Heat Pipe-Based Cooling Enhancement for Photovoltaic Modules: Experimental and Numerical Investigation

Abstract

High temperatures in photovoltaic (PV) modules lead to the degradation of electrical efficiency. To address the challenge of reducing the temperature of photovoltaic modules and enhancing their electrical power output efficiency, a simple but efficient photovoltaic cooling system based on heat pipes (PV-HP) is introduced in this study. Through experimental and numerical investigations, this study delves into the temperature characteristics and power output performance of the PV-HP system. Orthogonal tests are conducted to discern the influence of different factors on the PV-HP system. The experimental findings indicate that the performance of the PV-HP system is superior to that of the single system without heat pipes. The numerical simulation shows the effects of system structural parameters (number of heat pipes, angle of heat pipe condensation section) on system temperature and power output performance. The numerical simulation results show that increasing the angle of the heat pipe condensation section and the number of heat pipes leads to a significant drop in system temperature and an increase in the efficiency of the photovoltaic cells.

1. Introduction

Relying solely on traditional energy sources cannot meet human needs; there is also a need to develop renewable energy sources [1]. With the emergence of solar energy technology worldwide in regions with hot weather and intense sunlight, the high temperature of photovoltaic (PV) cells has become one of the primary concerns [2]. Research indicates that approximately 9% to 12% of the sunlight incident on the surface of PV cells is directly converted into electrical energy, while the remaining approximately 80% is converted in the form of heat energy [3]. Additionally, the electricity generation efficiency of PV modules is influenced by their temperature. A temperature increases of 1 °C results in a decrease in the electricity generation efficiency of PV modules by 0.3% to 0.5% [4].

Researchers have long been interested in finding efficient cooling methods for PV panels [5]. Photovoltaic cell cooling methods can generally be categorized into active cooling [6] and passive cooling [7]. Active cooling systems require external power to operate devices such as fans or pumps, which then act on the surface of the cells to remove heat. The main forms of active cooling include forced-air cooling [8,9], water cooling [10], and nanofluid cooling [11]. Due to the use of active components, active cooling demonstrates higher heat dissipation capacity during PV cooling processes compared to passive cooling, making it more effective in improving the electrical efficiency of photovoltaic cells. Passive cooling systems do not require additional power for cooling PV panels and do not incur parasitic energy consumption [12]. The temperature of PV cells is regulated by various methods including phase change material (PCM) [13], heat pipe [14], liquid immersion [15], radiative cooling [16], etc. The aforementioned cooling techniques primarily focus on efficiently dissipating heat from PV cells. And there is extensive research exploring PV cooling systems using spectral beam-splitting technology (BSPT) [17]. By employing spectral beam-splitting filters, it is possible to selectively absorb useful solar radiation, effectively mitigating the issue of excessive temperature in PV cells [18]. Beam-splitting technology is typically utilized in concentrated PV systems. This technique, through concentrating and splitting sunlight, effectively enhances the energy utilization efficiency of PV systems [19]. Analyzing various types of cooling systems reveals that heat pipe cooling consumes no additional energy and possesses excellent thermal conductivity, effectively reducing the temperature of PV cells. Theoretical and experimental investigations have been conducted to understand the thermal performance of PV modules employing heat pipes. Alizadeh et al. [20] conducted a numerical investigation on a pump heat pipe (PHP)-based PV cooling system. The results revealed that the use of heat pipes as passive cooling mechanisms improves the yield, resulting in an 18% increase in electrical power output and a 10% reduction in payback period compared to an active water-cooled PV system. Additionally, Amri et al. [21] conducted a systematic theoretical analysis of the heat transfer process in heat pipe-based flat-plate solar collectors and determined experimentally the optimal ratio between the evaporation and condensation sections of the heat pipe. Du et al. [22] designed a system consisting of solar cells and nano-coated heat pipe plates for thermal management. Using a conjugate heat transfer model, they calculated the temperature of the solar cells and the corresponding evaporative heat flux density. The results indicated that heat pipes can provide sufficient cooling for solar cells under varying solar irradiance levels. Moradgholi et al. [23] proposed a photovoltaic/thermal (PV/T) hybrid system that utilizes heat pipes to absorb excess heat from solar PV cells and maintain isothermal conditions. During springtime, the average electricity generation of the PV/T system was found to be 5.67% higher compared to a standalone PV system. Koundinya et al. [24] utilized finned heat pipes to reduce operating temperatures. They conducted experiments on a prototype and compared the results with computational simulations. The findings indicated that employing this method can achieve a maximum temperature reduction of 13.8 K. There is a mismatch between the instantaneous presence of solar energy and the user’s energy needs, and phase change materials can store some of the energy [25]. Zhou et al. [26] proposed a new configuration for a photovoltaic–thermal management system utilizing phase change materials (PCMs) coupled with heat pipes (PV-PCM/HP). Experimental results demonstrated that the performance of the coupled PCM/HP system surpassed that of a single system. Soliman et al. [27] conducted an experimental study on the performance of concentrated solar cells using flat heat pipes for cooling. The results showed that photovoltaic cell efficiency and output power increased with an increase in the length of the heat pipe condenser and decreased as the length of the adiabatic section was reduced. Ji et al. [28] proposed a new type of heat pipe system with dual condensers and analyzed its performance under different climatic conditions. The results indicate that the system exhibits stable performance and is suitable for various climate conditions. Fu and his team [29] examined the performance of the proposed novel vacuum tube PV/T system with heat pipes through experiments and solving the system’s energy model. The results show that the new vacuum tube PV/T system can significantly reduce the photovoltaic temperature, and the overall efficiency can reach 68.44%.

