Enhancing the performance of concentrator photovoltaic systems using Nanoparticle-phase change material heat sinks

Energy Conversion and Management 179 (2019) 229–242

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Enhancing the performance of concentrator photovoltaic systems using Nanoparticle-phase change material heat sinks

T

Ismaila Zarmaa, Mahmoud Ahmeda,b, , Shinichi Ookawaraa,c ⁎

a

Department of Energy Resources Engineering, Egypt-Japan University of Science and Technology (E-JUST), P.O. Box 179, New Borg El-Arab 21934, Alexandria, Egypt Mechanical Engineering Department, Assiut University, Assiut 71516, Egypt c Department of Chemical Science and Eng., Tokyo Institute of Technology, Tokyo 152-8552, Japan b

ARTICLE INFO

ABSTRACT

Keywords: Concentrator photovoltaic Nanoparticles Phase change materials Hybrid

In this research work, the performance of a concentrator photovoltaic Nanoparticle-phase change material (CPVNanoparticle-PCM) hybrid system is investigated at a solar concertation ratio (CR) of 20. The influence of different nanoparticles (Al2O3, CuO and SiO2) at loading ratios (1 wt% and 5 wt%) on the overall performance of a concentrator photovoltaic system is explored. A comprehensive two-dimensional hybrid model consisting of photovoltaic layers and a Nanoparticle-PCM heat sink is developed and numerically simulated. The predicted results are validated using the available experimental and numerical data. It is found that PCM’s thermal conductivity has significantly increased with the addition of Al2O3, compared with CuO, SiO2 nanoparticle which enhances the process of heat transfer, melting rate, and accordingly reduces the solar cell temperature. Furthermore, using Nanoparticle-PCM attains a higher temperature uniformity and electrical efficiency of the CPV system. It is found that utilizing Al2O3-PCM at 5 wt% attains an electrical efficiency of 8% and temperature uniformity of 12 °C compared to pure PCM (0 wt%) where the electrical efficiency reaches 6.36 % and a temperature uniformity of 20 °C. This novel CPV-Nanoparticle-PCM system can be recommended for residential and industrial applications due to its ability to save energy and offer safe operating conditions.

1. Introduction The technologies of concentrator photovoltaic (CPV) have recently drew researchers attention since they are consider as an efficient source of electrical energy and thermal storage of energy within phase change materials (PCM) [1]. The CPV technologies, which use highly efficient solar cells under concentrated solar irradiations, are solution for today’s high costs of electricity [2]. In technologies of CPV, low-cost materials like, mirrors and plastic lenses are considered to capture incoming solar irradiance from a wider range to be concentrated into a smaller cell [3]. Concentrator photovoltaic systems having high concentration ratios (CR) increase solar cell temperature, which could cause problems to the CPV systems. Currently, solar cells that are silicon-based are used in CPV systems converting only 18–20 % of solar irradiance available into electrical power, leaving the remainder to become heat energy. This results in temperature elevation in the PV cells, posing a challenge for the effective performance of the cells, and is possibly detrimental to

their longevity as well. In solar cells that are made of mono or polycrystalline silicon, high temperatures could lead to an elevation in current short circuit (0.06–0.1 % °C). Accordingly, it causes a much upper voltage drop (2–2.3 mV °C) with fill factor reduction (0.1–0.2 %), triggering the produced electrical power to drop by 0.4–0.5 % °C, [4,5]. This objectionable performance decline caused by the elevation in solar cells temperature, causes over-heating of solar cells, and therefore, should be controlled. However, damage caused by solar cells temperature elevation can be avoided with consideration of PCM with high-energy densities introduced in the system [6]. PCMs are resources utilized for heat captivation, storage, and recapture in alternative energy-based systems and can improve solar utilization in the areas of applied energy [7]. Also, solar cell temperature rise can passively be restricted with the use of PCMs [8], although PCMs poor thermal conductivities limit their effectiveness [9], likewise caused crystallisation and segregation throughout solidification. This results in slow transient response [10],

Abbreviations: CPV, Concentrated Photovoltaic; CR, Solar Concentration Ratio; EVA, Ethylene Vinyl Acetate; LHTES, Latent Heat Thermal Energy Storage; NanoPCM, Nanoparticles-enhanced PCM; PCM, Phase Change Material; TCE, Thermal Conductivity Enhancers; TDT, Tedlar; TES, Thermal Energy Storage ⁎ Corresponding author at: Department of Energy Resources Engineering, Egypt-Japan University of Science and Technology (E-JUST), P.O. Box 179, New Borg ElArab 21934, Alexandria, Egypt. E-mail addresses: [email protected], [email protected] (M. Ahmed). https://doi.org/10.1016/j.enconman.2018.10.055 Received 25 June 2018; Received in revised form 24 September 2018; Accepted 17 October 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclatures

Amush Cp G (t ) G g H h h1 k L npcm p Q q"w T t V u, v x, y ΔTm

wt

mush zone constant [kg/m3·s] specific heat at constant pressure [J/kg·k] concentration solar irradiance [W/m2] reference solar radiation, 1000[W/m2] gravitational acceleration [m/s2] height of the enclosure [mm] convention heat transfer coefficient [W/m2·k] sensible enthalpy [J/kg] thermal conductivity [W/m·K] length of the enclosure [mm] nano-PCM pressure stored thermal energy [J/kg] constant wall heat flux temperature [°C] time [min.] velocity [m/s] velocity in x and y-axis [m/s] cartesian coordinates melting temp. range, and equal to Tliquidus-Tsolidus

Subscripts amb ab Al Ai conv conv.,g-a Elec E g ini qi l m n p pcm rad rad.,g-s refl ref s sc sc, x T t th Vw Vi wall

Greek symbols

1

µ v

weight fraction Stephen-Boltzmann constant, 5.67 × 10−8 (W/(m2·K4))

absorptivity solar cell temperature coefficient [1/k] thermal expansion coefficient [1/k] emissivity transmissivity efficiency thickness [mm] viscosity [pa·s] kinematic viscosity [m2/s] density [kg/m3] liquid fraction Volume fraction

i

and makes it hard to quickly store and extract the energy stockpiled within the phase change material based thermal storage systems [11]. Even though PCMs that were made of metallic such as gallium and tin have extraordinary thermal conductivities, they are infrequently consider for commercial determinations based on their high density, excessive cost as well as elevated or low temperature phase change [12]. Consequently, PCMs weak thermal conductivity should be boosted by loading nanoparticles. Different types of nanoparticles are considered to improve the poor thermal conductivity with resultant enhancement in heat transfer of PCM-founded systems [13]. There are many studies recently that report on Nanoparticles-PCM systems and aim to enhance the PCMs weak thermal conductivity. Likewise, many techniques apart from loading nanoparticles to enhance the PCMs thermal conductivities were considered as reported in the literature. Enhancing PCMs thermal conductivity as well as controlling the increase in temperature in the cells of PV can be maintained by the application of immovable structures like fiber brushes, fins/cavities and porous/foams techniques, as discussed below. The first technique considered the use of fixed structure fins. Huang et al. [14] studied natural convection adapting internally-finned PCM heat sink created for photovoltaics thermal management. The study resolved that use of internal fins improved temperature control of the PV/PCM system. Khodadadi et al. [15] conducted a review on the latent heat energy storage systems (LHES) performance using fins with high thermal conductivity. Pakrouh et al. [16] explored PCM-founded pin fin heat sink. Their results revealed that enlarging the thickness, height,

