Performance characteristics of a photovoltaic panel integrated with PCM packed cylindrical tubes for cooling

ABSTRACT

The effect of an increasing volume of the phase change material (PCM) and large heat transfer area have been assessed for controlling the higher surface temperature of the photovoltaic (PV) module which influences conversion efficiency and power output. For this, a bed of multi-cylindrical copper tubes filled with PCM has been prepared. The performance evaluation has been done on three different configurations such as module ‘B’ integrated with 91 tubes in the first configuration, module ‘C’ integrated with 181 in the second configuration and module ‘D’ integrated with 271 in the third configuration. The results obtained from three configurations are compared with the reference module (module A). All the tested panels are found to be better than the reference panel, but panel D is found to be the best configured among all tested panels, which showed the average per cent reduction of around 20.76% in the cell temperature and average per cent increment in 6.49% in conversion efficiency and 6.67% in power output.

KEYWORDS:

• Photovoltaic
• heat transfer
• PCM
• efficiency
• power yield
• thermal performance

Nomenclature

PCM	=	Phase change material
TES	=	Thermal energy storage
LHS	=	Latent heat storage
Apm	=	Area of the photovoltaic module (m2)
has	=	Coefficient of heat transfer for the surrounding air (W/m2 K)
hbs-pv	=	Coefficient of convective heat transfer for the back surface of the tested PV panel (W/m2 K)
hpcm-t	=	Coefficient of convective heat transfer for the PCM infused tube (W/m2 K)
Tamb	=	Ambient temperature (°C)
Tbs	=	Back surface temperature of PV (°C)
TPCM	=	Temperature of PCM (°C)
Tsc	=	Temperature of solar cell surface (°C)
HPCM	=	Latent heat of PCM (J/kg)
MPCM	=	Mass of PCM (kg)
Csol	=	Specific heat of solid PCM (J/kg·K)
Cliq	=	Specific heat of solid PCM (J/kg·K)
ϵ	=	Emissivity factor
σ	=	Stefan–Boltzmann’s Constant (J/m2·s·K4)
αabs	=	Absorptive factor
ηce	=	Conversion efficiency (%)
Pmax	=	Power output (W)
Wv	=	Wind velocity (m/s)

1. Introduction

Over the last few years, a significant number of reports/articles have been published, focusing on sustainable development by using renewable energy resources. In the current market of renewable energy technology an increase in the efficiency of the system (Saxena et al. 2011; Saxena, Agarwal, and Srivastava 2013) is observed as the simplest and inexpensive method to improve the feasibility of these applications at different locations of the world (Saxena and Srivastava 2013; Saxena and Deval 2016; Saxena and Norton 2021). For instance, cooling of the solar cell surface in PV systems under peak solar hours has exposed a visible potential in order to improve its performance in terms of efficiency and power output.

In previous literature two types of techniques for cooling of the solar cell have been identified as potential techniques to control the temperature practically such as active technique and passive technique (Krauter 2004; Furushima and Nawata 2006; Ceylan et al. 2014; Wu and Xiong 2014; Ebrahimi, Rahimi, and Rahimi 2015; Chandrasekar and Senthilkumar 2016; Sainthiya, Beniwal, and Garg 2018; Bahaidarah et al. 2013; Smith et al. 2014; Nizetic et al. 2016; Schiro et al. 2017; Wu, Chen, and Xiao 2018; Atkin and Farid 2015; Stropnik and Stritih 2016; Hachem et al. 2017; Waqasa and Ji 2017). Tables 1–3 summarise some of the research work carried out previously on thermal management of PV systems around the globe.

Table 1. PV surface cooling by water.

Reference	PV Cooling mode	Investigation	Results
Krauter (2004)	Water cooling on the front surface of PV through pump	A thin film of fresh water is provided in continuous flowing film manner over the hot front PV surface with the help of a line arrangement of syringes for cooling of PV surface. The flow rate has been kept about 2L/m	The cell surface temperature is found to be reduced around 22°C through water cooling over the front surface with 10.3% of increased electrical yield
Furushima and Nawata (2006)	Back surface water cooling through a water jacket	Six PV panels are tested under water cooling by using a novel developed system used backside of the PV by employing siphonage. In order to save the energy by familiarising cooling water in to PV, siphonage from the top to bottom level of the building has been taken advantage of	The flow rate of the water has set for 55°C of the cell temperature. This kept the PV surface temperature below 55°C. The efficiency is found to be quite improved and hot water from the PV panel surface is reused in building for some hot water tasks
Ceylan et al. (2014)	Water cooling has been provided from backside of PV module	A PV/T system integrated with a copper made pipe placed on PV panel like a spiral heat exchanger for active cooling mode by using water	The solar cell efficiency is improved from 10% to 13% while power has improved from 32 to 46 W
Wu and Xiong (2014)	Water cooling through direct either by the rain or rain water stored in tank	A passive cooling system is developed for PV (250 W) by using the rainwater with a gas expansion device. Rain water has been chosen a cooling fluid which controlled through a gas expansion device. The gas expands thermally due to excessive irradiance which pushes the water stored in a tank to flow over the panel	The temperature is reduced up to 19°C and electrical efficiency is improved around 8.3% while the PBP of modified system is 14 years
Ebrahimi, Rahimi, and Rahimi (2015)	Backside cooling of PV through natural water vapour	A new method for solar cell cooling is investigated by using coolant (natural vapour) under simulated sunlight. The coolant encountered at backside of PV module in various distributions with different mass flow rates. It is notable the vapour to the backside of PV has been provided by a natural vapour generator	The maximum cell temperature drop is measured about 16°C at 5 gr min^−1 of mass flow rate. Results shown that electrical efficiency is about 22.9% at the same cell temperature
Chandrasekar and Senthilkumar (2016)	Back surface water cooling supported by long cotton wicks	A new technique is developed for cooling of PV. It is done with the help of metallic fins in combination with some cotton wicks at the backside of 25 Wp solar panel. One mini storage tank is installed at top of PV for supplying cold water while another on bottom to collect hot water	The PV module temperature got reduced to 43.3°C from 49.2°C. It corresponds to around 12% reduction in cell temperature and electrical yield is found to be increased by 14% due to water cooling
Sainthiya, Beniwal, and Garg (2018)	Front surface water cooling in winter and summer	A setup is modified for front cooling of a poly-crystalline panel (75 W) through water cooling under different flow rates. The water cooling is found better in summer season. One small diameter pipe is installed at top of PV for supplying cold water while another on bottom to collect hot water	PV efficiency is improved by 13% for winter season and 11% for summer season and the steady power output is obtained about 70 and 60 mW, respectively
Bahaidarah et al. (2013)	Back surface water cooling	A hybrid Photovoltaic system of 230 W has been cooled through back surface water cooling. The cooling water has stored in a tank and circulated through a water pump. A detailed numerical model has been developed with the help of EES software	The solar cell temperature has been dropped by 20% while the electrical efficiency has been improved about 9% by using the said cooling channel
Smith et al. (2014)	Front surface water cooling	A 175 W of PV module has been tested at different operating conditions to maintain its temperature about 40°C through uniform front surface water cooling. A pump is used to circulate the water	Maximum peak power enhancement has been observed about 43% that corresponding to a 60 W improvement by applying all the tested cooling as combined
Nizetic et al. (2016)	Front surface and back surface water cooling	A PV module of 50 W has equipped with a system of water spraying nozzles that mounted on the PV modules so that both the sides (front and rear) surface got the water spray distribution for proper cooling	Result showed that there is a net increase of 16.3% in electric power output and a net improvement about 14.1% in PV module electrical efficiency by using the new cooling mechanism
Schiro et al. (2017)	Front surface water cooling	A PV panel of 220 W has been integrated with a series of nozzles of water spray at the top of it. Water has been sprayed through a water pump over the front surface of PV. Readings have been taken on 03 conditions such as; varying irradiance, varying wind velocity and varying air temperatures	The maximum variation in cell temperature has been found on varying wind velocity conditions i.e. conventional panel temperature is found about 39.27°C while water cooled panel temperature is found about only 20.90°C
Wu, Chen, and Xiao (2018)	Front surface water cooling	A PV panel has been integrated with a series of nozzles (5 mm dia) of water spray at the top of it. The system has been studied for heat transfer characteristics by considering the effect of mass flow rate, the cooling channel height, inlet water temperature and effect of irradiance	Results showed that the Nu of bottom and top faces achieve opposed trend laterally the flow direction, and convective heat transfer of bottom is improved in comparison of top surface for practically all of the cases. The maximum exergy efficiency has been obtained about 0.003 kg/s (flow rate)

