Performance analysis of tilted photovoltaic system integrated with phase change material under varying operating conditions

doi:10.1016/j.energy.2017.05.150

Energy 能源

Volume 133, 15 August 2017, Pages 887-899
第 133 卷，2017 年 8 月 15 日，第 887-899 页

https://doi.org/10.1016/j.energy.2017.05.150 Get rights and content 获取权利和内容

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Highlights 亮点

• -
PV temperature can be reduced by 19 °C by using phase change material.
通过使用相变材料，光伏温度可降低 19 °C。
• -
Effects of operating conditions on the performance of system are analysed.
分析了运行条件对系统性能的影响。
• -
Increase in tilt of system leads to increase in rate of heat extraction by PCM.
系统倾斜度的增加会导致 PCM 热量提取率的增加。

Abstract 摘要

In photovoltaic (PV) cells, a large fraction of solar radiation gets converted into heat which raises its temperature and decreases its efficiency. The heat can be extracted by attaching a box containing phase change material (PCM) behind the PV panel. Due to large latent heat of PCM, it can absorb heat without rise in temperature. It will lower down the PV temperature and will increase its efficiency. The available numerical studies analysed the vertical PV-PCM systems. However, PV panels are generally tilted according to latitude of the place. Thus, in the current work, performance analysis of the tilted PV-PCM is carried out. The effects of tilt-angle, wind-direction, wind-velocity, ambient-temperature and melting-temperature of PCM on the rate of heat extraction by PCM, melting process of PCM and temperature of PV-PCM system are also studied. The results show that as tilt-angle increases from 0° to 90°, the PV temperature (in PV-PCM system) decreases from 43.4 °C to 34.5 °C which leads to increase in PV efficiency from 18.1% to 19%. The comparison of PV-PCM with only-PV is also carried out and it is found that PV temperature can be reduced by 19 °C by using PCM and efficiency can be improved from 17.1% to 19%.
在光伏（PV）电池中，大部分太阳辐射会转化为热量，从而使其温度升高，效率降低。可以在光伏电池板后面安装一个装有相变材料（PCM）的盒子来提取热量。由于 PCM 的潜热大，它可以在不升温的情况下吸收热量。这将降低光伏温度并提高其效率。现有的数值研究分析了垂直 PV-PCM 系统。然而，光伏电池板通常会根据当地的纬度而倾斜。因此，本研究对倾斜式 PV-PCM 进行了性能分析。还研究了倾斜角度、风向、风速、环境温度和 PCM 熔化温度对 PCM 热量提取率、PCM 熔化过程和 PV-PCM 系统温度的影响。结果表明，随着倾斜角度从 0°增加到 90°，光伏温度（在 PV-PCM 系统中）从 43.4 ° C 降至 34.5 °C，从而使光伏效率从 18.1% 提高到 19%。此外，还对 PV-PCM 和单纯 PV 进行了比较，发现使用 PCM 后，PV 温度可降低 19 °C，效率可从 17.1% 提高到 19%。

Keywords 关键词

Phase change material

Photovoltaic

Thermal management

相变材料光伏热管理

Nomenclature 术语

liquid fraction of PCM PCM 的液体分量

C_p

specific heat capacity (J/kgK)
比热容（J/kgK）

Dirac delta function 狄拉克三角函数

view factor between surfaces
面间视角系数

acceleration due to gravity (m²/s)
重力加速度（m ² /s）。

heat generation (W/m³)
发热量 (W/m ³ )

Grashof number 格拉肖夫数

convective heat transfer coefficient (W/m²K)
对流传热系数（W/m ² K）

I_T 我 _T

solar radiation on tilted surface (W/m²)
倾斜表面上的太阳辐射（W/m ² )

thermal conductivity (W/mK)
导热系数（W/mK）

L_ch

characteristic length (m)
特征长度（米）

L_h

latent heat (J/kg) 潜热（焦耳/千克）

pressure (Pa) 压力 (Pa)

Prandtl number of air
空气的普朗特数

Q_L

rate of heat loss from the top surface (W/m²)
顶面热损失率 (W/m ² )

Re 回复

Reynolds number 雷诺数

S_h

solar radiation converted into heat (W/m²)
转化为热量的太阳辐射（W/m ² )

time (s) 时间（秒）

temperature (K) 温度（千）

T_m

peak melting temperature of PCM (K)
PCM 的峰值熔化温度（K）

velocity of melted PCM (m/s)
融化的 PCM 速度（米/秒）

v_w

wind velocity (m/s) 风速（米/秒）

Greek symbols 希腊文符号

tilt angle of the panel (rad)
面板倾斜角度（rad）

β_c b _c

thermal expansion coefficient of PCM (/K)
PCM 的热膨胀系数（/K）

wind azimuth angle i.e. the angle made by wind stream with the projection of surface normal on horizontal plane (rad)
风方位角，即风流与地表法线在水平面上的投影所成的角度（弧度）

depth of PCM container (m)
PCM 容器深度（米）

Δn

distance between successive nodes (m)
连续节点之间的距离（米）

ΔT

phase change zone (K) 相变区 (K)

emissivity for long wavelength radiation
长波辐射发射率

η_PV 的 _PV

solar radiation to electricity conversion efficiency of PV
太阳辐射到光伏发电的转换效率

dynamic viscosity of air (kg/ms)
空气动态粘度（千克/米）

kinematic viscosity of air (m²/s)
空气运动粘度（m ² /s）

density (kg/m³)
密度（千克/米 ³ )

Stefan–Boltzmann constant (W/m² K⁴)
斯特凡-玻尔兹曼常数（W/m ² K ⁴ )

(τα)_eff (ta) _eff

effective product of transmissivity of glass cover and absorptivity of solar cell
玻璃盖板透射率与太阳能电池吸收率的有效乘积

Abbreviation 缩写

BICPV

building integrated concentrated PV
光伏建筑一体化

EVA 舱外活动

ethylene vinyl acetate 乙烯-醋酸乙烯

PCM

phase change material 相变材料

photovoltaic 光伏

Subscripts 下标

ambient 环境

critical 严重

for 对于

forced convection 强制对流

ground 地面

liquid phase 液相

nat 肤色

natural convection 自然对流

sky; solid phase 天空；固相

top surface 顶面

x direction x 方向

y direction y 方向

1. Introduction 1.导言

Electricity generation using photovoltaic (PV) cells is one of the economically feasible renewable technologies. However, the PV cells convert only a fraction of the incident solar radiation into electricity. A major fraction gets converted into heat and raises the temperature of the cell. The temperature rise reduces the solar to electricity conversion efficiency of the cell [1]. The use of phase change material (PCM) for the thermal management of the PV cells by extracting the heat has been reported by some studies.
利用光伏电池发电是经济上可行的可再生技术之一。然而，光伏电池只能将部分入射太阳辐射转化为电能。大部分转化为热量，使电池温度升高。温度升高会降低电池的太阳能转换效率[1]。一些研究报告称，可以使用相变材料 (PCM) 通过提取热量对光伏电池进行热管理。

The studies presented the one-dimensional (1-d) numerical models for the PV-PCM system are as follows: Brano and his co-workers [2], [3] have presented a finite difference method for the thermal modelling of the PV-PCM system. Mahamudul et al. [4] have analysed the PV-PCM system for Malaysian whether. Smith et al. [5] have computed the power output from the PV-PCM system for countries all over the globe. Atkin and Farid [6] have analysed the thermal management of the PV using PCM infused graphite integrated with finned heat sink. Kibria et al. [7] have compared the performance of the PV-PCM using three different PCMs. Park et al. [8] have analysed the effect of the thickness of PCM layer behind the PV panel on the performance of the system. Aelenei et al. [9] have studied the building integrated PV-PCM system.
有关 PV-PCM 系统一维 (1-d) 数值模型的研究如下：Brano 和他的同事[2]、[3] 提出了 PV-PCM 系统热建模的有限差分法。Mahamudul 等人[4] 分析了马来西亚的 PV-PCM 系统是否适用。Smith 等人 [5] 计算了全球各国 PV-PCM 系统的功率输出。Atkin 和 Farid [6] 分析了使用注入石墨的 PCM 与鳍片散热器集成的光伏热管理。Kibria 等人 [7] 使用三种不同的 PCM 比较了 PV-PCM 的性能。Park 等人[8] 分析了光伏面板后 PCM 层的厚度对系统性能的影响。Aelenei 等人 [9] 研究了建筑物集成 PV-PCM 系统。