ambient absorbed aluminum area of layer i convection convection loss from glass to ambient electricity EVA glass initial internal heat generation per unit volume of layer i Liquid PCM melting nanoparticle-enhanced PCM nanoparticle solid phase change materials radiation radiation loss from glass to sky temp. reflection reference conditions, G = 1000 W/m2/T = 250 solid PCM silicon solar cell local solar cell tedlar top surface thermal wind speed volume of layer i wall transmissivity of layer above the layer i

number of the fins can significantly reduce the heat sink base temperature and the operating time. Abdulateef et al. [17] conducted experimental and numerical evaluated PCM melting procedure in a heat exchanger made of triplex tube with fins made of triangular/longitudinal. Their results reveal that a substantial improvement was practical, while using exterior triangular, interior-exterior, and interior fins at 15%, 12%, and 1% respectively, when compared with cases where fins that are longitudinal were used. The second technique relies on fiber brushes. Fukai et al. [18] examined the influence of carbon-fiber brushes in PCMs during conductive heat transfer. The outcomes showed that the PCMs thermal conductivity around heat transfer tubes remained improved. Abbas et al. [19] evaluated the impact of time for charging and discharging in thermal energy storage units using metallic brushes. The outcomes established that introduction of fiber brushes in phase change materials based systems can enhance the PCM performance. The third technique utilizes a porous/foam structure placed in the PCMs. Further details were reported by Hu et al. [20], Alshaer et al. [21], Zhao et al. [22], Moeini et al. [23] and Savija et al. [24]. Kant et al. [25] evaluated PCMs with graphene nanoparticles heat transfer process. El Qarnia et al. [26] studied the transient behavior of melting Nanoparticles-PCM in a rectangular container. Arasu et al. [27] considered CuO and Al2O3 nanoparticles for the paraffin wax’s thermal performance enhancement. The results confirmed that loading nanoparticles (Al2O3) in a lesser volumetric fraction increased the rate of heat transfer, with thermal efficiency of paraffin wax enhanced; meanwhile, the use of CuO did not 230

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produce a significant of an enrichment in the thermal efficiency. Auriemma et al. [28] numerically examined melting process in paraffin wax loaded with Al2O3, CuO and ZnO nanoparticles in a rectangular container. The outcomes showed that the paraffin wax thermal performance was improved with nanoparticles loading. Khodadadi et al. [29] performed numerical and experimental investigations on PCM/ nanoparticles suspension exposed to a heat flux in a square container. Minea et al. [30] numerically evaluated three nanofluids based hybrid (Al2O3, TiO2 and SiO2). Radwan et al. [31] studied thermal management of concentrator photovoltaic sytems using microchannel heat sink with nanofluids, and Sadegh et al. [32] experimentally examined the solidification development of a PCM dispersed with TiO2 nanoparticles used during thermal energy storage. Recently, Brano et al. [33] developed a model of thermal storage system fixed with a PV device. Al-Waeli et al. [34] experimentally showed that Nanoparticle-PCM and nanofluid photovoltaic thermal (PVT) scheme could reduce the cell temperature, which positively impacted the PV/T performance. Emam et al. [35] studied an inclined concentrator photovoltaic-PCM heat sink performance. The fallouts specified that the CPV-PCM at an inclination angle of 45 °C exhibited a minimum mean temperature with greater uniformity of local cell temperature. Most rrecently, Emam et al. [36] examined cooling mechanisms of CPV systems using different configuration of PCM heat sinks. The outcomes showed that using five cavities parallel arrangement produced a significant reduction in the solar cell temperature when relates with single cavity and three cavity-series arranged heat sink configurations. In view of aformentioned, The CPV-Nanoparticle-PCM system plays a key role in enhancing the PCM thermal conductivity and consequently reduces the temperature rise of the CPV system. Accordingly, the addition of nanoparticles in a pure-PCM integrated with CPV systems remarkably enhances the solar cell temperature uniformity, decreases local cell temperature and in return improves the electrical efficiency as well as preventing potential damage caused by high temperatures. However, to the best of the authors’ knowledge, no published work related to concentrator photovoltaic Nanoparticles-PCM (CPVNanoparticles-PCM) systems thermal management. The originality of the current work is underlined by the novelty of the CPV-NanoparticlesPCM system. The key objective of this paper is the enhancement in PCM thermal conductivity and the reduction in the concentrator photovoltaic temperature rise to acquire efficient and optimal performance. This goal can be realized by loading of nanoparticles to address PCMs weak thermal conductivity. This in supplementary, controls the escalation in the temperature of PV cells that occurs when consider high solar concentration ratio (CR) which is define as the ratio of the solar irradiance incident on the cell target area relative to a certain solar irradiance of 1000 W/m2 (1 Sun)”. During the current simulation, the CR was selected to be 20 suns (20,000 W/m2) while the nanoparticles loading weight percent is varied from 1 wt% to 5 wt%, which significantly leads to decrease the temperature of solar cell and the risk for the CPV systems been damage. The thermal model for PV layers and the thermo-fluid model for Nano-PCM are developed and numerically simulated to predict a transient melting process, which takes notes of the phase-change phenomena by means of enthalpy method, heat loss boundary condition, and solar incident irradiance conversion into electricity. The focus of the current study is on the effect of the insertion of different nanoparticles in PCMs for CPV systems thermal regulation. However, the thermal regulations period can be increased by increasing the thermal mass of the employed nano-PCM to maintain the PV cell temperature at a lower value through the daytime. The study considered three types of metalic-oxide nanoparticles; the aluminum trioxide (Al2O3), copper oxide (CuO) and silicon dioxide (SiO2) dispersed in inorganic PCMs, calcium chloride hexahydrate. The examined nanoparticle loadings in PCM are at 1 wt% and 5 wt%. In this study, the PCMs with Al2O3, CuO, and SiO2 particle loadings are termed as NanoPCM1, Nano-PCM2 and Nano-PCM3, respectively.

Fig. 1. Schematic illustration of rectangular CPV-Nanoparticle-PCM system with PV cell layers.

2. Description of the hybrid concentrator photovoltaicNanoparticle-phase change material systems A schematic diagram of the CPV-Nanoparticle-PCM hybrid system with dimensions and boundary conditions is shown in Fig. 1. The system of the photovoltaic module with five layers is vertically positioned and coupled to a rectangular container of aluminum with 3 mm. walls thickness to improve Nanoparticles-PCM heat sink thermal conductivity and to provide uniform temperature distribution on the solar cell surface. The container has an interior height (H) of 125 mm on the y direction and length (L) of 100 mm on the x direction and is occupied with Nanoparticles-PCM composites with dispersed nanoparticles considered at specific weight fractions. Also, the three other sides of the container are presumed to be adiabatic, so that there will be symmetrical heat flow over the perpendicular path within CPV-NanoparticlesPCM system. In the current paper, the preferred PCM is calcium chloride hexahydrate. It is used because of the following criteria: a fixed melting point of temperature 28.9 °C [37] which is nearby 25 °C [38], usual required temperature for PV system operation, high latent heat, high density, non-flammable, good crystallization rate, reversible phase change, and cost effective. Three types of metalic-oxide nanoparticles Al2O3, CuO and SiO2 dispersed at changed weight fractions were considered and the impacts on phase transition temperature, thermal conductivity and melting rate are investigated. The solar concentrated irradiance reaching the system is presumed to be uniformly distributed [39]. The solar concentration ratio (CR) is considered to be 20 as the mean solar irradiance in the concentrated beam incident on the focus, while the reference value of 1 Sun is 1000 W/m2 [40]. The values of heat transfered by the captivated energy of each layers can be estimated using Eq. (2) by means of solar total irradiation incident on the glass cover [41] diffused into the Nanoparticles-PCM composite in the container, leaving some part vanished by radiation and convection back to the surroundings. The materials optical properties [42], considered in PV module are obtainable from Table 1. The PCM, nanoparticles, and aluminum thermophysical properties used are represented in Table 2. 3. Theoretical analysis The present CPV-Nanoparticles-PCM systems consist of PV layers of glass cover, tedlar layer, silicon cell and upper/lower EVA, integrated with a Nanoparticle- PCM heat sink as exhibited in Fig. 1. The model is established to envisage the melting fraction, transient temperature distribution throughout melting process in Nanoparticle-PCM composites and the mean transient temperature along with the local solar cell 231

