Applied Thermal Engineering 141 (2018) 958–975

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Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Numerical study of an inclined photovoltaic system coupled with phase T

change material under various operating conditions
⁎
Meriem Nouira , Habib Sammouda
Laboratory of Energy and Materials (LabEM) (LR11ES34), University of Sousse, ESSTHSousse, Abbassi Lamine Street, 4011 Hammam Sousse, Tunisia

H I GH L IG H T S

• APhase
numerical study of PCM layer attached behind PV panel is performed.
• 9 g/m change process of a PCM is studied under Tunisian climate.
• Wind direction
2
of dust deposition reduces PV panel power output of about 3 W at midday.
• increase from 30° to 60° rises PV panel temperature from 64 °C to 69 °C.

A R T I C LE I N FO A B S T R A C T

Keywords: Photovoltaic panels suffer from high temperatures. A large part of absorbed solar radiation is converted into
PCM heat, which causes heating of PV cells and therefore leads to decrease PV efficiency. The effect of integrating
PV-PCM panels different PCMs with different thicknesses is studied. Coupling photovoltaic panel with the suitable macro-
BIPV encapsulated phase change material layer is important for having better thermal regulation of PV panel. In the
Efficiency
current thermodynamic investigation, melting and solidification processes of the selected PCM are carried out.
Thermal regulation
To achieve a realistic simulation of heat and mass transfer of PV-PCM system, it is very important to analyze the
Dust deposition density
effects of the following exterior operating conditions on PV panel performance: wind direction, wind speed and
dust accumulation. Dust deposition density of 3 g/m2, 6 g/m2, and 9 g/m2 reduces electrical power of about
1.2 W, 2.8 W and 3 W, respectively. Moreover, the increase of wind speed leads to increase the heat losses due to
forced convection and therefore reduces PV panel temperature. Eventually, wind azimuth angle increase causes
an increase in the operating temperature of the PV panel.

1. Introduction electrical efficiency and to increase its power output. So far, several
methodologies have been used for thermal regulation of PV panel such
One of the renewable energy technologies that are being promoted as active cooling or passive cooling methods.
is solar energy; such energy is known to have the potential of gen- Active cooling methods require external devices, such as pumps to
erating electricity directly by using solar photovoltaic or by converting pump water or fans to force air, in order to maintain the temperature of
heat into electricity from solar thermal energy. Photovoltaic cells can the BIPV system at a level consistent with higher power output. For
absorb up to 80% of the incident solar radiation available in the solar instance, pumping water for cooling in locations characterized by great
spectrum. However, only a limited amount of the absorbed incident potential of solar energy, like deserts, may be unsuitable because water
energy is converted into electricity depending on the conversion effi- is rare. Moreover, it causes an insupportable maintenance that leads to
ciency of the PV cell technology. The high temperature of PV modules increase the operating costs.
reduces the efficiency of a PV system by 0.4–0.5% per K [1,2]. The To reduce the temperature rise of a BIPV system using active
operating temperature of the PV panel usually varies between 40 °C and techniques, Yun et al. [5] have studied the effect of ventilated wall-
85 °C in hot climates [3] and could exceed the upper range in some real integrated PV system with an opening behind the PV. The findings have
cases in summer as presented in [4]. Several studies have considered PV led to a rise of about 2.5% in the electrical output of PV panel.
panel as a building element. Therefore, thermal regulation of a building Lu et al. [6] studied the annual thermal performance of a BIPV
integrated photovoltaic (BIPV) module is required to enhance its system. In this paper, authors have discussed mainly the impact of the

⁎
Corresponding author.
E-mail address: nouiramariem1@gmail.com (M. Nouira).

https://doi.org/10.1016/j.applthermaleng.2018.06.039
Received 2 November 2017; Received in revised form 22 April 2018; Accepted 12 June 2018
1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

Nomenclature β thermal expansion coefficient of PCM (1/K)

βref temperature coefficient (1/K)
A upper surface of the PV panel (m2) Δτ transmittance reduction
Apv surface area of PV panel (m2) εglass surface emissivity of the glass
Ai anisotropy index εal aluminum emissivity
B liquid fraction of PCM γpv PV panel orientation (°)
Cp specific heat capacity (J/kg K) γw wind direction (°)
D Dirac delta function ηpv electrical efficiency
F the view factor μ dynamic viscosity (Pa s)
FT absorbed solar radiation with dust deposition (W/m2) ν kinematic viscosity (m2/s)
FF fill factor ρ density (kg/m3)
f correction coefficient ρg ground reflectance (albedo)
Gr Grashof number ρD dust deposition density (g/m2)
GT incident solar radiation (W/m2) σ Stefan–Boltzmann constant (W/m2 K4)
g acceleration due to gravity (m/s2) τ transmittance of polluted panel
k thermal conductivity (W/m K) (τα )(θ) transmission/absorptance product
K τα Incidence angle modifier θ incidence angle of solar radiation (°)
Lf latent heat (J/kg) θr refraction angle (°)
Lc characteristic length (m)
M air mass modifier Abbreviation
Mref reference air mass modifier
P pressure (Pa) AM air mass
Pr Prandtl number BIPV building integrated photovoltaic
Q internal heat generation (W/m3 K) HDKR Hay, Davies, Klucher, Reindl
Re Reynolds number PCM phase change material
Ra Rayleigh number PV photovoltaic
T temperature (°C) PV-PCM Photovoltaic phase change material
Te,amb exterior ambient temperature (°C) STC standard test conditions
Tsky sky temperature (°C)
TPV PV panel temperature (°C) Subscripts
Tref temperature at standard condition (°C)
Tf fusion temperature (°C) a air
TES thermal energy storage al aluminum
T time (s) b beam radiation
u velocity of PCM in x direction (m/s) b,n beam radiation at normal incidence angle
v velocity of PCM in y direction (m/s) c characteristic
vair wind velocity (m/s) d diffuse
vpv,cell volume of the PV cells (m3) e,amb exterior ambient
ΔT transition temperature (°C) g ground
liq liquid phase
Greek symbols n normal incidence angle
r refraction
α angle of inclination with the horizontal (°) solid solid phase
αp thermal expansion factor of air (1/K) T titled
αp absorptivity of the glass cover

thickness of an air duct on the thermal performance of the system. PCMs are mainly classified as non-organic, organic and eutectics
A global comprehensive review could be observed in the researches PCMs [12].
of Sargunanathan et al. [7]. Non-organic PCM: Hydrated salts are the most frequently used PCM
Passive cooling methods are based on the application of absorbing in this category. They have high latent heat storage capacity, non-
materials of heat excess released by the photovoltaic panel. The in- flammable and they are available at low prices. However, their main
tegration of PCM on the back side of a PV panel is a preferable passive disadvantage is that their super cooling problem during phase change
cooling method since it needs less operating and maintenance costs process which leads to irreversible transition phase [13].
compared to active cooling techniques [8], it does not require any in- Organic PCMs: Paraffin, carbohydrate and fatty acids are the most
tervention of external devices and additional energy [9] thanks to its used PCMs for thermal energy storage in this group. Being recyclable,
ability of storing and releasing heat [10]. having the ability of melting congruently, having high heat of fusion
PCMs undergo a reversible phase change process depending on their and freezing without much under-cooling compared to inorganic PCMs
fusion temperature. They absorb/release heat during their fusion/soli- [14] are their most known advantages. However, they have low
dification phase change. The selection of the ideal PCM for a better thermal conductivity in their solid state and can be available at high
thermal regulation of PV panel is very important. Hence, an appropriate prices [11].
PCM for such application must bear several criteria: large latent heat of Eutectic: Eutectic is a mixture of pure compounds with a volumetric
fusion, high thermal conductivity, chemically stable, non-corrosive, storage density slightly higher than organic substances. However, their
non-toxic and its melting temperature must be within the PV system’s thermo-physical properties data are limited because the use of such
operating range [11]. materials is new for energy storage applications.

