Thermal management of photovoltaic panel with nano-enhanced phase change material at different inclinations

Photovoltaic (PV) panel, coupled with phase change material (PCM), has attracted broad attention for the panel’s thermal management. Despite the higher energy storage capability of PCMs, the main disadvantage is their low thermal conductivity which is compensated to an extent with the nano-enhanced PCMs (NEPCMs). In this study, numerical simulations are carried out to compare the heat transfer phenomena and thermal response of PV-NEPCM with simple PV-PCM for various tilt angles. CuO nanoparticles with mass concentrations of 1%, 3% and 5% are selected for NEPCM. The thermal performance of PV-NEPCM at inclinations of 0°, 15°, 30° and 45 ∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document} is compared with a simple PV-PCM system to know the effect of mass concentration of nanoparticles and inclination. The average temperature of PV, liquid fraction and thermal energy stored in PCM, the pattern of isotherms and streamlines and performance of PV are compared for PV-PCM and PV-NEPCM systems. Results show that the loading of nanoparticles increases the heat transfer rate to PCM in all the configurations. It has also been shown that at lower inclinations, the use of NEPCM is more effective due to the presence of conduction heat transfer. At higher tilt angles, heat transfer from the PV module takes place by natural convection. By using NEPCM, the maximum decrease in PV temperature of 1.26 ∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ{\rm C}$$\end{document} and maximum improvement in the liquid fraction of 8.25% are achieved when θ=0∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uptheta =0^\circ$$\end{document} with 5% mass concentration of nanoparticles compared to simple PCM. Enhancement of thermal energy stored in PCM increases upon adding nanoparticles, and the highest improvement is obtained for θ=0∘.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uptheta =0^\circ .$$\end{document} Maximum enhancement of efficiency of PV module is found to be 1.75% for θ=0∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uptheta =0^\circ$$\end{document} inclination on adding nanoparticles of 5% mass concentration.


Introduction
Energy utilisation is growing exponentially in the present era of rising population, and the demand for renewable energy has been increasing significantly from the last decade onwards. Solar energy, which is derived from the sun, is the most abundant renewable energy which can easily meet today's demands. Solar energy from the sun that falls on the earth's surface can be transformed into electrical energy with the help of photovoltaics based on the direct energy conversion method. Photovoltaic (PV) cells, also referred to as solar cells, are solid-state devices that directly convert solar energy into electricity. Depending on the cell material and climatic conditions, a standard PV cell converts 6-20% of the incident solar radiation into electricity, and the remainder is converted to thermal energy, which increases the temperature of the PV cell to 50 • C above ambient (David Tan 2011). The temperature coefficient of power is an important differentiator in solar PV efficiency, particularly in hot climates. The efficiency of PV cells degrades as the temperature of the cells increase (Luque and Hegedus 2003). Wysocki and Rappaport (1960) theoretically investigated energy conversion in solar PV cell over a temperature range of 0-400 • C by varying band gaps and found that the maximum conversion efficiency occurs with materials having high bandgap. Radziemska and Klugmann (2002) experimentally showed that the product of V oc I sc of PV cell degrades about 0.8% for every 1 K increase in temperature. Power output of crystalline solar cell decreases by 0.4% for every 1 K rise in temperature (E. Radziemska 2002). Skoplaki and Palyvos (2009) presented correlations for PV's power and efficiency as a function of its operating temperature. The PV module's degradation rate is doubled for every 10 °C rises in its temperature (Otth and Ross 1983). So, temperature management of PV panels is very much essential for its best performance.
Temperature regulation of PV using phase change material (PCM) has received much attention in the passive cooling of PV module as the cooling process is very efficient using PCMs. A typical solid-liquid PCM with an appropriate melting point and heat of fusion is mounted to the backside of the PV panel to establish a PV-PCM system. PCM in the PV-PCM system absorbs the excessive thermal energy generated by the PV panel in the form of latent heat and ensures lower PV panel temperature and higher electrical efficiency. Hasan et al. (2010) evaluated the performance of PV integrated with five different PCMs with three insolations and showed that mass and thermal conductivity of PCM along with thermal conductivity of PCM container play a significant role in the PV-PCM system's performance. Park et al. (2014) carried out an experimental and numerical analysis to examine the performance of a vertical PV-PCM system and compared it with a standard PV module under actual outdoor climate conditions. The results showed an increase of 1-1.5% in electric power generation of PV module.