Furthermore, the energy on the photovoltaic cells that is not used for electricity generation can be stored and utilized [30]. Soliman et al. [31] designed a sliding window system integrating phase change materials (PCMs) with photovoltaic cells. Through heat transfer facilitated by the phase change materials, this design not only reduces the temperature of the photovoltaic cells but also lowers the temperature of the inner walls. Meanwhile, Wang et al. [32] designed a solar energy insulation system for buildings using flat-plate heat pipes and phase change materials (PCMs). Their results indicate that increasing the tilt angle of the flat-plate heat pipe condensation section prolongs the complete melting time of the PCM. Ji et al. [28] conducted simulation analyses of a heat pipe PV/T system operation in various regions during summer and winter. The results indicate that in the summer heating water mode, the system can heat water from 25 °C to 46.1 °C. In winter heating mode for colder regions, the average air outlet temperature at the condensation section can reach 17.4 °C.

Based on the existing literature review, using heat pipes for photovoltaic (PV) cooling combined with forced-air cooling can effectively and rapidly reduce the temperature of PV cells. However, the anti-gravity performance of heat pipes directly affects their heat transfer efficiency. Therefore, this study integrates heat pipes with good anti-gravity performance with PV modules to design the PV-HP system, allowing PV modules to be installed at any angle and thereby expanding their range of applications. Additionally, an experimental testing system was constructed, and performance experiments were conducted to validate the superiority of the proposed system. Furthermore, simulation studies were carried out to analyze the impact of system structural parameters on system performance.

2. Experimental Setup

The schematic diagram of the PV-HP module is illustrated in Figure 1. The system mainly consists of a glass cover, PV layer, thermal conductive silicone layer, aluminum absorber plate, insulation cotton, and heat pipes. The heat pipes are adhered to the back of the PV modules with high-temperature resistant thermal conductive silicone grease and aluminum absorber plate, ensuring tight contact between the evaporation section of the heat pipe and the absorber plate. Additionally, insulation cotton is applied to the back of the photovoltaic panel, while the condensation section protrudes from the side of the panel to exchange heat with the surrounding environment.

The operating principle of the entire system is as follows: Solar energy absorbed by the PV modules is converted into heat, which is then transferred to the evaporation of the heat pipes. The heat is further transferred through the phase change of the working fluid inside the heat pipes, ultimately reaching the condensation of the heat pipes.

2.1. Experimental Setup

The experimental setup includes photovoltaic modules with dimensions of length = 1080 mm, width = 450 mm, and thickness = 30 mm. Additionally, to demonstrate the superiority of the established PV cooling system in temperature control and efficiency enhancement, a comparative experiment has been conducted using a PV module of the same size as a reference. Figure 2 depicts the schematic diagram of the PV-HP system. The main parameters of the PV-HP modules are listed in

Table 1. Major parameters of the PV-HP module.

Component	Parameter	Value
PV module	Maximum power	100 W
	Voltage at maximum power	17.10 V
	Current at maximum power	5.85 A
	Size	1080 mm × 450 mm
	Effective PV cell area	0.398 m2
Heat pipe	Size	600 mm × 15 mm × 1.5 mm
	Condensation	150 mm
	Evaporation	400 mm
	Insulation	50 mm
	Max heat transfer power	60 W
	Average heat transfer thermal resistance	0.07 °C/W
Heat-absorbing plate	Thickness	0.5 mm
Silicone	Average thickness	0.4 mm
Thermal insulation cotton	Thickness	30 mm
	Thermal conductivity	0.074 W/(m·°C)

. The heat pipes are constructed of copper, with pure water serving as the internal working fluid. The cross-sectional dimensions of the heat pipes are 15 mm × 1.5 mm. The lengths of the evaporation section, condensation section, and adiabatic section of the heat pipes are 400 mm, 150 mm, and 50 mm, respectively. This heat pipe exhibits a thermal resistance of less than 0.1 °C/W, indicating high efficiency in thermal conduction.

The experiment was conducted in the Changchun area, Northeast China, with the performance testing period from 10:00 to 16:00 under clear to partly cloudy weather conditions. An experimental test system for the PV-HP module was constructed outdoors, as shown in Figure 3. Measurements in the experimental setup primarily include temperature, electrical power, and environmental parameters, with all data being transmitted to a computer for processing.

Temperature measurements were conducted using K-type thermocouples, which respectively record the temperature data of the PV modules’ surface and the heat pipes data, and the data were collected by a data logger. The measurement positions of the thermocouples are shown in Figure 4. Additionally, temperature cloud maps of the PV modules were generated by infrared camera. The I-V recorder was used to record the power generation status of the photovoltaic cells. The solar radiation received by the solar cells was recorded by a pyranometer, while the wind speed was recorded by a radiation detector. Using 5 identical cooling fans for air cooling, each fan has a power of 3.6 W, and the power supply for fans is provided separately. The parameters of the measuring instruments are listed in

Table 2. Parameters of the measuring instruments.