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Table 1 The PV module optical and thermophysical properties of the materials used. Materials

Absorptivity [42]

Reflectivity [42]

Transmissivity [42]

Emissivity [42]

Glass EVA Cell TPT

0.04 0.08 0.9 0.13

0.04 0.02 0.08 0.86

0.92 0.9 0.02 0.012

0.9 – – 0.9

Density [37]

Thermal conductivity [37]

Specific heat capacity [37]

Thickness [37]

3000 kg/m3 960 kg/m3 2330 kg/m3 1200 kg/m3

2 W/mK 0.35 W/mK 148 W/mK 0.2 W/mK

500 J/kg K 2070 J/kg K 677 J/kg K 1250 J/kg K

3 mm 0.5 mm 0.2 mm 0.3 mm

Glass EVA Cell TPT

Table 2 PCM, Nanoparticle and aluminum thermophysical properties. Thermo-physical properties

PCM, Aluminum and Nanoparticles PureSalt Hydrate (CaCl2·6H2O)[35]

Aluminum (Al) [36]

Aluminum Oxide (Al2O3) [30]

Copper Oxide (CuO) [29]

Silicon dioxide (SiO2)[30]

Thermal cond. (W/mK) Solid Liquid

1.08 0.56

211 –

40 –

18 –

1.2 –

Density (kg/m3) Solid Liquid

1710 1560

2675 –

3970 –

6510 –

2200 –

Spec. heat cap. (kJ/kg K) Solid Liquid Melting point (°C) Heat of fusion (kJ/kg) Thermal exp. coefficient (l/k) Diameter (nm)

1.4 2.1 29.8 191 0.0005 –

0.903 – – – – –

765 – – – – 59

540 – – – – 29

703 – – – – 30

temperature at altered nanoparticle loadings. In this proposed theoretical assessment, the succeeding assumptions are considered to originate the governing equations.

layers, conduction is the main means of heat transfer. Therefore, explaining the heat transfer diffusion equation is very important. The general form of the diffusion equation in the Cartesian coordinate system can be articulated as [37]:

1. The PCM composite is unsteady and 2-Dimentional, Newtonian, and incompressible in its liquid form. 2. The means of heat transfer in the Nanoparticles-PCM composites are controlled by conduction and convection. 3. The nanoparticles in the PCM are homogeneously dispersed. 4. The solar cell is expected to receive concentrated solar irradiance with uniform intensity. 5. The PV layers, PCM, nanoparticles and aluminum thermos-physical properties in solid form, are considered isotropic and temperature independent.

i C p,i

Ti (x, y) = ki ( t

2T (x, i x2

y)

+

2T i(x,y) ) y2

+ qi where, i = 1, 2, 3, (1)

. , n

where Ti (x , y ) represents the temperature; Cp, i , i , qi and ki are the specific heat, density, interior heat generation and thermal conductivity of the layer i, respectively. Also, in the current model, the heat changed due to the captivated solar irradiance of each layer in the solar cell can be obtained by means of Eq. (2) [36] and used in the heat transfer equation as interior heat generation, qi .

The investigated solar cell in this work is a polycrystalline cell as specified by Sandia National Laboratory. The PV module is assembled of layers comprising of tempered glass, the upper EVA and the lower EVA, silicon cell, and tedlar foil. The glass cover is made of 3 mm. thickness of tempered glass with anti-reflective coating layer of 100 µm. thickness been used. This is because silicon can reflect up to 35% of incident radiation. The embedded silicon layer in transparent EVA layers is to create PV cells moisture resistant and electrically isolated. The tedlar, which is made of polymer is photostable layer with a thickness of 400 µm, which also provides moisture protection and electrical insulation.

qi =

(1

sc ) G (t ) i j Ai

Vi

(2)

where qi represents the interior heat generation per unit volume of the layer i; G(t) is the solar concentrated irradiance; sc is the electrical efficiency of the silicon layer in the solar cell, with value replaced to zero for all layers; i , Vi , Ai are absorptivity, volume, and area of the layer i, respectively; while i symbolizes the transmissivity of the layers over the layer i. Also, within the CVP cell layers, the glass cover interior heat generation is reliant on the incident solar irradiance concentration, and the glass absorptivity. More so, the top EVA layer interior heat generation is reliant on the received solar irradiance concentration, the EVA absorptivity, and the glass transmissivity. Nevertheless, the silicon cell layer interior heat generation term is reliant on the received solar irradiance concentration, the transmissivity of its EVA layers over the

3.1. Aluminum enclosure and concentrator photovoltaic layers In the aluminum enclosure coupled with concentrator photovoltaic 232

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silicon layer, and the glass, as well as the electrical efficiency of solar cell. Also, on the supplementary pointer, CPV cell layers under the silicon layer (i.e. TPT back sheet and bottom EVA layers) are not directly open to the received solar irradiance concentration, because of weak transmissivity of the silicon layer. Thus, the interior heat generation in the back sheet of the TPT and the bottom EVA layers is very minor and might be ignored [42]. The solar cell electrical efficiency, sc is expressed as [43]. sc

=

ref

(1

1, ref

(Tsc

Tref ))

operating temperature, and o represent operating density. The density and operating temperature are considered to be o = l and To = Tm , respectively. The Sx and Sy parameters are Darcy's law damping terms that are supplemented to the momentum equation because of phase change impact of convection. These terms reliant on both the existing constant Amush and liquid fraction (λ), that can be articulated as follows [35]:

(3)

The terms ref , and 1, ref are the reference silicon cell efficiency and the silicon cell temperature coefficient (1/k), respectively at a reference temperature Tref of 25 °C. The solar irradiance reference, G is equivalent to 1000 W/m2 or 1 sun. Usually, such standards are specified by the manufacturer in its data sheet and are obtainable for most solar PV cells on use [44]. To find the electrical efficiency of solar cell with respect to temperature at the standard solar irradiance, Eq. (3) is usually used. Also, numerous researchers reported that this equation can appropriately envisage the electrical efficiency of solar cell at changed values of concentration ratio [37]. The silicon cell power productivity per unit width can be inscribed as in Eq. (4) [45]:

Pelec =

sc G(t)H1,sc g E

=

ref

(1

ref

(Tsc

Tref ))G(t)H1,sc

g E

(4)