The numerical analysis and experimental investigation by Mahamudul et al. (2016) showed that with RT35 as a PCM layer of 0.02-m thickness, the module's surface temperature is reduced by 10 • C for 4-6 h. The effects of inclination angle, concentration ratio and PCM thickness on the performance of a CPV-PCM system were studied numerically by Emam et al. (2017) using CaCl 2 -6H 2 O as PCM. Khanna et al. (2017) analysed the effects of tilt angle of PV-PCM system, wind direction, wind velocity, ambient temperature and phase transition temperature on the rate of PCM heat extraction and temperature of PV-PCM system. The PV panel temperature in the PV-PCM system dropped from 43.4 to 34.5 • C . Gkouskos et al. (2012) presented an experimental study of a PV-PCM system to decrease the temperature of the PV panel and to increase the overall efficiency of the PV-PCM system. PV temperature, when coupled with RT27 as PCM, was found to be close to 25 • C.
A three-dimensional numerical model was simulated, and the results were compared and validated with the results of the two-dimensional model and experimental studies by Huang et al. (2006). Brano et al. (2013) developed a onedimensional numerical model based on an explicit finite difference method for formulating energy balance for the PV-PCM system to increase its performance. The results of the numerical simulation were in good agreement with the data obtained from the real-time monitoring device. Ceylan et al. (2017) examined the effectiveness of paraffin wax on reducing the temperature of CPV panels, and it was reported that the panel temperature was reduced by 15 ℃ on an average compared to the system without paraffin. Nouira and Sammouda (2018) conducted a numerical study to know the impact of integrating different PCMs with different thicknesses on the system's performance. Kant et al. (2016) numerically studied the natural convection effect on melting of PCM (RT35HC) and its influence on PV performance using COMSOL Multiphysics 5.5 software. The effects of wind velocity and angle of inclination on the performance of the PV-PCM system were also investigated and reported a temperature drop of 3 ℃ for the PV-PCM system when compared to simple PV. Singh et al. (2020) considered a PV-PCM heat sink and finned PCM (FPCM) heat sink for PV panel cooling and observed that the PCM incorporated with heat sinks could reduce the maximum temperature by 13 • C , whereas FPCM can enhance cooling by 19 • C.
Since PCMs generally have low thermal conductivity, different strategies are employed to improve it using composite PCMs, incorporating metal foams and using multiple PCMs. Klemm et al. (2017) numerically showed that temperature could be reduced by approximately 2 • C compared to bare PV using a composite PV-PCM (PCM-filled metallic fibre structure) system. Maiti et al. (2011) incorporated a thick bed of metal-embedded paraffin wax as PCM and maintained the PV temperature at 60-65 ℃ for 3 h. This led to a gain in overall power output of 55%. The system was found to be beneficial even with low-velocity conditions. By integrating micro-fins, PCM and nano-enhanced PCM, Sourav et al. (2019) numerically and experimentally studied the effect of passive cooling technique (n-PCM) to lower PV temperature. Luo et al. (2017) developed a PV-PCM device using shape-stable composite paraffin PCM and found that form-stable composite PCM helps to control PV panels' temperature easily. Atkin and Farid (2015) have experimentally modelled and tested the use of PCM infused graphite with an external finned thermal sink for the temperature control of PV panels. The PV panel without any cooling technique, the PV panel along with PCM infused graphite attached to the rear and the PV with a combination of PCM infused graphite and the finned heat sink attached to the bottom were studied in four situations. The latter was found to be beneficial since the reduction in temperature and increase in efficiency are more in this. The effect of using white petroleum jelly (pure form) and composite PCM consisting of white petroleum jelly, copper and graphite on the thermal and electrical behaviour of a PV panel was explored by Hachem et al. (2017). The overall performance of a concentrated PV (CPV) nanoparticle-PCM was studied by Zarma et al. (2019) with different nanoparticles (Al 2 O 3 , CuO and SiO 2 ). Nanoparticles were found to be enhancing the thermal conductivity of PCM and thereby reduce the temperature of CPV.