Apparatus	Type	Measured Data	Measurement Range	Measurement Error
Thermocouple	ZW-K	Temperature	0–200 °C	±0.2 °C
I-V recorder	SZCW-DW-81	Current	0.999–9.999 A	≤±1 mA
		Voltage	9.999–600 V	≤±1 V
Radiation detector	SANPO-ST8916	Solar radiation	0.1–1999.9 W/m2	±5 W/m2
Anemometer	SMART-VT110	Wind speed	0.15–30 m/s	±3%
Data collector	MEACON-MIK-R8000D	-	-	-

.

2.2. Experimental Results

2.2.1. Performance Comparison of Experiment Results

To investigate the overall daily performance of the PV-HP system, an outdoor experimental test was conducted on 10 June 2023, from 10:00 to 16:00. The experiment utilized a PV without cooling as the reference (PV-ref). The PV-HP system was set at an inclination angle of 40°. The solar irradiance and ambient temperature variations throughout the day are depicted in Figure 5a. On the experimental day, solar irradiance exhibited significant fluctuations between 11:30 and 12:30, with minor fluctuations during the remaining time periods. The maximum irradiance recorded was 937.12 W/m², with an average of 591.79 W/m², and irradiance levels above 650 W/m² accounted for 50% of the total. Additionally, ambient temperature fluctuated within normal ranges, generally exhibiting an upward trend followed by a decline. The average temperature during the experimental period was 30.75 °C.

According to the curves depicted in Figure 5b, due to the thermal management effect of the heat pipes on the PV modules, the surface average temperature of the PV modules T_(PV-HP) is lower compared to T_(PV-ref). The temperature difference between them fluctuated within the range of 3 to 10 °C. The maximum value of T_(PV-HP) recorded on the surface was 58.58 °C, with an average value of 45.32 °C. Conversely, the maximum value of T_(PV-ref) observed on the PV module surface was 65.28 °C, with an average value of 52.79 °C. Throughout the entire experimental period, the average temperature difference between the two PV modules was 5.47 °C, representing a relative decrease in temperature of 10.36%. This reduction in temperature is equivalent to a potential increase in the theoretical power generation efficiency of the photovoltaic cells by 2.81%.

Figure 5c depicts the daily variation curves of the PV power (P_(PV-HP) and P_(PV-ref)). Due to the cooling effect of the heat pipes, the surface temperature of the PV modules in the PV-HP system is lower, resulting in an increase in power output during system operation. Throughout the entire experimental phase, the maximum value of the P_(PV-HP) was recorded as 35.78 W, with an average value of 27.6 W. In comparison, the maximum value of P_(PV-ref) was 32.75 W, with an average of 25.29 W. The maximum difference between the P_(PV-HP) and P_(PV-ref) was 5.24 W, with an average difference of 2.31 W. Instances where the power difference exceeded 2.5 watts accounted for 41.67% of the entire phase. The photovoltaic power output of the PV-HP system was thus 9.13% higher compared to the PV-ref.

2.2.2. Impact of Air Cooling on the Performance of the PV-HP System

To investigate the impact of activating air cooling on the PV-HP system, an experiment was conducted on 2 September 2023, lasting 180 min. The experiment comprised two phases: the first 90 min without air cooling and the subsequent 90 min with air cooling (wind speed of the fan is 2.1 m/s). According to the variation curves of the PV modules surface temperature shown in Figure 6a, during the initial 0–90 min period, there was a significant difference between the values of the T_(PV-HP) and T_(PV-ref), with a maximum difference of 6.56 °C and an average temperature difference of 4.74 °C. Following the activation of air cooling during the 90–113 min period, both T_(PV-HP) and T_(PV-ref) rapidly decreased to their lowest points. Between 113 and 130 min, both of them experienced a slight rise, and from 130 to 180 min, the values of T_(PV-HP) and T_(PV-ref) fluctuated in response to variations in solar irradiance. After turning on the fan for 90–180 min, the average temperature difference between T_(PV-HP) and T_(PV-ref) was 1.42 °C, lower than the period before turning on the fan. This discrepancy can be attributed to structural factors. Specifically, the condensing section of the heat pipe is less affected by wind speed, resulting in smaller differences in cooling rates between the two temperatures.

Figure 6b shows the power variation of two PV modules. During the experiment, there were significant fluctuations in power generation at approximately the 33rd, 70th, and 150th minutes due to brief cloud cover. In the first 90 min of the experiment, the maximum value difference between P_(PV-HP) and P_(PV-ref) was 4.63 W, with an average difference of 2.49 W. The PV-HP exhibited a 10.15% improvement in power generation efficiency compared to the PV-ref. Between the 90th and 115th minutes, the addition of air cooling resulted in an improvement in power output; both PV-HP and PV-ref quickly reached their peak power output levels at the 103rd minute, and then fluctuated mainly in response to changes in solar radiation from the 120th minute until the end of the 180 min experiment. In the latter 90 min, the power generation efficiency of PV-HP was, on average, 5.36% higher than that of PV-ref.