3.2. Nanoparticles-phase change materials

u v + =0 x y

P + µl, npcm x

=

y

direction: =

2u

x2

l,npcm

P + µl, npcm y

+

v + t

2v

x2

+

l,npcm u 2u

y2

u + x

2v

y2

l,npcm v

+ FB + Sy

where

o (1

1

1 (T

To )) g

H + t

l,npcm u

H + x

l,npcm v

2T H = kl,npcm ( 2 + y x

2T H = k s,npcm ( 2 + t x

2T

y2

)

2T

y2

)

(11)

(12)

(13)

H = h1 + H T

h1 = href +

Tref

Cp dT

(14)

where href is the enthalpy reference at temperature reference Tref and latent heat term can be stated in forms of the heat of the NanoparticlesPCMs L as: (15)

H= L

where ΔH can vary from zero (solid) to L (liquid). Therefore, the liquid fraction λ can be articulated as: H L1 H L

(6)

=

=0

T < Tm

T

Tsolidus Tliquidus Tsolidus H L

u l,npcm v y

=1

Tm < T < Tm + Tm T > Tm + Tm

(16)

where Tm is the temperature melting point of the Nanoparticles-PCM and Tm is the range between phase transition which can be well-defined as the variance between liquidus and solidus. Also, in the model, the mean temperature of the cell and stock thermal energy of the CPV-Nanoparticle-PCM system for a stage from initial time (ti ) to the extreme melting time (tm ) are obtained based on given Eqs. (17) and (18) [37]:

(7)

where l, npcm is density of the liquid mixture of nanoparticles and phase change materials; u , v are velocities of liquid phase in the x and y axis, respectively; µl, npcm is dynamic viscosity of the liquid mixture of nanoparticles and phase change materials; P is pressure and FB is a buoyancy force specified by the Boussinesq approximation [45].

FB =

(10)

where: H is the enthalpy of the Nanoparticles-PCMs and is the total value of the sensible enthalpy, h1, and then latent heat ΔH:

u y

+ Sx

v + l,npcm u x

(1 )2 . Amush . v ( 3+ )

s,npcm

Momentum equations:

u + t

Sy =

Energy equation for solid phase:

(5)

l,npcm

(9)

l,npcm

The principle of the enthalpy-porosity method [46,47] is consider simulating phase change processes of Nanoparticle-PCM. The interface in solid- liquid is not pursued explicitly when using this technique. The mushy zone for solid-liquid is considered as a “pseudo” porous zone having quantity branded as a liquid fraction λ as its “porosity” with suitable momentum sink terms augmented to momentum equations, which is the reason for the pressure drop as results of solid materials presence. The Nanoparticle-PCM liquid density difference in buoyancy term is simulated by means of Boussinesq approximation to achieve thermal buoyancy. Therefore, the 2-D transient laminar flow including buoyancy driven convention governing equations could be articulated as follows: Continuity equation:

direction:

(1 )2 . Amush . u ( 3+ )

where: γ is a minor number, naturally about 10 3 established to avoid division by zero, and the mushy zone constant Amush clarifies how steeply its velocity is condensed to zero when the material solidifies, and its value reliant on the morphology of the medium. This value is frequently high and ranges between 10 4 and 10 8. Also, the same can be said when the local liquid friction turns to be high and the velocity is condensed to zero. In the current work, Amush is presumed to be constant throughout the entire simulations and is established to be 106, where it achieves the best conformity amongst the predicted, experimental and numerical data as presented in the subsequent model validations. Also, many researchers recommend considering the Amush value of 106 where it provides the best overall relationship between their experimental and numerical data [37]. Energy equation for liquid phase:

where H1, sc represents the height of solar cell; E and g are the EVA layers transmissivity over the silicon cell and glass layers.

x

Sx =

T¯sc, avg =

(8)

Q¯ th, avg,

represents thermal expansion coefficient; To represents 233

1 tm

npcm

t = tm

ti =

t = ti

1 tm

Tsc (t ) dt t = tm

ti

t = ti

Qth (t ) dt

(17) (18)

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th, npcm

=

Q¯ th, avg

Note that, the constant b empirically-resolute is estimated using the study performed by Wakao and Kaguei [49]. Thus, the thermal conductivitykn , of the colloid can be obtained by:

npcm Xmnpcm

G (t ) XAsc X (tm

(19)

tl )

The transport of Nanoparticles-PCM composites is considered in modelling. The liquid or solid phase is observed by means of a quantity known as liquid fraction where nanoparticles are supposed to be distributed uniformly and homogenously in PCM. The occurrence of the nanoparticles only impacts the PCM thermo-physical properties. These properties of a multi-component system are reliant on the volume fraction of nanoparticles. Eq. (20) is considered for change between the weight fraction and the volume fractions ( wt to ∅) [29]: wt pcm

=

wt pcm + (1

wt

= wt

wt ) p

/

/

where ko is the thermal conductivity of Nanoparticle-PCM composites and kd represents the thermal conductivity improvement because of thermal diffusion. 3.3. Boundary conditions The schematic diagram of physical domain as represented in Fig. 1 exhibits a no-slip boundary condition applied at the solid-liquid interface: 0, At x = Al, (L Al ); y = 0; H1 for t

p

p + (1

(20)

wt )/ pcm

while, the weight fraction of PCM is constant regardless of the form of PCM phase, the volume fraction of PCM will differ according to the method of PCM phase because of density variance between the liquid phase and solid phase of PCM. The density of Nanoparticles-PCM [29] is articulated by Eq. (21): npcm

= (1

)

+

pcm

u=v=0 at x = Al ; y = 0 for t 0, The initial condition is:

u (x , y , 0) = v (x , y , 0) = 0

(21)

p

The model with solid Nanoparticles-PCM composite preserved at an early temperature, Tini which is less than the melting temperature, Tm of the engaged Nanoparticles-PCM and corresponds to 20 °C. Also, for all solid-solid boundaries exist, a thermally joined boundary condition is considered. Moreover, the adiabatic boundary condition is considered at the lower as well as the upper ends of the CPV-Nanoparticles-PCM system, as previously presented in Fig. 1. The front surface CPV cell thermal boundary condition had combined losses from convection and radiation. Furthermore, a convective coefficient of heat transfer, exterior radiation temperature with surface exterior emissivity, and ambient temperature, can be correctly quantified. However, the back-exterior boundary is exposed to convective heat loss for the CPV-Nanoparticle-PCM system. Furthermore, the external back and front surfaces applied boundary conditions can be articulated as follows [37]: On the CPV cell fore surface.

The density of the founded PCM is expressed as;

pcm

=

s ( s + l) 2

T < Tm Tm < T < Tm + Tm T

l

Tm = Tliquidus

Tm + Tm

(22) (23)

Tsolidus

The heat capacity of Nanoparticles-PCM composites and part of the Boussinesq term can be obtained using Eqs. (24) and (25) as represented below:

( Cp )npcm = (1

(

)npcm = (1

)( Cp )pcm +

)(

)pcm +

( Cp )p

(

(24) (25)

)p

Also, the latent heat can be estimated as:

(

)npcm = (1

)(

(26)

)pcm

( CP )s ( Cp )pcm =

2

+

T

s+ l

2

( ), Tm

( Cp )l

Tm

Tm + Tm

kal

µn =

hconv, g

The stagnant effective thermal conductivity (kO ) of NanoparticlesPCM composites can be formulated by means of Maxwell model [29] as given in Eq. (29):

knpcm kpcm

=

kp + 2kpcm

2 (kpcm

kp)

kp + 2kpcm + 2 (kpcm

kp)

ks (ks + kl ) , 2

T

sky (Tsky

Tg )

(33)

T = hconv, al x

amb (Tamb

Tal )

(34)

amb

= 5.7 + 3.8Vw

(35)

This relationship was originated based on the basic theory of heat transfer and wind tunnel measurement. Also, this equation was effective for wind speed Vw up to 5 m/s and was considered by numerous researchers to achieve the coefficient of heat transfer from the upper surfaces of PV [50]. Furthermore, the radiation coefficient of heat transfer amongst the glass cover and the sky (hrad.,g -sky), and that of the TPT back cover and the sky (hrad,T-sky) were acquired by means of Eqs. (36) and (37) as reported in [37] based on the statement that the sky is a black body with temperature, Tsky :

(28)

)2.5

(1

Tg ) + hrad, g

More so, the glass cover layer convective heat transfer coefficient to the atmosphere (hconv, g - amb) due to the influence of wind was evaluated by the following correlation given in Eq. (35) [37].