Table 2. PV surface cooling by phase change materials (PCM).

Reference	PV Cooling mode	Investigation	Results
Atkin and Farid (2015)	Back surface PCM based cooling	PCM infused graphite is used through an exterior finned heat sink that is attached to backside of panel for cooling. Thickness of the layer of PCM is about 30 mm. The system has been tested under a flux of 1000 W	Maximum overall efficiency is found around 12.97% under the 920 W/m^2 of insolation. The simulation study is also carried out with MATLAB modelling
Stropnik and Stritih (2016)	Back surface PCM based cooling	An attempt has made to enhance the power output as well as overall efficiency by using a RT28HC (pure PCM) for cooling of solar panel (250 W). For this, PCM has been filled at the backside of PV in the form of thick layer	Result showed that temperature of panel without PCM incorporation is found to be around 35.6°C in comparison of panel with PCM incorporation and an electrical output increase of 9.2% is obtained through cooling by PCM
Hachem et al. (2017)	The backside of PV has been converted into a container and filled with PCM	The effect of a white petroleum jelly (pure PCM) and the same jelly with copper and graphite is used (combined PCM) is studied experimentally for cooling of a solar PV (30 W) which is attached at the back surface of PV. Combined PCM has been found more efficient than pure PCM	Result shown that the electrical efficiency is increased for 3% by using pure PCM with a dropping of 2.7°C in surface temperature while electrical efficiency is increased for 5.8% by using combined PCM along with a temperature drop of 5.6°C
Waqasa and Ji (2017)	PCM has been filled in small containers (rotatable shutters) and attached to the back surface of PV	The effect of a commercial grade PCM (RT44) has been studied on electrical output and working temperature of solar panel. Rotatable shutters carrying the PCM and attached to the backside of PV in the form of 1.5 mm thin layer	Modeling revealed that PV temperature is reduced to 42°C from 64°C by using PCM filled shutters and efficiency is found to be enhanced by 9% during the summers and 2.2% in winters
Nizetic et al. (2018)	Backside surface cooling through a conventional PCM and pork fat	The pork fat is considered as a quality PCM for passive type cooling of solar panel and the cooling effect of pork fat is compared with another pure PCM. The pork fat is attached in the form of thin layer to the backside of PV	It is concluded that the pork fat can be considered as an economic and efficient PCM for thermal degradation of solar cells
Khanna, Reddy, and Mallick (2018)	Backside surface cooling through PCM and extended fins	An attempt is made to remove the heat from PV through PCM integrated fins. The most suitable depth for PCM filling has been investigated to be 2.8 cm at instantaneous irradiance = 3 kWh/m^2/day. The fins have been placed inside the large PCM container	For effective cooling of panel, the best thickness of fin is notified as 2 mm with a gap of 25 cm between two successive fins
Nada, El-Nagar, and Hussein (2018)	Backside surface cooling through PCM and Al2O3 nanoparticles	Two different PV panels of (30 W) have been tested with PCM and PCM with Al2O3 nanoparticles for cooling of solar cells. PCM filled container has attached to the backside of PV. Both the configurations reduced the significant amount of surface temperature of PV	PV with pure PCM and enhanced PCM has been found appropriate for cooling. Both the modules results for reducing surface temperature about 8.1 and 10.6°C, respectively as well as increasing its efficiency about 5.7 and 13.2%, respectively
Nada and El-Nagar (2018)	Back surface PCM based cooling is done	For experimentations two panels by 30W have been taken and cooling of BIPV is done by mixing a PCM (RT55) and Al2O3 nanoparticles inside a container which is attached to the backside of PV	Results showed that (i) PV with PCM reduced the cell temperature from 75°C to 62°C and PV with PCM added nanoparticles reduced the cell temperature about 59°C, and (ii) integrating the BIPV with PCM enhances daily average efficiency about 7.1%
Nasef, Nada, and Hassan (2019)	Back surface PCM (RT35HC) cooling with closed loop water cooling	The integrative active and passive cooling performance of low concentrated PV has been assessed theoretically with the help of a mathematical model	Results showed that the suggested passive-active integrated system attained an average temperature reduction of PV by 60%, and an improvement in the system efficiency is about 224% after 1200 s on running condition. Furthermore, this system reduced the PCM melting period about 33%
Darkwa et al. (2019)	Back surface PCM integrated thermoelectric cooling	A mono-crystal silicon solar module of 5 W has been tested and a numerical model has developed. For cooling of PV, a 50 mm layer of PCM (melting point 45°C) integrated with thermoelectric generators has been attached to the backside of PV	Results showed a worthy agreement between experimental results and predicted values. In comparison of conventional PV, the modified PV gives 9.5% more power i.e. 51.4%
Siahkamari et al. (2019)	Back surface PCM based cooling	A PV panel of 10 W has been tested for cooling operations through a composite of sheep fat (PCM, melting point – 47°C) + CuO nanoparticles and paraffin wax (PCM, melting point – 53°C). For cooling of PCM a network of small copper pipes has been passed by thick layer of PCM	Results revealed that composite of sheep fat + CuO nanoparticles have given the best output. By using this as a PCM, power has been increased about 26.2%
Choubineh, Jannesari, and Kasaeian (2019)	Back surface PCM based cooling	A PV panel integrated with PCM (32°C melting point) at backside has been tested in a form of absorber of a solar air collector. Experiments for cooling have been done on natural and forced convection. The air passes beneath the panel which cools PCM also	Results indicated that on natural convection the back surface temperature down about 4.3°C and ƞelect has been found to be improved by 11%. These parameters have been found about 3.4°C and 11.5% for forced convection
Zhao et al. (2019)	Back surface PCM cooling	A PV panel of 100 W integrated with PCM (20°C melting point) at backside has been tested in climatic conditions of Shanghai for cooling performance. Single dimension (1-D) model has been developed in MATLAB R2018a for heat transfer studies	Results revealed for a year round performance and the power output has been found to be improved about 2.46%

Table 3. PV surface cooling by natural convection techniques.