Figure 6c indicates the temperatures of the evaporation and condensation sections (T_(HPV) and T_(HPC)) of the four heat pipes (as shown in Figure 2). It can be observed that the trends in temperature variation among the curves are consistent, and the differences are relatively small. After activating the air cooling, both T_(HPV) (1,2,3,4) and T_(HPC) (1,2,3,4) decreased rapidly. Between the 90th and 114th minutes, the temperatures of each evaporation and condensation section decreased to their lowest points at a relatively high rate. The average value differences between the T_(HPV) and T_(HPC) (1,2,3,4) were less than 1.8 K, indicating that the heat transfer capability of the heat pipes is good, and heat can effectively transfer from the evaporation sections to the condensation sections.

2.2.3. Impact of Angle of HPC on the Performance of the PV-HP System

The thermal conductivity of a gravity heat pipe is influenced by gravity. Tilting the heat pipe at a certain angle relative to the ground will facilitate the return of liquid working fluid at the condensation section, thereby accelerating heat transfer. In this study, the photovoltaic cells were placed horizontally, and only the condensation section of the heat pipe was bent at a certain angle to simplify the system. Additionally, to avoid damage to the outer wall of the heat pipe due to repeated bending, during the experiment, the condensation section of the heat pipe was bent to 30° in one step, while other angles (10°, 20°) were simulated through computational modeling, as shown in Figure 7.

The experiment was conducted from 11:00 to 14:00 on 11 September 2023. The temperature curves of PV-HP and PV-ref are shown in Figure 8a. In the first 90 min of the experiment, the maximum value difference between T_(PV-HP) and T_(PV-ref) was 4.27 °C, with an average difference of 2.8 °C. Between 90 and 115 min, T_(PV-HP) and T_(PV-ref) gradually decreased; from the 115th minute to the 180th minute, there were fluctuations in solar radiation, causing changes in T_(PV-HP) and T_(PV-ref). In the second 90 min, the maximum temperature difference between the two was 7.25 °C, with an average difference of 3.91 °C, compared to the first 90 min, there was an increase in the average temperature difference between T_(PV-HP) and T_(PV-ref). This increase is attributed to setting the condensing section to 30°, which allowed the airflow from the fan to not only affect the surface of the PV modules but also the condensation section of the heat pipes. The cooling effect of the airflow accelerated the phase change heat transfer within the pipes, facilitating better heat dissipation from the condensation section of the heat pipes.

Figure 8b illustrates the power variation between the PV-HP and the PV-ref when the angle of the condensation sections of the heat pipe are set to 30°. Between 0 and 90 min, air cooling was not employed, and the values of both P_(PV-HP) and P_(PV-ref) mainly followed variations in solar radiation, and P_(PV-HP) was 5.25% higher than P_(PV-ref). After activating the air cooling at the 90th minute, the temperature of the PV modules decreased, leading to an improvement in PV power output. P_(PV-HP) and P_(PV-ref) reached their maximum values at the 117th minute. Subsequently, as solar radiation fluctuated, PV power also began to fluctuate and decrease from the 117th minute to the 180th minute. During the period from 90 to 180 min, P_(PV-HP) was 6% higher than P_(PV-ref).

The temperature variation curves of the HPCs and HPVs are shown in Figure 8c. The trends in values of both T_(HPC) and T_(HPV) (1,2,3,4) remained consistent with the surface temperature variation trend of the PV modules. Within the period of 90 to 118 min after the implementation of air cooling, their values gradually decrease and reach their lowest point around 118 min.

Comparative analysis between Figure 6a and Figure 8a revealed that with the use of air cooling, different variations are observed in the temperature difference between T_(PV-HP) and T_(PV-ref). These differences are summarized in

Table 3. Average difference between T_(PV-HP) and T_(PV-ref).

Average Difference between T(PV-HP) and T(PV-ref)	Before Using Air Cooling	After Using Air Cooling
At 0° of HPCs	4.75 °C	1.42 °C
At 30° of HPCs	2.80 °C	3.91 °C

.

2.3. Analysis of Experimental Errors

Inevitable errors may occur during the experimental process, so it is necessary to assess whether the experimental errors are within a reasonable range. The following equations are used to determine the errors [33]:

$$R_I={({\displaystyle \frac{W_I^2}{3}})}^{0.5}$$

(1)

$$R_E={\displaystyle \frac{dy}{y}}={\displaystyle \frac{\partial f}{\partial x_1}}{\displaystyle \frac{d{x}_1}{y}}+{\displaystyle \frac{\partial f}{\partial x_2}}{\displaystyle \frac{d{x}_2}{y}}+\dots +{\displaystyle \frac{\partial f}{\partial x_n}}{\displaystyle \frac{d{x}_n}{y}}$$

(2)

$$R_{ME}={\displaystyle \frac{{\displaystyle {\sum }_1^N\left|R_E\right|}}{N}}$$

(3)

where $R_I$ means the error of directly measurable physical quantity; $W_I$ is the accuracy of the measuring instrument; $R_E$ is the error of indirectly measurable physical quantity; $x_i(i=1,2,3,\dots ,n)$, the directly measurable physical quantities that cause errors in indirectly measurable physical quantities; ${\displaystyle \frac{\partial f}{\partial x_i}}(i=1,2,3,\dots ,n)$, error transmission coefficient of directly measurable physical quantities; $R_{ME}$ is relative average error.