3
In general, the critical takeaway is that PCM is immensely helpful in regulating PV panel temperature by absorbing excessive thermal energy of PV, which is not converted into electrical energy and stored as latent heat of PCM. The major drawback of paraffin PCM is its low thermal conductivity. So, it is necessary to adopt different methods which will help to improve the thermal conductivity of PCM and help to augment the heat transfer rate from the PV module and rate of execution of the phase change process of PCM in the system. The inclusion of nanoparticles in the PCM is an option to improve the thermal conductivity of the PCM. It is evident from the literature survey that there is a need to explore the effectiveness of loading nanoparticles in PCM on the performance of the PV-PCM system with respect to a primary operating condition like the inclination of the system. In this paper, numerical modelling and simulation of the system are carried out to analyse the overall thermal behaviour and its consequent effect on the performance of the PV-NEPCM system with different mass fractions of CuO nanoparticles. RT25HC PCM with mass concentrations (φ wt ) 1%, 3% and 5% are considered to establish different NEPCMs. The main objectives of the present work are to determine the heat transfer characteristics such as the transient mean temperature of the PV panel, variation of the pattern of isotherms and streamlines in NEPCM, liquid fraction and thermal energy storage related to NEPCM and to evaluate the effect on the performance of the PV module of PV-NEPCM system with different inclinations and mass concentration of nanoparticles by comparing with that of the PV-PCM system. Figure 1 shows the schematic diagram of the geometry of the PV-NEPCM system. The PV module consists of five different layers. PCM with nanoparticles is attached to the bottom of the PV module with the help of aluminium plates to establish the PV-NEPCM system. When the concentration of the nanoparticles is zero, the PV-NEPCM system will become a typical PV-PCM system. The tilt angle of the system is the angle made by the system with the horizontal plane. The tilt angle of the PV-NEPCM system ( θ) is varied in addition to the mass concentration of nanoparticles to get different operational configurations of the system for analysing its performance. The following assumptions are considered for the mathematical modelling of the PV-NEPCM system:

Physical system description and mathematical formulation
• The incident radiation on the PV module is uniform for all the configurations of the system. • The temperature and velocity fields of the PV-NEPCM system are two-dimensional in the x-y plane.
• PCM in the fluid state is assumed as Newtonian.
• The flow of melted PCM is unsteady, two-dimensional, laminar and incompressible. • Materials of different layers of PV module are treated as isotropic and homogeneous. • Dust and rain effects are not considered. • Resistive losses in the PV cell are not considered. • The effect of radiation heat transfer is neglected.
The portion of incident solar radiation ( G T ) that transmits through the glass cover and is absorbed by the PV cell is where ( ) eff is the effective product of the glass cover's transmissivity and the PV cell's absorptivity. The other major portion of this is converted into thermal energy and available for heat transfer ( Q g ), which can be written as where Q g is the heat generation per unit volume in W∕m 3 and PV is the electric efficiency of PV cell and can be defined as (Evans and Florschuetz 1977)

Solid domain
The only mode of heat transfer that exists in all solid domains is conduction (PV and aluminium layers), and hence the diffusion heat transfer equation is applicable to the solid parts of the system. Governing equation for temperature distribution of different layers of PV module is where Q g is the heat source term which is applicable to the silicon layer of PV only.

Modelling of NEPCM
Energy-porosity technique (Brent et al. 1988) (Voller and Prakash 1978) along with Boussinesq approximation (Mat et al. 2013) is used to model the PCM, which predicts both the melt front's location and morphology at different instants with modest computational requirements. The temperature and the instantaneous velocities of the melted PCM can be modelled using thermal energy equation, Navier-Stokes equation and continuity equation for Newtonian incompressible fluid, and they are: where , c p , k, and are the density, specific heat, thermal conductivity, dynamic viscosity and thermal expansion coefficient of the PCM, respectively. Velocities of melted PCM in the x and y directions are represented with uandv , respectively. The function B(T) is used to model liquid fraction and thermo-physical changes in PCM (Biwole et al. 2013) B(T) is 0 and 1 in the solid and liquid phases, respectively, and linearly varies from 0 to 1 in the transition region. Thermo-physical properties of PCM are modelled as (Biwole et al. 2013) The modified specific heat accounts for the latent heat of fusion for the PCM when it melts, and it is modelled as Modified specific heat is defined as the common specific heat of the PCM. D(T) is used to create modified specific heat. Its primary role is to distribute latent heat in the transition region, and it is expressed as (Biwole et al. 2013) This function D has a value of 0 at every region except over the interval (T m − ΔT∕2) and (T m + ΔT∕2) , and its integral over the range of transition temperature is equal to 1 so as to satisfy the energy balance in the transition region. The additional volumetric forces in the laminar flow are (Biwole et al. 2013) where A(T) is a porosity operator and is derived from the Carman-Kozeny equation for a porous media flow and was introduced by Brent et al. (1988). Overall viscosity modification of PCM and handling momentum equation for solid PCM was done by using A(T) (Biwole et al. 2013) which is The value of A(T) is zero for liquid phase of PCM. C m is a constant that represents a mushy medium, and it depends on the type of the PCM. The constant is a small value used to avoid division by zero. A(T) is also used to define the viscosity of PCM as where l is absolute viscosity of PCM in liquid phase.