Reference	PV Cooling mode	Investigation	Results
Akbarzadeh and Wadowski (1996)	Gravity assisted heat pipe based cooling	The coiling mechanism contains 02 heat exchangers (HEx) which are evacuated and full of refrigerant. The lower HEx (evaporator), filled with refrigerant while the upper one (condenser) holds saturated vapour. PV cells have been attached to the evaporator and condenser exposed to the air cooling naturally. The nature of thermosyphon fluid is contingent on temperature range required such as; for 20–100°C range refrigerant R-11, R-22 are suitable while water is suitable from the point of view of heat transfer effectiveness	The developed system is exposed to the sun for four hours and the PV cell temperature is found to be closed around 46°C, Voc is around 34 Volt, Isc is around 1.7 amp and electricity output is 20.6 W
Teo, Lee, and Hawlader (2012)	Air cooling has been provided beneath the PV	A PV/T (55 W) system has been developed with some specially designed ducts on the backside of PV panel for active cooling through the air. To improve heat transfer rate from the backside some extended fins has also attached to support air cooling	The PV module temperature got reduced to 38°C from 68°C. Efficiency and total power output is improved by 14% and 12.5%, respectively
Soliman, Hassan, and Ookawara (2019)	Backside air cooling with the help of extended and randomly oriented aluminium fins of ‘L’ shape profile	Two PV panels of 50 W have been tested for cooling of its surface via randomly oriented fins attached on the backside of PV. Five different configurations have been developed (along with wind velocity variations) to observe the significance of wind velocity on different positioned fins on the performance of PV	Results showed that randomly oriented fins has given an average improvement about 2% in the efficiency (relatively peak power output for a specific time) in comparison of parallel arrangement of the fins
Deaver and Edenburn (1983)	Backside natural air cooling through extended fins type heat exchanger	A PV panel has been cooled through a heat exchanger via natural cooling mode. The design of heat exchanger, wind speed and its directions are the main parameters to be studied. Correlation between Nu and Re has been developed	Results revealed that the designs of heat exchanger and wind speed are the main parameters that effect the natural cooling of a PV system. The coefficient of heat transfer from (h) extended fins to surroundings is found about 20 W/m^2 °C
Do et al. (2012)	Backside natural air cooling through a flat plate fins type heat sink	A PV panel of 50 W has been cooled through a heat sink (attached on backside of PV) via natural cooling mode. The design specifications of heat sink are; L = W = 240 mm, H = 50 mm and t = 1 mm	A general correlation has been developed to estimate thermal performance of a heat sink with respect to sink design, input supply, and orientation angle for CPV module cooling. The optimum space between the two fins has been observed about 10.5 mm
Radwan, Ookawara, and Ahmed (2016)	Backside natural air cooling through a micro channel heat sink	A micro channel heat sink has been designed for cooling of a low concentration PV (CR ranges 1–40) and attached at backside. The system has been studied for observing the; effect of water cooling, effect of Tamb, effect of mass flow rate, effect of wind velocity etc.	Results revealed that at CR of 40 the modified system’s electrical efficiency and thermal efficiency has been found about 18.5% and 62.5%, respectively
Popovici et al. (2016)	Cooling through back side air cooled heat sink	An air cooled heat sink (made of high thermal conductive material) is designed which is composed by ribbed wall for cooling of PV. The study has been done for various angles of the ribbed wall to the base plate of sink	By using the new heat sink the peak power output is obtained about 90% to the nominal one for angles of the ribbed walls from 90° to 45°
Ali et al. (2017)	Air cooling of both the top and back surface of PV	Two PV panels of 10 W have been tested for its surface temperature reduction under the high windy conditions (0 to 15 m/s) through a tunnel and the flux has been generated through solar simulator. Thermal model has been developed with the help of ANSYS-FLUENT for validation of results	Results showed that PV surface temperature has dropped by 17.21% while the power output has been increased about 12%
Soliman, Hassan, and Ookawara (2019)	Backside air cooling with the help of heat sink integrated with extended aluminium fins	A polycrystalline solar cell of 6 Volt has been cooled through aluminium finned heat sink composed of 18 fins (specific dimension 180 mm × 100 mm × 45 mm). The heat has been removed through natural and forced convection from the sink. A 12 V DC fan has been used for providing the air over the sink. The flux has been generated through solar simulator	Results showed that the temperature of top surface has reduced by 5.4 and 11% respectively on natural and forced convection. The efficiency and power has been increased about 8% and 16%, respectively
Amr et al. (2019)	Backside air cooling with the help of extended aluminium fins	A PV panel of 250 W has been tested theoretically (heat transfer analysis through energy balance equations) and experimentally. The significance of fin cooling has been observed under the still air cooling and ventilated air cooling	Results showed that the temperature of top surface has reduced by 4–5°C. The power has been found about 180.9 W from 159.9 W under ventilated air which has been found the best cooling mode
Siyabi et al. (2020)	Backside air cooling with the help of microchannel heat sink	A CPV has been cooled by attaching a microchannel heat sink at the backside of CPV. These microchannel plates have been made by aluminium for a specific size about 30 mm (length) and 32 mm (width). The heat transfer fluid has been varied from 30 ml/min to 300 ml/min for performance evaluation	The cell temperature has been maintained up to 60°C and the extracted heat from the CPV is about 12.85 W which shows of 74.9% of the total produced power while the fluid flow rate is 30 ml/min

It is clear from Saxena and Norton (2021), (Krauter (2004), (Furushima and Nawata (2006), Ceylan et al. (2014), Wu and Xiong (2014), Ebrahimi, Rahimi, and Rahimi (2015) and Chandrasekar and Senthilkumar (2016) that the efficiency of photovoltaic panels decreases as the panels’ temperature increases, which results in the deduction of electricity generation. In order to reduce this effect, different cooling methods have been proposed and investigated (Tables 1–3). The present paper reviews the previous work on cooling PV cells and concludes that cost-effectiveness, design feasibility and minimal energy consumption are the important design consideration for cooling systems. Based on these considerations, this paper reports a passive cooling method that utilises PCM properties along with extended fins principles for effective cooling of the PV system. The present heat sink is found to be better comparatively with other designs (Tables 1–3) which are complicated in design, therefore need much space for installation and also require a pump which increases the overall cost of the system. Another foremost issue is the replacement of the PCM which is not easy in most systems (if required) while the present heat sink is easy to maintain, less space required, no pumping cost and easy replacement of PCM through fins and lastly much-improved performance of the PV panel.

Apart from this, it has been noticed from the available literature on solar thermal systems that the latent heat storage (LHS) materials are progressive in recent years to be used as potential techniques for thermal energy storage for efficient enhancement (Saxena et al. 2011; Saxena, Agarwal, and Srivastava 2013; Saxena and Srivastava 2013; Saxena and Deval 2016; Saxena and Norton 2021) especially in solar energy systems (Agyenim et al. 2010).

