RECUEIL DE MÉCANIQUE VOL... N°.. (2022)..–..

ISSN: 2507-7589 ○ EISSN: 2507-7619

Research Paper DOI : 10.5281/zenodo…… Open access

Hybrid nano improved phase change material for latent thermal energy
storage system: Numerical study.
Mohamed Lamine Benlekkam b.c , Nassira Cheriet* a,c, Driss Nehari b, Sahraoui Kherris a,c
a
Mechanical Engineering, Materials and Structures Laboratory, TISSEMSILT university, Tissemsilt, Algeria,
b
Laboratory of Smart Structure, University of Ain Temouchent, AinTemouchent, Algeria.
c
Faculty of science and technology, TISSEMSILT university, Tissemsilt, Algeria,

ARTICLE INFO ABSTRACT

Article history : Due to the very low thermal conductivity of phase change materials (PCMs), the thermal
conductivity can be improved by utilizing hybrid nanoparticle-enhanced phase change
Received …
materials (HNPCM). In this study, a small mass fraction of hybrid nanoparticles TiO2-
Received in revised form … CuO was dispersed in PCM in a (50%-50%) ratio with five mass concentrations of 0%,
0.25%, 0.5%, 0.75%, and 1% to enhance the thermal performance of the hybrid nano-
Accepted …
PCM (HNPCM) used for thermal energy storage (TES). The numerical model created in
this study was successfully validated using experimental data from the literature. The
findings demonstrated that the addition of hybrid nanoparticles enhanced the effective
Keywords: thermal conductivity and density of HNPCM. Accordingly, the average charging time
Phase change material (PCM) Latent heat was reduced by 12.04%, 19.9%, 23.55%, and 27.33%, respectively, when the mass
storage, Melting and solidification, fraction of HNPCM increased by 0.25%, 0.5%, 0.75%, and 1%. On the other hand, the
Thermal energy storage, Hybrid Nano-
particles, LHTESS. more the HNPCM dynamic viscosity increases, the more the hybrid nanoparticles' mass
concentration is increases. Consequently, the phase change rate underwent a decline due
to the slower motion of the liquid HNPCM, which breaks down the natural convection
effect. Moreover, the amount of energy saved decreased by 0.83%, 1.67%, 2.83%, and
3.88%, respectively.

1. Introduction
Phase change materials (PCMs) are utilized in latent heat storage (LHS) to store and release thermal energy during their
melting and solidification cycles [1][1]. However, the PCM suffers from its low thermal conductivity (0.1–0.7 W/m.K),
which decreases the thermal performance of TES systems. Therefore, several researchers try to develop an improved
technique to increase the heat transfer rate inside the PCM such as fins, TES system orientation, and nanoparticles additives
[2]–[4][2-4].
Despite the significant thermal improvement, the fins increase the net weight of the TES system. Hence, the use of
nanoparticles dispersed into the pure PCM can also improve its thermophysical properties. NS. Dhaidan et al [5][12]
presented an experimental and numerical investigation of NePCM inside a cross-section of two concentric cylinders. They
reported that the inclusion of nanoparticles accelerated the melting time by increasing the PCM's effective thermal
conductivity for low concentration. However, the high nanoparticles quantities make it longer due to the increment of
nanoparticles agglomeration and viscosity effects. They recommended using an eccentric configuration geometry by

* Corresponding author. Tel.: +213 780497444.