The equation which relates mass and volume fractions ( φ wt andφ ) is The modified properties are modelled as Thermal conductivity of the NEPCM where where is the volume fraction of nanoparticles and b, and d np are constant for Brownian motion, Boltzmann constant and diameter of the nanoparticle, respectively. T ref ,np is the reference temperature.
The boundary conditions at the top and bottom of the PV-NEPCM system can be expressed, respectively as where g is the absorptivity of the glass cover. T g , T al and T a are the temperatures of glass cover, aluminium backplate and atmospherere, respectively.h t and h b are top and bottom convective heat transfer coefficients, respectively.
The boundary condition for sidewalls The boundary condition at the interfaces with reference to different layers is where m and n represent two different layered materials on either side of an interface in the system.
The initial conditions of the system are Numerical procedure, grid independence study and validation of the model Polycrystalline PV-module is considered in the PV-NEPCM system of the present work. The properties and dimensions of each layer of PV module and aluminium plates are given in Table 1. The commercially available PCM RT25HC from Rubitherm GmbH enhanced with CuO nanoparticles is attached to the bottom of the PV panel with the help of aluminium plates. Thermo-physical properties of the RT25HC PCM and CuO are shown in Table 2. The mass concentrations of nanoparticles considered in the NEPCM are 0% (pure PCM), 1%, 3% and 5%. For PV-PCM ( φ wt = 0% ) and PV-NEPCM ( φ wt = 1%, 3%and5% ) systems, the inclination angle is changed from 0to45 • in the steps of 15 • .
COMSOL Multiphysics 5.5 software is used for the simulation of both PV-PCM and PV-NEPCM systems. The systems are simulated for predicting the temperature distribution, the pattern of isotherms and streamlines in PCM and NEPCM, melting of PCM and NEPCM, convection patterns in liquid PCM/NEPCM and performance of the PV module in all the configurations of the systems. The simulation is carried out for 3-h duration against the constant radiation 1 3 incident on the PV module for each configuration of PV-PCM ( φ wt = 0% ) and PV-NEPCM ( φ wt = 1%, 3%and5% ) systems. The other inputs required to carry out the simulation are specified in Table 3. For the grid dependency study, variation of average PV temperature (in PV-NEPCM system for 45°) with time for different mesh element size combinations (maximum size, minimum size) are shown in Fig. 2. The findings suggest that the decrease in minimum size beyond 4.76×0.0161 mm does not change the outcome, and the same is selected as the optimum for the entire study. The final complete mesh consists of 76262 domain elements and 6912 boundary elements. The time-stepping method is selected as Backward Euler. The maximum and minimum orders of backward differentiation are 5 and 1, respectively. The initial time step is fixed at 0.001 s, and the maximum time step constraint is 2 s. Absolute tolerance is given as 0.001 s. A tolerance factor of 0.5 is used under a fully coupled option with a damping factor of 0.75.
The numerical findings are compared with the experimental results of Huang et al. (2011) for the variation of the average temperature on the system's front surface with time in Fig. 3(i) for the PV-PCM validation. The simulated predictions are found to be in reasonably good agreement with the experimental results. The NEPCM system model is validated by comparing the simulation findings with experimental results of Dhaidan et al. (2013) by tracing the variation of the liquid fraction of a nano-enhanced square PCM cavity of size 25.4 mm with time in Fig. 3(ii). The comparison shows that simulated predictions of the PV-NEPCM system are in excellent agreement with experimental results available in the literature.

Results and discussion
Numerical simulations are carried out to compare the thermal performance of different configurations of PV-NEPCM systems for tilt angles of the system from 0 to 45 • in steps of 15 • as well as 0% , 1%, 3% and 5% mass concentrations of nanoparticles in the system. PV-NEPCM system with 0% mass concentration of nanoparticles is PV-PCM system. The inclination of the system and mass concentrations of nanoparticles in the system are varied to study the effect of natural convection inside PV-PCM and PV-NEPCM systems and the consequent performance of the PV module.
The results are obtained in terms of the transient mean temperature profile of the PV module, the pattern of isotherms and streamlines in NEPCM, the liquid fraction of NEPCM, thermal energy storage in NEPCM and performance of the PV module, which provide a better vision of the heat transfer process in the systems.