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

Hence, using paraffin for solar system cooling, requiring high latent 1.0–1.5% compared to the conventional PV panel.
heat storage is preferable. But, such materials have usually low thermal Laura et al. [27] have studied a BIPV-PCM prototype, installed on
conductivity leading then to poor performance of the TES system. Solar XXI office building's vertical façade, under Lisbon outdoor con-
For this reason, Chaichan et al. [15] have studied the effect of im- ditions.
proving the thermal conductivity of paraffin wax with different mass Hasan et al. [28] have investigated experimentally the performance
fractions of nanoparticles of Al2O3 and TiO2. They have found that of PV-PCM system for Dublin, Ireland and Vehari, Pakistan locations.
increasing the mass fraction leads to an increase in its thermal con- They have observed a reduction of 7 °C and 10 °C in PV panel' tem-
ductivity and thus increasing the heat release rate of the studied ma- perature using salt hydrate (CaCl26H2O) and a eutectic mixture of fatty
terial. acids with Capric-palmitic acid as PCMs respectively.
He et al. [16] have investigated experimentally new nanofluids Browne et al.[29] have investigated a novel PV-T-PCM system under
PCMs. Its thermal conductivity is enhanced and its supercooling degree Dublin, Ireland environmental conditions. They have found that using
is reduced by adding TiO2 nanoparticles in BaCl2-H2O (aqueous BaCl2 PCM leads to improve heat extraction amount from PV panel about 7
solution). The studied TiO2-BaCl2-H2O can be considered as a pro- times. An experimental investigation carried out by Browne et al.
moting candidate for cooling storage. [30,31] show that coupling PV-PCM system with a pipe network filled
Chaichan et al. [17] have performed an experimental study, in with water could be a good approach to utilize the heat stored by PCM.
Baghdad-Iraqi weathers, to enhance the thermal conductivity of par- Al-Waeli AH et al. [32] have showed in his paper that the use of 3 wt
affin wax by adding aluminum powder as an additive and therefore to % Nano-SiC-water improves the electrical efficiency by up to 24.1% in
enhance its heat transfer rate. An improvement on its thermal con- comparison with the reference system and the thermal efficiency
ductivity is found as compared to the pure PCM. The different types of reached 100.19% in comparison with the reference system. Moreover,
PCMs, mentioned previously, have been used for several applications. Al-Waeli AH et al. [33] have investigated experimentally the effect of
For instance, Sharma et al. [18] have considered the use of PCM in SiC nanoparticles added in paraffin as a PCM on the efficiency of the
various building components. Sun et al. [19] have studied the effect of PV/T systems. This investigation has showed that the studied system
its integration in Trombe walls. reduces PV cell temperature to 30 °C and therefore increases its power
Lin et al. [20] have studied the use of PCM for floor heating. output from 61.1 W to 120.7 W.
Moreover, several studies have recently been studying the use of PCMs Apart from the experimental researches, several studies have re-
for thermal regulation of BIPV panel. Such application to decrease the ported numerical studies of PV-PCM system. Most numerical studies do
rise of PV panel temperature has recently been studied. not take into account the convective heat transfer inside the PCM.
Most experimental investigations on PV-PCM modules have been However, Liu et al. [34] have mentioned the vital role of convective
studied under controlled external conditions. The following investiga- heat transfer mode on the phase change process. Taking into account
tions have revealed the experimental studies of the PV-PCM system. the presence of convective mode for macro-encapsulated phase change
The first experimental and numerical study of a BIPV system cou- material allows the displacement of macroscopic fluid particles and
pled with paraffin wax (RT25) as a PCM has been carried out by Huang therefore leads to speeding up fusion process and enhancing the ex-
et al. under externally controlled conditions [21]. In this research, a traction of heat from PV panel.
macro encapsulated PCM into aluminum container has been attached The following studies have considered only the conductive heat
behind a solar selective absorbing material and exposed to transfer mode:
750–1000 W/m2 of solar radiation. Their numerical results have been
compared with the numerical results and a good agreement has been Park et al. [26] have analyzed the effects of orientation on vertical
found. BIPV-PCM system as well as the thickness of PCM on PV panel's
Hasan et al. [8] have investigated the use of various types of PCM electrical output.
for thermal regulation of four different cell-size BIPV systems under Elarga et al. [35] have studied a one dimensional numerical model
500–1000 W/m2 of solar radiation. They have found that the use of of a PV-PCM system with double skin façade in different climates. A
pure salt hydrate mixed with Eutectic mixture of Capric-lauric acid, reduction within 20–30% in the monthly cooling requirement is
commercial blend and Eutectic mixture of palmitic acid and paraffin found for hot climates. Additionally, about 8% of an increase in peak
wax reduce PV panel's temperature to about 18 °C, 16 °C and 14 °C, value of PV efficiency is noticed when the double skin façade is
respectively. combined with the PV-PCM system.
Maiti et al. [22] have studied the effect of integration PCM (paraffin Atkin and Farid [9] have studied the thermal regulation of the PV
wax) on the back side of PV system. PV panel's temperature is reduced panel using infused graphite as PCM integrated with finned heat
to 65–68 °C at 2300 W/m2 while it attains 90 °C without using PCM. sink. Results show that using PCM creates a shift in temperature
Biwole et al. [23] have revealed in his investigation that the in- peak. Moreover, the efficiency of PV cell rises to 13% using PCM for
tegration of a PCM layer behind PV panel leads to reduction of PV PV panel.
panel's temperature to 40 °C. Smith et al. [36] have analyzed from a global numerical study the
Sharma et al. [24] have investigated the thermal regulation of a electrical power output from the PV-PCM system for countries all
building integrating concentrated PV system using PCM. An enhance- over the globe. They have found an improvement of 6% on PV panel
ment in its electrical efficiency has been observed by 6.80%, 4.20% and power output in different countries such as eastern Africa and
1.15% under 1200, 750 and 500 W/m2 respectively. Mexico.
Atkin and Farid [25] have analyzed through an experiment, the Ho et al. [37,38] have studied numerically a three dimensional
thermal response of a PV-PCM panel under controlled peak incident- model of PV system coupled with microencapsulated PCM and
light of 960 W/m2. Four different techniques have been studied to taking into account only the conductive heat transfer mode into the
analyze the efficiency of the studied PV-PCM system. PCM.
A few experimental studies have been investigated under actual Kibria et al. [39] have investigated a one-dimensional numerical
environmental conditions. For instance, Park et al. [26] have examined study of a BIPV-PCM system. The thermal response of BIPV-PCM has
a vertical BIPV-PCM module in an experiment under actual climatic been treated using various PCMs, neglecting wind speed effect and
conditions. Their results reveal that adding a PCM layer behind the PV convective mode effect in PCM on PV panel power generation.
panel decreases the PV temperature rise coming from overheating by
absorbing a considerable amount of heat during the phase change. In All the previous numerical studies mentioned below do take into
addition, the amount of electric power generation is increased by consideration neither the effect of wind orientation on PV-PCM panel