E-mail address: mohamed_benlekkam@yahoo.fr

Recueil De Mécanique © 2022

2 RECUEIL DE MÉCANIQUE VOL.. N°.. (2022)..–..

lowering the center of the internal cylinder to increase the surface area and the amount of NePCM exposed to the
buoyancy-driven convective flow effect. Changda Nie et al [6]conducted a parametric study on the charging process for the
vertical TES unit. They found the HTF upside injection was more effective in convection domination, whereas the bottom
injection was better for the conduction. Besides, the nanoparticles inclusion improved the conduction heat and decreased
the total energy storage. P.M Kumar et al-b investigated the effect of using Hybrid nanoparticles (SiO2-CeO2) into Paraffin
with 0, 0.5, 1.0, and 2.0 mass fractions on its thermophysical properties. They found that the dispersion of hybrid
nanoparticles in PCM did not affect its chemical structure. Moreover, the relative thermal conductivity and stability of
HNPCM were boosted by 115.49% and 165.56%, respectively. Further, they noticed that the supercooling was reduced by
more than 35% for 2% of hybrid nano-additive. Besides, they recommended 1% of hybrid nanoparticles within Paraffin for
getting a better thermal performance of low-temperature solar thermal systems due to its low change in thermal storage
capacity.
Although various researchers [5], [7]–[9]have studied the nano-improvement of shell and tube for LHS system with a
single type of nanoparticles. However, the use of two types of nanoparticles has not been widely studied. Moreover, an
improvement based on a single type of nanoparticle is solely dependent on its thermophysical properties, especially thermal
conductivity and viscosity. For the present work, we used the TiO2 and CuO metal oxide, which has several outstanding
properties like stability and chemical inertness. Therefore, the employment of TiO2-CuO can offer a better improvement.
In this study, we carefully investigated the effect of hybrid nanoparticles on the thermal performance of shell and tube
TES unit. Similar quantity of TiO2-CuO was dispersed in PCM based (paraffin) with five mass concentrations of 0, 0.25,
0.5, 0.75, and 1 wt %. The present study aims to properly evaluate the effect of hybrid nanoparticles mass concentration on
the liquid fraction, complete time, and the total stored energy for the charging process

2. Mathematical model
The configuration of the LHS system under investigation Fig.1, which is studied by Hosseini et al [10]for their experiment.
LHS system is composed of a shell and a copper tube heat exchanger. The length, outer and inner diameter of the shell and
tube are 1m, 0.085 m, and 0.022 m, respectively. While the exterior of the unit is completely insulated. We kept the same
configuration of [10]in our numerical study. The space between the shell and the tube was filled by PCM, which is Paraffin
[11]A hybrid TiO2-CuO nanoparticles is dispersed within PCM for enhancing its thermal properties. Water flows through
the inner tube as HTF to transfer thermal energy with the HNPCM during the melting process. The initial temperature of
the whole system is T0=25°C. The HTF temperature is set to be THTF= 70°C with a flow rate of 0.017 kg/s.The
thermophysical properties of the PCM and the nanoparticles used in the present study are presented in Table1. For
equivalent quantity of TiO2-CuO hybrid nanoparticles. five mass concentration of 0%, 0.25%, 0.5%, 0.75% and 1 mass%
are used in this study.

Fig. 1 - Schematic diagram of the numerical TES system.

Table 1-Thermo-physical properties of PCM [11], Water, Nanoparticles TiO2 [12] and CuO [12]

Nanoparticles
Propriety Paraffin HTF (water)
TiO2 CuO

Density (kg.m-3) 778 977.36 4250 6460

Specific heat capacity 2100 4066.8 686 536

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(J.kg-1.K-1)

Thermal conductivity 0.231 0.6627 8.954 10.042

(W.m-1.K-1)

Melting temperature (°C) 58-62 - - -

Latent heat (J.kg-1) 189470 - - -

Viscosity (mPa.s) 9.27 - - -

Dilatation coefficient (1/K) 0.0006 - - -

3. Governing equations
The following assumptions are taken into account to conduct all the numerical simulations on the charging and discharging
process of HNPCM in the LHTES unit.