TES materials have been used in photovoltaic systems owing to the excellent TES capacity. Buddhi et al. (1988) carried out some experiments on different TES materials. Among all TES materials tested for performance enhancement paraffin was found to be the most economic and efficient TES material for solar applications. Chandel and Agarwal (2017) studied the various cooling techniques applied to PV for performance enhancement. Results show that PCM is a cost-effective solution for controlling PV temperature and besides this a melting point around 30°C or more is capable to sustain a constant temperature of the PV panel which results in improved panel efficiency.

References (Chandrasekar and Senthilkumar 2016; Sainthiya, Beniwal, and Garg 2018; Bahaidarah et al. 2013; Smith et al. 2014; Nizetic et al. 2016; Schiro et al. 2017; Wu, Chen, and Xiao 2018; Atkin and Farid 2015; Stropnik and Stritih 2016; Hachem et al. 2017; Waqasa and Ji 2017) show that paraffin wax is not only a simple material but also economically energy storage material for solar electrical/thermal applications. In paraffin wax, solar energy is stored through a phase change in the TES material through two common thermal processes such as melting and freezing. In melting, the heat is stored as latent heat of fusion and in freezing this heat is liberated. A lot of research has been carried out on the suitability of different compounds of paraffin especially on wax as an LHS for solar energy systems (He and Setterwall 2002; Silakhori et al. 2013; Saxena, Agarwal, and Cuce 2020; Kyriaki et al. 2017; Kousksou et al. 2010). The wax has been found to improve much better the overall performance of improved heat transfer, system efficiency, power output, heat storage capacity, durability and life cycle of the solar applications. Due to this reason, a common compound of paraffin wax (RT-28HC) has been considered in the present work as a capacitive TES material (Table 3). Apart from this, it is essential to retain the operative temperature as low as conceivable to improve the efficiency of a PV system (rather at the level of STC or 25°C) and in Moradabad city, T_amb at 6:00 h mainly in the months of May and June is about 26–27°C. Therefore, PCM is selected for a melting point of about 27°C which starts to absorb the heat of the PV panel from early in the morning to the long hours of noon (daily).

2. Materials and methods

2.1. Experimental set-up

In the present article, efforts have been made to observe the effect of cylindrical copper tubes encapsulated with PCM on the thermal response of a solar PV module for better performance. For this, a special bracket of galvanised iron has been designed to support the copper tubes attached to the backside of PV. The area of the bracket (1.5 m × 0.75 m) is slightly less than the area of the PV back surface (1.58 m × 0.81 m) so that it can be attached properly to the backside or PV can be easily fitted above it. To develop the PCM cooling mechanism, a total of three thin flat sheets (thickness = 0.8 mm) of cooper are taken for the specific dimension of 1.57 m × 0.27 m. On these sheets, copper tubes of 1.8 cm diameter and 15 cm length are vertically positioned and soldered (Figure 1(a)) to behave like a pin fin heat sink. Copper material has been taken because of good thermal conductivity (386 W/m-°C) and specific heat (380 J/kg-°C). The one end is completely closed through soldering while the other end is opened to be encapsulated by PCM (Figure 1(b)).

Figure 1. (a) PCM tubes in vertical positioned on copper sheet (heat sink) and (b) copper tube sealing arrangement.

After filling the PCM, the other end is closed (or fully sealed) through an aluminium nut with the principle of nut and bolt (Figure 1(b)) to avoid any kind of leakage. These PCM containing tubes are placed on equidistance (4.4 cm from all sides) from all four sides over the thin sheet of copper to prepare the PCM-based pin fin heat sink. These copper tubes have been filled with 90% of PCM to avoid leakage/damage due to thermal expansion of the PCM under higher temperatures. Now, the sheet integrated with the encapsulated tubes has been placed at the mid centre of the designed bracket (Figure 2). A thin layer of thermal conductive glue (Silcotherm™: thermal conductivity 3.1 W/m·K, density 2.91 g/cm³, thermal resistance 24 mm²·K/W, minimum working temperature (−50°C), maximum working temperature (200°C) and type-paste) is pasted over the sheet and then it has been attached to the backside of PV (Figure 3). The rigid bracket provides strength to the sheet carrying tubes which results in conformance of no air gap between the new designed bracket and the backside of PV, which results in better heat transfer from the backside of the panel through the tubes. A flexible stand (Figure 4(c)) has been designed in such a manner that the PV panel can be easily placed on it at the inclination angle of 43° (Saxena, Agarwal, and Srivastava 2013; Elshafei 2010) from the horizontal plane.

Figure 2. Experimental set-up of a 91 PCM-encapsulated tubes (pin fin heat sink).

Figure 3. PCM cooling of PV at the backside by (a) 271 pin fin heat sink (b) 181 pin fin heat sink (c) 91 pin fin heat sink.

Figure 4. (a) Experimental set-up of PV cooling with 91 PCM-encapsulated tubes (b) with 271 PCM-infused fins (c) special designed flexible PV stand.

All the investigations have been carried out on the actual ambient conditions of Moradabad city (28.83°N and 78.78°E) of India. Total four same specifications solar panels of 180 W_p manufactured by CEL, Sahibabad, India, have been installed at MIT, Moradabad, for conducting experiments. From these solar panels, three configurations have been developed, consisting of different numbers of PCM-encapsulated tubes for performance enhancement evaluation.

The fourth panel is reference panel A, which has been tested simultaneously with panels B, C and D for comparison of results in the following manner;

First configuration: In the first configuration, reference panels A and B (panel with 91 PCM-encapsulated tubes) have been tested on 19 June 2019 from 06:00 to 18:00 h.

Second configuration: In the second configuration, reference panels A and C (panel with 181 PCM-encapsulated tubes) have been tested on 20 June 2019 from 06:00 to 18:00 h.

Third configuration: In this, reference panels A and D (panel with 271 PCM-encapsulated tubes) have been tested on 21 June 2019 from 06:00 to 18:00 h.

It is notable that in each configuration there is an additional tube (i.e. 90 + 1 = 91, 180 + 1 = 181 and 270 + 1 = 271) which carried a 0.6 mm drilled hole below 03 cm distance from the top edge (which is connected to the copper sheet) to measure the temperature of filled PCM inside the tube through a thermocouple sensor (Figure 5). The location of additional tubes is shown in Figure 3. At these points, where additional tubes are located, T_bs has its minimum value with respect to other points, which confirmed the melting of PCM inside all tubes. These tubes, attached at the backside of the PV panel, acted as a pin fin heat sink for the individual PV system.

Figure 5. Heat transfer mechanism of the pin fin heat sink.

Specifications of the PV module and tested PCM are given in Tables 4 and 5, respectively. Readings of the experiments have been taken for an interval of 30 min in all the configurations and discussed for an interval of 01 h in graphical presentation. To measure the temperature variations at the various points of set-up, a 12 point K type copper constantan thermocouple sensor with an accuracy of ±2.2°C (±0.75%) has been used due to its better sensitivity. To record the velocity of wind around the testing place an anemometer (model-WD9819) has been used with an accuracy of ±3%. A potential solarimeter ‘Surya-mapi’ (CEL™-201 and range = 0–1200 W/m²) with an accuracy of ±1 W/m² has been used to measure solar radiation. A sensitive weigh balance (linearity ± 0.2 mg) has been used for measuring the quantity of tested PCM and a commercial multi-meter of EXTECH™ (model-EX410A) with an accuracy of ±0.5% has been used to measure the output of the PV panel.