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

temperature nor the effect of dust on the electrical power produced of Table 1
PV-PCM panel. Great interest has been paid to thermal PV-PCM systems PV panel material properties [35,36].
in recent years. However, researches on such modules under actual Thermo-physical properties of PV panel and aluminum layer
environmental conditions in hot regions like Tunisia have seldom been
found. To the best of our knowledge, the study of the effect of wind Density Specific heat Thickness (m) Thermal
direction as well as the effect of dust on the performance of the system (kg/m3) (J/(kg K)) conductivity (W/
(m K))
has been rarely studied in the open literature. In order to deepen the
study of the PV-PCM, further improvements have been made in the Glass 3000 500 0.003 1.8
present study, including convective heat transfer into the liquid PCM to EVA 960 2090 0.0005 0.35
study its phase change process (fusion and solidification), heat loss by Silicon cells 2330 677 0.0003 148
Tedlar 1200 1250 0.0005 0.2
forced and natural convection from both sides of the PV-PCM panel to
Aluminum 2675 903 0.002 211
the environment, radiation heat loss, actual climatic conditions using
the Hay, Davies, Klucher, Reindl (HDKR) to model solar radiation re-
ceived by an inclined PV-PCM system, wind speed, wind direction and Table 2
dust deposition on the performance of the system have been in- Thermo-physical properties of the PCM used by Park et al. (2014) [15].
vestigated. The current work is organized as follows: A numerical
Thermo-physical properties Value
model description is presented in Section 2. The mathematical model of
the considered PV-PCM system is given in Section 3. The current results Thermal conductivity (solid) (W/(m K)) 0.2
have been validated against previous experimental results from litera- Density (solid) (kg/m3) 880
ture in Section 4. In Section 5, the effect of the integration of different Density (liquid) (kg/m3) 760
Specific heat capacity (kJ/(kg K)) 2.1
PCMs behind PV panel as well as the effect of its thickness on operating Melting temperature (K) 298
PV-PCM panel temperature has been investigated. Additionally, the Latent Heat of Fusion (kJ/kg) 184
effects of the operating conditions such as wind direction, wind speed,
dust deposition density on the temperature of PV-PCM system, on its
efficiency and on its electrical power generation have been studied. frame which its effects are not considered in the model because its
Eventually, conclusions have been yielded in Section 6 and future work surface area in comparison with the panel area is very low, thus, it have
direction is given in Section 7. Thus, an evaluation of the system be- a negligible effect on the variation of PV panel temperature [40]. The
havior under various operating conditions could be assessed from the angle α represents the tilt angle relative to the horizontal. The thermo-
current thermodynamic work by studying the influence of pretty im- physical properties of each layer used in the current study are given in
portant factors that have not been taken into consideration hitherto. Table 1. Moreover, the thickness of the chosen PCM layer used in the
present work is macro encapsulated in 2 mm thick aluminum sheets.
2. Numerical model description The properties of the selected PCM are presented in Table 2. The above
described thermal model was studied for a selected city, namely Sousse
As usual, a PV module is composed of five layers depending on the (35.82539_N, 10.63699_E) for Tunisian climate on July 15th.
photovoltaic technology used as presented in Fig. 1. The PV module in
this work is polycrystalline and it is assumed to be fixed in a metal

Fig. 1. Physical model of PV/PCM panel.

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3. Thermal equations and boundary conditions (36). σ is the Stefan–Boltzmann constant, εglass is the surface emissivity of
the glass cover taken as 0.91 [41], Ff-sky and Ff-g are correspond to the
The processes that describe the phenomenon of electricity produc- view factors between the PV panel front surface and the sky or the
tion at the level of the semiconductor material as well as the operating ground, respectively.
temperature of the photovoltaic module are very intricate. In fact, the Tglass, Te,amb and Tsky are, respectively, the glass, the exterior am-
electricity production and the extra heat released by the photovoltaic bient and the sky temperatures.
module occur by the bombardment of photons onto the solar cell. For On the bottom surface of PV-PCM system, long wave radiation heat
these reasons, the following assumptions have been considered: loss from aluminum layer to the ground and convection term heat loss
had been considered as follows:
(i) Properties of each layer in PV panel are considered to be isotropic
∂T
and homogeneous. −kal ⎛ ⎞ = (hb, free + hb − forced )(Te, amb−Tal ) + σεal Fb − g (Tg 4−Tal 4 )
⎜ ⎟

(ii) The solar radiation falling on the front surface of the PV panel is ⎝ ∂y ⎠
equally distributed. + σεal Fb − sky (Tsky 4−Tal 4 ) (4)
(iii) The contact resistances in the PV cell are not taken into account in
this work. where Tal and Tg are, respectively, the aluminum back layer surface and
(iv) The flow of the melted PCM is considered Newtonian, in- ground temperature. The value of the aluminum surface emissivity, εal ,
compressible and unsteady. is set to 0.85 [42]. Ff-sky and Ff-g are the view factors between the PV
(v) All absorbed solar radiation that is not converted to electricity will panel back surface and the sky or the ground, respectively.
be dissipated into heat.
(vi) The fusion of PCM is controlled by the convection and conduction 3.2.1. Radiation modeling
modes of heat transfer. The total solar radiation absorbed by the PV-PCM panel depends
(vii) Rain effect, which probably affect dust accumulation density, is effectively on the incident radiation on the front surface of the panel
not considered studied and on the total radiation produced by the PV-PCM panel. Thus,
the total resulting radiated energy can be estimated as:
The simulation of the variation of the temperature of the PV module
qrad = qirradiance−(q ground + q sky) (5)
is performed by considering the heat transfer from the module to the
surroundings and the energy absorbed by the PCM. where qirradiance, qground and qsky define, respectively, the solar radiation
absorbed by the PV-PCM panel, the heat loss leaving the panel towards
3.1. Within solid domains the ground and sky.
The irradiance model input on the PV-PCM panel’s front surface
The conduction mode is the only mode that governs the heat depends on cover glass’s absorptivity and can be calculated as follows:
transfer in all solid domains (PV and aluminum layers). Hence, the
diffusion heat transfer equation applied to the solid parts of the system, qirradiance = αglass G T A (6)
after simplifications using hypothesis cited above, is expressed by Eq.
All the necessary equations for the calculation of the incident solar
(1):
radiation on the front PV panel and absorbed solar radiation by the PV-
∂T ∂ 2T ∂ 2T PCM panel are mentioned below.
ρCP = k⎛ 2 + 2 ⎞ + Q
⎜ ⎟
∂t ⎝∂ x ∂ y⎠ (1)
where Q is a heat source and it is applied to the heat transfer equation
• Solar radiation modeling on the level of the PV panel surface
of the PV cells layer as an internal heat generation. As mentioned in the The prediction of real PV cells variation requires information on the
above assumptions, the remaining absorbed solar radiation that is not solar energy radiation received by an inclined PV panel. To mimic a real
converted to electricity will be dissipated into heat. Hence, an increase time application, the daily solar radiation incident on inclined PV panel
in PV panel temperature is obtained because of this internal heat surface, GT, is simulated in this paper using the HDKR model (Hay,
source. Q is evaluated using the expression below: Davies, Klucher, Reindl model) [43]. In details, the hourly total in-
(1−ηPV )FT A cident irradiance on inclined surface consists of three components as
Q= presented in Eq. (7) [44]:
VPVcell (2)
where FT is the absorbed solar radiation as properly expressed in Eq. G T = (G T,b + G T,d + G T,ref ) (7)
(25), ηpv is the electrical efficiency of the PV cells which is defined in Eq. In details:
(54), A is the upper surface of the PV panel and Vpv,cell is the volume of Beam radiation GT,b : The beam radiation on titled surface describes
the PV cells in the panel. the solar radiation traveling from the sun, passing through the atmo-
sphere without any scattering and directly received by the surface. As
3.2. On the level of the PV panel surface presented in Eq. (8), GT,b can be estimated by multiplying the value of
beam radiation received by horizontal surface, Gb, by the geometric
At the upper interface of the PV panel, we have considered the solar factor, Rb.
radiation, the long-wave radiation of the glass surface and the con-
vection terms as presented below: GT , b = Gb Rb (8)

∂T where Rb denotes a geometric factor depending on the zenith and in-

k glass ⎛ ⎞ = αglass GT + (hcvfree + hcvforced )(Te, amb−Tglass )
⎜ ⎟
cidence angles. Rb is calculated using the following expression [45-47].
⎝ ∂y ⎠
+ σεglass Ff − sky (Tsky 4−Tglass 4 ) + σεglass Ff − g (Tg 4−Tglass 4 ) (3) cos(θ)
Rb =
cos(θz ) (9)
where αglass and GT are the absorptivity of the glass cover and the in-
cident solar radiation on the PV-PCM panel (expressed in Eq. (7)) re- where θ and θz are the incidence angle and the zenith angle respectively
spectively. hcvfree and hcvforced are, respectively, the heat transfer coef- and both of them can be evaluated according to [45]. Thus, the beam
ficient for natural and forced convection as expressed in Eqs. (35) and radiation received by titled surface, GT,b, is giving by:

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cos(θ) ⎞ GT = GT , b + GT , d + GT , ref
GT , b = Gb ⎛⎜ ⎟

⎝ cos(θz ) ⎠ (10) = Gb Rb + Gd ⎡ (1−Ai ) ( 1 + cos α

) (1 + f sin ( ) ) + A R ⎤⎦ + ρ G (
3 α
i b g
1 − cos α
)
⎣ 2 2 2
Gb is the beam radiation incident on horizontal surface which can be
(17)
expressed as follow [48]:
G b = G b,ncos(θz) (11) • Absorbed solar radiation without dust deposition
where Gb,n is the energy of solar radiation falling with right angle on
The absorbed solar radiation without dust deposition is evaluated
square meter of the ground in a unit of time and can be calculated
using the radiation and optical model. In details, it is a function of the
according to [48].
incident radiation on titled PV panel surface GT, air mass M and in-
Diffuse radiation GT,d: describes the sunlight that reach the sloping
cidence angle modifier K τα . The model is defined by the following
surface after its dispersion through molecules and particles into the
equation [44]:
atmosphere. It should be known that modeling the sky diffuse compo-
nent on titled surface is considered the most complex problem. In fact, GT , ref
ST GT , b GT , d
this diffuse component is characterized by its anisotropic and not uni- = M (τα )n ⎜⎛ K τα, b + K τα, d + K τα, g ⎞⎟
Sref G
⎝ ref Gref Gref ⎠ (18)
formity of its distribution in the sky over the time. Many researchers
used many models in order to evaluate this component which is basi-
where (τα )n is the transmittance/absorptance product of the PV cover
cally classified on three types: Isotropic, circum-solar and anisotropic
for incoming solar radiation at a normal incidence angle. Gref is the
models. The isotropic models assume that the distribution intensity of
solar radiation at standard conditions (1000 W/m2) where
this component is isotropic and uniform over the entire hemisphere sky.
sref = Gref (τα )n and Mref = 1[44]. M and Mref are the air mass modifier
Many authors evaluated solar radiation on titled surface for any or-
and the reference air mass modifier respectively. The air mass modifier
ientation using the isotropic diffuse sky model [49,50]. In spite of its
is modeled using the empirical relation expressed by the below equa-
popularity, this model should not be used because it does not give a real
tion [60]:
picture of solar conditions in comparison with other theoretical as well
as with other experimental results [51]. The second type model (the M
4

circum-solar model) assumes that the diffuse component is evaluated

Mref
= ∑ ai (AM )i
similarly to the direct component [52,53]. However, it is not preferable i=0 (19)
to use this model because it could only be applied for totally clear skies where AM is the air mass which is given according to [60] as presented
[53]. Finally, the anisotropic model presumes the anisotropy of this in Eq. (20), a0, a1, a2, a3 and a4 are constants for different PV cells
component in the circumsolar region as well as the isotropy diffuse materials and their values for polycrystalline PV cells are 0.918093,
component distribution from the rest of the sky dome. This model is 0.086257, −0.024459, 0.002816, −0.000126 respectively [60].
pretty used for clear and cloudy days [46]. Many researchers used a
large number of models considering the anisotropic model [54–58]. In 1
AM =
this paper, the diffuse radiation received by titled surface is modeled cos(θz ) + 0.5057(96.080−θz )−1.634 (20)
using the HDKR (Hay, Davies, Klucher, Reindl) model [51]. According
to HDKR model, the diffuse radiation received by inclined surface is K τα, b , K τα, d and K τα, g are the incidence angle modifiers for beam, diffuse
expressed as: and ground-reflected radiation components, respectively, where the
incidence angle modifier is defined as:
1 + cos α ⎛ α
GT , d = Gd ⎡ (1−Ai ) ⎛ ⎞ 1 + f sin3 ⎛ ⎞ ⎞ + Ai Rb⎤
(τα )
⎢
⎣ ⎝ 2 ⎠⎝ ⎝ 2 ⎠⎠ ⎥
⎦ (12) K τα =
(τα )n (21)
where α is the inclination angle of the considered surface relative to the
horizontal. Ai and f are the anisotropy index and the correction coef- where (τα )(θ) is the transmission/absorptance product through a PV-
ficient, respectively, which are given as follow [59]: PCM cover system by a simple air-glazing model. (τα )(θ) is calculated
according to [61]:
Gb
f=
G (13) 1 sin2 (θ −θ) tan2 (θr −θ) ⎞ ⎤
(τα )(θ) = e−(KL /cos θr ) ⎡1− ⎛ 2 r ⎜ + ⎟
⎢ 2 ⎝ sin (θr + θ) tan2 (θ + θ ) ⎥
r ⎠⎦ (22)
Gb ⎣
Ai =
Go (14) -1
where θ and θr are the incidence and refraction angles, K (m ) is the
here G is the global radiation received by horizontal surface. It is cal- glazing extinction coefficient, and L (m) is the glazing thickness. The
culated using the Eq. (15) below: refraction angle is defined as θr = sin−1 (θ /(nr / n)) where the refraction
index (nr/n) for glass is set to 1.526.
G = Gb + Gd (15)

Go is the horizontal extraterrestrial radiation over a time step and it can • Absorbed solar radiation with dust deposition
be calculated referring to [59]. ▪ Transmittance-Dust deposition modeling
Ground reflected component GT,ref: describes the reflected solar
radiation by the ground and reached by the tilted surface. All models Many previous experimental investigations studied the effect of dust
presume that this component is isotropic as expressed below deposition density on PV panel transmittance and therefore on PV pa-
[46,47,52,53] nel’s efficiency. In this context, the decreasing of PV’s performance due
to the increasing of the dust concentration on PV panel surface has been
1−cos α
GT , ref = ρg G ⎛ ⎞ investigated in [62–64]. Several experimental studies investigated the
⎝ 2 ⎠ (16)
effect of dust deposition density on the transmittance. Therefore, var-
where ρg is the ground reflectance (albedo). ious correlations were derived for the evaluation of transmittance re-
Thus, as mentioned previously, the HDKR model will be applied in duction in [65–68]. Thus, the correlation quoted in [68] is used in the
this paper and the total solar radiation incident on oblique surface can present study due to its application in various regions and various
be expressed as: weather conditions and it is given by Eq. (23):

963
M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

Δτ (%) = −0.001335ρD6 + 0.04398ρD5 −0.5427ρD4 + 3.05ρD3 −7.703ρD2 surfaces of the PV panel, respectively.