All the above numerical studies consider only the conductive energy flow inside the PCM. However, the convective energy flow inside the melted PCM has significant effect on the thermal performance of the PV-PCM system [10]. The following studies have considered it and presented the two-dimensional (2-d) thermal models. Huang et al. [11] have analysed the effect of ambient temperature, insolation and the thickness of PCM layer on the performance of the system. Huang [12] has analysed the PV temperature in the PV-PCM system considering two different PCM materials in same container. Ho et al. [13] have studied the performance of the PV system integrated with microencapsulated PCM. Biwole et al. [14] and Groulx and Biwole [15] have presented a mathematical model to capture the rapid change in the thermal properties of the PCM during phase change period.
上述所有数值研究都只考虑了 PCM 内部的传导能量流。然而，融化的 PCM 内部的对流能量流对 PV-PCM 系统的热性能有重大影响 [10]。以下研究考虑了这一点，并提出了二维 (2-d) 热模型。Huang 等人[11] 分析了环境温度、日照和 PCM 层厚度对系统性能的影响。Huang [12] 分析了 PV-PCM 系统中的 PV 温度，考虑了同一容器中两种不同的 PCM 材料。Ho 等人[13] 研究了与微胶囊 PCM 集成的光伏系统的性能。Biwole 等人 [14] 以及 Groulx 和 Biwole [15] 提出了一个数学模型，用于捕捉相变期间 PCM 热特性的快速变化。

The above studies have considered the side walls of the PCM container to be thermally insulated (using adiabatic condition). Thus, the temperature variations are considered only along the thickness and the height of the system. Thus, the 2-d analysis have been carried out by them. However, Huang et al. [16], [17] have considered the heat losses from the side walls of the container and, thus, presented the three-dimensional (3-d) analysis of the system. Ho et al. [18], [19] have presented the 3-d analysis of the PV system integrated with microencapsulated PCM considering only the conductive energy flow inside the PCM.
上述研究认为 PCM 容器的侧壁是隔热的（使用绝热条件）。因此，只考虑了系统厚度和高度的温度变化。因此，他们进行的是 2-d 分析。不过，Huang 等人[16]、[17] 考虑了容器侧壁的热损失，因此提出了系统的三维（3-d）分析。Ho 等人[18]、[19] 仅考虑了 PCM 内部的传导能量流，对集成了微胶囊 PCM 的光伏系统进行了三维分析。

Apart from the numerical modelling, the following studies have carried out the experimental investigation of the PV-PCM system. Huang et al. [20] have analysed the effect of fins on the performance of the PV-PCM system. Huang et al. [21] have studied the effect of crystalline segregation of the PCM on the performance of the system. Hasan et al. [22] have investigated the PV-PCM system using various types of PCM. Indartono et al. [23] have analysed the PV-PCM system using yellow petroleum jelly as phase change material. Hachen et al. [24] have studied the system using pure PCM (white petroleum jelly) and compared with mixed PCM (mixture of white petroleum jelly, copper and graphite). Stropnik and Stritih [25] have studied the PV integrated with RT 28 HC phase change material. Hasan et al. [26] have analysed the performance under two different climatic conditions. Sharma et al. [27] have studied the thermal management of the building integrated concentrated PV (BICPV) using PCM. Browne et al. [28], [29] have integrated a pipe network with the PV-PCM system so that water can be flowed inside the pipes to utilize the heat stored by PCM. Some review studies [30], [31], [32], [33], [34] are also available in literature on the use of PCM for the thermal management of the PV. Lamnatou and Chemisana [35] have presented a review of the studies which include environmental issues.
除数值建模外，以下研究也对 PV-PCM 系统进行了实验研究。Huang 等人[20] 分析了翅片对 PV-PCM 系统性能的影响。Huang 等人 [21] 研究了 PCM 结晶偏析对系统性能的影响。Hasan 等人[22] 研究了使用各种类型 PCM 的 PV-PCM 系统。Indartono 等人[23] 分析了使用黄色凡士林作为相变材料的 PV-PCM 系统。Hachen 等人[24] 研究了使用纯 PCM（白凡士林）的系统，并与混合 PCM（白凡士林、铜和石墨的混合物）进行了比较。Stropnik 和 Stritih [25] 研究了集成 RT 28 HC 相变材料的光伏系统。Hasan 等人 [26] 分析了两种不同气候条件下的性能。Sharma 等人 [27] 研究了使用 PCM 的建筑一体化聚光光伏 (BICPV) 的热管理。Browne 等人[28]、[29] 将管网与 PV-PCM 系统集成在一起，这样水就可以在管道内流动，从而利用 PCM 储存的热量。文献 [30]、[31]、[32]、[33]、[34] 中也有一些关于使用 PCM 进行光伏热管理的综述研究。Lamnatou 和 Chemisana [35] 综述了包括环境问题在内的研究。

From literature, it has been found out that the numerical studies are carried out for the vertical PV-PCM systems. However, the PV panels are generally tilted according to the latitude of the place. Thus, in the current work, the tilted PV-PCM system has been analysed. The mathematical model of the PV-PCM system is presented in section 2. The results obtained from the proposed model have been validated against the existing reported ones in section 3. The effects of the operating conditions (tilt angle of the system, wind direction, wind velocity, ambient temperature and melting temperature of the PCM) on the rate of heat extraction by PCM, melting process of PCM and temperature of PV-PCM system have been studied in section 4 and the only PV and PV-PCM systems have been compared. The conclusions have been listed down in section 5. Thus, from the current work, one can evaluate the system behaviour in different operating conditions.
从文献中可以发现，数值研究是针对垂直 PV-PCM 系统进行的。然而，光伏板通常会根据当地的纬度而倾斜。因此，本研究对倾斜的 PV-PCM 系统进行了分析。第 2 节介绍了 PV-PCM 系统的数学模型。在第 3 部分中，根据现有的报告对所提出的模型得出的结果进行了验证。第 4 节研究了运行条件（系统倾斜角度、风向、风速、环境温度和 PCM 熔化温度）对 PCM 热量提取率、PCM 熔化过程和 PV-PCM 系统温度的影响，并对仅有的 PV 系统和 PV-PCM 系统进行了比较。结论列于第 5 节。因此，通过目前的研究工作，我们可以评估系统在不同运行条件下的表现。

2. Methodology 2.方法论

The system considered in this work consists of a polycrystalline PV panel integrated with a box containing PCM as shown in Fig. 1. The tilt angle of the system is denoted by β. The PV panel is considered to be made up of five layers. At the back of the panel, the PCM container is attached. The depth of the container is denoted by δ. The top wall of the container is made up of aluminium (4 mm thick). The bottom and side walls of the container are considered to be thermally insulated. Thus, the temperature variations are only along the thickness (y direction) and height of the system (x direction).
如图 1 所示，本研究中考虑的系统由一个多晶硅光伏板和一个装有 PCM 的盒子组成。系统的倾斜角度用 β 表示。光伏板由五层组成。在面板的背面，连接着 PCM 容器。容器的深度用 δ 表示。容器的顶壁由铝制成（4 毫米厚）。容器的底壁和侧壁被认为是隔热的。因此，温度变化只沿着系统的厚度（y 方向）和高度（x 方向）。

The following assumptions have been made in this work
在这项工作中做出了以下假设

(i)
The heat losses from the bottom and side walls are neglected as they are considered to be well insulated
底部和侧壁的热损失被忽略，因为它们被认为隔热性能良好
(ii)
The incident solar flux is uniformly distributed over the surface of the PV
入射太阳光通量均匀地分布在 PV 表面上
(iii)
The contact resistances in the PV cell are not considered
不考虑光伏电池中的接触电阻

The fraction of the incident solar radiation (I_T) that gets transmitted through the glass cover and absorbed by the solar cell can be written as (τα)_eff x I_T where (τα)_eff is the effective product of transmissivity of the glass cover and absorptivity of the solar cell. Out of the absorbed one, only a small fraction gets converted into electricity and the rest of the solar radiation gets converted into heat (S_h) which can be written as(1)

S_{h} = {(τ α)}_{e f f} I_{T} - η_{c e l l} I_{T}

where η_cell is the solar radiation to electricity conversion efficiency of the cell. Some fraction of the heat is lost to surroundings due to convective and radiative losses from the top surface of the panel which can be written as(2)