(27)

The colloid containing weak suspensions of minor rigid sphereshaped particles viscosity is specified by Brinkman [48] with Eq. (28):

µl

amb (Tamb

On the CPV-Nanoparticles-PCM system back-exterior surface.

Tm < T < Tm + Tm T

T = hconv, g x

kg

Therefore, the liquid fraction λ can be evaluated using Eq. (16). The adapted heat capacitance of the PCM is determined as follows: ( Cp )s + ( Cp )l

(32)

kn = k o + kd

(29)

Tm

(Tg4

4 Tsky )

(Tg

Tsky )

(TT4

4 Tsky )

(TT

Tsky )

hrad, g

sky

=

g

The thermal conductivity improvement because of thermal diffusion can be estimated with Eq. (31) and Eq. (33) [29]:

hrad, T

sky

=

T

kd = b ( Cp )n u2 + v 2 dp

The optical values and characteristics of CPV cells and designed parameters considered in this contemporary study of the CPV-

kpcm =

kl

Tm < T < Tm + Tm T

Tm + Tm

(30)

(31) 234

(36) (37)

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Nanoparticles-PCM system is represented in Table 2.

correction, and thermal energy under-relaxation factors for were accordingly considered. The calculation from the present simulation model, in terms of melting front, followed the same trend when compared with the calculations done by Khodadadi et al. [29] experimentally and numerically. Furthermore, this justifies clearly that the present studied model is in high agreement, therefore, this comparative study puts a stringent test of the consistency of our model and its predictions before using it further.

4. Numerical methodology In this current paper, a hybrid model that incorporates transient melting-solidification thermo-fluid model for Nanoparticles-PCM and CPV layers thermal model, was considered along with initial and boundary conditions. The developed model was numerically simulated using ANSYS 19.0 software [51]. The semi-implicit method for pressure-linked equations (SIMPLE) scheme was considered to determine the pressure-velocity coupling equations in Nanoparticles-PCM. The first-order upwind scheme was adopted to estimate the energy and momentum equations. Moreover, the governing equations solved at each time step, an updated liquid mass fraction was achieved.

4.2. Model validation In the current study, the numerical findings are validated by means of the experimental measured and numerical results. The assessments extensively exam the consistency and accuracy of the present established model before adopting and proceeding ahead. During the validation step, the same systems geometry, boundary conditions, operating conditions and materials were applied in the model.

4.1. Grid independence and time step study In this research, several grid independence tests have been conducted to ensure independency of the solution on grid density before large number of calculations are performed for the investigated model of integrated PV layers and Nano-PCM heat sink. The model consists of two domains coupled together, one for PV layers and the other for aluminum container. The model has quad-type meshing of square unit, which under goes unsteady melting process. The square quad-element is deployed with regards to the heating wall. Five different meshes of increasing quantities are considered and their corresponding evolution of liquid fraction. By comparison, the grid size (number of nodes,) element size (mm.) and the time steps ( t ) for this unsteady calculation is also checked and the results on relative error percentage (%) obtained from the five increasing grid size, elements size and time steps have been presented in Table 3. Comparisons were made with the minimum one, the time step, t = 0.1 s, the calculation errors corresponding to t = 0.2 s, t = 0.3 s, t = 0.4 s and t = 0.5 s are 0.10, 0.16, 0.32 and 0.38% respectively. Though the errors increase with an increase in time steps which result to increase in cost, but they are still within the acceptable range. In current simulations, the consumed time for calculations to reach the complete melting phase using a Dell Precision T7500 workstation with an Intel Xeon® processor of 3.75GH, 12core, and 32-MB installed memory is about 24 h and 15 h while using 0.1 and 0.2 s time step, respectively. The mesh size is selected after a careful examination of results to achieve the grid independence and accommodate both the required solution accuracy and convergence at a relatively low run time. This is accomplished by calculating the time required for a complete melting at different time steps. Results showed that an increase of the computational time for a complete melting is observed as time step is increased from t = 0.1–0.5 s. Further increase of that time step results in a slight change in the time reached at complete melting. Accordingly, a time step t = 0.2 s, is noticed to be adequate for the needed accuracy with reasonable computing time. Accordingly, the time step is carefully chosen to be as small as 0.2 s. Also, numbers of grids were considered after several trails to accommodate the required solution accuracy and achieve grid independency at comparatively low run time during the simulation. Five different of grids with total nodes: 1,777,716; 446,080; 198,852; 112,741; and 71,799 having element size of 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm and 0.5 mm respectively are developed and examined. It is observed that grid with nodes 71,799 using time steps of 0.2 s exhibits only marginal change with further addition of grid numbers. More so, the physical domain is discretized by the 71,799 nodes with 267.95 and 267.95 in x and y axis, respectively and is observed to be adequate for required accuracy and for comparison to justify the consideration of the time step 0.2 s and the grid number 71,799. Furthermore, these model characteristics are considered based on grid and time step independence studied to balance between running time and accuracy. More so, at each step during the simulation, convergence is checked at the criterion of 10−6 for the variables. The velocity, pressure

4.2.1. Phase Change Material-Nanoparticle model validation Fig. 2 presented the comparisons of melting fraction among present predicted and numerical results [25]. The PCM (CaCl2·6H2O) dispersed with nanoparticles (graphene) at 5 wt% is considered. The results as exhibited confirmed that the time required for the numerical result [25] to achieved a complete melting fraction is 20 min., while the predicted time is about 18.9 min. A difference of 1.1 min. is observed. However, this difference could be a result of modeling assumptions. The predicted and experimental results [29] for liquid fraction and the current calculated results at different time instants are validated as presented in Fig. 3a. The PCM (n-octadecane) dispersed with CuO nanoparticles at 5 wt% is used. Comparison illustrates a good concurrent between predicted and measured results. Fig. 3b present the comparison between the measured transient temperature of [29] and the current determined values for CuO nanoparticle dispersed in n-octadecane PCM at 3 wt%. The results disclose that the difference in temperature is about 1.8 %, which is in good agreement despite the two kind results being originated from different methods. Further, the variance recorded may have been due to some experimental errors. The PCM and nanoparticles thermo-physical properties consider in the validation is obtainable in Table 4. 4.2.2. Phase Change Material-Photovoltaic validation of model The predicted data are validated considering the experimental results [14] by relating the mean and measured temperatures on the systems front with respect to time, as exhibited in Fig. 4. The employed PCM is RT27 (organic paraffin wax) which is an organic paraffin-based material provided by RUBITHERM®, Germany [52] with a melting point temperature of 28 °C, an average surrounding temperature of 19 °C and a solar irradiance incident of 750 W/m2 was used. Moreover, the back, bottom and top surfaces were presumed to be adiabatic. The results shown that a concurrent agreement was achieved amongst the present simulated and experimental measured results with an observed maximum error of 1.0 °C translating to around 2.3 % (considering at 50 min., the predicted temperature is 37.87 °C and the experimental measured temperature is 36.8 °C). The properties of the materials considered in the PV module is obtainable in Table 1 and the PCM thermophysical properties is provided in Table 2. Table 3 Time step-step dependence of the numerical solution.