Effect of mass concentrations of nanoparticles and inclination on the mean temperature of PV module
The transient mean temperature trends at different inclinations and different mass concentrations for PV-NEPCM systems are shown in Fig. 4. The mean temperature of the panel is highest for θ = 0 • , and the mean temperature of PV decreases with the increase in tilt angle. This is because, for a horizontal system (θ = 0 • ) , heat transfer to the NEPCM takes place by conduction mechanism. Convection heat transfer is not present in the horizontal system due to the existence of the thermally stable state of the PCM, which will not give rise to the buoyancy force and the consequent natural convection currents. The low thermal conductivity of the PCM in the PV-PCM system leads to a lower heat transfer rate to the PCM (φ wt = 0%) . For the inclined system, the temperature difference existing in the melted PCM between the location nearer to the bottom of the PV module and the location far from it gives rise to establishing the gravitational field and consequent existence of buoyant force. This buoyant force is dominant over the inertial and viscous forces, which establishes the natural convection current and the existence of natural convection heat transfer within the melted PCM. This leads to an obvious enhancement of the rate of heat extraction by PCM from the PV module, resulting in lower PV temperature for an inclined system compared to the horizontal system for a specific mass concentration of nanoparticles in the system. As the tilt angle increases, the temperature difference within the PCM increases, which increase in density difference in PCM, increase in the strength of the gravitational field and existence of buoyant force, which in turn causes increase in the strength of natural convection current and higher convection heat transfer rate to PCM. Hence, the mean temperature of the PV module decreases with the increase in the inclination of the system for a specific volumetric concentration of nanoparticles in the system. The addition of nanoparticles in the PCM improves the thermal conductivity of the PCM. Heat transfer to PCM takes place in conduction mode for horizontal system ( θ = 0 • ). Hence, improvement in thermal conductivity of PCM with the addition of nanoparticles causes a higher conduction heat transfer rate to NEPCM, and consequently, the mean PV temperature when integrated with NEPCM is low compared to mean PV temperature with PCM (without nanoparticles, φ wt = 0% ) for the horizontal system. The effective thermal conductivity of NEPCM increases with an increase in the mass concentration of nanoparticles. For systems with inclinations greater than zero, the combined existence of natural convection and higher thermal conductivity of NEP-CMs seems to regulate the temperature of the module better compared to horizontal systems. However, the addition of nanoparticles leads to an increase in viscosity of NEPCM, which comes into play during the motion of NEPCM in the liquid phase, in addition to an increase in thermal conductivity of NEPCM. Higher viscosity results with the addition of nanoparticles in the PCM lead to higher fluid friction, and hence, the strength of natural convection current will not increase proportionally to increase in thermal conductivity with the addition of nanoparticles at higher inclinations of PV-NEPCM systems. Reduction in strength of natural convection current in the NEPCM systems causes lower heat transfer rate to PCM at higher inclinations than anticipated, and finally, the decrease in mean PV temperature reduces with the inclination. Moreover, the addition of nanoparticles lowers the latent heat of NEPCM, which affects the thermal regulation period. After the complete melting of the NEPCM, the average PV temperature increases again at a rate higher than in simple PCM. The higher the tilt angle, the lower the thermal regulation period, which can be seen in Fig. 4. The highest reduction in mean PV temperature is obtained as 1.26 • C for horizontal systems ( θ = 0 • ), with φ wt = 5%, and the temperature reduction decreases with the increase in inclination and nanoparticle concentration, as shown in Fig. 5. Maximum temperature reduction with the addition of nanoparticles is 0.78 • C when θ = 45 • for the PV-NEPCM system with φ wt = 5% . For PV-NEPCM with φ wt = 1% , maximum temperature reductions are 0.72 • C and 0.372 • C for θ = 0 • and θ = 45 • , respectively. Figure 6 shows the evolution of temperature