Q_{L} = h [T_{a t y = 0} - T_{a}] + σ ε_{t} F_{t_s} [T_{a t y = 0}^{4} - T_{s}^{4}] + σ ε_{t} F_{t_g} [T_{a t y = 0}^{4} - T_{g}^{4}]

where h is the convective heat transfer coefficient of the top surface which is the combination of natural and forced convection. T_a is the ambient temperature. σ is the Stefan–Boltzmann constant. ε_t is the emissivity for long wavelength radiation of the top surface. F_{t_s} and F_{t_g} are the view factors of the top surface with respect to sky and ground respectively. T_s and T_g are the sky and ground temperature respectively. Following Kaplani and Kaplanis [36], h can be written as follows(3)

h = {\begin{array}{l} h_{f o r}; i f G r / R e^{2} \leq 0.01 \\ {| h_{n a t}^{7 / 2} + h_{f o r}^{7 / 2} |}^{2 / 7}; i f 0.01 < G r / R e^{2} < 100, β = 0 ° \\ {| h_{n a t}^{3} + h_{f o r}^{3} |}^{1 / 3}; i f 0.01 < G r / R e^{2} < 100, β > 0 ° \\ h_{n a t}; i f G r / R e^{2} \geq 100 \end{array}

where Gr is the Grashof number and Re is the Reynolds number. h_nat and h_for are the heat transfer coefficients of the top surface due to natural and forced convection respectively and can be written as follows(4)

h_{n a t} = {\begin{cases} [0.13 \{{(G r P r)}^{1 / 3} - {(G r_{c} P r)}^{1 / 3}\} + 0.56 {(G r_{c} P r \sin β)}^{1 / 4}] k_{a} / L_{c h}; i f β > 30 ° \\ [0.13 {(G r P r)}^{1 / 3}] k_{a} / L_{c h}; i f β \leq 30 ° \end{cases}

(5)

h_{f o r} = 0.848 k_{a} {[\sin β \cos γ v_{w} \Pr / ν]}^{0.5} {(L_{c h} / 2)}^{- 0.5}

where Pr is the Prandtl number of air, Gr_c is the critical Grashof number = 1.327 × 10¹⁰ exp{−3.708(π/2−β)}, k_a is the thermal conductivity of air, L_ch is the characteristic length i.e. the length of the surface along the direction of air flow, γ is the wind azimuth angle (the angle made by wind stream with the projection of surface normal on horizontal plane), v_w is the wind velocity and ν is the kinematic viscosity of air.
入射太阳辐射（I _T ）中透过玻璃盖板并被太阳能电池吸收的部分可以写成 (τα) _eff x I _T 其中 (τα) _eff 是玻璃盖板透射率和太阳能电池吸收率的有效乘积。在被吸收的太阳辐射中，只有一小部分转化为电能，其余的太阳辐射转化为热能（S _h ），可写成 (1)

S_{h} = {(τ α)}_{e f f} I_{T} - η_{c e l l} I_{T}

其中 η _cell 是太阳能电池从太阳辐射到电能的转化效率。由于电池板顶面的对流和辐射损失，部分热量会散失到周围环境中，可写成 (2)

Q_{L} = h [T_{a t y = 0} - T_{a}] + σ ε_{t} F_{t_s} [T_{a t y = 0}^{4} - T_{s}^{4}] + σ ε_{t} F_{t_g} [T_{a t y = 0}^{4} - T_{g}^{4}]

其中 h 是顶面的对流传热系数，是自然对流和强制对流的组合。T _a 是环境温度。 σ 是斯蒂芬-玻尔兹曼常数。 ε _t 是顶面的长波辐射发射率。F _{t_s} 和 F _{t_g} 分别是顶面相对于天空和地面的视角系数。T _s 和 T _g 分别是天空和地面温度。根据 Kaplani 和 Kaplanis [36]，h 可写成 (3)

h = {\begin{array}{l} h_{f o r}; i f G r / R e^{2} \leq 0.01 \\ {| h_{n a t}^{7 / 2} + h_{f o r}^{7 / 2} |}^{2 / 7}; i f 0.01 < G r / R e^{2} < 100, β = 0 ° \\ {| h_{n a t}^{3} + h_{f o r}^{3} |}^{1 / 3}; i f 0.01 < G r / R e^{2} < 100, β > 0 ° \\ h_{n a t}; i f G r / R e^{2} \geq 100 \end{array}

，其中 Gr 是格拉肖夫数，Re 是雷诺数。 h _nat 和 h _for 分别是自然对流和强制对流引起的顶面传热系数，可写成 (4)

h_{n a t} = {\begin{cases} [0.13 \{{(G r P r)}^{1 / 3} - {(G r_{c} P r)}^{1 / 3}\} + 0.56 {(G r_{c} P r \sin β)}^{1 / 4}] k_{a} / L_{c h}; i f β > 30 ° \\ [0.13 {(G r P r)}^{1 / 3}] k_{a} / L_{c h}; i f β \leq 30 ° \end{cases}

(5)

h_{f o r} = 0.848 k_{a} {[\sin β \cos γ v_{w} \Pr / ν]}^{0.5} {(L_{c h} / 2)}^{- 0.5}

其中 Pr 是空气的普朗特数，Gr _c 是临界格拉肖夫数 = 1.327 × 10 ¹⁰ exp{-3.708(π/2-β)}, k _a 是空气的热导率，L _ch 是特征长度，即表面沿气流方向的长度，γ 是风的方位角（风流与表面法线在水平面上的投影所成的角度），v _w 是风速，ν 是空气的运动粘度。

The temperature of the PV-PCM system and the velocities of the melted PCM in x and y directions at any time t can be found out by solving below equations and the values of the parameters used for the calculations are presented in Table 1 and Table 2.(6)

ρ C_{p} \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} (k \frac{\partial T}{\partial x} - ρ C_{p} u_{x} T) + \frac{\partial}{\partial y} (k \frac{\partial T}{\partial y} - ρ C_{p} u_{y} T) + G

(7)

ρ (\frac{\partial u_{x}}{\partial t} + u_{x} \frac{\partial u_{x}}{\partial x} + u_{y} \frac{\partial u_{x}}{\partial y}) = - \frac{\partial p}{\partial x} + μ (\frac{\partial^{2} u_{x}}{\partial x^{2}} + \frac{\partial^{2} u_{x}}{\partial y^{2}}) + ρ g_{x}

(8)

ρ (\frac{\partial u_{y}}{\partial t} + u_{x} \frac{\partial u_{y}}{\partial x} + u_{y} \frac{\partial u_{y}}{\partial y}) = - \frac{\partial p}{\partial y} + μ (\frac{\partial^{2} u_{y}}{\partial x^{2}} + \frac{\partial^{2} u_{y}}{\partial y^{2}}) + ρ g_{y}

(9)

\frac{\partial u_{x}}{\partial x} + \frac{\partial u_{y}}{\partial y} = 0

where ρ is the density, C_p is the specific heat capacity, k is the thermal conductivity, u_x and u_y are the velocities of melted PCM in x and y direction respectively, G is the heat generation, p is the pressure, μ is the dynamic viscosity and g_x and g_y are the accelerations due to gravity in x and y direction respectively.
PV-PCM 系统的温度以及熔化的 PCM 在任意时间 t 在 x 和 y 方向上的速度可通过求解以下方程得出，计算所用的参数值见表 1 和表 2。 (6)

ρ C_{p} \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} (k \frac{\partial T}{\partial x} - ρ C_{p} u_{x} T) + \frac{\partial}{\partial y} (k \frac{\partial T}{\partial y} - ρ C_{p} u_{y} T) + G

(7)

ρ (\frac{\partial u_{x}}{\partial t} + u_{x} \frac{\partial u_{x}}{\partial x} + u_{y} \frac{\partial u_{x}}{\partial y}) = - \frac{\partial p}{\partial x} + μ (\frac{\partial^{2} u_{x}}{\partial x^{2}} + \frac{\partial^{2} u_{x}}{\partial y^{2}}) + ρ g_{x}

(8)

ρ (\frac{\partial u_{y}}{\partial t} + u_{x} \frac{\partial u_{y}}{\partial x} + u_{y} \frac{\partial u_{y}}{\partial y}) = - \frac{\partial p}{\partial y} + μ (\frac{\partial^{2} u_{y}}{\partial x^{2}} + \frac{\partial^{2} u_{y}}{\partial y^{2}}) + ρ g_{y}

(9)