Table 4. Specifications of installed PV.

Electrical parameters	PM 180
Nominal power rating
Pmax. (Wp)	180
Rated current IMPP (A)	05.00
Rated voltage VMPP (V)	36.00
Short circuit current ISC (A)	05.30
Open circuit voltage VOC (V)	44.80
Size (mm)
Length (L)	1580
Width (W)	805
Depth (D)	42
Weight (kg)	14.2
No. of cells (nos.)	72

Table 5. Properties of tested PCM.

Properties	Value
Melting temperature	27.5°C
Congealing area	29–27°C
Heat storage capacity	250 kJ/kg
Specific heat capacity	2 kJ/kg K
Density solid (at 25°C)	0.88 kg/L
Density liquid (at 80°C)	0.77 kg/L
Heat conductivity (both phases)	0.2 W/m·K
Volume expansion	12.5%
Flash point	>165°C
Max. operation temperature	51°C

2.2. Data analysis

A comparative assessment of the experimental study of three different configured (but of the same specifications) multi-crystalline panels of 180 W_p has been carried out. Experiments on all three configurations have been carried out simultaneously with the same specifications’ reference panel for result comparison on consecutive days. In all configurations, reference panel ‘A’ got cooled naturally by surrounding air while the rest of the panels B, C and D got cooled by operating the system on different numbers of PCM-encapsulated tubes (Figure 4). It has been observed the heat accumulated at the backside of the solar panel is transmitted to the PCM-encapsulated tube through conductive heat transfer where the PCM absorbs the heat and undergoes a solid to liquid phase conversion and stored a significant amount of waste heat from PV (Figure 5). The energy balance for the heat transfer can be shown by assuming that (i) the coefficient of heat transfer remains the same for the duration of the entire over the experimental settings, (ii) solar radiation is uniformly distributed on the PV module and (iii) natural convection heat transfer occurs at both sides of the module; (1) $Q_{\mathrm{in}}\times \mathrm{\Delta }t=Q_{\mathrm{conv}}+Q_{\mathrm{rad}}+Q_{\mathrm{pv}\text{-}\mathrm{sc}}+Q_{\mathrm{pcm}}+Q_{\mathrm{panel}}$(1)

The net energy input to the system is the product of time duration/frame of the experimental study (Δt) and net received solar power (Q_in). According to the PV test standard conditions (STC), manufacturers of solar PV panels establish to the extent their products efficiency is about 15–16% for a typical standard silicon single P–N junction (Ingersoll 1986; Tiwari and Dubey 2010). Here, the Q_pv is taken to be 16% of total energy (Q_in × Δt) and the remainder (waste heat) has been absorbed through the PV panel (Ingersoll 1986). The value of solar power (Q_in) can also be expressed as (Duffie and Beckman 2013) (2) $Q_{\mathrm{in}}=I\cdot A_{\mathrm{pm}}\cdot {\alpha }_{\mathrm{abs}}$(2)

The heat transfer through the radiation and convection provides the surrounding heat loss mechanisms as well as it acts like cooling resource for reference panel A, therefore; (3) $Q_{\mathrm{conv}}=h_{\mathrm{sa}}(T_{\mathrm{pv}\text{-}\mathrm{sc}}-T_{\mathrm{amb}})$(3) (4) $Q_{\mathrm{rad}}=\epsilon \cdot \sigma \cdot (T_{\mathrm{pv}\text{-}\mathrm{sc}}^4-T_{\mathrm{amb}}^4)$(4)

Besides this, the remainder waste heat is assumed to be completely absorbed through the PCM-encapsulated tubes through heat transfer. In panels B, C and D, the solid to liquid phase change has been followed when the T_pcm reaches its melting point (T_melt). During this phase change of the PCM, the temperature remains constant and the heat is captivated as latent heat of fusion. The values are different from the specific heat for both the states i.e. solid and liquid and have a significance effect on the increase of T_pcm. Therefore, the heat transfer mode can be expressed as follows:

For the solid phase: $T_{\mathrm{amb}}\prec T_{\mathrm{pcm}}\prec T_{\mathrm{melt}}$ (5) $Q_{\mathrm{pcm}}=M_{\mathrm{pcm}}\cdot C_{\mathrm{sol}}\cdot (T_{\mathrm{pcm}}^{}-T_{\mathrm{amb}}^{})$(5)

For solid to liquid phases: $T_{\mathrm{pcm}}=T_{\mathrm{melt}}$ (6) $Q_{\mathrm{pcm}}=M_{\mathrm{pcm}}\cdot C_{\mathrm{sol}}\cdot (T_{\mathrm{melt}}^{}-T_{\mathrm{amb}}^{})+H_{\mathrm{pcm}}$(6)

For the liquid phase: $T_{\mathrm{pcm}}\succ T_{\mathrm{melt}}$ $Q_{\mathrm{pcm}}=M_{\mathrm{pcm}}\cdot C_{\mathrm{sol}}\cdot (T_{\mathrm{melt}}^{}-T_{\mathrm{amb}}^{})+H_{\mathrm{pcm}}+M_{\mathrm{pcm}}\cdot C_{\mathrm{liq}}\cdot (T_{\mathrm{pcm}}^{}-T_{\mathrm{amb}}^{})$ (7) $\Rightarrow Q_{\mathrm{pcm}}=M_{\mathrm{pcm}}\cdot [C_{\mathrm{sol}}\cdot (T_{\mathrm{melt}}^{}-T_{\mathrm{amb}}^{})+C_{\mathrm{liq}}\cdot (T_{\mathrm{pcm}}^{}-T_{\mathrm{amb}}^{})]+H_{\mathrm{pcm}}$(7)

2.3. Thermal response of the PCM tube

The net energy transferred (${\dot{Q}}_{\mathrm{net}}$) from the heated back surface of PV to the heat sink (tube network) by both components i.e. convection (${\dot{Q}}_{\mathrm{conv}}$) and the radiation (${\dot{Q}}_{\mathrm{radi}}$) therefore (Elshafei 2010) is (8) ${\dot{Q}}_{\mathrm{net}}={\dot{Q}}_{\mathrm{conv}}+{\dot{Q}}_{\mathrm{radi}}$(8)

While the rate of heat exchanged is the difference of net input to the heat sink and conductive losses from the panels back surface; therefore, (9) ${\dot{Q}}_{\mathrm{net}}={\dot{Q}}_{\mathrm{input}}-{\dot{Q}}_{\mathrm{loss}}$(9)

By ignoring the conductive heat losses, the radiative component can be obtained by (Elshafei 2010) (10) ${\dot{Q}}_{\mathrm{rad}}={\displaystyle \frac{\sigma A_{\mathrm{hs}}(T_{\mathrm{ms}}^4-T_{\mathrm{sur}\cdot \mathrm{w}}^4){\epsilon }_{\mathrm{hs}}}{(1-{\epsilon }_{\mathrm{hs}})+{\displaystyle \frac{A_{\mathrm{hs}}}{A_{\mathrm{sur}\cdot \mathrm{w}}}}}}$(10) where A_hs = area of the heat sink (total PCM tubes area + area of the copper sheet attached to the back surface of PV), T_ms is the mean temperature of the heat sink, A_sur·w is the area of surrounding small walls and the value of ${\epsilon }_{\mathrm{hs}}$ is 0.15 for the heat sink (Joo and Kim 2015).

