capacity and maintain the
product at a desired temperature is thermal energy storage by
phase change materials (PCM). A PCM is a substance that
* Corresponding author. Tel.: þ33 1 40 96 65 02; fax: þ33 1 40 96 60 75.
E-mail address: hong-minh.hoang@irstea.fr (H.M. Hoang).
www.iifiir.org
Available online at www.sciencedirect.com
ScienceDirect
journal homepage: www.elsevier.com/locate/ijrefrig
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 5 2 ( 2 0 1 5 ) 1 5 1 e1 6 0
http://dx.doi.org/10.1016/j.ijrefrig.2014.07.002
0140-7007/© 2014 Elsevier Ltd and IIR. All rights reserved.

2. undergoes a phase transition (e.g. fusion/crystallization) at a
specific temperature or in a narrow range of temperature. It
can have a high enthalpy of phase transition and then is
capable of storing and releasing large amounts of energy
(Rentas et al., 2004). The surplus heat can be absorbed by the
phase transition of the material so that the augmentation of
the product temperature could be limited.
In general, chilled food products are often stored between
0 and 6
C. Thus, the PCM phase change temperature should
be chosen in the temperature range of 4e8
C. The PCM is
therefore liquid at room temperature so its handling is
complicated and becomes an issue for some applications. To
limit its leakage while changing from the solid to the liquid
state, the PCM should be contained in some recipient. One
solution is to encapsulate the PCM inside a shell material
(Cheng et al., 2012) or a micro/nanostructured material (Perez-
Masia et al., 2013). The PCM is then protected against the in-
fluences of the outside environment by a shell that increases
the heat transfer area, withstands changes in volume when
the phase change occurs and, much better, allows the
handling of the liquid phase of PCM. Among the encapsulation
technologies, micro, submicro and nanoencapsulation pre-
vent volatile losses, allow a greater dispersion and minimize
the amount of non-encapsulated product. Electrospinning
technique has proven to be a suitable method for micro/
nanostructured encapsulation. Compared to micro encapsu-
lation, submicro and nanoencapsulation provide higher spe-
cific areas which can increase the heat transfer area of the
PCM. Moreover, nanomaterials could be easily dispersed in
the packaging matrices without affecting the physical prop-
erties of the packaging. Many compounds, including
biomedical substances or functional food ingredients, have
been encapsulated in polymeric matrices by means of this
method (Goldberg et al., 2007; Lopez-Rubio and Lagaron, 2012).
The aim of the present work is to study the heat transfer
behaviour of a plate made from submicro-encapsulated PCM
material. The phase transition can be modelled by many
methods based on the energy balance equation: tracking of
the solideliquid interface (Azzouz et al., 2008), enthalpy (Zhou
et al., 2010; Melone et al., 2012) and apparent heat capacity
(Antony Aroul Raj and Velraj, 2011). In this study, the enthalpy
method was chosen. This method simplifies the solution of
the phase change problem avoiding the explicit tracking of the
solideliquid interface. The model was validated by experi-
mental heating and cooling tests under controlled tempera-
ture conditions.
Finally, the PCM phase transition model was applied to
evaluate the influence of packaging on the product tempera-
ture evolution along the cold chain. Simulations were carried
out for a product in which two choices of packaging were
tested: encapsulated PCM material and cardboard. A realistic
air time-temperature profile of the cold chain retrieved from
the Cold Chain Database (www.frisbee-project.eu/
coldchaindb) was used as input data. The result of the ther-
mal model along with the time-temperature profile of the
packaging, was then applied to the “Cold Chain Predictor
software” (Lun et al., 2012) in order to estimate the remaining
shelf-life of a refrigerated food product (ham) in both cases
(PCM material packaging and cardboard).