According to the above formulas, the relative average errors for the photocurrent and the photovoltaic efficiency are calculated to be 3.51% and 4.12%, respectively.

3. Numerical Modeling

Due to constraints such as experimental time, equipment, and environmental conditions, it is not possible to comprehensively experimentally study all factors of the PV-HP system. Therefore, the operational characteristics of the PV-HP system using simulation methods have been chosen for investigation. In this study, a physical model and a mathematical model based on the constructed PV-HP experimental system have been developed. Figure 9 depicts a cross-sectional schematic of the physical model.

Table 4. Thickness and thermodynamic parameters of each layer of the PV-HP [34].

Component	Thickness (mm)	Conductivity (W/(m·°C))	Density (kg/m3)	Specific Heat (J/(kg·°C))
Glass	3.2	1.15	2200	830
PV	0.5	168.00	2330	757
Silicone	0.4	2.40	2000	700
Plate absorber	0.5	202.40	2719	871
Thermal insulation cotton	30	0.074	2300	381
Heat pipe	1.5	9000	8960	386

displays the main information for each layer of the PV-HP.

3.1. Mathematical Model

For the PV-HP system, the following assumptions are made to facilitate numerical analysis:

• Solar light incidence is perpendicular to the surface of the photovoltaic panel.
• Photovoltaic assembly considers only the glass cover and the cell layer, which are closely integrated, neglecting any contact thermal resistance.
• The aluminum frame is not considered, only the effective generating area is taken into account.
• Thermal insulation cotton provides effective insulation, and there are no additional heat losses in the system.
• Temperature distribution in the evaporation section of the heat pipe is uniform, disregarding any longitudinal heat conduction.

Based on the aforementioned assumptions, the energy transfer model for the PV-HP system is as follows [28]:

For glass cover

$${\rho }_g{c}_g{\sigma }_g{\displaystyle \frac{{\partial }_{Tg}}{{\partial }_t}}=h_a(T_a-T_g)+h_{sky}(T_{sky}-T_g)+h_{g,PV}(T_{PV}-T_g)+G{\alpha }_g$$

(4)

where ${\rho }_g$ is the density of glass, ${\mathrm{kg}/\mathrm{m}}^3$; $c_g$ is the specific heat capacity of glass (J/(kg·°C)), ${\sigma }_g$ is the thickness of glass, m; $T_a$ is the ambient temperature, °C; $T_{sky}$ is the temperature of sky, °C, $T_{sky}=0.0552T_a^{1.5}$; $T_g$ is the temperature of glass, °C; $T_{PV}$ is the temperature of PV, °C; $G$ is the solar radiation, ${\mathrm{W}/\mathrm{m}}^2$; ${\alpha }_g$ is the absorptivity of glass, 0.04; $h_a$ is the heat transfer coefficient between glass and the ambient environment; $h_{sky}$ is the heat transfer coefficient between glass and the sky; $h_{g,PV}$ is the heat transfer coefficient between glass and the PV, (W/(m²·°C)).

$h_a$, $h_{sky}$, $h_{g,PV}$ can be calculated using the following formula:

$$h_a=2.8+3.8v$$

(5)

$$h_{sky}={\epsilon }_g\sigma (T_{sky}^2+T_g^2)(T_{sky}+T_g)$$

(6)

$$h_{g,PV}=\sigma (T_{PV}^2+T_g^2)(T_{PV}+T_g)$$

(7)

where $v$ is the wind speed, m/s; ${\epsilon }_g$ is the emissivity of the glass, 0.85; σ is the Stephen Boltzmann constant.

For the PV module

To simplify calculations, photovoltaic (PV) cells are assumed to be uniform and homogeneous. Materials such as Tedlar, EVA, PET, etc., within the PV module are not considered. Using an overall modeling approach to derive the energy balance equation for the PV panel, as follows:

$${\rho }_{PV}{c}_{PV}{\sigma }_{PV}{\displaystyle \frac{{\partial }_{T_{PV}}}{\partial t}}=h_{g,PV}(T_g-T_{PV})+G\tau {\alpha }_{PV}+{\displaystyle \frac{(T_{al}-T_{PV})}{R_{si}}}-E_{PV}$$

(8)

where ${\rho }_{PV}$ is the density of PV, ${\mathrm{kg}/\mathrm{m}}^3$; $c_{PV}$ is the specific heat capacity of PV, (J/(kg·°C)); ${\sigma }_{PV}$ is the thickness of PV, m; $T_{al}$ is the temperature of plate absorber, °C; $R_{si}$ is the thermal resistance of silicone, (m²·°C)/W; $E_{PV}$ is the electric power of the PV cell, can be calculated using the following formula:

$$E_{PV}=G\tau {\alpha }_{PV}{\eta }_{PV}$$

(9)

where $\tau$ is the transmissivity of glass, 0.91; ${\alpha }_{PV}$ is the absorptivity of the photovoltaic panel to solar radiation, 0.9; ${\eta }_{PV}$ is the PV’s photoelectric conversion efficiency, has a linear relationship with the temperature of the photovoltaic panel as follows:

$${\eta }_{PV}=\eta (1-0.0045(T_{PV}-25))$$

(10)

where $\eta$ is the photoelectric conversion efficiency of the photovoltaic cell under standard conditions ($T_{PV}$ = 25 °C, G = 1000 W/m²), assumed to be 0.15 in this paper.