Now by putting the value of ${\dot{Q}}_{\mathrm{radi}}$ in Equation (8), the rate of convective heat transfer in steady state can be obtained through (11) ${\dot{Q}}_{\mathrm{conv}}=(h_{\mathrm{bs}\text{-}\mathrm{pv}}\cdot A_{\mathrm{bs}\text{-}\mathrm{pv}}+h_{\mathrm{pcm}\cdot \mathrm{t}}\cdot A_{\mathrm{pcm}\cdot \mathrm{t}}\cdot {\eta }_{\mathrm{pcm}\cdot \mathrm{t}})(T_{\mathrm{bs}}-T_{\mathrm{air}})$(11)

Now, by introducing the overall tube efficiency (${\eta }_{\mathrm{over}}$) in Equation (11) and assuming that $h_{\mathrm{bs}\text{-}\mathrm{pv}}=h_{\mathrm{pcm}\cdot \mathrm{t}}=\overline{h}$, Equation (11) becomes (12) ${\dot{Q}}_{\mathrm{conv}}=\overline{h}\cdot A_{\mathrm{hs}}\cdot {\eta }_{\mathrm{over}}\cdot (T_{bs}-T_{air})$(12)

Now, the overall tube efficiency (${\eta }_{\mathrm{over}}$) can be obtained through (13) ${\eta }_{\mathrm{over}}=⟨1-{\displaystyle \frac{A_{\mathrm{pcm}\cdot \mathrm{t}}}{A_{\mathrm{hs}}}(1-{\eta }_{\mathrm{pcm}\cdot \mathrm{t}})}⟩$(13)

Besides this, the average heat transfer coefficient through convection depended on the total surface area for heat transfer can be obtained as (Elshafei 2010; Joo and Kim 2015) (14) $\overline{h}={\displaystyle \frac{{\dot{Q}}_{\mathrm{conv}}}{A_{\mathrm{hs}}\cdot {\eta }_{\mathrm{over}}}(T_{bs}-T_{air})}$(14)

And the thermal resistance (R_th) can also be evaluated by using the following equation (Joo and Kim 2015): (15) $R_{\mathrm{th}}={\displaystyle \frac{1}{(h_{\mathrm{bs}\text{-}\mathrm{pv}}\cdot A_{\mathrm{bs}\text{-}\mathrm{pv}}+h_{\mathrm{pcm}\cdot \mathrm{t}}\cdot A_{\mathrm{pcm}\cdot \mathrm{t}}\cdot {\eta }_{\mathrm{pcm}\cdot \mathrm{t}})}}$(15)

In Equation (15), the PCM-encapsulated tube cum fin efficiency can be calculated by (16) ${\eta }_{\mathrm{pcm}\cdot \mathrm{t}}={\displaystyle \frac{\tanh \cdot (mH)}{mh}={\displaystyle \frac{\tanh \cdot \left(\sqrt{{\displaystyle \frac{4h_{\mathrm{pcm}\text{-}\mathrm{t}}}{k\cdot D}\cdot }}.H\right)}{\left(\sqrt{{\displaystyle \frac{4h_{\mathrm{pcm}\text{-}\mathrm{t}}}{k\cdot D}}}\cdot h\right)}}}$(16) where H is the height of the copper tube and D is its diameter.

For a detailed analysis, one can go through the work of Amr et al. (2019) and Bayrak, Oztop, and Selimefendigil (2019). Both the authors have discussed the energy balance equations with a detailed model for PV panels without extended fins and with ‘n’ numbers of fins surrounded by PCM.

2.4. Power generation

The electrical yield of the solar module (P_max) can be estimated through Equation (17) if the conversion efficiency of the PV is given as (17) $P_{max}={\eta }_{\mathrm{conv}}\cdot A_{\mathrm{pm}}\cdot I$(17)

It has been noticed experimentally that as the surface temperature of the cell is increased, the cell conversion efficiency (ƞ_conv) is decreased (Ingersoll 1986). Therefore, the relationship between the temperature rise and ƞ_conv drop can be designated through Equation (18) (Amr et al. 2019) (18) ${\eta }_{\mathrm{conv}}={\eta }_{\mathrm{ref}}^{}[1-{\beta }_{\mathrm{ref}}(T_{\mathrm{pv}}-T_{\mathrm{ref}})]$(18) where ${\eta }_{\mathrm{ref}},{\beta }_{\mathrm{ref}}\mathrm{and}{T}_{\mathrm{ref}}$ are the conversion efficiency, coefficient of temperature and the cell surface temperature of the reference panel at the standard test condition (STC), while T_pv is the actual temperature of the tested solar panel.

3. Result and discussion

In the present work, the thermal performance evaluation of the 180 W_p solar PV module has been carried out by operating with different configurations of PCM-encapsulated tubes which are attached at the backside of the panel through a flat copper sheet to be worked as a pin fin heat sink (Joo and Kim 2015). The concept of using the PCM-encapsulated tubes is to produce the fin effect which is highly favourable for a better convective heat transfer (commonly approached in solar air heaters; Saxena, Varun, and El-Sebaii 2015) from the backside of the solar module mainly after the complete melting of PCM inside the tube (Duffie and Beckman 2013). It captivates and releases a large amount of latent heat during its phase change state at a constant temperature. Here, only the thermal behaviour of the solar panel has been investigated by using PCM tubes heat sink. Conversion efficiency (ƞ_conv) of the panel and power output (P_max) are the two major characteristics of the present work which have been experimentally studied under the peak solar hours.

Testing has been carried out on three consecutive days of the month June 2019 at MIT, Moradabad (India). All the readings have been discussed for an interval of 1 h from 06:00 h in the morning to 18:00 h in the evening. In all configurations, the reference panel (A) had been cooled via natural cooling while the other panels B, C and D have got cooled under passive type cooling through the PCM. All the instruments have been well checked for proper functioning and error-free mode before starting the experiments. Wind velocity has been observed to be varied between 1.0 and 1.2 m/s therefore it has been considered for a fixed value of 1.1 m/s in experiments.

3.1. PV module testing on the first configuration

In this configuration, reference panels A and panel B with 91 PCM-encapsulated tubes have been experimentally studied simultaneously for performance enhancement (Figure 4). The experiments have been conducted from the morning (6:00 h) to the evening (18:00 h) on the first day i.e. 19 June 2019. Readings have been taken to measure the temperature variations in T_amb, T_sc-A, T_sc-B and T_pcm to calculate the conversion efficiency and power yield of both panels A and B.

Experiments have been started around 6:00 h when the T_amb is notified as 26.9°C and irradiance ‘I’ is noted to be 475 W/m². The surface temperature of both the panels is almost the same before experimentation. After starting the experiments T_sc-A is found to rise swiftly in comparison to T_sc-B. The value of T_sc of both the panels is found to be normally varied coinciding with solar radiation ‘I’. Increasing from an almost identical value with T_amb in the morning, it extended to its highest value in solar noon and then decreased with respect to the dropping of the T_amb and solar radiation. The maximum value of T_sc-A and T_sc-B is found to be 58.93°C and 53.9°C around the 13:05 h, respectively (Figure 6).

Figure 6. Temperature variations for panels A and B.