1.1. Cold chain predictor software
Cold Chain Predictor (CCP v1.1) is software developed by
IRSTEA (National Research Institute of Science and Technol-
ogy for Environment and Agriculture, former CEMAGREF) and
NTUA (National Technical University of Athens) in the
framework of FRISBEE project. The purpose of the CCP soft-
ware is to simulate a food cold chain by building a time-
temperature history from time-temperature profiles contrib-
uted to the Cold Chain Database. The Cold Chain Database
(www.frisbee-project.eu/coldchaindb) has been constructed
in order to develop a user friendly on line platform where
collected data from all cold chain stages of the food supply
chain can be retrievable and available to be used from
candidate users. The CCP software in conjunction the Cold
Chain Database allows the user to estimate the distribution
graph of (effective) temperature for a specific stage of a
selected food product and to calculate the remaining shelf life
of the food product at different stages of the cold chain, if
quality decay kinetic data is available.
2. Materials and methods
2.1. Encapsulated PCM materials
Rubitherm RT5 was selected as PCM material since it has a
phase transition around 5
C, a suitable temperature for
chilled food keeping. PCM capsules were made through
electro-hydrodynamic processing also known as “electro-
spinning”. The process uses high voltage electric fields to
produce electrically charged jets from viscoelastic polymer
Nomenclature
cp Heat capacity, J kgÀ1
KÀ1
E Plate thickness, m
h Convective heat transfer coefficient, W mÀ2
KÀ1
DH Enthalpy of phase change, kJ kgÀ1
k Heat conductivity, W mÀ1
KÀ1
M Number of mesh points
t Time, s
T Temperature,
C
TS Surface temperature,
C
Ta Air temperature,
C
x Mass fraction
y Dimension of the plate thickness, m
Greek symbols
a Thermal diffusivity, mÀ1
sÀ2
ε Porosity
εi Volume fraction of component i of the material
r Density, kg mÀ3
Subscripts
a air
l liquid
PC phase change
s solid
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3. solutions which on drying, by the evaporation of the solvent,
produce micro, submicro (also called ultrathin) or nano-
structured polymeric structures. The electrospun materials
were produced in a Fluidnatek LE-500 high throughput model
of Bioinicia S.A., Spain (www.bioinicia.com). A significant
advantage of the technique is the suitable use of biomass-
derived materials and of biodegradable polymers as encap-
sulating elements, with the corresponding environmental
benefits. Different biopolymers were tested and finally poly-
caprolactone (PCL) was selected as the most suitable shell
material, since this material was able to encapsulate the
biggest amounts of PCM. Fig. 1 presents images of the ultra-
thin materials morphology obtained by scanning electron
microscopy (SEM). The structures obtained by electrospinning
vary from the micro to the nano-level. In this case, the “nano”
refers to the size of the significant fraction of capsules that
contain the PCM and not to the size of the superior fibre like
architecture. However, since there appears to be a distribution
of sizes, the “submicro” term was used.
Different concentrations of polymer and PCM were tested
in order to obtain the most efficient encapsulated systems in
terms of encapsulation efficiency (defined as the percentage of
PCM in the suspension with the polymer that goes into the
capsules). The selected fibre mats were put together and
lightly pressed using a hot-plate hydraulic press to form
0.5e1 cm thickness plates. In this study, two plates of different
PCM mass fraction (30% for the plate 1 and 38% for the plate 2,
Table 1b) were tested experimentally. The experimental re-
sults were compared to the numerical model's results in
section 3.1. Their characteristics (density, heat capacity, heat
conductivity, porosity …) were reported in the Table 1.
The effect of storage temperature (4
C and 25
C) and time
(90 days) on the PCL/RT5 material was studied in Chalco-
Sandoval et al., 2014. No significant changes of RT5 mass
fraction during ageing were observed in encapsulated PCM
material stored at 4
C during 90 days. For the same material
stored at 25
C, the mass fraction of RT5 reduced from 41% to
33% at the internal zone and from 35% to 31% at the external
zone.