\frac{\partial u_{x}}{\partial x} + \frac{\partial u_{y}}{\partial y} = 0

其中，ρ 为密度，C _p 为比热容，k 为热导率，u _x 和 u _y 分别为熔化 PCM 在 x 和 y 方向的速度、G 是发热量，p 是压力，μ 是动态粘度，g _x 和 g _y 分别是 x 和 y 方向的重力加速度。

Table 1. Thermo-physical properties of PV [37] and aluminium layer [14]
表 1.光伏层 [37] 和铝层 [14] 的热物理性质

Empty Cell	Glass 玻璃	EVA	Silicon 硅	Tedlar	Aluminium 铝
C_p (J/kg-K)	500	2090	677	1250	903
k (W/m-K)	1.8	0.35	148	0.2	211
Thickness (mm) 厚度（毫米）	4	0.5	0.3	0.1	4
ρ (kg/m³)	3000	960	2330	1200	2675

Table 2. Thermal properties of PCM (RT 25 HC) [14] and values of other parameters used for calculations
表 2.PCM 的热性能（RT 25 HC）[14] 和用于计算的其他参数值

Parameter 参数	Value 价值	Parameter 参数	Value 价值	Parameter 参数	Value 价值	Parameter 参数	Value 价值
C_p (J/kg-K)	1800/2400 (solid/liquid phase) 1800/2400（固/液相）	T_a (°C)	20	β_c (K⁻¹)	0.001	η_PV (%) _PV (%)	20 [1−0.005(T_cell-25) +0.085 ln (I_T/1000)] 20 [1-0.005(T _cell -25) +0.085 ln (I _T /1000)]。
I_T (W/m²)	1000	T_m (°C)	26.6	γ (°)	0	μ (kg/m-s)	10⁵/0.001798
k (W/m-K)	0.19/0.18	v_w (m/s) v _w （米/秒）	4	ΔT (°C)	2	ρ (kg/m³)	785
L_h (J/kg) L _h （焦耳/千克）	232000	β (°)	45	ε	0.85	(τα)_eff (ta) _eff	0.9

For solid regions of the system (PV and aluminium layer), only Eq. (6) is solved by using u_x = u_y = 0 m/s. For PCM, all the above four equations (Eqs. (6), (7), (8), (9)) are solved. The portion of PCM where temperature is below solidification temperature (T_m-ΔT/2), the viscosity is used as 10⁵ kg/m-s so that the PCM portion will act as solid and the portion of PCM where temperature is above liquidification temperature (T_m + ΔT/2), the viscosity is used as μ_l (viscosity of PCM in liquid phase) so that it will act as liquid. T_m is the peak melting temperature of PCM and ΔT is the phase change zone. During the period of phase change, PCM will absorb the latent heat (L_h). The latent heat can be modelled as change in the specific heat of PCM during the phase change period. The rapid change in the thermal properties of PCM during phase change has to be handled carefully for the convergence. Biwole et al. [14] have presented two functions to capture this rapid change smoothly as follows(10)

C_{p, P C M} (T) = C_{p, P C M, s} + (C_{p, P C M, l} - C_{p, P C M, s}) B (T) + L_{h} D (T)

where C_p,PCM,s and C_p,PCM,l are the specific heat capacity of PCM in solid and liquid phases respectively. B(T) is the liquid fraction of the PCM. It is 0 for solid phase and 1 for liquid phase and can be written as(11)

B (T) = {\begin{array}{l} 0 i f T < (T_{m} - Δ T / 2) \\ \frac{T - (T_{m} - Δ T / 2)}{Δ T} i f (T_{m} - Δ T / 2) \leq T \leq (T_{m} + Δ T / 2) \\ 1 i f T > (T_{m} + Δ T / 2) \end{array}

对于系统的固体区域（PV 和铝层），仅使用 u _x = u _y = 0 m/s 求解公式 (6)。对于 PCM，上述四个方程（公式 (6)、(7)、(8)、(9)）都要求解。温度低于凝固温度的 PCM 部分 (T _m -ΔT/2)，粘度取为 10 ⁵ kg/m-s，这样 PCM 部分就会像固体一样；温度高于液化温度的 PCM 部分 (T _m + ΔT/2)，粘度取为 μ（PCM 在液相中的粘度），这样它就会像液体一样。T _m 是 PCM 的峰值熔化温度，ΔT 是相变区。在相变期间，PCM 将吸收潜热 (L _h )。潜热可模拟为相变期间 PCM 比热的变化。相变期间 PCM 热属性的快速变化必须谨慎处理，以确保收敛性。Biwole 等人[14]提出了两个函数来顺利捕捉这种快速变化，如下所示 (10)

C_{p, P C M} (T) = C_{p, P C M, s} + (C_{p, P C M, l} - C_{p, P C M, s}) B (T) + L_{h} D (T)

其中 C _p,PCM,s 和 C _p,PCM,l 分别是 PCM 在固相和液相中的比热容。B(T) 是 PCM 的液态部分。固相为 0，液相为 1，可写成 (11)

B (T) = {\begin{array}{l} 0 i f T < (T_{m} - Δ T / 2) \\ \frac{T - (T_{m} - Δ T / 2)}{Δ T} i f (T_{m} - Δ T / 2) \leq T \leq (T_{m} + Δ T / 2) \\ 1 i f T > (T_{m} + Δ T / 2) \end{array}

D(T) (in Eq. (10)) is the Dirac delta function which is used to capture the latent heat during phase change. It has value 0 everywhere except in the phase change region and can be written as(12)

D (T) = \frac{e^{- {(T - T_{m})}^{2} / {(Δ T / 4)}^{2}}}{\sqrt{π {(Δ T / 4)}^{2}}}

D(T)（在公式 (10) 中）是狄拉克三角函数，用于捕捉相变过程中的潜热。除相变区域外，它在任何地方的值都为 0，可写成 (12)

D (T) = \frac{e^{- {(T - T_{m})}^{2} / {(Δ T / 4)}^{2}}}{\sqrt{π {(Δ T / 4)}^{2}}}

In Fig. 2, the graphical representation of Eq. (10) can be seen which shows the change in specific heat capacity of PCM with temperature. The area under the curve from T_m-ΔT/2 to T_m + ΔT/2 is almost equal to the latent heat which ensures that all the latent heat is captured in the phase change zone.
从图 2 中可以看到公式 (10) 的图示，其中显示了 PCM 比热容随温度的变化。从 T _m -ΔT/2 到 T _m +ΔT/2 的曲线下面积几乎等于潜热，这确保了所有潜热都被相变区吸收。

3. Validation 3.验证

Biwole et al. [14] have analysed the thermal performance of PCM in a vertical aluminium box and reported the temperature of the front surface of the system. For validation, the calculations have been carried out using the methodology of the current work by using the same parameters as used by them. The variation in the temperature of the front surface with time is plotted in Fig. 3 along with their reported values. The results show that the values computed using the current work differ from those of Biwole et al. [14] within the range of ±1.5°C.
Biwole 等人[14] 分析了垂直铝箱中 PCM 的热性能，并报告了系统前表面的温度。为进行验证，我们采用了与他们相同的参数，并使用当前工作的方法进行了计算。图 3 显示了前表面温度随时间的变化及其报告值。结果表明，使用当前方法计算出的数值与 Biwole 等人[14]的数值相差在 ±1.5°C 的范围内。

4. Results and discussion
4.结果和讨论

The variations in the temperature of the PV-PCM system with time, melting of the PCM, energy extraction by PCM, heat losses from the system and efficiency of PV in the PV-PCM system and only PV system have been computed. The effects of tilt angle of the system, wind azimuth angle (wind direction), wind velocity, ambient temperature and melting temperature of the PCM on the performance of the system have been analysed.
计算了 PV-PCM 系统的温度随时间的变化、PCM 的熔化、PCM 的能量提取、系统的热损失以及 PV-PCM 系统和仅 PV 系统的 PV 效率。分析了系统倾斜角、风方位角（风向）、风速、环境温度和 PCM 熔化温度对系统性能的影响。

ANSYS Fluent 17.1 is used to solve the equations. It is found that the results do not change much with decrease in the values of energy, velocity and continuity residuals beyond 10⁻⁸, 10⁻⁴ and 10⁻⁴ respectively. Thus, for the convergence of the solution, these values of residuals are considered as the accepted ones.
ANSYS Fluent 17.1 用于求解方程。结果发现，当能量、速度和连续性残差值分别超过 10 ⁻⁸ 、10 ⁻⁴ 和 10 ⁻⁴ 时，随着残差值的减小，结果变化不大。因此，为了使解法收敛，这些残差值被视为可接受的残差值。