 The flow in HTF and liquid phase of HNPCM inside the container is laminar, incompressible and Newtonian.
 The thermophysical properties are assumed to be constant with temperature except the density.
 Boussinesq approximation is adopted to take into account the density variation.
 Volumetric expansion or contraction of samples associated with phase transition in a shell container is neglected.
 The HNPCM is homogeneous and isotropic.
 The external shell wall container is considered perfectly insulated, and the shell material is not taken into account in
the computational domain.
 Due to the higher thermal conductivity relative to the copper tube, the thickness of tubes is neglected, and inlet
temperature variations of HTF are also ignored.
 The continuity

(1)

 The momentum

(2)

 The energy

(3)

 The total volumetric enthalpy H is calculated by:

(4)
(5)
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(6)

Where ΔH latent heat of the material and h is the sensible heat of PCM.

h0 is the PCM sensible enthalpy at the reference temperature T 0, γ refers to liquid fraction that indicates the fraction of a cell
volume in liquid form and is associated with each cell in the domain given by Eq. (7).

{
0 T <T s
γ = T s<T <T l (7)
1 T >T l

Boussinesq approximation was adopted to calculate the change in PCM density as a function of temperature in the liquid
density given by:

(8)

And the relationship of buoyancy forces in the momentum equation is given by:

(9)

Where ρ0 is the reference density at melting temperature Tm and β is the thermal expansion.

3.1. Thermal performance index.

The total energy stored by the HNPCM during the charging process is defined by:

(10)

Where Tinlet represents the inlet temperature of the HTF, m is the effective mass of HNPCM, and is defined by (Eq 5).

The instantaneous stored energy of HNPCM is defined by [8]:

(11)

We can use the dimensionless form of H(t) dividing it by the maximum value Htotal using (Eq. (10)). H(t)/ Htotal

Also, we can define a stored energy rate by (Eq. (11)) as follow:

(12)

3.2. Thermophysical properties of hybrid Nano-PCM

Overall, to determine the nanofluid thermophysical properties, almost all of the literature studies have used the classical
models of Maxwell. However, a hybrid nanofluid lacks some models to define its properties. In fact, there is a model
proposed by SS Ghadikolaei et al [13] based on the classical ones. The mass concentration ∅ for the two different types of
nanoparticles (TiO2 and CuO) dispersed in PCM is calculated from eq. (10) and the other thermal properties are calculated
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by the equations shown in Table 2. However, these classical models cannot estimate the hybrid thermophysical properties
of the HNPCM with good precision. Which makes it difficult to have a clear idea of the hybrid nanoparticles' influence on
pure PCM. Accordingly, the thermal conductivity and viscosity of HNPCM for all mass concentrations are taken from the
measured experimental data of S. Harikrishnan et al [11] for the present numerical computations.

∅ = ∅TiO 2 + ∅ CuO (13)

Table 2 - Thermophysical properties of hybrid NanoPCM [3], [14]

NanoPCM Hybrid NanoPCM

[
ρnPCM =ρPCM (1−∅ ) + ∅
( )]ρPCM
ρs
(14)
[
ρhnPCM = ρPCM ( ( 1−∅ 2 ) ) ( 1−∅ 1) + ∅ 1 ( )]
ρs
ρ PCM
1
+ ∅2 ρ s 2
(19)

[
ρCp nPCM =ρCp PCM ( 1−∅ ) + ∅
( ρCp s
ρCp PCM )] (15)
[
ρCp hnPCM =ρCp PCM ( 1−∅ 2 ) ( 1− ∅1 ) + ∅1 ( ρCp s
ρCp PCM
1

)] + ∅(20)
2 ρCp s 2

μ PCM μ PCM
μnPCM = 2. 5 (16) μhnPCM = 2. 5 2 .5 (21)
( 1− ∅ ) ( 1− ∅1 ) ( 1−∅ 2 )

ρL f bPCM =ρL f bPCM ( 1− ∅ ) (17) ρL f HNPCM =ρL f bPCM ( 1− ∅ 2) ( 1−∅ 1 ) (22)

k hnPCM k s + ( S−1 ) k bPCM −( S−1 ) ∅2 ( k bPCM −k s )