• For the top side of the PV panel, the convective heat transfer coef-
+ 11.19ρD −2.25 (23)
where ρD is the dust deposition density in (g/m ). 2 ficient, hf-pv, is given as:
Once the transmittance reduction is evaluated, the transmittance of hf − pv = hf , free + hf − forced (33)
polluted PV panel can be calculated as follows:
where hf,free and hf-forced are the natural and forced convective heat
τ = (1−Δτ )(τα )(θ) (24)
transfer coefficients for the front PV panel surface respectively. hf-pv is
Here (τα )(θ) present the transmission of a clean glass cover, and its given below as follows [71]
evaluation is deduced from the Eq. (22). Thus, the absorbed solar ra-
diation by a photovoltaic module under the effect of dust deposition, FT, ⎧ hf − forced ifGr / Re 2 ⩽ 0.01
is expressed as follows: ⎪ (h
⎪ f , free 7/2 + h 7/2 ) 2/7if 0.01 < Gr / Re 2 < 100, α = 0∘
f − forced
hf − pv =
⎨ (hf , free + hf − forced3)1/3if 0.01 < Gr / Re 2 < 100, α > 0∘
3
GT , b GT , d GT , ref ⎪
FT = (1−Δτ ) Sref M (τα )n ⎛⎜ K τα, b + K τα, d + K τα, g ⎞⎟ ⎪ hf , free ifGr / Re 2 ⩾ 100
Gref Gref Gref (25) ⎩ (34)
⎝ ⎠
where Re is the Reynolds number and Gr is the Grashof number. The
3.2.2. Thermal radiation heat losses modeling heat transfer coefficient due to natural convection the top surface is
The effective heat loss from front and back sides of the studied PV given as follows [72]
panel radiated towards the ground and sky follows the
⎧ [0.13{(GrPr )1/3−(GrC Pr )1/3} + 0.56(GrC Pr sin α )1/4] K a
Stefan–Boltzmann's law. It depends essentially on the surface emis- ⎪
sivity, the exterior ambient temperature, the upper and rear surface hf , free = / Lc if α > 30∘
⎨
temperatures of the PV panel and tilt angle. The net heat loss radiation, ⎪ [0.13(GrPr )1/3] K a/ Lc if α ⩽ 30∘ (35)
⎩
qrad, to the ground is expressed as follows:
where Grc is the critical Grashof number which can be given as:
qground = εal Fb − g σA (Tg 4−Tal 4 ) + εglass Ff − g σA (Tg 4−Tglass 4 ) (26) GrC = 1.327 × 1010 exp(−3.708(π /2−α )) , this critical number correspond
to the transition zone from laminar to turbulent flow, Pr define the
In the present study, the ground temperature is considered to be
Prandtl number, ka is the air thermal conductivity, Lc is the char-
equal to the exterior ambient temperature. The net heat loss radiation,
acteristic length. The evaluation of heat losses by forced convection
qsky, is described as follows:
caused by the wind speed is very important for calculating the thermal
qsky = εglass Ff − sky σA (Tsky 4−Tglass 4 ) + εal Fb − sky σA (Tsky 4−Tal 4 ) (27) response of the studied PV panel. The appropriate empirical equation of
the heat transfer coefficient due to forced convection is given by the
The sky temperature, Tsky, can be calculated by the modified re- following equation [71]:
lationship of [69] as expressed in Eq. (28):
hf − forced = 0.848ka [cos α w vair Pr / υ]0.5 (Lc /2)−0.5 (36)
Tsky = 0.037536 Te,amb1.5 + 0.32Te,amb (28)
where υis the kinematic viscosity of the air and vair is the wind velocity.
The exterior ambient temperature could be modeled as a sinusoidal
αw is the wind incident angle and defined as the angle between the
function of the form [70]:
wind direction vector and the normal to the PV module surface vector
2πt ⎞ as figured out in Figs. 13 and 14. In order to determine the wind in-
Te, amb = Tamb + ΔTamb sin ⎛ ⎜ ⎟
cident angle, Eq. (37) below is derived from spherical trigonometry and
⎝ TS ⎠ (29)
used as following [71]:
where Tamb and ΔTamb are, respectively, the average value and the os-
cillation amplitude of the exterior ambient temperature during a period cos(α w ) = cos(90−α ) cos(γ ) = sin(α ) cos(γ ) (37)
of time TS (one day = 24 h). where γ is the angle given as γ = |γpv−γw |, as shown in Figs. 13 and 14.
The view factor F acts on the heat loss of the PV-PCM structure and γw is the wind direction and γpv donates PV panel orientation with re-
it is properly expressed as follows: ference to the south (angle between south direction and the horizontal
1 projection of normal to PV panel where γpv = 0 for south orientation).
⎧ Ff − sky = 2 (1 + cos α ) ⎫
⎪ ⎪ Hence, the heat transfer coefficient due to forced convection is
1
⎪ Ff − g = 2
(1−cos α ) ⎪ given by the following equation:
⎨ Fb − sky = 1 (1 + cos(π −α )) ⎬ hf − forced = 0.848ka [sin α cos γvair Pr /υ]0.5 (Lc /2)−0.5
⎪ 2 ⎪ (38)
⎪ Fb − g = 1 (1−cos(π −α )) ⎪
(30)
⎩ ⎭
• At the back side of the PV panel, the overall convective heat transfer
2

coefficient, hb-pv, is given as:

3.2.3. Convective heat losses modeling
hb − pv = hb, free + hb − forced (39)
At the top and back surfaces of the PV panel, convective heat losses
are taken into account for the present research. The heat transfer by where hb,free and hb,forced are the natural and forced convective heat
convection mode takes place by the combination between natural and transfer coefficients for the back side of the PV panel, respectively.
forced convection heat transfer. Thus, the heat losses, qf-convection and The heat transfer coefficient due to natural convection, hb,free , is
qb-convection, due to convection mode in this case for the front and for the obtained by evaluating the Eq. (40) as follows [72]:
back sides, respectively, are defined as follows:
2
qf − convection = hf − pv (Tpv−Te, amb) A (31)
⎧
⎪
⎪
⎣
(
⎡ 0.825 + 0.387(Ra . sin α )
1/6
)
(1 + (0.492 / Pr )9/16)8/27
⎤ ka/ Lc if α ⩾ 30
⎦
qb − convection = hb − pv (Tal−Te, amb) A (32) hb, free = [0.56(Ra. sin α )1/4] ka/ Lc if 2 < α < 30 and 105 < Ra.
⎨
⎪ sin α < 1011
where hf-pv and hb-pv are the overall convective heat coefficients that ⎪ 1/5 6 11
include both natural and forced convection for the front and back ⎩ [0.58(Ra) ] ka/ Lc if 0 ⩽ α ⩽ 2 and 10 < Ra < 10 (40)

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

where Ra and αp are the Rayleigh number and the thermal expansion state, it absorbs the latent heat (Lf) which can be modeled as a change
factor, respectively, which are given as: in its specific heat during the phase transition period.
gαp ρ2 cP |TPV −Tamb |Lc 3 0 T < (Tf −ΔT )
Ra = ⎧
ka μ (41) ⎪ (T − Tf + ΔT )
B (T ) = (Tf −ΔT ) ⩽ T < (Tf + ΔT )
⎨ 2ΔT
1 ⎛ ∂ρ ⎞ ⎪ 1 T > (Tf + ΔT ) (47)
αp = ⎜ ⎟
⎩
ρ ⎝ ∂TPV ⎠P (42)
The latent heat and the latent heat of the selected PCM are modeled
The heat transfer coefficient due to forced convection at the back as follows
side of the PV panel surface is given as [73] and [74]:
Cp (T ) = Cp, solid + (Cp, liq−Cp, solid ) B (T ) + Lf D (T ) (48)
k
⎧ (0.664 Re1/2 Pr 1/3) Lae for la min ar flow (Re<4. 105 and Pr ⩾
⎪ where Cp,liq and Cp,solid are the specific heat capacities of the chosen
⎪ 0.6) PCM in liquid and solid phases respectively. D(T) is Dirac delta function
⎪ k and its main role is to distribute the latent heat of fusion in a similar
⎪ (0.037 Re 0.8Pr 1/3) Lae for turbulent flow (5.105 < Re < 108
⎪ manner nearby the melting point of PCM. It is set to 0 everywhere
hb − forced = and 0.6 ⩽ Pr ⩽60) except in interval [Tf − ΔT,Tf + ΔT] and can be modeled as follows:
⎨
⎪ ((0.037 Re 0.8 - (0.037 Re 0.8 - 0.664 Re 0.5 )) Pr 1/3) ka for mixed
c c
⎪ Le −(T − Tf )2
⎪
⎪ flows (4.10 5 < Re < 5.10 5 and 0.6⩽ D (T ) = e
⎛
⎜
( ΔT 2 ) ⎞
ΠΔT 2 ⎟
⎪ Pr ⩽ 60) ⎝ ⎠ (49)
⎩
(43) Moreover, Wx and Wy are the Darcy’s law source terms in x and y
Vair x
directions that are added to modify the momentum equations in the
where Re = the Reynolds number (x is the position along the
νair
is mushy zone and can be written as:
panel), Pr is the Prandtl number and Rec is the critical Reynolds number
which is set to 4 · 105. Wx = −A(T)·u
Wy = −A(T)·v (50)
3.3. PCM modeling
where A(T) is used in order to mimic Carman-Kozeny equations for flow
By applying the heat transfer diffusion equation and the Navier- in a porous media and it is defined as follows[75]:
Stokes equations for Newtonian and incompressible fluid as presented (1−B(T))2
in equations below, the temperature of the studied PV-PCM system as A(T) = C
(B3 (T) + q) (51)
well as the instantaneous velocities of the melted PCM can be found:
where the constant q is typically a small number and it is fixed to 10-3 in