2.2. Differential scanning calorimetry (DSC)
Differential scanning calorimetry (DSC) analyses were per-
formed on a Perkin Elmer DSC 7 (US) under a nitrogen atmo-
sphere using a subambient cooling accessory for the plates 1
and 2 (Fig. 2). Different heating and cooling rates were tested
in order to find the rate that accomplished with the RAL
standard. This standard or procedure ensures that the mea-
surement is not dependent on heating and cooling rate and on
the sample mass because the procedure guarantees the
thermal equilibrium in the sample and the sample holder
(Lazaro et al., 2013; Sharma et al., 2014). The heating and
cooling rate was set at 2
C minÀ1
and each DSC analysis was
done in triplicate. Analysis of a DSC thermogram enables the
determination of two important parameters: the phase tran-
sition temperature range and the denaturation enthalpy (or
phase change enthalpy e DH). Fig. 2 shows that the phase
change enthalpy DH of the plate 2 (containing 38% of PCM) is
Fig. 1 e Encapsulated RT5 e PCL morphology with different scales.
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4. greater than of the plate 1 (containing 30% of PCM). For both
plates, hysteresis was observed: the crystallization began at a
lower temperature compared to the end of the melting.
The multiple peaks observed in the DSC analysis during the
crystallization of the plate 2 (Fig. 2) could be attributed to the
rotator phase transition. A rotator phase is defined as lamellar
crystals which exhibit long-range order in the molecular axis
orientation and center-of-mass position, but lack rotational
degrees of freedom of the molecules about their long axis
(Kraack et al., 2000; Sirota and Herhold, 2000). Two or three
peaks can be observed on the DSC cooling curves. These peaks
can be attributed to the heterogeneously nucleated liquid-
erotator transition, the rotatorecrystal transition and the
homogeneously nucleated liquidecrystal transition, respec-
tively. When there are two peaks, the second and the third
transitions are included in only one peak. This phenomenon
which appears due to the confinement of the PCM in the
micro- and nanometer fibers is not important for the plate 1 in
which the PCM mass fraction is lower.
2.3. Heat transfer model development
2.3.1. Enthalpy model
The enthalpy model (Zhou et al., 2010) was applied to study
the heat transfer phenomenon. The y dimension corresponds
to the plate thickness: it was assumed that the plate thickness
(E) is a lot smaller than its length and width so that the 1D
model can be used.
r
vHðy; tÞ
vt
¼
v
vy
k
vTðy; tÞ
vy
; 0 y E (1)
The enthalpy H is in function of the temperature T as:
H ¼
ZT
T0
cp;sdT when T T1
ZT1
T0
cp;sdT þ
ZT
T1
cp;PCdT when T1 T T2
ZT1
T0
cp;sdT þ
ZT2
T1
cp;PCdT þ
ZT
T1
cp;ldT when T T2
8
:
(2)
where: T0 is the reference temperature where H(T0) ¼ 0,
[T1, T2] is the temperature range in which the phase
transition occurs.
cp,s, cp, PC, cp,l are the heat capacities of the solid, phase
transition and liquid states.
As example, the Fig. 3 shows the enthalpy evolutions in
function of temperature for the two plates in which the three
states (liquid, phase transition and solid) can be easily iden-
tified; the greater change of enthalpy corresponds to the phase
change region.
Table 1 e Materials properties.