contours and streamlines for t = 45 min, 90 min, 135 min and 180 min for different inclinations for PV-PCM and a PV-NEPCM system with φ wt = 5% . As the mass concentration of nanoparticles and time increases, the physical state of the PCM in the PV-PCM system and NEPCM in the PV-NEPCM system changes, which alter the pattern of isotherms and streamlines. In the beginning, PCM and NEPCM are in solid state in their respective systems, and isotherms are almost parallel near the PV, implying the presence of the conduction as the heat transfer mechanism from PV module to PCM and NEPCM. This is observed in horizontal configurations and all the inclined configurations. Due to the effect of loading the nanoparticles, the thermal conductivity of the PCM has increased; thereby, the heat transfer rate has increased. As a result, a faster rate of phase front movement occurs in NEPCM compared to PCM at the beginning in horizontal and all inclined configurations of the system. For systems with θ = 0 • (horizontal orientation), the isotherm moves uniformly from top to bottom throughout with the variation of time in PV-PCM and PV-NEPCM systems as conduction is the only heat transfer mechanism involved throughout in this situation. The nanoparticles' loading makes the isotherm move faster in NEPCM than pure PCM (refer to Fig. 6 (i)) in horizontal systems. Better heat transfer rate to the NEPCM from the PV module leads to lesser temperature of the module in this compared to pure PCM, and this leads to better performance of horizontal PV-NEPCM system over PV-PCM system. The effect of NEPCM is visible clearly at t = 135 min and t = 180 min for the horizontal system. Natural convection plays a crucial role for inclined systems for heat transfer rate from the PV module (refer Fig. 6 (ii) to (iv)) due to the buoyancy effect, as evident from t = 90 min onwards. The effect of buoyancy force increases with the increase in inclination, which ultimately increases the heat transfer rate in PCM and NEPCM in their respective systems. As a result, the natural convection flow occurs on the left side and proceeds upwards close to the high-temperature PV, affecting the thermal field and, as a result, the speed and form of the travelling phase front in the PCM and NEPCM. The average velocity of melted PCM is higher in inclined systems, as shown by the streamlines. Here, enhancing the relative heat transfer rate inside PCM by loading nanoparticles is more effective for horizontal orientation than configurations of the systems with inclined orientation.

Effect of mass concentration of nanoparticles and inclination on the liquid fraction of the system
The variations of liquid fraction with time at various inclinations and mass concentrations of nanoparticles are shown in Fig. 7. The melting rate is slower for θ = 0 • in both PV-PCM and PV-NEPCM systems due to the lower heat transfer rate from PV module in both systems by virtue of the existence of conduction mechanism in horizontal systems. The melting rate is faster in inclined PV-PCM and PV-NEPCM systems compared to their respective versions of horizontal systems. This is due to the presence of convection heat transfer which leads to a higher heat transfer rate from the PV module in inclined systems. As inclination increases, the melting rate also increases because of the enhanced energy transfer rate owing to increased buoyant force by virtue of gravitation field and thereby convection current in both PV-PCM and PV-NEPCM systems. For a given inclination, the melting rate improves with an increase in the mass concentration of nanoparticles as it effectively increases the thermal conductivity of NEPCM.
For the PV-NEPCM systems, the melting occurs faster for all tilt angles compared to the corresponding PV-PCM systems. The effect of adding nanoparticles is more pronounced for the horizontal system compared to all the inclined systems. For horizontal systems, conduction is the mechanism of heat transfer existing in the PV-PCM and PV-NEPCM systems. The addition of nanoparticles in the PCM for the PV-NEPCM system will not lead to any consequence that reduces the conduction heat transfer rate in horizontal systems, and it only leads to increasing the thermal conductivity of NEPCM. This causes the maximum benefit with the addition of nanoparticles in the form of higher relative heat transfer rates from the PV module that leads to cause the maximum difference of melting rates between PV-PCM and PV-NEPCM systems for horizontal configurations only.