4.1. Grid independence study
4.1.电网独立性研究

The variations in the temperature of PV (in PV-PCM system) with time for various grid sizes are plotted in Fig. 4. The grid size is defined by the distance between successive nodes (Δn). The results show that the decrease in Δn beyond 1 mm does not improve the results much. Thus, Δn = 1 mm is chosen for all calculations henceforth.
图 4 中绘制了不同网格大小的 PV（PV-PCM 系统中）温度随时间的变化情况。网格大小由连续节点之间的距离 (Δn)定义。结果表明，当 Δn 减小到 1 毫米以上时，结果并没有太大改善。因此，以后的所有计算都选择 Δn = 1 毫米。

4.2. Transient analysis of the system
4.2.系统瞬态分析

The variation in the temperature of the PV-PCM system with time is presented in Fig. 5. The corresponding variations in the temperature of the PV with time and the rate of heat extraction by PCM are plotted in Fig. 6 respectively. The results show that, initially, the temperature of the PV increases rapidly with time. It is due to the fact that, initially, the PCM is in solid phase and its thermal conductivity is very low. Thus, the PCM extracts very less amount of heat from the PV and leads to rapid increase in the PV temperature with time. The results show that, beyond t = 10min, the increase in the PV temperature slows down because the PCM starts melting and absorbing the latent heat. Thus, the PCM starts extracting large amount of heat from the PV without increase in temperature. Beyond t = 150min, the temperature of the PV again increases rapidly with time. It is due to the fact that, now, the PCM is almost fully melted and absorbed all the latent heat which leads to decrease in the rate of heat extraction by PCM and increase in the PV temperature.
图 5 显示了 PV-PCM 系统的温度随时间的变化情况。图 6 中分别绘制了光伏温度随时间的相应变化和 PCM 热量提取率。结果显示，最初，PV 的温度随着时间的推移迅速升高。这是由于 PCM 最初处于固相状态，导热率非常低。因此，PCM 从光伏中提取的热量非常少，导致光伏温度随时间迅速升高。结果表明，超过 t = 10 分钟后，PV 温度的上升速度会减慢，因为 PCM 开始融化并吸收潜热。因此，PCM 开始从光伏中提取大量热量，而温度并没有升高。超过 t = 150 分钟后，PV 的温度又会随着时间的推移而迅速升高。这是因为，此时 PCM 几乎完全融化并吸收了所有潜热，导致 PCM 抽取热量的速度降低，光伏温度升高。

4.2.1. Effect of tilt angle of system
4.2.1.系统倾斜角度的影响

The variations in the temperature of the PV (in PV-PCM system) with time for various tilt angles of the system (β) are plotted in Fig. 7, Fig. 8. The corresponding melting process of the PCM for various tilt angles is presented in Fig. 9. The results show that as tilt angle of the system increases, the PV temperature decreases. This is due to the fact that when tilt angle is very small, the energy flow inside the PCM due to convection is very less (Fig. 9). Energy flow is mainly due to conduction. Since conductivity of the PCM is very less, the energy extraction from PV is very low. With increase in tilt, the energy flow due to convection increases. Thus, the energy extraction by PCM increases which results in decrease in the PV temperature.
图 7 和图 8 中绘制了在系统不同倾斜角度 (β)下，光伏温度（PV-PCM 系统中）随时间的变化情况。图 9 显示了 PCM 在不同倾角下的相应熔化过程。结果表明，随着系统倾角的增加，光伏温度降低。这是因为当倾斜角度很小时，PCM 内部由于对流而产生的能量流非常小（图 9）。能量流主要来自传导。由于 PCM 的传导率非常低，因此从 PV 提取的能量也非常低。随着倾斜度的增加，对流导致的能量流也随之增加。因此，PCM 的能量提取增加，导致光伏温度降低。

4.2.2. Effect of wind azimuth angle
4.2.2.风向方位角的影响

The variations in the temperature of the PV (in PV-PCM system) with time for various values of wind azimuth angle (γ) are plotted in Fig. 10. The results show that as wind azimuth angle increases, the PV temperature increases. It is due to the fact that when wind azimuth angle is very less, wind flows almost normal to the surface which leads to larger heat losses due to forced convection and, thus, results in lesser temperature.
图 10 中绘制了在不同风方位角 (γ) 值下，光伏温度（在 PV-PCM 系统中）随时间的变化情况。结果表明，随着风方位角的增大，光伏温度也随之升高。这是因为当风向方位角很小时，风几乎以法线方向流向表面，这会导致强制对流造成更大的热量损失，从而降低温度。

The variations in the rate of heat extraction by PCM with time for various values of wind azimuth angle (γ) are plotted in Fig. 11. The results show that, initially, the rate of heat extraction by PCM is higher for higher wind azimuth angle. However, after a certain time, the rate of heat extraction by PCM is lesser for higher wind azimuth angle. It is due to the fact that, initially, for higher wind azimuth angle, the heat losses are lesser which leads to higher rate of heat extraction by PCM. Thus, for higher wind azimuth angle, the PCM melts in shorter duration. After melting, the rate of heat extraction decreases. Thus, beyond a certain time, the PCM is fully melted for higher wind azimuth angle which leads to lesser rate of heat extraction by PCM.
图 11 中绘制了不同风方位角 (γ) 值下 PCM 热量提取率随时间的变化情况。结果表明，最初，风方位角越大，PCM 的萃热率越高。然而，经过一段时间后，风方位角越大，PCM 的萃热率越低。这是由于风方位角越大，热量损失越小，从而导致 PCM 的萃取率越高。因此，风方位角越大，PCM 熔化的时间越短。融化后，汲取热量的速度会降低。因此，超过一定时间后，风方位角越大，PCM 就会完全融化，从而导致 PCM 的析热率越低。

4.2.3. Effect of wind velocity
4.2.3.风速的影响

The variations in the temperature of the PV (in PV-PCM system) with time for various values of wind velocity (v_w) are plotted in Fig. 12 and the corresponding PV-IV curve is plotted in Fig. 13 for v_w = 5 m/s. The results show that as wind velocity increases, the PV temperature decreases. It is due to the fact that when wind velocity is very less, the heat losses due to forced convection are very less which results in higher temperature.
图 12 中绘制了不同风速值（v _w ）下光伏温度（PV-PCM 系统中）随时间的变化情况，图 13 中绘制了 v _w = 5 m/s 时相应的 PV-IV 曲线。结果表明，随着风速的增加，光伏温度会降低。这是由于当风速非常小时，强制对流造成的热损失非常小，从而导致温度升高。

The variations in the rate of heat extraction by PCM with time for various values of wind velocity (v_w) are plotted in Fig. 14. The results show that, initially, the rate of heat extraction by PCM is higher for lesser wind velocity. However, after a certain time, the rate of heat extraction by PCM is lesser for lesser wind velocity. It is due to the fact that, initially, for lesser wind velocity, the heat losses are lesser which leads to higher rate of heat extraction by PCM. Thus, for lesser wind velocity, the PCM melts in shorter duration. After melting, the rate of heat extraction decreases. Thus, beyond a certain time, the PCM is fully melted for lesser wind velocity which leads to lesser rate of heat extraction by PCM.
图 14 中绘制了不同风速值 (v _w ) 下 PCM 热量提取率随时间的变化情况。结果表明，最初风速较低时，PCM 的析热率较高。然而，经过一段时间后，风速越小，PCM 的析热率越低。这是因为，最初风速较低时，热量损失较少，从而导致 PCM 的析热率较高。因此，风速越小，PCM 融化的时间越短。融化后，汲取热量的速度会降低。因此，超过一定时间后，风速较小的 PCM 将完全融化，从而导致 PCM 的析热率降低。