a. Pure materials
RT5 e liquid RT5 e solid PCL ePolycaprolactone
Density (k gmÀ3
) 770
(Manufacturer)
880
(Manufacturer)
1094
(Agarwal and Speyerer, 2010)
Heat capacity (J kgÀ1
KÀ1
) 2170
(Manufacturer)
e 1500
(Minakov and Schick, 1999)
Heat conductivity (W mÀ1
KÀ1
) 0.2
(Manufacturer)
e 0.4
(Minakov and Schick, 1999)
b. PCM encapsulated (measured or calculated from pure materials properties)
Plate 1 Plate 2 Plate 3 Plate 4 (cardboard)
Mass fraction of RT5 0.30 0.38 0.30 e
Dimensions (m) 0.050 Â 0.050 Â 0.010 0.037 Â 0.037 Â 0.005 ∞ Â ∞ Â 0.040 ∞ Â ∞ Â 0.040
Mass (g) 12.34 2.68 e e
Porosity 0.47 0.62 0.47 e
Density at 20
C (k gmÀ3
) 520 356 520 144
Density below the crystallization
region (k gmÀ3
)
546 378 546 144
Heat capacity (J kg-1
KÀ1
) 1701 1755 1701 1400
Heat conductivity
(W m-1
KÀ1
)
0.08 0.11 0.08 0.07
Fig. 2 e DSC results of the two plates (at the heat flow rate
of 2
C min¡1
).
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5. The plate's properties (density, heat capacity, heat con-
ductivity …) are considered to be spatially homogeneous, i.e.
no heterogeneous structure caused by the polymers, PCM and
air distribution are considered.
The initial condition at time t ¼ 0 was considered as
Tðy; t ¼ 0Þ ¼ T0ðyÞ (3)
The convective heat transfer boundary condition was
applied at the surfaces:
k
vT
vy
y¼0
¼ hðTa À Tðy ¼ 0; tÞÞ (4)
k
vT
vy
y¼E
¼ hðTa À Tðy ¼ E; tÞÞ (5)
2.3.2. Numerical solution
The equation system (Eqs. (1)e(5)) was solved numerically
using the finite volume method coupled with the fully implicit
finite difference scheme. The spatial and temporal domains
were discretized uniformly in M grids (1 i M) and N time
steps (1 n N). The discretized equation system takes the
following form:
The 'enthalpy_function' corresponds to Eq. (2) and the
'inverse_enthalpy_function' is its inverse form.
Note that the system (6) resolves both enthalpy and tem-
perature at each time step. This system is numerically solved
by using over relaxation iteration algorithm (Zhou et al., 2010)
with a relaxation factor of 1.5. When the enthalpy difference
between two iterations
PM
i¼1ðDHn
i Þ2
is less than the given pre-
cision (0.0001 J kgÀ1
), the obtained enthalpy and temperature
are recorded and the calculation proceeds to the next time
step. The spatial grid sizes are 0.00056 m (plate1) and
0.00028 m (plate 2) and the time step is 0.1 s (for both plates).
Further refinement of either space grids and time steps shows
no effect on the results.
2.4. Thermal properties of the plates
The thermal properties of the plates were calculated from the
properties of the PCM (RT5) and of the polycaprolactone PCL.
2.4.1. Porosity
The porosity ε was obtained from the density of each
component (Table 1a) and the PCM mass fraction.
ε ¼ 1 À r
xRT5
rRT5
þ
xPCL
rPCL
(7)
Tnþ1
1 ¼
Tnþ1
a þ
k
hDy=2
Tnþ1
2
0
1 þ
k
hDy=2
Hnþ1
1 ¼ enthalpy function
À
Tnþ1
1
Á
Hnþ1
2 ¼ Hn
2 þ
Dt
rDy2
kTnþ1
3 À
k þ
1
1=ðhDyÞ þ 1=ð2kÞ
Tnþ1
2 þ
Tnþ1
a
1=ðhDyÞ þ 1=ð2kÞ
!
Tnþ1
2 ¼ inverse enthalpy function
À
Hnþ1
2
Á
Hnþ1
i ¼ Hn
i þ
kDt
rDy2
À
Tnþ1
iþ1 þ Tnþ1
iÀ1 À 2Tnþ1
i
Á
for 3 i M À 2
Tnþ1
i ¼ inverse enthalpy function
À
Hnþ1
i
Á
for 3 i M À 2
Hnþ1
MÀ1 ¼ Hn
MÀ1 þ
Dt
rDy2
kTnþ1
MÀ2 À
k þ
1
1=ðhDyÞ þ 1=ð2kÞ
Tnþ1
MÀ1 þ
Tnþ1
a
1=ðhDyÞ þ 1=ð2kÞ
!