The thermal conductivity increase with the inclusion of nanoparticles is valid for all the inclined configurations in addition to horizontal systems. However, heat transfer takes place from the PV module by convection mechanism due to the existence of bulk motion in all the inclined configurations in contrast to horizontal systems. The inclusion of nanoparticles in PCM leads to an increase in viscosity of the fluid in addition to thermal conductivity, and this will come into play in the dynamic condition of the fluid only. The increase in thermal conductivity and viscosity due to the inclusion of nanoparticles leads to a higher heat transfer rate from the PV module and greater melting rates in inclined systems compared to their PV-PCM counterparts. But, the relative increase in heat transfer rate is not as high as it is seen in the horizontal systems due to the reduction in strength of the natural convection current inside PCM by virtue of increased viscosity with nanoparticles. The effect of viscosity comes into play in all inclined systems with the involvement of the bulk motion in them, and hence the effect of the inclusion of nanoparticles is not as pronounced as in horizontal systems. The higher the inclination of the configuration, the stronger the tendency to the bulk motion, the greater the relative resistance to fluid motion with increased viscosity, the lower the relative increase in heat transfer rate with inclusion of nanoparticles and the lower the melting rate enhancement compared to PV-PCM systems. In addition, an increase in nanoparticles reduces the latent heat of the NEPCM and consequent reduction in the thermal regulation period at higher inclinations which can be seen with lower slopes of liquid fraction trends. From Fig. 8, it is clear that the enhancement in the liquid fraction when adding CuO nanoparticles is highest (8.25%) for the horizontal system with φ wt = 5% , and it decreases with an increase in the inclination of the system. The enhancement is 3.2% for θ = 45 • when t = 150 min for the same mass concentration over their PV-PCM counterparts. For φ wt = 1% , the highest and lowest enhancements are 6.2% and 2.8% for θ = 0 • and θ = 45 • , respectively. Figure 9 shows the temporal evolution of thermal energy stored at different inclinations and 1 3 different mass concentrations for PV-NEPCM systems ( φ wt = 0%, 1%, 3%and5% ). The energy stored is strongly related to the liquid fraction. As the inclination angle increases, the heat transfer rate from the PV module increases, the melting rate increases, the liquid fraction increases and the rate of energy stored in the system is also increased. The amount of energy stored is lowest for the horizontal system compared to all the configurations with inclination greater than zero as the melting is carried out mainly by the presence of conduction heat transfer mechanism in the horizontal configuration.

Effect of mass concentration of nanoparticles and inclination on energy stored in the system
The addition of nanoparticles leads to an increase in heat transfer rate in horizontal configuration and all the inclined configurations compared to their corresponding configurations with pure PCM (φ wt = 0%) . But, the relative increase in heat transfer rate with the inclusion of nanoparticles is more in a horizontal configuration, and hence the highest difference in the trends of energy stored can be seen with this configuration. The rate of relative increase in heat transfer with the inclusion of nanoparticles reduces with increase in inclination, leading to a decrease in the difference between the trends of energy stored with an increase in inclination of the configuration.
Variation of energy stored in NEPCM at t = 150 min is shown in Fig. 10 for both the PV-PCM and PV-NEPCM systems at various inclinations. The thermal energy stored in simple PCM is 400.5 kJ against 419.48 kJ for NEPCM with φ wt = 5% , at θ = 0 • . There is only a slight increase in the amount of energy stored for higher tilt angles with the loading of nanoparticles in the system, as natural convection is affected by high viscosity and lower latent heat in NEPCM. For φ wt = 5% , the improvement in thermal energy stored is 1.67% for the PV-NEPCM system with an inclination of 45 • compared to 4.81% for the horizontal system.

Effect of mass concentration of nanoparticles and inclination on the performance of the system
The variations of electrical efficiency of the PV module at various inclinations and mass concentrations of nanoparticles are shown in Fig. 11. The temperature of the PV module dictates its efficiency. The mean temperature of the module is highest for the horizontal PV-PCM φ wt = 0% system, and hence the efficiency is lowest in this case. Heat transfer rate from the module is higher in all inclined configurations of PV-PCM system compared to horizontal case due to the prevailing heat transfer mechanism for inclined systems, and this leads to the reduction in temperature and consequent increase in efficiency of the PV module for inclined systems. The higher the inclination, the higher the rate of heat transfer from the module, the lower the temperature of the module and the higher the efficiency of the module. Hence, the best trend of efficiency of the PV-PCM system is for the configuration with an inclination of 45 • .
The inclusion of nanoparticles in the PCM causes enhancement of heat transfer rate from the module for horizontal and all the inclined configurations. This leads to a reduction in the temperature of the module and a consequent increase in efficiency of the module for all the configurations of the PV-NEPCM systems compared to their counterparts of the PV-PCM system. As the temperature drop is highest for horizontal PV-NEPCM systems with φ wt = 5%, the maximum enhancement in the efficiency of the PV module (1.75%) is also highest for the PV-NEPCM system with θ = 0 • (see Fig. 12). This is due to the conduction involved for heat transfer from the module to PCM in horizontal configurations and the increase in thermal conductivity of the NEPCM with the inclusion of nanoparticles. The relative increase in the efficiency of the module is less for inclined systems compared to the horizontal configuration as the involvement of convection heat transfer mechanism for heat transfer from the module in the inclined systems. Convection heat transfer rate depends on the nature of the fluid, fluid properties, nature of the flow, surface conditions and geometry. Except for the fluid properties, the remaining factors are similar for PV-PCM and PV-NEPCM systems at an inclination. Among the fluid properties, thermal conductivity and viscosity lead to increase and decrease in the rate of convection heat transfer, respectively. An increase in inertial and viscous forces will offset the increasing tendency of buoyant force strongly with the increase in inclination, and this results in lower relative enhancement of heat transfer rate at higher inclinations. As convection heat transfer becomes prominent for higher inclinations, the effect of thermal conductivity becomes lesser due to increase in fluid friction by virtue of viscosity and inertia, as explained earlier, which leads to less increase in efficiency with time in PV-NEPCM systems over PV-PCM systems.