235

Time steps t , (s)

Complete melting time (s)

Relative error (%)

0.1 0.2 0.3 0.4 0.5

3122 3119 3117 3112 3110

– 0.1% 0.16% 0.32% 0.38%

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5. Results and discussion The obtained numerical outcomes from the current study are reported and analyzed in this section. The results, as illustrates in Figs. 5–9 are represented in three subsections to comprehensively appraise the performance of the CPV-Nanoparticle-PCM system. In the first subsection, the impact of nanoparticles on phase change materials’ melting fractions, transient mean temperature differences and velocity magnitude within the container, are demonstrated. The second subsection demonstrates the impact of nanoparticles on concentrated photovoltaic system regarding transient variation of the mean solar cell temperature and local solar cell temperature. In addition, the last subsection recapitulates the impact of percentage weight fraction on melting fraction of Nanoparticles-PCM in addition to the transient temperature variation in solar cell for the developed CPV-Nanoparticles-PCM system. 5.1. Impact of nanoparticles on Phase Change Material

Fig. 2. Comparison between the predicted results on melting fraction for graphene nanoparticles dispersed in CaCl2·6H2O PCM at 5 wt% and the corresponding numerical results [25].

5.1.1. Melting fraction The comparisons of the development of the solid-liquid melting process in terms of melting fraction for pure-PCM (CaCl2·6H2O) and one dispersed with Al2O3, CuO and SiO2 at 1 wt% and 5 wt% are presented in Figs. 5 and 6. Based on the Figures, higher weight fractions improve the heat transfer process and in return accelerate the melting rate of Nano-PCM1-3. Fig. 5a exhibits the times to reach the complete melting point, which are 78 min., 80 min., and 85 min., for pure-PCM dispersed with Al2O3, CuO, and SiO2 at 1 wt%, respectively. For the pure-PCM, the time required to reach the complete melting point is 88 min. The difference in time required by all the Nano-PCM1-3 to reach complete melting fraction is caused by the increase in PCM thermal conductivity. This result can be considered because of loading of nanoparticles, which leads to the improvement of thermal conductivity, and accordingly, heat transfer process. Increasing the weight fraction of the same nanoparticles to 5 wt% in the PCMs, as exhibited in Fig. 5b, decreases in time need to achieve complete melting with Al2O3, and CuO, and SiO2 recorded at 70 min., 76 min., and 84 min., respectively. This is due to the improve of thermal conductivity and consequently speeds up the melting rate. When compared with Nano-PCM1-3 at 1 wt% and 5 wt%, the Al2O3 nanoparticles have the highest enhancement capability and the SiO2 nanoparticles have the lowest enhancement capability. This can be attributed to the reality that Al2O3 have greater thermal conductivity enhancement capability than CuO and SiO2 nanoparticles. Based on Fig. 5a and 5b, by raising the percentage of weight fraction of nanoparticles from 1 wt% to 5 wt% on PCMs throughout the melting procedure, the melting rates quickened as weight fraction increased. This justifies that enhancement in PCM thermal conductivity can be achieved by increasing the weight fraction of nanoparticles. However, loading higher dose of nanoparticles in PCMs has a negative effect, because of the agglomeration and sedimentation experiences. This can be, based on the fact adding weight fraction of nanoparticles in PCMs steadily raises the dynamic viscosity of NanoparticlesPCM composites. Therefore, there is a need to obtain an optimal percentage of nanoparticles loading in PCMs. It is observed during the study that for Nano-PCM1-3 there is little or no significant difference in heat transfer rates during the first few minutes. This also confirms that heat transfer is regulated by conduction within that first phase and then, as the PCM melts, the domain mechanism changes to natural convection, when the viscosity impact is higher. Finally, it can be stated that Nanoparticles-PCM thermal conductivity is greater than the purePCM, since Nanoparticles-PCM has a higher rate of heat transfer when related with equal mass of the pure-PCM sample. Therefore, viscosity of the Nanoparticles-PCM rises with the expansion in volumetric concentration of nanoparticles. The overall results are in agreement with experimental studies carried out by Khodadadi et al.[53] and Kant et al. [25]. The summary of discussed results on liquid fraction is showed in

Fig. 3a. Comparison between the predicted results on melting fraction for CuO nanoparticle dispersed in n-octadecane PCM at 5 wt% and the corresponding experimental results [29].

Fig. 3b. Comparison between predicted result on average temperature variations within cavity for CuO nanoparticle dispersed in n-octadecane PCM at 3 wt % and the corresponding experimental measured results [29].

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Table 4 PCM and nanoparticles thermophysical properties. Thermo-physical properties

PCM and Nanoparticles n-octadecane [29]

Thermal cond. – solid/liquid Density-solid/liquid Spec. heat cap. solid/liquid Melting point Heat of fusion Thermal exp. coefficient Diameter

0.358 W/mK 0.148 W/mK 865 kg/m3 770 kg/m3 1934 kJ/kg K 2196 kJ/kg K 28 °C 243 kJ/kg 9.1 × 10−4 l/k –

Pure salt hydrate-CaCl2·6H2O [25]

Paraffin-based RT-27 [14] −1

1.008 W/mK 0.561 W/mK 1802 kg/m3 1562 kg/m3 1.4 kJ/kg K 2.1 kJ/kg K 29.8 °C 192 kJ/kg 1 × 10−3 l/k –

−1

0.2 W m /K 0.2 W m−1/K−1 880 kg/m3 760 kg/m3 1.566 kJ m−3 K−1 1.800 kJ m−3 K−1 25–28 °C 184,000 J kg−1

Fig. 4. Comparison amongst the predicted results on mean temperature variation in the central vertical line of the PV/PCM with the experimental measured results [14]

Copper Oxide (CuO) [29]

Graphene [25]

18 W/mK

5000 W/mK

6510 kg/m3

2200 kg/m3

540 kJ/kg K

0.790 kJ/kg K

N/A N/A 1.67 × 10−5 l/k 29 nm

– – – –

Fig. 5b. Comparison of the melting processes of Nano-PCM1-3 at 5 wt% and pure-PCM at complete melting.

slower. This indicates that heat transfer is dominated by conduction mode. However, when time increases, the natural convection heat transfer mode becomes dominant in the systems. Accordingly, comparing loadings of Al2O3, CuO and SiO2 nanoparticles in pure-PCM at 1 wt% and 5 wt% is presented. The results show that within the cavity at 60 min the temperature could reach 77 °C for pure-PCM and the temperature of the Nano-PCM1-3 at 1 wt% was 84 °C, 82 °C and 79 °C, respectively. By further dispersing at 5 wt.%, the temperature reached 87 °C, 83 °C and 81 °C, respectively. However, it is shown that the increase in temperature has a flat profile during the first 30 min before melting takes place with little or no difference in the rate of heat transfer recorded at first 10 min interval, since the heat transfer process is regulated by conduction means. Again, as the Nanoparticles-PCM composites melts, the dominant process changes to natural convection. The melting process is only dominated by conduction at early stages and at later instances, natural convection becomes more pronounced, leading to a significant increase in temperature. Summary of comparisons/analysis of discussed results on liquid fraction/percentage of enhancement and temperature rise in cavity is presented in Table 5.