=
2 2

k bPCM k s + ( S−1 ) k bPCM + ∅ 2 ( k bPCM −k s )

k nPCM k s + ( S−1 ) k PCM −( S−1 ) ∅ ( k PCM −k s ) 2 2

= (18) Where (23)

k PCM k s+ ( S−1 ) k PCM + ∅ ( k PCM −k s ) k s + ( S−1 ) k PCM −( S−1 ) ∅ 1 ( k PCM −k s )
k bPCM
=
1 1

k PCM k s + ( S−1 ) k PCM + ∅ 1 ( k PCM −k s )

1 1

Table 3 - Thermophysical properties of hybrid NanoPCM for each fraction

TiO2-CuO

Total fraction 0% 0.25% 0.5% 0.75% 1%

Density (kg.m-3) 778 789.48 800.95 812.4 823.83

Heat capacity (J.kg-1.K-1) 2100 2074.41 2049.6 2025.51 2002.13

Thermal conductivity (W.m-1.K-1) 0.231 0.265 0.298 0.322 0.345

Viscosity (mPa.s) 0.00927 0.00936 0.00947 0.00962 0.00984

Thermal expansion coefficient (1/K) 0.0006 0.00059 0.00058 0.00057 0.00056

Latent heat (J.kg-1) 197620 196220 194680 192340 190060

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4. Numerical method and validation

4.1. Numerical method

A 2D implicit finite volume method was used to solve the governing equations in section 2.1 for a heat transfer conjugated
with a solid-liquid phase change process. The governing equations are solved by using the commercial code Ansys Fluent.
The phase change phenomena were modeled by the enthalpy-porosity formulation [14]. In this method, the solid liquid
interface is modeled as a porous medium. The liquid fraction varies smoothly across this porous so-called mushy zone,
where the porosity takes the values 0 and 1 in the liquid and solid phases, respectively. The mushy zone is modeled via the
phase fractions incorporated in the source terms in the governing equations to account for the phase change phenomena.
The pressure-velocity coupling is accounted by using SIMPLE algorithm [15], whereas the Quick scheme was adopted for
convective discrimination, and the PRESTO scheme was selected for pressure correction. Besides, the Boussineq
approximation was adopted to take into account the change in density of the PCM in the liquid phase as a function of
temperature eq (7). Further, the convergence criterion of 10 − 6 for the momentum and continuity equations and 10 − 8 for the
energy equation were taken.

4.2. Validation

The present model has been validated successfully with numerical and experimental data of Hosseini et al [10]. Our
validation has been performed with the same initial and boundary conditions, material properties and geometry of Hosseini
et al [10]. The total temperature of PCM for the charging process has been used for the validation. According to the figure
2, a good agreement was obtained. Therefore, it can be concluded that the present numerical model could be acceptable to
predict the behavior of the PCM during the charging and the discharging process.

Fig. 2 - Comparison of the average PCM temperatures for the charging process of numerical and experimental of [10], [16]
and the present study.
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5. Results and discussion

5.1. Charging/Melting process:

Fig. 3 - Liquid fraction of the HNPCM samples during charging process.

The effect of dispersed hybrid nanoparticles in PCM samples from 0 to 1wt % in the range of 0.25 wt% on the melting
process is presented in Fig.3. As we can see, the melting time decreased by 12 %, 20 %, 23.5% and 27.3 %, respectively.
This is due to the hybrid nano improvement which enhances the effective thermal conductivity of PCM. Furthermore, the
hybrid nanoparticles accelerate the sensible heating process due to its high thermal conductivity. Despite the HNPCM
thermal conductivity increased by about 50% from 0.231 for pure PCM to 0.345W/m. K for 1wt% of hybrid nanoparticles.
The melting rate does not accelerate as we expected because of the viscosity increment by about 6.14% compared to pure
PCM. Which is slowing down the molten HNPCM motion, then reduced the natural convection effect. Therefore, not only
the thermal conductivity improvement can accelerate the phase change but also its low dynamic viscosity.