⎪ ∂t ∂x ∂x (
⎧ ρcp ∂T = ∂ k ∂T −ρcp uT + ∂ k ∂T −ρcp vT
∂y ∂y ) ( ) order to make the PCM density effective even when the melt fraction is
zero. C defines the mushy zone constant and its value depends on the
⎪ ∂u
( ∂u ∂u ∂P ∂2u
) ∂2u
⎪ ρ ∂t + u ∂x + v ∂y = − ∂x + μ ∂x 2 + ∂y 2 + Wx
⎪
( ) morphology of the medium. The mushy zone constant describes how
steeply the velocity is totally reduced to zero when the material be-
⎪ + ρliq (1−β (T −Tf )) gx sin α
comes completely solid. The value of C is often varying between 104
⎨ and 108 kg/m3 s. In this research, the value of C is taken 106 because of
⎪ρ
⎪
( ∂v
∂t
∂v ∂v
)
+ u ∂x + v ∂y = − ∂y + μ
∂P
( ∂2v
∂x 2
+
∂2v
∂y 2 )+W y
the high viscosity of solid PCM.
⎪ + ρliq (1−β (T −Tf )) gy cos α
⎪
∂u ∂v
⎪ + =0 3.4. Electrical efficiency and power output
⎩ ∂x ∂y (44)

where ρ, cp and k are the density, the specific heat capacity and the The power output of PV cells can be simulated using the following
thermal conductivity of the PCM respectively. u and v represent the correlation [76]:
velocities of the fused PCM in x and y direction respectively. P is the
Pout = Imp Vmp = (FF ) Isc Voc = ηpv APV FT (52)
pressure, g is the acceleration due to gravity, β is the thermal expansion
coefficient and μ is the dynamic viscosity. The density, ρ(T), as well as where Imp and Vmp are the current and voltage output at maximum
the thermal conductivity, k(T), of PCM are modeled using the following power output, respectively. Apv is the surface area of the PV panel. FF is
equations: the fill factor; Isc and Voc are the open circuit current and voltage re-
ρ (T ) = ρsolid + (ρliquid −ρsolid ) B (T ) (45) spectively. Also, the PV cell electrical output efficiency is a function of
PV cell power output, solar radiation and PV cell surface area as shown
K (T ) = Ksolid + (Kliq−Ksolid ) B (T ) (46) in Eq. (53):

where ρliq and ρsolid describe the density of the PCM at its liquid and ηPVcell = Pout /(APV FT ) (53)
solid phase respectively. Moreover, ksolid and kliq are the thermal con-
Moreover, the module efficiency can be represented as follows [77]:
ductivity of the PCM at its solid and liquid phases respectively. The
function, B (T) as mentioned in Eq. (47), is defined as the liquid fraction ηPV = ηref (1−βref (TPV −Tref )) (54)
of the PCM in order to model the modifications of the thermo-physical
properties that appear during the phase transition. It is clear that from where ηref, βref, and Tref are respectively the panel’s electrical efficiency,
Eq. (47) B(T) takes zero as value when the PCM is totally in solid state temperature coefficient, and temperature at STC. The value of βref is
and takes 1 as value when it becomes fully melted. During the phase 0.004 1/K for polycrystalline PV panel [78]. Thus, the total power
transition, B(T) increases linearly from 0 to 1between the two states output is given by:
[75]. Here, Tf and ΔT are the fusion temperature and the transition
Pout = ηref (1−βref (Tpv−Tref )) AFT (55)
temperature of PCM respectively. When the PCM begins to change its

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

4. Numerical procedure, mesh independence study and model investigation are presented in the following subsections: (5.1) Transient
validation study of PV-PCM panel (5.2) Effect of the integration of different PCMs
on operating PV panel temperature (5.3) Effect of thickness of PCM
COMSOL Multiphysics software is used to solve numerically the layer (5.4) Effect of wind azimuth angle (wind direction) (5.5) Effect of
concurrent equations mentioned previously in Section 3 and subjected wind velocity on PV panel’s temperature (5.6) Effect of dust deposition.
to the boundary conditions based on the finite element method. The
dimensions of PV-PCM layers as well as the PCM thermo-physical 5.1. Transient study of PV-PCM system
properties were properly defined in the commercial software COMSOL
Multiphysics. The numerical simulation is carried out according to the The variation in temperature and velocity field in PCM (RT44HC)
following steps: Discretization of the considered domain (size, element domain at various time intervals is shown in Fig. 6. The results show
and type), defining the appropriate time step as well as the relative and that, at the initial state, the PCM is totally in solid phase due to the fact
absolute tolerances and use the appropriate solver techniques. In order that the solar radiation falling on PV panel surface does not exist. At
to get the most suitable solution, a mesh dependence study was per- daytime, PV panel temperature starts increasing with time and PCM
formed carefully for the current investigation. A triangular meshing starts absorbing and storing energy extracted from PV panel in the form
with a regular refinement method was used for the global mesh as of sensible heat in its solid state. In this situation, heat extracted from
shown in Fig. 2. For all domains, maximum element size and element PV panel is very low. After a period of time, PV panel temperature
growth rate are set to 0.03 and 1.1 respectively. 26,852 finite elements decreases due to the fact that the PCM starts melting and the energy is
are considered initially for the entire model and mesh sizes of 31,048 stored in the form of latent heat. When PCM is totally melted, the total
and 48,628 finite elements are considered when using a finer mesh. It is latent heat is absorbed and the PV panel temperature grows rapidly
well noted that were not a significant difference in the obtained results with time. As figured out in Fig. 6, the movement of the melted PCM
for all mesh sizes. For better precision and exactness, a mesh size with due to natural convection is represented by arrows. The melted PCM
48,628 elements will be chosen for our research. The Backwards dif- which characterized with high velocity is represented with large arrow
ferentiation formulas (i.e. Backward Euler) time stepping method is size and the melted PCM with low velocity is represented with small
selected for the time-dependent resolution. The maximum and arrow size. When solar radiation decreases with time, solidification
minimum order of backwards differentiation principles are 5 and 1 process starts when PCM reaches its solidification temperature and fi-
respectively. An absolute tolerance of 0.00001 and a relative tolerance nally it become fully in solid phase with absence of arrows (zero ve-
of 0.001 are applied. The time stepping is selected with an initial time locity).
step of 0.01 s and a maximum time step of 100 s. The initial tempera-
ture for all PV-PCM layers is set to 293.15 K. The two dimensional si- 5.2. Effect of integration of different PCMs
mulated model was performed for the atmospheric conditions of July
15th
, for the City of Sousse, Tunisia (35.82539_N, 10.63699_E). The In order to study the effect of different PCMs on PV cells tempera-
variation of exterior ambient temperature and solar radiation for the ture and on the produced electrical power, three PCMs were selected
considered day are plotted in Fig. 3. where their thermo physical properties are listed in table 3. The cor-
For validation, initial calculations were carried out using the de- responding variations of PV cells temperature with time for different
veloped methodology of the present research for which similar system PCMs along two consecutive days are plotted in Fig. 7. Interestingly, the
geometry, boundary conditions and the same material properties were results in Fig. 7 show that the RT44HC which is characterized with a
used as defined by Park et al. [26]. The thermo physical properties of melting temperature of 44 °C leads to lower PV temperature at daytime.
the PCM used for the validation of our thermodynamic model are These results can be justified by the latent thermal energy of RT44HC
presented in Table 2. The PV-PCM model is validated against the ex- which is higher compared to RT25HC and RT35HC. The variation in
perimental results of Park et al. [26]. As plotted in Figs. 4 and 5, a good temperature of PV panel and velocity field in different PCMs at t = 11
match between the simulated temperature of PV cell, with and without AM are shown in Fig. 9. It can be seen that at 11 AM, RT25HC and
PCM, along three days using the present work and between those of RT44HC are almost in liquid phase and in solid phase respectively.
Park et al. [26] with a difference within the range of ±2 °C. Hence, from Figs. 7 and 9 it can be illustrated that fusion process of
RT25HC is much faster and starts earlier than RT35HC and RT44HC
5. Results and discussion because RT25HC has the lowest fusion onset temperature of about
26.6 °C. The liquid fraction variation with time of different PCMs is
The performance of the PV and PVPCM systems had been analyzed shown in Fig. 8. It is well observed that the melting and solidification
in the current paper. The results and discussion of the current phenomenon of PCMs for variable solar irradiation starts at different

Fig. 2. Mesh at different number of element of the numerical model.