For the plate absorber

$${\rho }_{al}{c}_{al}{\sigma }_{al}{\displaystyle \frac{{\partial }_{al}}{{\partial }_t}}={\displaystyle \frac{(T_{PV}-T_{al})}{R_{si}}}+(1-\beta )h_{al,a}(T_a-T_{al})+\beta {\displaystyle \frac{(T_{Heva}-T_{al})}{R_{si}}}$$

(11)

where ${\rho }_{al}$ is the density of the plate absorber, ${\mathrm{kg}/\mathrm{m}}^3$; $c_{al}$ is the specific heat capacity of the plate absorber, (J/(kg·°C)); ${\sigma }_{al}$ is the thickness of the plate absorber, m; $\beta$ is the ratio of the evaporator area of the heat pipe to the area of the photovoltaic backplane; $T_{Heva}$ is the temperature of the heat pipe evaporator, °C; $h_{al,a}$ is the heat transfer coefficient between the absorber plate and the surrounding environment, being calculated by the following formula:

$$h_{al,a}={\displaystyle \frac{1}{\frac{{\kappa }_s}{{\lambda }_s}+\frac{1}{h_s}}}$$

(12)

where ${\lambda }_s$ is the thickness of thermal insulation cotton, m; ${\kappa }_s$ is thermal conductivity of insulation cotton, W/(m·°C); $h_s$ is the surface convective heat transfer coefficient between insulation cotton and air, W/(m·°C).

For the heat pipe

This paper simplifies the energy transfer of heat pipes, disregarding internal phase changes and wall thermal resistance.

$${\rho }_{Heva}{c}_{Heva}{\sigma }_{Heva}{\displaystyle \frac{{\partial }_{T_{Heva}}}{{\partial }_t}}={\displaystyle \frac{(T_{Hcon}-T_{Heva})}{R_{eva,con}}}+\beta {\displaystyle \frac{(T_{al}-T_{Heva})}{R_{si}}}+\beta h_{Heva,a}(T_a-T_{Heva})$$

(13)

where ${\rho }_{Heva}$ is the density of the heat pipe evaporator, ${\mathrm{kg}/\mathrm{m}}^3$; $c_{Heva}$ is the specific heat capacity of heat pipe evaporation, (J/(kg·°C)); ${\sigma }_{Heva}$ is the thickness of heat pipe evaporation, m; $R_{eva,con}$ is thermal resistance between the evaporator section and the condenser section of the heat pipe, (m²·°C)/W; $T_{Hcon}$ is the temperature of the heat pipe condensation, °C; $h_{Heva,a}$ is the overall heat transfer coefficient between the evaporator section of the heat pipe and the air, being calculated by using following equations:

$$h_{Heva,a}={\displaystyle \frac{1}{\frac{{\kappa }_h}{{\lambda }_h}+\frac{{\kappa }_s}{{\lambda }_s}+\frac{1}{h_s}}}$$

(14)

where ${\kappa }_h$, ${\lambda }_h$ are the thickness (m), and thermal conductivity (W/(m·°C)), respectively, of the heat pipe.

$${\rho }_{Hcon}{c}_{Hcon}{\sigma }_{Hcon}{\displaystyle \frac{{\partial }_{T_{Hcon}}}{{\partial }_t}}={\displaystyle \frac{(T_{Heva}-T_{Hcon})}{R_{eva,con}}}+\theta h_{Hcon,a}(T_a-T_{Hcon})$$

(15)

where ${\rho }_{Hcon}$ is the density of heat pipe condensation; $c_{Hcon}$ is the specific heat capacity of heat pipe condensation, (J/(kg·°C)); ${\sigma }_{Hcon}$ is the thickness of heat pipe condensation, m; $h_{Hcon,a}$ is the overall heat transfer coefficient between the condensation section of the heat pipe and the air, being calculated by Equation (16).

$$h_{Hcon,a}={\displaystyle \frac{1}{\frac{{\kappa }_h}{{\lambda }_h}+\frac{1}{h}}}$$

(16)

Some important parameters and their values used in the mathematical model are shown in

Table 5. Some major parameters used in the mathematical model.

Parameters		Value	Unit
	Absorptivity	0.04	——
Glass	Emissivity	0.85	——
	Transmissivity	0.91	——
PV	Absorptivity	0.9	——
Solar radiation intensity		800	W/m2
Ambient temperature		26.85	°C
Wind speed		2	m/s
Sky temperature		7.68	°C

.

3.2. System Performance

The photovoltaic–electric (PV-HP) system’s photovoltaic efficiency is defined as the ratio of the electricity generated by the photovoltaic panel to the total solar radiation received by the photovoltaic panel, and the equation is:

$${\eta }_{PV}={\displaystyle \frac{UI}{GA}}$$

(17)

where $U$ is the PV’s output voltage, V, and $I$ is its output current, A; $A$ is the photovoltaic cell area, m².