The effect of nanoparticles on the increase in efficiency of the module continuously increases with time for horizontal systems since the phase change of PCM and NEPCM was not completed in the respective systems for the duration considered in the simulation. Contrary to this, the thermal regulation period reduces due to reduction in latent heat for NEPCMs, which causes the reduction in efficiency of the module compared to PCM (φ wt = 0%) after the completion of the phase change process in PV-NEPCM systems. The improvement in PV efficiency is observed up to the melting period of NEPCM for all the inclinations. Maximum percentage enhancement in the efficiency of the module decreases with an increase in inclination as the value is only 0.89% for θ = 45 • , at ( φ wt = 5%) as shown in Fig. 12. Figure 13 shows the PV power output (in kW∕m 2 ) of the PV module for PV-PCM and PV-NEPCM systems at different inclinations at different instants t = 45min, 90min, 135min and 180min. Just like efficiency, the PV power output of the PV module is higher for the PV-NEPCM systems over the PV-PCM system for all the orientations. The relative increase in power output is higher for lower orientations compared to higher orientations. For θ = 0 • and φ wt = 5%, the highest power increment obtained is 0.221 kW∕m 2 at t = 135 min, and for θ = 45 • , it is only 0.027 kW∕m 2 when compared to the PV-PCM system ( φ wt = 0% ). Since the presence of nanoparticles in PCM increases the melting rate and decreases the thermal regulation time, the enhancement is almost negligible for t = 180 min, especially for higher inclinations.

Conclusions
In the present work, numerical investigations of a PV integrated with pure PCM (PV-PCM system) and nano-enhanced PCM (PV-NEPCM) systems with a mass concentration of 1%, 3% and 5% are carried out for 180 min duration. The outcomes of the study can be summarised as follows: • At an early stage, heat transfer takes place from the PV module by conduction mechanism in all the configurations of PV-PCM and PV-NEPCM systems. • The melting process of PCM and NEPCM is mainly executed by conduction and convection heat transfer mechanisms from the PV module for horizontal configurations and inclined configurations, respectively, for PV-PCM and PV-NEPCM systems. • The performance of the system is improved with the inclusion of nanoparticles in the PCM for horizontal as well as inclined configurations of the system. The effec- tive thermal conductivity of NEPCM increases with an increase in the mass concentration of nanoparticles. • Temperature contours and velocity streamlines indicate the heat transfer inside PV-PCM and PV-NEPCM systems and also the natural convection fluid motion inside melted PCM and NEPCM. • PV module integrated with nano-enhanced PCM is more effective for lower tilt angles. The maximum average temperature reduction of the PV module when φ wt = 5% is 1.26 • C is obtained when θ = 0 • . • The percentage increase in the liquid fraction for NEPCM ( φ wt = 5%) compared with PCM ( φ wt = 0%) is 8.25% for θ = 0 • as compared to 3.2% for θ = 45 • att = 150min. • For NEPCM with φ wt = 5% , the percentage increase in the amount of energy stored when compared with PCM is 4.81% for horizontal system against 1.67% for the system with an inclination of 45 • at t = 150 min. • The efficiency and power output of the PV module is enhanced with the inclusion of nanoparticles in the PCM. The highest maximum enhancement in the effi- ciency of 1.75% is obtained when φ wt = 5% for the system with θ = 0 • inclination. • It is observed that the thermal regulation period of the PV module is reduced with the inclusion of nanoparticles in the PCM by maintaining the volume of the PCM compartment the same. In order to have the maximum thermal regulation period and obtain the maximum benefit of the inclusion of nanoparticles, increasing the size of the PCM compartment is an option. Author contribution Unnikrishnan Karthamadathil Sasidharan has contributed to the main conceptual idea, study design and full article writing. Rohinikumar Bandaru has involved in the technical discussions, checked the review connectivity and improved the write-up.

Data availability
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations
Ethics approval and consent to participate Not applicable.

Competing interests
The authors declare no competing interests.