4.2.4. Effect of melting temperature of PCM
4.2.4.PCM 熔化温度的影响

The variations in the temperature of the PV (in PV-PCM system) with time for various values of melting temperature of PCM (T_m) are plotted in Fig. 15. The corresponding variations in the rate of heat extraction by PCM with time are plotted in Fig. 16. The results show that the PCM with lesser T_m can maintain the PV at lower temperatures. Thus, the appropriate PCM will be the one having T_m closer to the ambient temperature. However, the results also show that after a certain time, the PV temperature becomes higher for the system with lesser T_m. It is due to the fact that the system with lesser T_m experiences lesser heat losses and, thus, higher rate of heat extraction by PCM (Fig. 16) which leads to melting of the PCM in shorter duration. Thus, after melting, the PV temperature starts increasing rapidly. It should also be noted that the duration for which the PV is maintained at lower temperature can be increased by increasing the quantity of the PCM used (i.e. the depth of the PCM container) and the latent heat of the PCM.
图 15 中绘制了 PCM 不同熔化温度值 (T _m ) 下 PV（PV-PCM 系统中）温度随时间的变化情况。图 16 中绘制了 PCM 热量提取率随时间的相应变化。结果表明，T _m 较小的 PCM 可以在较低温度下保持 PV。因此，合适的 PCM 应该是 T _m 更接近环境温度的 PCM。然而，结果还显示，在一定时间后，T _m 较小的系统的 PV 温度会变高。这是由于 T _m 较小的系统的热损失较小，因此 PCM 的吸热率较高（图 16），从而导致 PCM 在较短时间内熔化。因此，熔化后 PV 温度开始迅速升高。还应注意的是，可以通过增加 PCM 的使用量（即 PCM 容器的深度）和 PCM 的潜热来延长 PV 保持较低温度的时间。

4.2.5. Effect of ambient temperature
4.2.5.环境温度的影响

The variations in the temperature of the PV (in PV-PCM system) with time for various values of ambient temperature (T_a) are plotted in Fig. 17. The results show that as ambient temperature increases, the PV temperature increases because of decrease in the heat losses.
图 17 中绘制了不同环境温度值（T _a ）下光伏温度（PV-PCM 系统中）随时间的变化情况。结果表明，随着环境温度的升高，由于热损失的减少，光伏温度也随之升高。

The variations in the rate of heat extraction by PCM with time for various values of ambient temperature (T_a) are plotted in Fig. 18. The results show that, initially, the rate of heat extraction by PCM is higher for higher ambient temperature. However, after a certain time, the rate of heat extraction by PCM is lesser for higher ambient temperature. It is due to the fact that, initially, for higher ambient temperature, the heat losses are lesser which leads to higher rate of heat extraction by PCM. Thus, for higher ambient temperature, the PCM melts in shorter duration. After melting, the rate of heat extraction decreases. Thus, beyond a certain time, the PCM is fully melted for higher ambient temperature which leads to lesser rate of heat extraction by PCM.
图 18 中绘制了不同环境温度值 (T _a ) 下 PCM 的汲取热量率随时间的变化情况。结果表明，最初，环境温度越高，PCM 的析热率越高。然而，经过一段时间后，环境温度越高，PCM 的析热率越低。这是因为，最初环境温度越高，热量损失越小，从而导致 PCM 的萃取率越高。因此，环境温度越高，PCM 熔化的时间越短。熔化后，汲取热量的速度会降低。因此，超过一定时间后，环境温度越高，PCM 就会完全融化，从而导致 PCM 的析热率降低。

It must also be noted that a PCM with lesser melting temperature can be used in winters to maintain the PV at lower temperature. But, this PCM cannot be used in summers as it will remain melted due to higher ambient temperature. Thus, in future work, two PCMs in same container will be explored which can work effectively in summers as well as in winters.
还必须注意的是，熔化温度较低的 PCM 可在冬季使用，以将光伏维持在较低温度。但是，这种 PCM 无法在夏季使用，因为较高的环境温度会使其继续融化。因此，在今后的工作中，将探索在同一容器中使用两种 PCM 的方法，这两种 PCM 在夏季和冬季都能有效工作。

4.2.6. Comparison of PV-PCM system with only PV system
4.2.6.PV-PCM 系统与仅有 PV 系统的比较

The variations in the temperature of the PV in PV-PCM system and only PV system with time are plotted in Fig. 19. The corresponding PV-IV curves and solar radiation to electricity conversion efficiencies of the PV are plotted in Fig. 20, Fig. 21 respectively. The results show that the temperature of the PV reduces by 19 °C by using PCM and power increases from 171W to 190W and, thus, the solar to electricity conversion efficiency of the PV increases from 17.1% to 19%.
图 19 中绘制了 PV-PCM 系统和纯 PV 系统中光伏温度随时间的变化情况。图 20 和图 21 分别绘制了相应的 PV-IV 曲线和太阳辐射到光伏发电的转换效率。结果表明，使用 PCM 后，光伏温度降低了 19 °C，功率从 171W 增至 190W，因此，光伏的太阳能转换效率从 17.1% 增至 19%。

5. Conclusions 5.结论

In the current work, a mathematical model for a tilted PV-PCM system has been presented. Heat transfer due to all the three modes (conduction, convection and radiation) is considered. The rapid change in the thermal properties of the PCM during phase change is smoothly captured by a mathematical model. The variations in the temperature of the PV-PCM system with time, melting process of the PCM, energy extraction by PCM, heat losses from the system and comparison of the PV-PCM and only PV systems have been analysed. The effects of tilt angle of the system, wind azimuth angle (wind direction), wind velocity, ambient temperature and melting temperature of the PCM on the performance of the system have been studied. The conclusions are as follows
在当前的研究中，提出了一个倾斜式 PV-PCM 系统的数学模型。该模型考虑了所有三种模式（传导、对流和辐射）的热传递。数学模型顺利捕捉到了相变过程中 PCM 热特性的快速变化。分析了 PV-PCM 系统的温度随时间的变化、PCM 的熔化过程、PCM 的能量提取、系统的热损失以及 PV-PCM 系统和纯 PV 系统的比较。还研究了系统倾斜角、风方位角（风向）、风速、环境温度和 PCM 熔化温度对系统性能的影响。结论如下

(i)
The temperature of PV can be reduced by using PCM and the solar to electricity conversion efficiency of PV can be increased.
使用 PCM 可以降低光伏的温度，提高光伏的光电转换效率。
(ii)
Increase in tilt angle of the system leads to increase in the rate of heat extraction by PCM which results in the decrement of PV temperature.
系统倾斜角度的增加会导致 PCM 热量提取率的增加，从而降低光伏温度。
(iii)
Increase in wind azimuth angle/wind velocity leads to decrease/increase in heat losses from top which leads to increase/decrease in the rate of heat extraction by PCM.
风方位角/风速的增加会导致顶部热量损失的减少/增加，从而导致 PCM 热量提取率的增加/减少。
(iv)
PCM with lesser melting temperature can maintain the PV at lower temperatures. Thus, the appropriate PCM will be the one having melting temperature closer to ambient temperature.
熔化温度较低的 PCM 可在较低温度下保持 PV。因此，合适的 PCM 应是熔化温度更接近环境温度的 PCM。

Acknowledgment 鸣谢

The authors gratefully acknowledge the financial support from EPSRC-DST funded Reliable and Efficient System for Community Energy Solution - RESCUES project (EP/K03619X/1). In support of open access research, all underlying article materials (such as data, samples or models) can be accessed upon request via email to the corresponding author.
作者衷心感谢 EPSRC-DST 资助的社区能源解决方案可靠高效系统 - RESCUES 项目（EP/K03619X/1）提供的资金支持。为支持开放存取研究，所有基础文章资料（如数据、样本或模型）均可通过电子邮件向通讯作者索取。