3.3. Solution Methods

This study simplifies the boundary conditions used in the simulation as follows: (1) The PV-HP assembly is axisymmetric along the length and width direction. (2) Radiative heat transfer is not considered. (3) Good connections between different materials are assumed, and contact thermal resistance is ignored. The boundary conditions are set as shown in Figure 10.

The use of a User-Defined Function (UDF) to describe the PV module surface’s photovoltaic conversion and heat transfer processes was proposed. During the simulation, the phase change heat transfer process inside the heat pipes was not considered. Based on the high thermal conductivity of the heat pipe, it would be treated as a high-conductivity solid entity. The equivalent thermal conductivity coefficient was obtained from the theoretical formula provided in reference [35], set to 9000 W/(m·°C) in this study.

The simulation was conducted on the ANSYS 2022 platform. It employed a pressure-based segregated implicit solver for steady-state numerical calculations. Absolute velocity is used during the computation, and a coupled algorithm was employed for pressure–velocity coupling iterative calculations. Second-order upwind schemes were utilized for the momentum equation, turbulent kinetic energy equation, and turbulent dissipation rate equation to enhance computational accuracy. The convergence criterion for the energy equation was set to 10⁻⁶, while for the momentum equation, continuity equation, k equation, and epsilon equation, were set to 10⁻⁴. Additionally, monitoring was performed on the average temperature and heat transfer rate on the surface of the PV.

The number of grids can affect the simulation results, and the average temperature of the PV surface was selected as the evaluation criterion for grid independence verification. The average temperature of the photovoltaic surface was calculated under the same conditions (8 heat pipes, wind speed = 2 m/s, ambient temperature = 26.85 °C, solar radiation intensity = 800 W/m²) with different numbers of grids. The results are shown in

Table 6. Effect of number of grids on simulation results.

No.	Number of Grids	Average PV Surface Temperature (°C)	|Ni+1 − Ni|
1	1,422,483	64.344	-
2	2,260,992	64.439	0.085 °C
3	3,189,463	64.447	0.008 °C
4	5,321,532	64.449	0.002 °C
5	10,572,064	64.446	0.003 °C

. Comparing the results of the third calculation with the fourth and fifth calculations, the temperature error values vary between 0.002 and 0.008 °C. Considering both computational accuracy and computing resources, a model with 3,189,463 grids was selected for further numerical research.

3.4. Validation of the Numerical Model

This study validated the accuracy of the simulation model. The data on September 10th were used for the simulation. The average values within each ten-minute interval of each stage were extracted and utilized as the boundary conditions for the simulation. Figure 11 compares the simulated temperature distribution with the actual temperature distribution, showing a close resemblance.

Table 7. Errors between experimental and simulated PV temperatures.

Time	Average Solar Radiation (W/m2)	Average Ambient Temperature (°C)	Average Temperature (Exp) (°C)	Average Temperature (Sim) (°C)	Average Errors (%)
10:55–11:05	869.46	30.14	57.32	62.2	8.56%
11:25–11:35	687.52	30.11	45.65	48.77	6.19%
11:55–12:05	420.15	30.65	44.15	46.27	4.87%
12:25–12:35	852.17	31.46	53.41	57.76	8.35%
12:55–13:05	735.55	31.73	50.68	52.56	6.57%
13:25–13:35	668.37	30.97	50.26	53.72	6.85%
13:55–14:05	334.08	30.14	43.02	44.14	4.70%
14:25–14:35	404.99	30.08	43.89	46.16	5.37%
14:55–15:05	447.37	29.64	45.32	47.53	4.46%
15:25–15:35	398.74	29.12	44.74	46.98	5.23%

shows the differences between the simulated values and the experimental values, with errors ranging from about 4% to 9%.

4. Results and Discussion

4.1. The Effect of Number of HP

Figure 12 represents the computational fluid dynamics (CFD) simulation surface cloud map of the PV module under conditions (solar radiation = 800 W/m²; ambient temperature = 26.85 °C; inlet velocity = 2 m/s; The number of heat pipes (N_(HP)), N_(HP) = 8,10,12,14). N_(HP) increased from 8 to 14 pcs, resulting in a decrease of 4.09 °C in the surface average temperature of the PV module. Meanwhile, the average temperature difference between the evaporation and condensation sections of the heat pipes decreased from 5.19 °C to 4.64 °C, as shown in Figure 13a. The reason for the reduction in the temperature difference between evaporation and condensation is that with the increase in the number of heat pipes, the heat transfer per individual heat pipe decreases. Consequently, each heat pipe transfers heat at a lower rate, leading to a decrease in the temperature difference between evaporation and condensation.

Figure 13b indicates that the increase in N_(HP) from 8 to 14 pcs resulted in the system’s photovoltaic power and efficiency increasing from 39.48 W to 40.76 W and from 12.34% to 12.74%, respectively, marking a 3.24% improvement in photovoltaic efficiency. This enhancement stems from the fact that under the same solar radiation conditions, the energy input to the system remained constant. However, the increase in N_(HP) allowed unconverted solar energy to be transferred more rapidly to the surroundings via the heat pipes. Consequently, the temperature of the PV modules decreased, leading to improved electricity generation efficiency and power.