Fig. 4 - The nanoparticles mass concentration effect on the dimensionless stored energy time evolution of the HNPCM
samples during the complete charging process.
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Fig. 5 - The HNPCM stored energy and its drop percentage.

From the above equations it should be mentioned that: As the mass concentration of hybrid nanoparticles increases, the
density and the thermal conductivity increase, while the latent heat and the specific heat capacity decrease. As a result, the
total thermal energy stored by the system decreased. The dimensionless stored energy of 0%, 0.25%, 0.5%, 0.75%, and 1%
HNPCM samples for the complete melting is presented in Fig.4. As the time elapsed, the H(t)/H total increases almost
linearly due to the sensible heating of the solid HNPCM. When the liquid fraction increases slightly with time due to the
phase change, the evolution of H(t)/Htotal becomes non-linear. At the end of the charging process, the H(t)/H total reaches the
steady-state taking the value 1 when the HNPCM average temperature approaches the HTF inlet temperature.

The increment of the hybrid nanoparticles mass concentration decreases the HNPCM latent heat capacity. Which
decreases the effective storage mass of pure PCM replaced by hybrid nanoparticles. As shown in Fig.5, the stored energy
decreases from 286 kJ/kg for the pure PCM to 275 kJ/kg for the HNPCM with =1% which decreases by about 3.86%.

Fig. 6 - The HNPCM melting time and its improvement.

The completely melting time of HNPCM samples is indicated by Fig.6. We can see that the melting time reduces by 12.04
%, 19.9 %, 23.55%, and 27.33 % when the mass concentration of hybrid nanoparticles increased by 0.25, 0.5, 0.75, and 1wt
%, respectively. This is because of the thermal conductivity improvement which rises from 0.231W/m.K for the pure PCM
to 0.345W/m.K for HNPCM (=1%). Besides, the effective heat transfer surface is significantly improved, which can
generate a higher charging rate.
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6. Conclusion:

The hybrid nano (50%-50%) improvement of shell and tube LHESS was numerically studied in this paper. The
numerical simulation has been conducted to evaluate the thermal performance enhancement in terms of charging (melting)
processes in the TES unit filled by PCM dispersed by equal quantity of TiO2-CuO as hybrid nanoparticles to improve its
thermal performance. The numerical model has been validated successfully by comparing the average melting PCM
temperature where a good agreement has been obtained. Also, the mathematical formulations have been used to estimate
the thermophysical properties of HNPCM.
Based on this study, the following conclusions are obtained:

 Mathematical formulations used in the literature to estimate the thermal properties of hybrid-nano PCM
cannot predict with a good precision the real ones. Especially the thermal conductivity and dynamic
viscosity because those parameters have a strong effect on the thermal behavior of the PCM for this
application. Accordingly, it is suitable to use realistic properties in such cases.
 In the charging process, when the HNPCM mass fraction increased by 0.25, 0.5, 0.75, and 1 wt% the
melting average time enhanced by 3.45 %, 10.34 %, 16.1 % and 28.73 %, respectively. In the same time
it reduced the stored energy by 0.83%, 1.67%, 2.83% and 3.88%, respectively.
 The stored energy decreases due to the increment of the hybrid nanoparticles which reduces the effective
storage mass of PCM. Therefore, it decreases by about 3.86% for =1 wt%.
 The HNPCM dynamic viscosity is increased when the hybrid nanoparticles' mass concentration is
increased. Hence, the phase change rate is reduced due to the slower motion of the liquid HNPCM, which
breaks down the natural convection effect. Consequently, the melting time does not decrease as we would
expect when the thermal conductivity of HNPCM increases.
 For the melting process, the conduction dominates the heat transfer at the first stage. Then, when the
liquid HNPCM mass increases with time, the convection drives the heat transfer but not as we expect due
to the increase of the dynamic viscosity.
Further studies will focus on the evaluation of several couples of metal oxides in order to determine the
optimum thermal properties needed to obtain the best performance of the TES.

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