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In recent years, researchers are fascinated to counter problem of PV-efficiency decline arising from high operating temperatures, especially in hot climates. This article conducts a comprehensive review of research activities performed in last 5 years, on cooling techniques with phase-change materials (PCMs), nanofluids and their combined use, leading to efficiency enhancement. By passive cooling approach with PCMs, it is found that maximum enhancement up to 20% in PV-efficiency can be achieved. Effectiveness of PCM for PV is more prominent in summer than in winter. Incorporations of fins inside PCM container at PV rear, results in much improved heat conduction within PCM. Now-a-days, researchers have grown interest in composite PCMs for PV cooling due to their enhanced thermal conductivity. Moreover, better heat regulation as well as PV-surface temperature uniformity can be achieved with two PCMs at a time having different melting points. Studies suggest that combination of passive & active cooling techniques helps in further lowering of PV-cell temperature, leading to enhancement in PV-efficiency with additional thermal power generation. PV-efficiency of water-based hybrid PV/T systems can be improved by 32% by integration with PCM. Although nanofluid-based PV/T systems have been proved to enhance PV-efficiency by more than 60%, but combined use of PCM & nanofluid is more effective approach for PV cooling than individual use of PCM or nanofluid. If combination is made between nanofluid & nano-PCM, electrical power & efficiency can further be enhanced. Nanofluids can also be considered a good spectral filter alternative as they require small thickness and are able to be tuned by varying nanoparticles conc. Finally, environmental impacts & economic viability of mentioned cooling techniques, were discussed. Studies show that PV/PCM systems become expensive & less feasible when operated in single junction due to long payback period up to 20 years. Economic feasibility can be increased by combining passive & active cooling techniques which can increase system compactness and lower its cost.
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In recent years, the utilization of phase change materials (PCMs) in photovoltaic (PV) module for thermal regulation has attracted wide attention in this field, as the hybrid PV-PCM technology can not only achieve higher photoelectric conversion efficiency but also make it possible to extract thermal energy stored in PCMs for cascade utilization. Although substantial research has been carried out on PV-PCM systems, the promise of practical application is still far from clear with some barriers unsolved, such as PCMs which need further improvements in both technical and economical view. In this paper, a comprehensive literature review of the state-of-the-art aspects of PV-PCM systems is presented, with the focus on technology overview and materials selection. The concept of hybrid PV-PCM system is first discussed with its general configuration and energy balance, to figure out the key factors affecting its performance. Besides, the development route of PV-PCM research is outlined through a comprehensive review of 104 research articles during 2004–2018, clarifying the representative achievements and existing problems in each stage. Furthermore, PCMs are highlighted in this paper with details on their classification, properties, and application in previous PV-PCM research. In particular a triangle about materials selection criteria and determination strategy of phase transition temperature is proposed. Finally, the challenges and prospects of future research on PV-PCM systems are raised, advocating that more attention should be addressed on new strategies to overcome the existing problems such as insufficient reliability and economic feasibility.
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In this paper, a comprehensive three-dimensional model of photovoltaic thermal system integrated with phase change material (PVT/PCM) is developed and simulated. The effect of some key parameters using parametric analysis on performance of PVT/PCM system with water as working fluid is investigated. Parameters considered in this study include the properties of PCM (i.e. melting temperature, enthalpy of fusion and thermal conductivity), solar radiation and mass flow rate. The parametric analysis ranges are selected according to the properties of the most of available PCMs on the market, which shows the practical application of the numerical research. Furthermore, a three-dimensional model of PVT system is simulated as well to compare its performance with PVT/PCM system. An enthalpy-porosity method is used to simulate the solidification and melting of PCM. To solve the governing equations, the pressure-based finite volume method using transient solver in ANSYS Fluent 16.2 is employed. Moreover, the SIMPLE algorithm is selected to provide the coupling between the pressure and velocity components. The results present that the PVT/PCM system has lower surface temperature and coolant outlet temperature compared to the PVT only system. The results also shows that enhancing the melting temperature of PCM from 40 °C to 65 °C increases the surface temperature from 51.53 °C to 58.78 °C, while it reduces the percentage of melted PCM from 82.7% to 9.6%. It is also concluded that as the thermal conductivity of PCM enhances, both electrical and thermal energy efficiency of PVT/PCM system increase.
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The deployment of phase change materials (PCMs) in practical applications is in large part limited by the low thermal conductivity of the available PCMs. Hence, in this study, enhancement in the melting rate of PCM by addition of fins in rectangular enclosures was experimentally investigated under different inclination angles. The melting process of lauric acid in side-heated enclosures with different numbers of fins was evaluated for inclination angles of 90° (vertical), 45° and 0° (horizontal). In order to visualize the melting process, the enclosure was fabricated from transparent acrylic material except one side made of an aluminum plate to heat the enclosure isothermally. Solid-liquid interface positions and temperature history of the PCM were recorded and applied to calculate the liquid fractions and heat transfer rates. The evolution of the interface in the inclined enclosures revealed that the development of vortical flow structures in the liquid PCM by decreasing the inclination angle significantly improves the melting rate. It was found that for both finned and unfinned enclosures the melting rate increases by reducing the inclination angle. Heat transfer enhancements obtained by the 0-fin horizontal and 3-fin vertical enclosures compared to the 0-fin vertical enclosure were 115% and 56%, respectively. This thermal behavior proposes that simply inclining the enclosure can be more effective to enhance the melting rate than adding fins to the vertical enclosure. Among the different cases studied, the 3-fin horizontal enclosure showed the maximum heat transfer rate and consequently the minimum melting time. The present investigation can contribute to a better understanding of PCM melting in the inclined finned enclosures and provide much-needed benchmark data for the future numerical simulations.
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[1] [1]
E. Skoplaki, J.A. Palyvos
On the temperature dependence of photovoltaic module electrical performance: a review of efficiency/power correlations
Sol Energy, 83 (2009), pp. 614-624
View PDF View article View in Scopus Google Scholar

[2] [2]
V.L. Brano, G. Ciulla, A. Piacentino, F. Cardona
Finite difference thermal model of a latent heat storage system coupled with a photovoltaic device: description and experimental validation
Renew Energy, 68 (2014), pp. 181-193
Google Scholar

[3] [3]
G. Ciulla, V.L. Brano, M. Cellura, V. Franzitta, D. Milone
A finite difference model of a PV-PCM system
Energy Procedia, 30 (2012), pp. 198-206
View PDF View article View in Scopus Google Scholar

[4] [4]
H. Mahamudul, M.M. Rahman, H.S.C. Metselaar, S. Mekhilef, S.A. Shezan, R. Sohel, et al.
Temperature regulation of photovoltaic module using phase change material: a numerical analysis and experimental investigation
Int J Photoenergy (2016), pp. 1-8
5917028
Crossref Google Scholar

[5] [5]
C.J. Smith, P.M. Forster, R. Crook
Global analysis of photovoltaic energy output enhanced by phase change material cooling
Appl Energy, 126 (2014), pp. 21-28
View PDF View article View in Scopus Google Scholar

[6] [6]
P. Atkin, M.M. Farid
Improving the efficiency of photovoltaic cells using PCM infused graphite and aluminium fins
Sol Energy, 114 (2015), pp. 217-228
View PDF View article View in Scopus Google Scholar

[7] [7]
M.A. Kibria, R. Saidur, F.A. Al-Sulaiman, M.M.A. Aziz
Development of a thermal model for a hybrid photovoltaic module and phase change materials storage integrated in buildings
Sol Energy, 124 (2016), pp. 114-123
View PDF View article View in Scopus Google Scholar

[8] [8]
J. Park, T. Kim, S.B. Leigh
Application of a phase-change material to improve the electrical performance of vertical-building-added photovoltaics considering the annual weather conditions
Sol Energy, 105 (2014), pp. 561-674
Google Scholar

[9] [9]
L. Aelenei, R. Pereira, H. Gonçalves, A. Athienitis
Thermal performance of a hybrid BIPV-PCM: modeling, design and experimental investigation
Energy Procedia, 48 (2014), pp. 474-483
View PDF View article View in Scopus Google Scholar

[10] [10]
K. Kant, A. Shukla, A. Sharma, P.H. Biwole
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Sol Energy, 140 (2016), pp. 151-161
View PDF View article View in Scopus Google Scholar

[11] [11]
M.J. Huang, P.C. Eames, B. Norton
Thermal regulation of building-integrated photovoltaics using phase change materials
Int J Heat Mass Transf, 47 (2004), pp. 2715-2733
View PDF View article View in Scopus Google Scholar

[12] [12]
M.J. Huang
The effect of using two PCMs on the thermal regulation performance of BIPV systems
Sol Energy Mater Sol Cells, 95 (2011), pp. 957-963
Google Scholar

[13] [13]
C.J. Ho, A.O. Tanuwijava, C.M. Lai
Thermal and electrical performance of a BIPV integrated with a microencapsulated phase change material layer
Energy Build, 50 (2012), pp. 331-338
View PDF View article View in Scopus Google Scholar

[14] [14]
P.H. Biwole, P. Eclache, F. Kuznik
Phase-change materials to improve solar panel's performance
Energy Build, 62 (2013), pp. 59-67
View PDF View article View in Scopus Google Scholar

[15] [15]
D. Groulx, P.H. Biwole
Solar PV passive temperature control using phase change materials
15th international heat transfer conference, August 10-15, 2014 (2014)
Kyoto, Japan
Google Scholar

[16] [16]
M.J. Huang, P.C. Eames, B. Norton
Comparison of a small-scale 3D PCM thermal control model with a validated 2D PCM thermal control model
Sol Energy Mater Sol Cells, 90 (2006), pp. 1961-1972
View PDF View article View in Scopus Google Scholar