Fig.5a. Comparison of the melting processes of Nano-PCM1-3 at 1 wt% and pure-PCM at complete melting

5.1.2. Velocity magnitude variations within interior cavity Figs. 6a and 6b illustrate a comparison of the simulated velocity magnitude between the pure-PCM and the Nanoparticles-PCM1-3 at 1 wt % and 5 wt% within the interior cavity at 80 min. The velocity magnitude is exported from the ANSYS results based on simulated average weight velocity magnitude obtained at various time instants. For all Nanoparticles-PCM1-3, results show that velocity increases with the loading of nanoparticles. This might occur because of the rise in thermal conductivity which, in return, increases the rate of heat

Table 5. Thus, in the present study, the transient temperature variations for Nano-PCM1-3 composites within the interior cavity of the CPVNanoparticles-PCM system is observed. The predicted temperature variations within the interior cavity of the CPV-Nanoparticles-PCM heat sink for all the weight fractions of nanoparticles considered, one can observe that at initial phases of the melting procedure, the melting is 237

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Table 5 Summary of comparisons/analysis of discussed results on liquid fraction/percentage of enhancement and temperature rise in cavity.

Al2O3 CuO SiO2 PCM

Percentage (%) enhancement by nanoparticles on Nanoparticles-PCM1-3 at complete melting fraction

Temperature in cavity after 60 min

0 wt%

1 wt%-Time

% of enhancement

5 wt%-Time

% of enhancement

0 wt%-Temp.

1 wt%-Temp

5 wt%-Temp.

– – – 88 min

78 min. 80 min. 85 min. –

11% 9% 3% 0%

70 min. 76 min. 84 min. –

20% 14% 6% 0%

– – – 77 °C

84 °C 82 °C 79 °C –

87 °C 83 °C 81 °C –

Table 6 Equivalent thermophysical properties of the employed PCM-nanomaterial composites at 5 wt% based on the previously mentioned equations. Composites (Nano-PCM)

Fig. 6a. Comparison of average velocity magnitude within the interior cavity of Nano-PCM1-3 at 1 wt% and pure-PCM at 80 min.

Thermo-physical properties

CaCl2·6H2OAl2O3

CaCl2·6H2O-CuO

CaCl2·6H2O-SiO2

Thermal cond. (W/mK) Solid Liquid

1.1477 0.5932

1.1175 0.5903

1.0914 0.5803

Density (kg/m3) Solid Liquid

1760.09 1608.83

1775.45 1621.65

1729.25 1583.02

Spec. heat cap. (kJ/kg K) Solid Liquid

1368.25 2033.25

1357 2022

1365.15 2030.15

for different Nano-PCMs at 5 wt%. 5.2. The impact of nanoparticles on solar cell temperature Investigating the temperature variations in solar cell is important in achieving the optimal performance of CPV systems. Therefore, transient differences of the mean and local solar cell temperatures are observed throughout the melting process, with the aim to comprehend how Nanoparticles-PCM might be considered to maintain a better CPV system cooling. There are three levels of temperature variations within solar cell that can be linked to phase change in the cooling process. The first level notes a rise in mean temperature of solar cell with a gradual elevation noted over period. This is probably because of sensible heating of the Nanoparticle-PCM composites due to the conducted heat transfer via the front wall of aluminum. The phase transition of the Nanoparticles-PCM adjacent to the aluminum wall occurs, where the Nanoparticles-PCM then served as a padding material to the CPV

Fig. 6b. Comparison of the average velocity magnitude within the interior cavity between Nano-PCM1-3 at 5 wt.% and pure-PCM at 80 min.

transfer where leading to a higher volumetric force variance amongst the liquid and solid Nanoparticles-PCM composite. The PCM dispersed with Al2O3 attains a higher velocity because of the thermal conductivity improvement capability when compared with pure PCM or PCM enhanced with CuO and SiO2. To further explain the reason, Eqs. (21), (22), (24), and (29) were used to calculate thermophysical properties (density, specific heat capacity, viscosity and thermal conductivity) of the composites as given in Table 6. The calculated values were implemented in the ANSYS FLUENT software to determine the liquid fraction and the average solar cell temperature up to complete melting point. Based on the calculated values, it is found that the calculated thermal conductivity of CaCl2.6H2O-Al2O3 is higher than that for CaCl2.6H2O-CuO, and CaCl2.6H2O-SiO2 which attains a faster rate of melting and consequently higher velocity, and lower average solar cell temperature as shown latter. The trends of these outcomes conform with the research work done by Kant et al. [25] on variations of velocity

Fig. 7a. Comparison of the transient mean solar cell temperature with different types of Nanoparticles-PCM at 1 wt.% and pure-PCM. 238

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temperature cell. Also, when heat transfer becomes fully active due to conduction, it leads to elevation in temperature of the CPV cells. The second level charts a further rise in time, and notes a reduction in the mean cell temperature, which then continues to be constant for some time. This signals the commencement of convective heat transfer, then stabilized the conductive heat transfer, at this stage, natural convention acts so significantly in the liquid Nanoparticles-PCM that there is a rise in melting fraction. The third level shows that as time progresses, the cell temperature starts to rise progressively until the point when Nanoparticles-PCM composites achieve complete melting fraction due to natural convention. This may result to low heat transfer from the hot to the liquid section in the CPV-Nanoparticles-PCM system.

temperature for Nano-PCM1-3 composites at 1 wt% and 5 wt% and purePCM. Generally, it agrees that increasing nanoparticle weight fractions, significantly decreases the local solar cell temperatures and improves uniformity of distribution of temperature within the CPV cell height. Also, as exhibited in Figs. 8a or 8b, it is observed that the local solar cell temperature for pure-PCM could have a difference of 20 °C amongst upper and lower parts of solar cell. For dispersed PCM with Al2O3, CuO, and SiO2 nanoparticles at 1 wt%, the temperature difference achieved can be 15 °C, 17 °C and 18 °C, respectively, as demonstrated in Fig. 8a. With further dispersing of the same nanoparticles at 5 wt%, the temperature variance amongst the maximum and the minimum can be reduced to 12 °C, 14 °C, and 15 °C, respectively, as revealed in Fig. 8b. The slight differences in temperature uniformity might be due to loading of nanoparticles. This justifies that while increasing the nanoparticles weight fractions, the local solar cell temperature reduces and improves its uniformity. The reduction in local solar cell temperature rise because of increase in thermal conductivity, which enhances the rate of heat transfer of PCM, thereby, reducing local solar cell temperature rise as reported in [55]. This also confirms that dispersing nanoparticles in CPV-PCM could reduce the thermal stratification within the systems, therefore yielding greater efficiency in the solar cell, which is mainly a role of cell temperature that is typically below 100 °C [36]. Comparison of nanoparticles with higher and lower enhancement capability at 1 wt% and 5 wt%, and pure-PCM with those reported by [35,44], show a good agreement. This further justifies how important Nanoparticles-PCM could be for the use in the cooling of CPV. The summary of these outcomes on the local solar cell temperature is obtainable in Table 8.