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

40 1200
Exterior ambiant temperature
38 Solar radiation
1000
36

Exterior ambiant temperature (°C)

Solar radiation (W/m )

34 800

32
600
30

28 400

26
200

2
24

0
22

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (hour)
Fig. 3. Exterior ambient temperature and solar radiation variation with time.

times. For instance, the fusion process of RT35HC and RT44HC starts at in the next day due to its low fusion temperature and because of its low
08:00 AM and at 09:30 AM respectively and both of them will be totally latent heat of fusion as plotted in Fig. 8. Hence, the amount of RT25HC
melted after three hours. Moreover, each PCM remains at his fully li- to be melted in the next day is not the same and the impact in tem-
quid state in a different period of time of about 5 h and 7 h for RT44HC, perature reduction is not the same (the panel temperature is lower by a
RT35HC respectively. Therefore, as shown in Fig. 7 the same reduction maximum of 9 °C and 8 °C in the first and in the next day respectively as
in PV cells temperature at daytime, for the two days, is obtained when shown in Fig. 7). For these reasons, the energy production increase is
using RT44HC and RT35HC due to the presence of the same amount of the same for the two days when using RT44HC and RT35HC but it is not
PCM to be melted in the first day and in the next day (i.e. RT44HC and the same reduction when using RT25HC as figured out in Fig. 10. For
RT35HC are totally at their solid state before the solar radiation starts instance, the maximum generated electrical power reaches of about
falling on PV panel surface as illustrated in Fig. 8 where the liquid 12.7 W at midday of the considered days when using RT44HC and it
fraction of those PCMs is zero). However, RT25HC remains at his fully reaches of about 12 W and 11.6 W in the first and next day when using
liquid state of about 10 h in the first day and of about 11 h in the next RT25HC, respectively.
day because the solidification process of RT25HC is not totally achieved RT44HC will be selected for the rest of the present research.

70
65 Present results
Park et al. results
60
55
PVPCM Temperature (°C)

50
45
40
35
30
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Time (h)
Fig. 4. PV-PCM panel temperature variation with time.

967
M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

75
Our results
70 Park et al. results
65
60
55
50
PV temperature (°C)

45
40
35
30
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Time (hours)
Fig. 5. PV panel temperature variation with time without PCM.

Fig. 6. Variation in temperature (°C) and velocity field of PV-PCM panel at various time intervals.

5.3. Effect of thickness of PCM layer plotted in Fig. 11. The operating temperature variation depends on the
thickness of PCM layer for constant wind velocity (1 m/s) as shown in
As mentioned in Section 5.2 above, RT44HC is used for our re- Fig. 11. The considered thermodynamic model is solved for different
search. The effect of thickness of PCM layer on PV panel temperature is PCM layer thickness i.e. 1 cm, 1.5 cm, 2 cm, 2.5 cm and 3 cm. From

Table 3
Thermo-physical properties of the selected PCMs [34].
Melting temperature (°C) Latent Heat of Fusion (kJ/kg) Specific heat (kJ/kgK) Density (kg/m3) Thermal conductivity (W/(m K))

RT25HC 26.6 232 1.8 solid phase 785 solid phase 0.19 solid phase
2.4 liquid phase 749 liquid phase 0.18 liquid phase
RT35HC 35 240 2 both phases 880 solid phase 0.2 both phases
770 liquid phase
R44HC 44 250 2 both phases 800 solid phase 0.2 both phases
700 liquid phase

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

80
without PCM
76
with RT25HC
72 with RT35HC
68 with RT44HC
64
60
56
Temperature (°C)

52
48
44
40
36
32
28
24
20
16
12

00
0 04
4 08
8 12 16 20 24
00 04
28 08
32 36
12 40
16 44
20 48
00
Time (h)
Fig. 7. Variation of PV cells temperature with time coupled with different PCMs.

these results, it is clearly shown that as the thickness of the PCM layer 5.4. Effect of wind azimuth angle
increases, the operating temperature of the PV panel decreases with a
half-hour offset at each increase of 0.5 cm of the selected PCM layer Prior to study the effect of the wind direction on the PV panel
thickness. These results can be explained due to the increase of PCM temperature, the wind incident angle should be evaluated. The wind
melting period. In fact, once the thickness of RT44HC increases, the incident angle is the angle comprised between the normal to PV module
storage time of the energy in the form of latent heat will be greater and vector and the wind direction vector as shown in Fig. 13. Hence, an
therefore the PV panel temperature will decrease as the thickness of the angle γ formed by the orientation vector of the PV panel, γpv , and the
PCM layer increases. Moreover, the variation of the PCM liquid fraction vector of the direction of the wind, γw , as figured out in Figs. 13 and 14,
and the PV panel temperature for two consecutive days for the case of should be determined. In our case (i.e. south orientation), γ = γw as
PCM with 3 cm thick is figured out in Fig. 12. Interestingly, at the end of shown in Fig. 14, because γpv = 0. The variation of average PV-PCM
the first day the PCM does not solidify completely as illustrated in panel temperature along the day for different wind azimuth angle for a
Fig. 12 (i.e. at 00:00 AM the liquid fraction is not zero (reaches 0.15)) clean system keeping south orientation and α = 30° are figured out in
until it remains at his fully solid state from 01:00 AM to 09:30 AM of the Fig. 15. On the basis of these results, it is clear that as wind azimuth
following morning (i.e. from 01:00 AM to 09:30 AM the melt fraction angle is higher, the average PV panel temperature increases. It's well
remains zero)). Therefore, the same amount of PCM to be melted the observed that the PV-PCM temperature increases with the increase of
next day will be the same at daytime (with the presence of solar ra- wind azimuth angle. These results can be explained as follows, when
diation falling on PV panel surface) and the impact in temperature re- the wind azimuth angle decreases, the wind flow will be almost normal
duction of the PV panel temperature is the same as shown in Fig. 12. at the surface of the panel and therefore heat losses due to forced

1,2
RT25HC
1,1
RT35HC
1,0 RT44HC
0,9
0,8
0,7
Liquid fraction

0,6
0,5
0,4
0,3
0,2
0,1
0,0
-0,1
00 04 08 12 16 20 00 04 08 12 16 20 00
Time (h)
Fig. 8. Variation of liquid fraction of different PCMs with time.

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

Fig. 9. Temperature (°C) and velocity field of PV panel coupled with different PCM at t = 11 AM.

13
without PCM
12 with RT44HC
with RT35HC
11 with RT25HC

10

9
DC power (W)

7
6

5
4

3
2

1
0
0
00 4
04 8
08 12
12 16 20 24
00 28
04 32
08 36
12 40
16 44
20 00
Time (h)
Fig. 10. Variation of DC power of PV power coupled with different PCM for two consecutive days keeping α = 30°, vair = 1 m/s and γw = 30° for south orientation.