Tnþ1
MÀ1 ¼ inverse enthalpy function
À
Hnþ1
MÀ1
Á
Tnþ1
M ¼
Tnþ1
a þ
k
hDy=2
Tnþ1
MÀ1
0
1 þ
k
hDy=2
Hnþ1
M ¼ enthalpy function
À
Tnþ1
M
Á
8
:
(6)
-10 -5 0 5 10 15 20
0.5
1
1.5
2
2.5
3
x 10
5
Temperature (°C)
Enthalpy(J/kg)
plate 1
plate 2
Fig. 3 e Enthalpy in function of temperature (for heating
process).
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6. 47% and 62% of porosity were obtained for the plates 1 and
2 respectively.
2.4.2. Density
The density of the plate was calculated in function of the
porosity, the mass fraction and the density of each
component:
1
r
¼
1
1 À ε
X
i
xi
ri
¼
1
1 À ε
xRT5
rRT5
þ
xPCL
rPCL
(8)
The density of the two plates at 20
C and below the crys-
tallization region was showed in Table 1b.
2.4.3. Heat conductivity
The heat conductivity was estimated as the mean value of the
parallel and series models:
kparallel ¼
X
i
kiεi ¼ r
X
i
kixi
ri
kseries ¼
X
i
εi
ki
!À1
k ¼
kparallel þ kseries
2
(9)
εi: volume fraction of component i
2.4.4. Heat capacity
The heat capacity of the plate was calculated from the heat
capacity of each component and the mass fraction:
cp ¼
X
xicpi (10)
During the phase transition, the heat capacity increases
greatly due to the phase change enthalpy:
cp;PC¼
DHPC
DTPC
(11)
2.5. Experimental validation
Experiments were carried out inside a temperature simulator
in order to study the temperature evolution of the two plates.
During the experiments, the air temperature inside the
simulator was maintained constant. Two types of experi-
ments were carried out for both plates: heating and cooling.
2.5.1. Thermal histories simulator
An experimental thermal histories simulator (Fig. 4) that can
reproduce cold chains at laboratory scale was developed in the
Frisbee project (Derens and Osswald, 2011). This device was
Fig. 4 e The thermal histories simulator (a) and the roll to put the products (b).
Fig. 5 e Temperature evolution of the plate 1 during 4
repetitions of cooling experiment (a) At plate surface (b) At
plate center.
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7. designed and constructed to provide a controlled temperature
and airflow that is used to rebuild the observed temperature
histories in the cold chain for selected food products. This
control system allows different temperature setting levels and
heating or cooling rates to be programmed.
2.5.2. Convective heat transfer coefficient measurement
The convective heat transfer coefficient was measured using
an aluminium heating object as described by Alvarez and Flick,
1999 where the Biot number is lower than 0.1 (thermal con-
ductivity 237 WmÀ1
KÀ1
, diameter 0.07 m, emissivity 0.12). The
object, instrumented by a thermocouple (T-type) and an elec-
trical heater, was placed inside the simulator at the same place
as the plates. It was heated by supplying power to the resis-
tance until its temperature was about 15e20
C above the air
temperature. The power supply was then turned off and the
object was cooled by forced convection by the air flow gener-
ated by the simulator. The convective heat transfer coefficient
obtained, h (W mÀ2
KÀ1
) was calculated from the slope of the
curve describing the evolution of temperature in function of
time and it was around 10 W mÀ2
KÀ1
(Hoang, 2012a).