4.2. Effect of Angle of Condensation

Figure 14 represents the CFD simulation surface cloud map of the PV module under conditions (solar radiation = 800 W/m²; ambient temperature = 26.85 °C; inlet velocity = 2 m/s; the angle of the condensation (An_(HPC)), An_(HPC) = 0, 10, 20, 30). Figure 15a shows that as An_(HPC) increases from 0° to 30°, the temperature of the PV modules decreased from 65.47 °C to 61.34 °C, with a temperature decrease of 4.13 °C. As the An_(HPC) increased, the heat pipes’ heat transfer capability were improved. Simultaneously, the average temperature difference between the evaporation and condensation sections of the heat pipes increased from 3.7 °C to 5.34 °C. This phenomenon occurred because the heat transfer capability of the heat pipes improves, resulting in an increase in heat transfer power and, consequently, an increase in the average temperature difference between the evaporation and condensation sections of the heat pipes.

The increase in the An_(HPC) coincided with a synchronous increase in the PV-HP system’s output power and efficiency, shown as Figure 15b. As the An_(HPC) increased from 0° to 30°, the photovoltaic power and efficiency increased from 39.04 W to 39.93 W and from 12.27% to 12.55%, respectively. This results in a 2.28% improvement in the PV module’s power output efficiency.

4.3. Comparative Analysis

To validate the performance of the PV-HP system, we compared it with the PV-PCM/HP system proposed in Reference [26]. Both this study and the literature established a PV-ref baseline. By analyzing the temperature difference between the system and PV-ref, under higher irradiance levels than those reported in Reference [26], the cooling effect of the PV-HP system surpasses that of the PV-PCM/HP system. Furthermore, the maximum temperature of the PV-HP system reached 58.58 °C, whereas in Reference [26], it was 66.85 °C. However, when comparing the performance after incorporating air cooling, the cooling system in the Reference [36] used more heat pipes, resulting in better cooling performance than the PV-HP system. In Reference [23], researchers added an additional cooling jacket to the heat pipe PV/T system, resulting in a maximum temperature reduction of 15 °C during the summer. The overall efficiency improved by 44.38%. However, the study noted limitations in power generation due to the use of low-power photovoltaic cells (20 W).

Based on the research from relevant literature, the thermal performance of existing heat pipe PV/T systems is briefly summarized. In Reference [28], the heat pipe extracts heat from a 200 W photovoltaic cell to heat 150 L of water from 25 °C to 46.1 °C. the overall efficiency in summer can reach 60.6% and in winter reaches 55.4%. In Reference [36], heat from the PV cells (365 W) is dissipated using a fan. The system achieves an overall efficiency of 53.4% in winter. In Reference [37], adding phase change materials at the condensation section of the heat pipe can increase the overall efficiency of the heat pipe PV/T system to 56.45%. Solar energy can be used in other forms. Compared with the PV-HP system, a solar air heater has a higher thermal energy utilization efficiency but is at a disadvantage in electricity generation [30].

5. Conclusions

This study proposes a novel heat pipe-based PV cooling system and experimentally verifies its performance. In order to investigate the effect of the number of heat pipes and the inclination angle of the condensing section of the heat pipes on the performance of the system, three-dimensional CFD simulations are performed. The main conclusions of this study are as follows:

(1)

The experimental findings’ performance comparison indicates that the temperature of photovoltaic cells mainly fluctuates with solar radiation intensity. The use of heat pipes effectively reduces the temperature of photovoltaic cells, with a temperature difference of 5.47 °C between the PV-HP system and the reference photovoltaic cells, representing a temperature decrease of 10.36%. The PV-HP system increases its average output power by 9.13% when compared to the reference photovoltaic cells. The findings emphasize the PV-HP system’s significant effectiveness in temperature control and efficiency improvement.

(2)

The performance of PV-HP with reference PV cells after adding air cooling is analyzed comparatively. When the fan was turned on for 13 min, the temperature of the PV-HP was reduced from 51.28 °C to 43.16 °C, and its power was increased by 10.15%. Furthermore, the fan’s activation reduced the average temperature difference between PV-HP and PV-ref from 4.75 °C to 1.42 °C. The air-cooling contributes positively when An_(HPC) is zero.

(3)

The effect of the heat pipe condensing section angle of 30° on the performance of PV-HP was analyzed. The experimental results reveal that when the An_(HPC) is 30°, the average surface temperature difference between the PV-HP and the PV-ref rises from 2.8 °C before the fan turns on to 3.91 °C after the fan turns on. This means that adjusting the inclination angle can help the heat be transferred more effectively.

(4)

The N_(HP) has decreased from 8 to 4, resulting in an average temperature reduction of PV cells from 64.45 °C to 58.54 °C, while the PV efficiency has increased from 12.34% to 12.74%. Meanwhile, the An_(HPC) increased from 0° to 30°, reducing the average temperature of PV cells from 65.47 °C to 61.34 °C and increasing PV efficiency from 12.27% to 12.55%. When the number of heat pipes is 14 and the inclination angle of the condensation section of the heat pipe is 30 °C, the PV-HP system achieves its maximum photovoltaic power output. However, increasing the number of heat pipes increases the cost.

(5)

The heat pipe can combine with other working fluids to collect and utilize the heat from PV cells. This paper did not collect heat through the condensation section of the heat pipe; future research could explore this aspect to enhance energy utilization efficiency.