[17] [17]
M.J. Huang, P.C. Eames, B. Norton
Comparison of predictions made using a new 3D phase change material thermal control model with experimental measurements and predictions made using a validated 2D model
Heat Transf Eng, 28 (2007), pp. 31-37
Crossref View in Scopus Google Scholar

[18] [18]
C.J. Ho, W.L. Chou, C.M. Lai
Thermal and electrical performance of a water-surface floating PV integrated with a water-saturated MEPCM layer
Energy Convers Manag, 89 (2015), pp. 862-872
View PDF View article View in Scopus Google Scholar

[19] [19]
C.J. Ho, W.L. Chou, C.M. Lai
Application of a water-saturated MEPCM-PV for reducing winter chilling damage on aqua farms
Sol Energy, 108 (2014), pp. 135-145
View PDF View article View in Scopus Google Scholar

[20] [20]
M.J. Huang, P.C. Eames, B. Norton
Phase change materials for limiting temperature rise in building integrated photovoltaics
Sol Energy, 80 (2006), pp. 1121-1130
View PDF View article View in Scopus Google Scholar

[21] [21]
M.J. Huang, P.C. Eames, B. Norton, N.J. Hewitt
Natural convection in an internally finned phase change material heat sink for the thermal management of photovoltaics
Sol Energy Mater Sol Cells, 95 (2011), pp. 1598-1603
View PDF View article View in Scopus Google Scholar

[22] [22]
A. Hasan, S.J. McCormack, M.J. Huang, B. Norton
Evaluation of phase change materials for thermal regulation enhancement of building integrated photovoltaics
Sol Energy, 84 (2010), pp. 1601-1612
View PDF View article View in Scopus Google Scholar

[23] [23]
Y.S. Indartono, A. Suwono, F.Y. Pratama
Improving photovoltaics performance by using yellow petroleum jelly as phase change material
Int J Low-Carbon Technol, 0 (2014), pp. 1-5
Google Scholar

[24] [24]
F. Hachem, B. Abdulhay, M. Ramadan, H. El Hage, M.G. El Rab, M. Khaled
Improving the performance of photovoltaic cells using pure and combined phase change materials - experiments and transient energy balance
Renew Energy, 107 (2017), pp. 567-575
View PDF View article View in Scopus Google Scholar

[25] [25]
R. Stropnik, U. Stritih
Increasing the efficiency of PV panel with the use of PCM
Renew Energy, 97 (2016), pp. 671-679
View PDF View article View in Scopus Google Scholar

[26] [26]
A. Hasan, S.J. McCormack, M.J. Huang, J. Sarwar, B. Norton
Increased photovoltaic performance through temperature regulation by phase change materials: materials comparison in different climates
Sol Energy, 115 (2015), pp. 264-276
View PDF View article View in Scopus Google Scholar

[27] [27]
S. Sharma, A. Tahir, K.S. Reddy, T.K. Mallick
Performance enhancement of a Building-Integrated Concentrating Photovoltaic system using phase change material
Sol Energy Mater Sol Cells, 149 (2016), pp. 29-39
View PDF View article Crossref View in Scopus Google Scholar

[28] [28]
M.C. Browne, K. Lawlor, A. Kelly, B. Norton, S.J. McCormack
Indoor characterisation of a photovoltaic/thermal phase change material system
Energy Procedia, 70 (2015), pp. 163-171
View PDF View article View in Scopus Google Scholar

[29] [29]
M.C. Browne, D. Quigley, H.R. Hard, S. Gilligan, N.C.C. Ribeiro, N. Almeida, et al.
Assessing the thermal performance of phase change material in a photovoltaic/thermal system
Energy Procedia, 91 (2016), pp. 113-121
View PDF View article Google Scholar

[30] [30]
M.C. Browne, B. Norton, S.J. McCormack
Phase change materials for photovoltaic thermal management
Renew Sustain Energy Rev, 47 (2015), pp. 762-782
View PDF View article View in Scopus Google Scholar

[31] [31]
T. Ma, H. Yang, Y. Zhang, L. Lu, X. Wang
Using phase change materials in photovoltaic systems for thermal regulation and electrical efficiency improvement: a review and outlook
Renew Sustain Energy Rev, 43 (2015), pp. 1273-1284
View PDF View article View in Scopus Google Scholar

[32] [32]
D. Du, J. Darkwa, G. Kokogiannakis
Thermal management systems for Photovoltaics (PV) installations: a critical review
Sol Energy, 97 (2013), pp. 238-254
View PDF View article View in Scopus Google Scholar

[33] [33]
A. Shukla, K. Kant, A. Sharma, P.H. Biwole
Cooling methodologies of photovoltaic module for enhancing electrical efficiency: a review
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Outline 概要

Cited by (151) 引用 (151)

Figures (21) 数字 (21)

Tables (2) 表格 (2)

Energy 能源

Highlights 亮点

Abstract 摘要

Keywords 关键词

Nomenclature 术语

Greek symbols 希腊文符号

Abbreviation 缩写

Subscripts 下标

1. Introduction 1.导言

2. Methodology 2.方法论

3. Validation 3.验证

4. Results and discussion
4.结果和讨论

4.1. Grid independence study
4.1.电网独立性研究

4.2. Transient analysis of the system
4.2.系统瞬态分析

4.2.1. Effect of tilt angle of system
4.2.1.系统倾斜角度的影响

4.2.2. Effect of wind azimuth angle
4.2.2.风向方位角的影响

4.2.3. Effect of wind velocity
4.2.3.风速的影响

4.2.4. Effect of melting temperature of PCM
4.2.4.PCM 熔化温度的影响

4.2.5. Effect of ambient temperature
4.2.5.环境温度的影响

4.2.6. Comparison of PV-PCM system with only PV system
4.2.6.PV-PCM 系统与仅有 PV 系统的比较

5. Conclusions 5.结论

Acknowledgment 鸣谢

References

Cited by (151)

Recent advancements in PV cooling and efficiency enhancement integrating phase change materials based systems – A comprehensive review

Photovoltaic panel integrated with phase change materials (PV-PCM): technology overview and materials selection

Numerical investigation and parametric analysis of a photovoltaic thermal system integrated with phase change material

Experimental investigation of melting behaviour of phase change material in finned rectangular enclosures under different inclination angles

A Comprehensive Review on Renewable Energy Development, Challenges, and Policies of Leading Indian States with an International Perspective

Latent Heat Thermal Energy Storage Systems with Solid–Liquid Phase Change Materials: A Review

Performance analysis of tilted photovoltaic system integrated with phase change material under varying operating conditions不同运行条件下集成了相变材料的倾斜式光伏系统的性能分析

Highlights 亮点

Abstract 摘要

Keywords 关键词

Nomenclature 术语

Greek symbols 希腊文符号

Abbreviation 缩写

Subscripts 下标

1. Introduction 1.导言

2. Methodology 2.方法论

3. Validation 3.验证

4. Results and discussion4.结果和讨论

4.1. Grid independence study4.1.电网独立性研究

4.2. Transient analysis of the system4.2.系统瞬态分析

4.2.1. Effect of tilt angle of system4.2.1.系统倾斜角度的影响

4.2.2. Effect of wind azimuth angle4.2.2.风向方位角的影响

4.2.3. Effect of wind velocity4.2.3.风速的影响

4.2.4. Effect of melting temperature of PCM4.2.4.PCM 熔化温度的影响

4.2.5. Effect of ambient temperature4.2.5.环境温度的影响

4.2.6. Comparison of PV-PCM system with only PV system4.2.6.PV-PCM 系统与仅有 PV 系统的比较

5. Conclusions 5.结论

Acknowledgment 鸣谢

References

Performance analysis of tilted photovoltaic system integrated with phase change material under varying operating conditions
不同运行条件下集成了相变材料的倾斜式光伏系统的性能分析

4. Results and discussion
4.结果和讨论

4.1. Grid independence study
4.1.电网独立性研究

4.2. Transient analysis of the system
4.2.系统瞬态分析

4.2.1. Effect of tilt angle of system
4.2.1.系统倾斜角度的影响

4.2.2. Effect of wind azimuth angle
4.2.2.风向方位角的影响

4.2.3. Effect of wind velocity
4.2.3.风速的影响

4.2.4. Effect of melting temperature of PCM
4.2.4.PCM 熔化温度的影响

4.2.5. Effect of ambient temperature
4.2.5.环境温度的影响

4.2.6. Comparison of PV-PCM system with only PV system
4.2.6.PV-PCM 系统与仅有 PV 系统的比较