2.5.3. Plate preparation
Maximum attention was taken to obtain a homogeneous
initial temperature for the tested product. For heating exper-
iment (plate initial temperature À10
C, air temperature in the
simulator 20
C), the plates were kept inside a home freezer at
À10
C for at least 12 h. For cooling experiment (plate initial
temperature 17
C, air temperature in the simulator À10
C),
the plates were kept at ambient temperature. When the
product was moved to the simulator, it was packed inside an
insulated box. Therefore, the initial center and surface tem-
peratures were almost the same (0.5
C of difference).
2.5.4. Instrumentation
T-type thermocouples (1 mm diameter, precision ±0.2
C) were
inserted in the plate's center and surface to measure its tem-
perature. Air temperature near the plate was also measured.
These thermocouples were previously calibrated at 5 different
temperatures (À25
C, À15
C, 0
C, þ15
C and þ25
C).
2.5.5. Experimentation repetitions
At least 2 repetitions were done for the heating or cooling
experiment of each plate. Fig. 5 shows the temperature evo-
lution of the plate 1 during 4 repetitions of the cooling
experiment; no significant difference was observed. The same
behaviour was observed for the repetitions of other experi-
ments and confirmed the stability of the material properties
during heating and cooling cycles.
3. Results and discussion
3.1. Comparison between experimental and numerical
results
Fig. 6 shows a comparison between experimental and nu-
merical results for the plate 1 during heating and cooling
Fig. 6 e Comparison between experimental and numerical temperature for plate 1 a) Temperature evolution during heating
process b) Temperature evolution during cooling process c) Correlation between experimental and numerical temperature
at plate center e heating process d) Correlation between experimental and numerical temperature at plate center e cooling
process.
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8. processes. The averaged plate's center and surface tempera-
tures of all repetitions were used to represent the experi-
mental data. For both processes, the phase change occurred
between À2
C and 10
C and stayed for around 1000 s, offering
a greater thermal inertia for the material in this range of
temperature. The hysteresis was observed, the melting
(Fig. 6a) began at a higher temperature compared to the end of
the crystallization (Fig. 6b) which agreed with the DSC results.
It can be observed that the model under predicts the surface
temperature during the heating process (maximum difference
of 1.9
C, Fig. 6a). The plate center temperature, however, was
relatively well predicted (maximum difference 0.8
C) for
both heating and cooling processes. The difference may relate
to the precision of the model input parameters (thermal
properties, heat transfer coefficient …). The correlation be-
tween numerical and experimental temperatures at the plate
center (Fig. 6c and d) confirmed a good agreement between the
simulation and experience.
The temperature evolution of the plate 2 obtained by the
simulation and experience during heating and cooling pro-
cesses is presented in the Fig. 7. In general, the model pre-
dicted well both the evolution of the center and surface
temperature (maximum difference of 1.2
C for the center and
2.2
C for the surface temperatures). A similar thermal
behaviour was observed compared to the plate 1 with the
same phase change temperature range.
Table 2 summarises the time for the phase change and for
the temperature equilibration between air and the plates for
both heating and cooling processes. Because of its smaller
dimensions and mass (plate 2: 0.037 m  0.037 m  0.005 m
and 2.68 g/plate 1: 0.050 m  0.050 m  0.010 m and 12.34 g),
the plate 2 takes only half of the time to attain the air tem-
perature compared to the plate 1. However, the time for phase
change takes 33% of the total time for the plate 2 (38% of PCM)
and only about 25% for the plate 1 (30% of PCM).