In panel B, the phase change effect has been noticed from 08:00 to 10:30 h. The PCM inside the tube is found to be completely melted around 10:30 h and the T_PCM is notified around 40°C at this time. During the experiments, T_sc-A is observed to be higher than T_sc-B at all times due to the PCM cooling. During the phase change effect, the T_sc-B is found to be much cooler than T_sc-A. Notably, the PCM-encapsulated tubes of copper act like extended fins on the flat plate which improves the heat transfer from the back surface of PV to the PCM-encapsulated tubes (Joo and Kim 2015). PCM inside the tubes absorbed the heat energy from the back surface of panel B and due to this the value of T_sc-B has not been found moreover it is 53.9°C throughout the day. It is also notable that the surrounding air carries the stored heat from the tubes’ external surface to the environment and helps the system to get cool more efficiently in comparison to panel A.

During the testing, a significant effect has been noticed on T_sc-A and T_sc-B due to variations in T_amb and I (W/m²). The average temperature reduction has been found to be 11.23% in panel B by using PCM cooling. The maximum value of η_ce-A and η_ce-B has been found to be 17.64% and 18.21%, respectively (Figure 7). The average percentage efficiency enhancement has been found to be 3.73% for panel B under PCM cooling on the first configuration. The maximum value of P_max-A and P_max-B has been found to be 99.66 and 103.91 W, respectively. The average percentage power yield improvement has been found to be 3.76% for panel B on the first configuration.

Figure 7. Variations in efficiency and power output for panels A and B.

3.2. PV module testing on second configuration

In this configuration, reference panels A and panel C with 181 PCM-encapsulated tubes have been experimentally studied simultaneously for performance improvement under the climatic conditions of Moradabad city, India.

Experiments have been started around 6:00 h and the T_amb is notified to be around 27°C and irradiance ‘I’ is observed to be 470 W/m². The surface temperature of both the panels (A and C) is almost the same before testing. After starting the experiments T_sc-A has been again noticed to rise expeditiously in comparison to T_sc-C. The maximum value of T_sc-A and T_sc-c has been observed to be 59.13°C and 48.7°C around the 13:02 h, respectively (Figure 8). In panel C, the phase change effect has been noticed from 08:10 to 10:45 h. The PCM inside the tube is found to be completely melted around 10:46 h and the T_PCM is notified around 45.8°C at this time. During the experiments, T_sc-A is observed to be higher than T_sc-C due to the PCM cooling. During the phase change effect, the T_sc-C is also found to be much cooler (like T_sc-B) than T_sc-A. The value of T_sc-C has not been found more than 48.71°C throughout the day.

Figure 8. Temperature variations for panels A and C.

During the experimental testing, a significant effect has been noticed on T_sc-A and T_sc-c due to variations in T_amb and I (W/m²) as in previous configuration testing. The average temperature reduction has been found to be 17.6% in panel C by using PCM cooling which is more than panels A and B because the quantity of PCM has been increased in comparison to 91 PCM-encapsulated tubes (more the amount of PCM in the heat sink, more the amount of heat energy absorbed). As well as the large contact area of the surface that improved the heat transfer. The maximum value of η_ce-A and η_ce-C has been found to be 17.63% and 18.27%, respectively (Figure 9). The average percentage efficiency enhancement has been found to be 5.97% for panel C under PCM cooling on 181 PCM-encapsulated copper tubes. The maximum value of P_max-A and P_max-B has been found to be 99.48 and 108.14 W, respectively. The average percentage power yield improvement has been found to be 5.79% for the panel C on the second configuration. Figures 8 and 9 show the significance of the amount of PCM used on the performance of panel C which is better over the panels A and B.

Figure 9. Variations in efficiency and power output for panels A and C.

3.3. PV module testing on the third configuration

In this last configuration, the reference panels A and panel D with 271 PCM-encapsulated tubes have been experimentally studied simultaneously for performance improvement at the same location.

An experimental study has been carried out from 6:00 h in the morning and the T_amb is notified around 28°C and irradiance ‘I’ is observed to be 480 W/m². The surface temperature of both the panels (A and D) is almost the same before conducting the tests. After starting the experiments, T_sc-A has been noticed to rise expeditiously along with the increase of T_amb and ‘I’ in comparison of T_sc-D. The maximum value of T_sc-A and T_sc-D is observed to be 61.02°C and 48.8°C around 14:01 h, respectively (Figure 10). In panel D, the phase change effect has been noticed from 08:20 to 11:00 h. The PCM inside the tube is found to be completely melted around 11:00 h and the T_PCM is notified around 46.9°C at this time. During the experiments, T_sc-A is observed to be higher than T_sc-D due to the PCM cooling through 271 PCM-encapsulated copper tubes attached at the back surface of panel D. During the phase change effect, the T_sc-C is also found to be much cooler (alike T_sc-C and T_sc-B) than T_sc-A. The value of T_sc-D has not been found moreover it is 48.8°C throughout the day.

Figure 10. Temperature variations for panels A and D.

During the experiments, besides the significant effect of ambient conditions on T_sc-A and T_sc-D, the effect of PCM quantity with increasing numbers of encapsulated tubes used for cooling has been marked clearly on the performance of new panel D along with a large surface area contact. The average surface temperature reduction has been found to be 20.76% in panel D by using PCM cooling which is more than panels A, B and C because the quantity of PCM has been increased with increasing numbers of encapsulated tubes which absorbed more heat energy from the back surface of panel D in comparison of 91 and 181 PCM-encapsulated tubes and provided better conductive and convective heat transfer due to contact in a large-sized heat sink. The maximum value of η_ce-A and η_ce-D is found to be 17.48% and 18.44%, respectively (Figure 11). The average percentage efficiency enhancement is found to be 6.49% for panel D under PCM cooling on 271 PCM-encapsulated copper tubes. The maximum value of P_max-A and P_max-D has been found to be 98.61 and 108.71 W, respectively. The average percentage power yield improvement is found to be 6.67% for panel D on the third configuration. Figures 8 and 9 show the significance of the amount of PCM used on the performance of panel D which is better compared to panels A, B and C.

Figure 11. Variations in efficiency and power output for panels A and D.

In the present article, the PCM infused cylindrical tubes have been used for cooling of a solar panel which acted as an air-cooled pin fin heat sink at the backside of PV. It can be seen from Figures 3 and 5 that the tubes have been arranged in such a manner that the possible airflow maintained through the tubes network from all the sides without blocking the air. It is remarkable that the convection heat coefficient on the PCM tube cannot be possibly defined accurately without direct airflow analysis and air temperature around exactly the tube position. Therefore considering the model (Grubisic-Cabo et al. 2018) for a wind speed around 1.1 m/s on the location of experiments, the mean convective heat transfer coefficient is found around 5.21 W/m² K. Figure 12 shows the results of all the tested configurations on different days for a better understanding of output results.

Figure 12. Efficiency and power output of panels B, C and D on different days (19, 20, and 21 June 2019).

About the overall performance of the panels operated on different configurations the third configuration is found the best among all. These tubes have a greater influence on the solidification process of the tested PCM than that of melting progression. Apart from this, thermal response of the panels B, C and D is found to be improved with enhancement in design of the attached mechanism.