5.2.1. Mean temperature of solar cell transient variations Fig. 7a presents a comparison between transient variations of mean temperature of solar cell for the CPV-Nanoparticles-PCM and purePCM-CPV system. These include the loading of Al2O3, CuO, and SiO2 nanoparticles in pure-PCM at 1 wt%. It is noted that by considering PCM heat sink with dispersed nanoparticles, a remarkable reduction in mean temperature of solar cell is achieved, compared to the pure-PCMCPV system. This could be attributed to PCM thermal conductivity that has been improved by the nanoparticles, which increases the rate of heat transfer of PCM. Furthermore, loading of nanoparticles improved the melting section in the systems. This leads liquid phase temperature to reasonably decrease, resulting in a rise in difference in temperature amongst the wall and the melted liquid. Eventually, more heat is relocated into the Nanoparticle-PCM domain from the CPV cell side, which exhibits a decreasing mean solar cell temperature. Results of the Nanoparticles-PCM-CPV system with Al2O3, CuO, and SiO2 nanoparticles loaded at 1 wt.% at complete melting fraction reveal that the mean temperature of solar cell reduced significantly to 141 °C at 78 min, 142 °C at 80 min, and 148 oC at 85 min, respectively. In distinction, a temperature of 153 °C for 88 min is examined when the PurePCM-CPV heat sink is considered because at that point latent heat has depleted, and the systems temperature starts to increase rabidly. Moreover, adding the Al2O3, CuO, or SiO2, nanoparticles from 1 wt% to 5 wt%, decreases the temperature at complete melting fractions of Nanoparticles-PCM-CPV from about 141 °C to 132 °C, 142 °C to 140 °C, and 148 °C to 146 °C, respectively, as revealed in Fig. 7b. The Pure-PCM temperature at complete melting point was 153 °C. However, the drops in temperature noted because of the improvement in PCM thermal conductivity while increasing nanoparticles. Subsequently, comparing the three Nanoparticle-PCM cases at two different loadings of nanoparticles, in terms of average solar cell temperature. Results show that at both weight fraction loading 1 wt% and 5 wt%, Al2O3 nanoparticles have the highest enhancement capability and nanoparticles SiO2 have the lowest enhancement capability, at complete melting fraction. The Al2O3 nanoparticles have an enhancement capability of about 11 % at 1 wt.%, and 20 % at 5 wt.%, with a temperature difference of 15 °C and 12 °C respectively. The SiO2 nanoparticles are the lowest, having an enhancement capability of about 3 % at 1 wt.%, as well as 6 % at 5 wt.% compared to Al2O3 nanoparticles. Also, the SiO2 exhibits a temperature difference of 18 °C and 15 °C. when dispersed in PCM. This further reveals that increasing the nanoparticles’ weight fraction in PCM result in enhancing thermal conductivity, consequently reducing the rise in solar cell temperature, as exhibited in Figs. 7a and 7b, to conform with required operating temperature levels of CPV [35]. These findings are in agreement with studies done by Emam et al. [34], Emam et al. [35], and Radwan et al. [54] where cases of temperature reduction in CPV were observed due to the introduction of numerous fins in the systems. The summary of discussed results on mean temperature of solar cell presented in Table 7.

5.3. Performance of concentrator photovoltaic-nanoparticle-phase change material systems To compare the performance and temperature uniformity of the CPV-Nanoparticle-PCM system, different types of nanoparticles at different weight fractions are utilized at a CR of 20. Fig. 9a illustrates the electrical efficiency of the solar cell using Al2O3-PCM, and SiO2-PCM, at 1 wt% and 5 wt%, in comparison to pure-PCM. Results reveal that, at 1 wt% Al2O3-PCM and SiO2-PCM, the electrical efficiency is 7.17 %, and 6.69 %, respectively. With further increase of nanoparticles to 5 wt%, the electrical efficiency rises to 8.0 %, and 6.9 % accordingly. On the other hand, using pure PCM attains electrical efficiency of 6.36 %. Consequently, using Nanoparticle-PCMs can achieve an improvement in solar cell electrical efficiency, which enhances cell performance. At a CR = 20, the CPV-Nanoparticle-PCM system with Al2O3-PCM at 5 wt% achieves the highest electrical efficiency with an enhancement

Fig. 7b. Comparison of the transient mean solar cell temperature with different types of Nanoparticles-PCM at 5 wt. % and pure-PCM.

5.2.2. Local solar cell temperature variation Figs. 8a and 8b present a comparison amongst the local solar cell 239

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Table 7 Summary of comparisons/analysis of discussed results on mean solar cell temperature.

Table 8 Summary of comparisons of discussed results on local solar cell temperature. Local solar cell temperature raises in Nano-PCM1-3 and PCM at 0.125 m height at 60 min

Average solar cell temperature for Nano-PCM1-3 and pure-PCM at a complete melting

Al2O3 CuO SiO2 PCM

0 wt.% Time

0 wt.% Temp.

1 wt.% Time

1 wt.% Temp.

5 wt.% Time

5 wt.% Temp.

– – – 88 min

– – – 153 °C

78 min 80 min 85 min –

141 °C 142 °C 148 °C –

70 min 76 min 84 min –

132 °C 140 °C 146 °C –

Al2O3 CuO SiO2 PCM

0 wt% Time

Temp difference (Top and base)

1 wt.% Time

Temp difference (Top and base)

5 wt.% Time

Temp. difference (Top and base)

– – – 60 min

– – – 20 °C

60 min 60 min 60 min –

15 °C 17 °C 18 °C

60 min 60 min 60 min –

12 °C 14 °C 15 °C –

Fig. 8a. Difference in local solar cell temperature with height for different types of Nanoparticle-PCM at 1 wt.% and pure-PCM.

Fig. 9a. Solar cell electrical efficiency using different Nanoparticles-PCMs

Fig. 8b. Difference in local solar cell temperature with height for different types of Nanoparticles-PCM at 5 wt.% and pure-PCM.

capability of 22 % compared to pure-PCM. In addition, the CPV-Nanoparticle-PCM system with Al2O3-PCM attains better solar cell performance compared to SiO2-PCM. The temperature variation along the solar cell height is an essential parameter to determine the thermal stresses associated with the temperature gradient to avoid hot spots. Temperature uniformity can be defined as the difference between the maximum and minimum temperature along the solar cell. Subsequently, the temperature uniformity of solar cell using Al2O3-PCM, and SiO2-PCM, at 1 wt% and 5 wt% is shown in Fig. 9b. As seen in the figure, the temperature uniformity is 20 °C via pure-PCM. By using Al2O3-PCM, the temperature uniformity decreases from 15 °C at 1 wt% to 12 °C at 5 wt%. A similar trend is

Fig. 9b. Temperature uniformity of solar cell using different NanoparticlesPCMs

observed for SiO2-PCM where the temperature uniformity reduces from 18 °C at 1 wt% to 15 °C at 5 wt%. To conclude, using Al2O3-PCM as a cooling medium of CPV at a 240

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concentration ratio of 20, attains the highest electrical efficiency of 8.0 % and temperature uniformity of 12 °C compared to pure PCM, where the electrical efficiency reaches 6.36 % and temperature uniformity of 20 °C. Accordingly, using nanoparticles not only enhances the electrical efficiency but the temperature uniformity as well.

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