3.2. Influence of packaging on thermal inertia and
product shelf-life
3.2.1. Effect of encapsulated PCM on thermal inertia
In order to evaluate the effect of encapsulated PCM material
on thermal inertia, a numerical simulation was carried out to
study the temperature evolution of an imaginary plate made
of this material along a cold chain (Plate 3, Table 1b). The air
time-temperature profile of the meat cold chain (Table 3) from
the Frisbee Cold Chain Database (Taoukis and Katsaros, 2011;
Hoang, 2012b) was used as input data. In the simulation, three
temperature peaks (20
C, 45 min) were added between the
links (transportation, distribution warehouse, display cabinet
and consumer domestic refrigerator) to represent the transi-
tion between them. It was assumed that the plate 3 had the
same thermal properties as the plate 1 and had a thickness of
4 cm; the other plate's dimensions (length and width) were
supposed to be large enough so that the 1D model was still
acceptable. This type of plate could be used for the external
packaging of a product pallet for example. Considering the
price of the encapsulated PCM (about 5V/kg), using this ma-
terial demands an additional investment of about 200V per m3
of volume of product. However, the packaging can be reused.
The temperature evolution at the center of the plate 3 was
compared to the one of a cardboard of the same dimensions
(plate 4, Table 1b); the result was shown in Fig. 8. During the
first two temperature peaks, the PCM plate temperature
increased up to 7.5
C; for the third peak, the PCM plate tem-
perature increased progressively to attain the temperature
level of the refrigerator (5.65
C). The cardboard temperature,
Table 2 e Time for phase change and for temperature equilibration of the 2 plates.
Time for melting
(min)
Time for
crystallization (min)
Total time (TT) for temperature equilibration between
air and plate (heating and cooling processes) (min)
Plate 1 13 (24% of TT) 12 (26% of TT) 52
Plate 2 8 (33% of TT) 8 (33% of TT) 25
Fig. 7 e Comparison between experimental and numerical temperature for plate 2 a) Temperature evolution during heating
process b) Temperature evolution during cooling process.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 5 2 ( 2 0 1 5 ) 1 5 1 e1 6 0158

9. however, attained 20
C during the three peaks. This result
demonstrated a better thermal buffering capacity of the
encapsulated PCM material compared to a standard one.
3.2.2. Product shelf-life
The result of the thermal model, the time-temperature pro-
files of the two types of packaging (encapsulated PCM and
cardboard), were applied to the “Cold Chain Predictor soft-
ware”. This software allows the calculation of the remaining
shelf-life of a food product taking into account the microbial
growth under specific time-temperature profiles correspond-
ing to different cold chain scenarios (Lun et al., 2012). Cooked
ham slices in modified atmosphere packaging were selected
as a case study. The specific food product has a shelf life of 29
days at 2
C and the specific spoilage organism that can be
used as a quality indicator is lactic acid bacteria growth. Ac-
cording to Kreyenschmidt et al. (2010) the end of shelf-life for
the specific food product can be considered as the time when
lactic acid bacteria reaches more than 7log10 (CFU gÀ1
).
Temperature sensitivity of lactic acid bacteria growth was
expressed through the activation energy (using Arrhenius ki-
netics), found to be equal to 110.7 kJ molÀ1
. The remaining
shelf-life was estimated at the end of the two temperature
profiles depicted in the Fig. 8, for cardboard and PCM pack-
aging, respectively using the Cold Chain Predictor Software.
According to the results the remaining shelf life of cooked
ham in cardboard and PCM packaging was 356 and 380 h,
respectively. This result confirmed the influence of the pack-
aging on the product quality and showed the possibility to
increase the product shelf-life by using a novel packaging
material (þ6.7% in the current condition). Further study would
be carried out to find the optimized thickness of the packaging
plate in function of the gains of product quality/shelf life and
the additional investment caused by the material.
4. Conclusion
A model of heat transfer for encapsulated PCM material (RT5 e
PCL) was developed. It took into account the variation of
thermal properties in function of temperature and the phase
change of the PCM material by the enthalpy method. The
validation of the model was carried out by experiments on two
plates of different mass fractions of PCM during heating and
cooling processes. The results showed that this material has a
better thermal buffering capacity compared to a standard
packaging material which can enhance the thermal protec-
tion of perishable products.
Acknowledgements
The research leading to these results has received funding
from the European Community's Seventh Framework Pro-
gramme (FP7/2007-2013) under grant agreement No. 245288.
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