Without RT44HC
80
1 cm
1,5 cm
70
2 cm
2,5 cm
60
PV panel temperature

3 cm

50

40

30

20

10

0 2 4 6 8 10 12 14 16 18 20 22 24
Time (h)
Fig. 11. Effect of thickness of PCM (RT44HC) layer for a clean system for south orientation keeping vair = 1 m/s and γw=30°.

970
M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

1,1 80
Liquid fraction
1,0 without RT44HC 75
with RT44HC
70
0,9
65
0,8
60

PV panel temperature (°C)

0,7
55
Liquid fraction

0,6 50

0,5 45

0,4 40

35
0,3
30
0,2
25
0,1
20
0,0 15

-0,1 10
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
Fig. 12. Effect of integration of a 3 cm of PCM (RT44HC) layer for a clean system for south orientation keeping vair = 1 m/s and γw = 30° for two consecutive days.

convection will be greater. Thus, a decrease in the average temperature 5.6. Dust effect
of the PV panel is obtained.
Several previous researches on thermal modeling of PV panels
coupled with PCMs had not considered the effect of dust on the per-
5.5. Effect of wind speed formance and the operating temperature of PV panels. Dust deposition
plays a vital role on the amount of solar energy absorbed by the panel
It is necessary to study the impact of various wind speed values on and therefore on the temperature of the PV cells. Thus, it is very im-
the operating temperature of PV panel (in PV-PCM system). The effect portant to consider the dust density deposition in our modeling The
of wind velocity on PV panel operating temperature variations with developed model with 2 cm thickness of the chosen PCM (RT44HC) is
time is plotted in Fig. 16. The developed thermal model is studied for studied for various dust deposition density i.e. 3 g/m2, 6 g/m2, 9 g/m2
various wind velocity (i.e. 1 m/s, 2 m/s, 3 m/s and 4 m/s) at 30° angle for south orientation keeping 30° as an inclination angle. . The effi-
of inclination for south orientation. From results in Fig. 16, it is well ciency variation of PV panels with time is plotted in Fig. 17. It can be
shown that as wind speed is higher, the PV panel operating temperature seen that as the density of dust deposition increases the efficiency of PV
decreases. These results are explained due to the increase of heat losses panel increases. These results are explained due to the reduction of the
due to forced convection when wind speed increases. absorbed solar energy when dust deposition increases as shown in

Fig. 13. PV panel orientation, wind incident angle and wind direction for PV panel not facing south.

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

Fig. 14. PV panel orientation, wind incident angle and wind direction for PV panel facing south (our case).

Fig. 18a. For instance, the maximum absorbed energy the PV-PCM 6. Conclusion
module reaches 922 W/m2, 850 W/m2, 705 W/m2 and 695 W/m2 for a
clean panel, 3 g/m2, 6 g/m2 and 9 g/m2 of dust deposition density, re- In light of the current investigation, the developed thermodynamic
spectively. Hence, a reduction in electrical power generated by the PV- PV-PCM model has been well investigated in order to recognize the
PCM panel of about 1.2 W, 2.8 W and 3 W is obtained as figured out in heat, mass and momentum transfer phenomena of a PCM attached
Fig. 18b for 3 g/m2, 6 g/m2 and 9 g/m2 of dust deposition density, re- behind PV panel. The simulated studies are performed for the month of
spectively. Therefore, the increase of the density of the dust deposition July and for the Tunisian climatic conditions of the City of Sousse
covering the panel reduces the quantity of the absorbed solar radiation (35.82539_N, 10.63699_E) which hold high quality PV panel installa-
and thus an improvement on the efficiency of the PV panel is obtained. tion potential. Some important findings and conclusions can be derived.
Consequently, a reduction in the produced electrical power is noticed. It is observed that at midday of the two considered days, the operating
temperature of the PV panel with the integration of RT35HC and

90
85 =15°
w
80 =30°
w
75 =45°
w
70 =60°
w
65 =75°
PV-PCM temperature (°C)

w
60 =90°
w
55
50
45
40
35
30
25
20
15
10
5
0 2 4 6 8 10 12 14 16 18 20 22 24
Time (h)
Fig. 15. Variation of average PV-PCM panel temperature over the day time for different wind azimuth angle for a clean system keeping vair = 1 m/s, south or-
ientation and α = 30°.

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M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

80
-1
With RT44HC and Vair=1ms
75 -1
With RT44HC and Vair=2ms
70 With RT44HC and Vair=3ms
-1

-1
65 With RT44HC and Vair=4ms
-1
Without RT44HC and Vair=1ms
60
Temperature (°C)
55
50
45
40
35
30
25
20
15
10
0 2 4 6 8 10 12 14 16 18 20 22 24
Time (h)
Fig. 16. Wind Speed effect on a clean panel operating temperature keeping α = 30° and γw = 30° for south orientation.

RT44HC behind its back surface is lower by about a maximum of 10 °C study reveal that the maximum operating temperature reaches ap-
and 12 °C, respectively, when attached to the conventional PV module. proximately 87 °C, 72.5 °C, 69 °C, 66 °C, 64 °C and 63 °C for wind azi-
However, the reduction in the maximum temperature of the PV panel is muth angle of 90°, 75°, 60°, 45°, 30° and 15° respectively. A dramatic
not the same when attaching RT25HC behind its back surface and it is decrease in the maximum operating temperature during peak time of
reduced by a maximum of 9 °C and 8 °C at midday of the first day and the day is illustrated reaching therefore 67 °C, 63 °C, 58 °C and 53 °C for
during peak time of the next day respectively. Hence, RT44HC is the wind speed of 1 m/s, 2 m/s, 3 m/s and 4 m/s respectively. As a final
appropriate PCM and leads to increase the produced electrical power to finding, the maximum PV-PCM efficiency reaches 13.1%, 13.4% and
a maximum of about 12.7 W. An obvious increase in the total period 13.5% for dust deposition density of 3 g/m2, 6 g/m2, and 9 g/m2 re-
required to reach the full liquid state of the PCM layer is observed due spectively leading therefore to a reduction in the maximum absorbed
to the increase of its thickness. Thus, the maximum operating tem- solar radiation of about 72 W/m2, 217 W/m2 and 227 W/
perature of the PV panel is reduced from 70.36 °C to 56 °C due to in- m2respectively. Hence, a reduction in PV panel power output is noticed
crease the PCM thickness from 1 cm to 3 cm. The results of the current of about 3 W, 2.8 W and 1.2 W at midday for 9 g/m2, 6 g/m2 and 3 g/m2

17,0

16,5

16,0

15,5

15,0
Efficiency (%)

14,5

14,0

13,5

13,0
clean and without RT44HC
12,5 clean and with RT44HC
-2
with RT44HC and D =3 gm
12,0 with RT44HC and D
=6 gm
-2

-2
with RT44HC and =9 gm
11,5 D

0 2 4 6 8 10 12 14 16 18 20 22 24
Time (h)
Fig. 17. Effect of dust deposition density keeping α = 30°, γw = 30° and vair = 1 m/s for south orientation on PV panel efficiency with time.

973
M. Nouira, H. Sammouda Applied Thermal Engineering 141 (2018) 958–975

1000
3,4
clean panel
2
3,2 3 g/m of dust deposition density
900 3 g/m2 of dust deposition density
2
6 g/m2 of dust deposition density 3,0 6 g/m of dust deposition density
2
800
2
9 g/m of dust deposition density 2,8 9 g/m of dust deposition density

2,6
700 2,4
Absorbed energy ( W/m )
2

2,2
600
2,0

Power reduction (W)

a) b)
500 1,8
1,6
400 1,4
1,2
300
1,0
0,8
200
0,6

100 0,4
0,2
0 0,0
0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 24
Time (h) Time (h)

Fig. 18. Effect of dust deposition density keeping α = 30°, γw = 30° and vair = 1 m/s for south orientation: (a) on the absorbed energy reduction and (b) on the
electrical power reduction with time.

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