The convective heat transfer takes place from a large surface area by increasing the number of PCM filled tubes in each new configuration which not only helps to cool down the T_pcm towards the solidification but reduces the back surface temperature of the PV panel and results in improved conversion efficiency and power yield (Table 6).

Table 6. Results of different configurations of PV panel cooling through PCM-encapsulated copper tubes.

Parameters	On 1stconfiguration	On 2ndconfiguration	On 3rdconfiguration
Numbers of PCM tubes	91	181	271
Tsc (Maximum value)	53.9°C	48.7°C	48.8°C
ηce (Maximum value)	18.21%	18.27%	18.45%
Pmax (Maximum value)	103.91 W	108.14 W	108.64 W
TPCM (Maximum value)	45.89°C	45.81°C	46.9°C

4. Economic analysis

The development of the cost-competitiveness of a PV system ended the years endures to initiate its interestas a worthwhile power generation alternate in the worldwide energy mix. In 2014, values of PV modules reduced about 75% in comparison with their prices in 2009 and as a consequence, refining the PV system plug parity. The total cost of the present project is shown in Table 7.

Table 7. Costs of different items of PV system.

Items	Cost in Indian rupees
PV panel	6500
PCM	700
Copper made fins	650
Copper sheet	500
Iron angle	500
Thermal conductive glue	600
Labour	500
Miscellaneous	50
Total cost	10,000/- INR = $131.11

Significant measures used in the economic assessment of a PV system considered in the present work are as follows.

4.1. Net present value (NPV)

The NPV is an economic tool that is used to assess cash outflows and incomes (revenues), and asset characteristics and choices especially for associating commonly exclusive projects. It is an algebraic sum of the net cash flows (CF_m) until the end of the project’s life cycle to the present, reduced by an applicable annual discount rate (r). It can be estimated as (Saxena and Srivastava 2012) (19) $\mathrm{NPV}=\sum _{m=0}^N{\displaystyle \frac{\mathrm{C}{\mathrm{F}}_m}{{(1+r)}^m}}$(19) where N is the analysis period.

Assumptions and facts:

1. 01 year electricity savings (kWh) is 1825 rupees ($24.25)

2. Electricity (kWh) price in our locations in 6.50 rupees

3. Total cost of the system is about 10,000/- rupees

4. Future value discount rate is about 20%

5. Annual output degradation (linear) – 0.5%

6. Electricity inflation price rate is about 1%.

From Equation (19) the NPV for 25 years is about 14,190 INR or $188.58 and for the present PV system the NPV is shown in Figure 13.

Figure 13. NPV of the present PV system for 25 years.

4.2. Life cycle cost (LCC)

LCC is a tool to estimate the inclusive cost of the project counting initial costs (C_I), fuel costs, operating cost and maintenance costs (C_OMR), replacement (C_repl) or repair costs, discarded or resale values (C_disc), the other finance charges (if any) and other costs (C_OC) (Duffie and Beckman 2013).

LCC can be estimated as (20) $\mathrm{LCC}=C_{\mathrm{I}}+C_{\mathrm{OMR}}+C_{\mathrm{OC}}+C_{\mathrm{repl}}-C_{\mathrm{disc}}$(20) = 12,266 INR or $163 (for one panel).

4.3. Payback period (PBP)

PBP is fundamentally the number of years obligatory to recuperate the initial investment. The small PBP is extremely desirable due to wealth gains that will be obtainable first and will decrease the risk of asset. PBP can simply be estimated as (Duffie and Beckman 2013) (21) $\mathrm{PBP}={\displaystyle \frac{\mathrm{Total}\mathrm{cost}\mathrm{of}\mathrm{the}\mathrm{system}}{\mathrm{Net}\mathrm{savings}\mathrm{by}\mathrm{the}\mathrm{system}}}$(21) = 10,000/1825 = 5.47 years.

5. Uncertainty analysis

The uncertainties in some measured performance indicators have been obtained from the errors of the measuring instruments used in the experiments indicated in Section 2 and it has been calculated with the help of the following equations (Soliman, Hassan, and Ookawara 2019):

For a mean value (x) (22) $\overline{x}={\displaystyle \frac{\sum _{i=1}^N(x_i)}{N}}$(22)

For the standard deviation (σ) (23) $\sigma =\sqrt{{\displaystyle \frac{1}{N-1}\sum _{i=1}^N{(x_i-\overline{x})}^2}}$(23)

Now, to compute the experimental uncertainty equation (22) is divided by Equation (23) and the following is obtained: (24) $={\displaystyle \frac{\overline{x}}{\sigma }}$(24)

The uncertainty in solar radiation (I − W/m²) has been found to be ±1.1% while that of ambient temperature (T_amb − °C) and the panel temperature (T_sc − °C) have been found around ±1.5% and ±2.1%, respectively. Uncertainty for the conversion efficiency (η_ce − %) and the power output (P_max − W) has been found to be ±1.81% and 2.01±, respectively during the experiments.

6. Conclusion

In the present work a special bracket stand of galvanised iron has been designed through which multi cylindrical copper tubes encapsulated with PCM (melting point 27–29°C) have been attached at the backside of the PV system for controlling of the surface temperature. Experiments have been conducted on three different configurations of PCM tubes such as on 91 tubes (panel B), 181 tubes (panel C) and 271 tubes (panel D). Overall, the results can be concluded as

1. Panel B with 91 PCM-encapsulated tubes is found to be better over reference panel A for the average per cent reduction about11.23% in the cell temperature and average per cent increment of 3.73% in the conversion efficiency and about 3.76% in the power output through experimentally testing under the same climatic conditions.

2. Panel C with 181 PCM-encapsulated tubes has been found better over panel A for the average per cent reduction of about 17.6% in the cell temperature, 5.97% in the conversion efficiency and 5.79% in the power output. This panel C is found to be better over panel B for the average per cent reduction of about 5.3% in the cell temperature, 1.74% in the conversion efficiency and 1.53% in the power output. The variations in these values of performance parameters are directly subjected to the ambient conditions because both the panels have been tested on different ambient conditions.

3. Panel D with 271 PCM-encapsulated tubes is found out to be the best configured which showed the average per cent reduction about 20.76% in the cell temperature, 6.49% in the conversion efficiency and 6.67% in the power output in comparison of the reference panel A. In a comparison of panels B and C, the average per cent reduction is obtained to be about 7.51% and 5.6% in the cell temperature, 2.3% and 0.54% in the conversion efficiency and 2.11% and 0.57% in the power output, respectively. It is notable that panels B and C have been tested on different ambient conditions.

7. Future work

1. The typical thermal characteristics of PCM used in cylindrical tubes can be further investigated for the charging and discharging processes.

2. The design optimisation of the novel bracket stand with fin geometry will result in a much better way.

3. The heat transfer characteristics and angle of tubes can be studied for accurate results.

4. The effects of wind velocity on the cooling of PV panel especially from the back surface integrated with PCM tubes.

5. Failure analysis of PV under the high tensile load of thermal attachment.

Acknowledgements

The valuable support of Dr Abhishek Saxena (Co-PI of this project) is highly appreciable.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Dr. A.P.J. Abdul Kalam University, Lucknow (India), under the Visvesarriya research promotion scheme [grant number Dr.APJAKTU/DeanPGSR/2017/4236-46].