# A Numerical Study of Dual-Inlet Air-Cooled PV/T Solar Collectors with Various Airflow Channel Configurations

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. Geometry Model

#### 2.2. Mathematical Model

_{amb}is a function of wind velocity and is extrapolated by the following empirical relationship [26], where υ is the speed of the air:

_{top}and h

_{bot}can be computed by the following equation:

_{air}is the thermal conductivity of air, Nu is the Nusselt number of the airflow, and D is the equivalent diameter. Nu can be estimated by the following correlation [27]:

_{a}

_{ir}and T denote the mean air temperature and the wall temperature of the tube, respectively; and L is the length of the front and back PV module. This correlation can fully satisfy engineering calculation accuracy under the following conditions:

#### 2.3. Numerical Model

^{2}, which is consistent with [24]. The effective utilization coefficient of solar energy and the packing factor of the solar cell is 0.8. The lower surface of the photovoltaic panel is defined as a constant heat flow boundary condition. The material used in the bottom insulation layer is a heat-insulating material, and the external heat exchange phenomenon is not considered, but it accepts the radiation heat transfer of the photovoltaic panel. When the surface temperature of the bottom plate increases, it will produce convective heat transfer with the air in the cavity. The steady simulation was employed using ANASY Fluent.

_{k}is the generation of turbulent kinetic energy due to mean velocity gradients, and Dk

_{eff}and Dε

_{eff}are the effective diffusivity for k and ε, respectively, which are calculated as shown below:

_{ε}is the turbulent Prandtl number for ε and is assumed as equal to 1.3. Furthermore, the constants C

_{1}

_{ε}, C

_{2}

_{ε}, and C

_{μ}have the following values:

_{k}is the generation of turbulent kinetic energy, which is common in most turbulence models and is given by:

_{ij}is written as:

## 3. Calculation Verification

#### 3.1. Mesh Independence Verification

#### 3.2. Comparison of Experiment and Simulation

## 4. Results and Discussion

#### 4.1. Effect of Cross-Sectional Area Ratio of the Inlet and Outlet

#### 4.2. Effect of the Length Ratio of the Front and Back Air Channel

#### 4.3. Effect of the Angle between the Photovoltaic Panel and the Bottom Panel in the Second Part

## 5. Conclusions

- (1)
- As the area of the second inlet increases, more air getting into the second inlet enhances the convection heat transfer as the cross-sectional area ratio X is reduced, and the temperature distribution in the back air channel is more uniform. The maximum thermal efficiency is about 45.36% at X = 0.562. The maximum photovoltaic efficiency is 11.25% at X = 0.5.
- (2)
- As the length ratio Y of the front and back air channel is reduced, the averaged outlet temperature first decreases and then increases. There is a minimum heat-exchanging quantity of the dual-inlet PV/T air collector between Y = 1.331 and Y = 0.799. The calculated maximum thermal efficiency is about 62.14% at Y = 1.865. The maximum photovoltaic efficiency is 11.19% at Y = 1.
- (3)
- Along with the increase in angle φ, the average temperature of the outlet gradually rises. Although the calculated maximum thermal efficiency is about 51.70% at φ = 4°, the photovoltaic efficiency is the smallest. A large amount of heat gathers in the upper part of the second air passage, which is not conducive to cooling the photovoltaic panels.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Nomenclature | |

A | area, m^{2} |

c_{p} | specific heat capacity, kJ/kg K |

Dk_{eff} | effective diffusivity for k |

Dε_{eff} | effective diffusivity for ε_{d} |

F | packing factor |

G_{k} | production of turbulent kinetic energy, J |

k | turbulent kinetic energy, J |

H | height, m |

h | convective heat transfer coefficient, W/m^{2} K |

I | solar radiation intensity, W/m^{2} |

L | Length, m |

m | mass flow rate, kg/s |

S_{ij} | strain-rate tensor |

T | temperature, ^{o}C |

v | flow velocity, m/s |

W | width, m |

X | cross-sectional area ratio of the front and back air channel |

Y | length ratio of the front and back air channels |

$\nu $ | kinematic viscosity, m^{2}/s |

${\nu}_{t}$ | turbulent kinematic viscosity, m^{2}/s |

α | absorption coefficient |

μ | dynamic viscosity, N·s/m^{2} |

η | photovoltaic efficiency |

λ | thermal conductivity, W/m K |

τ | transmission coefficient |

γ | kinematic viscosity, m^{2} |

ε | emissivity coefficient |

ε_{d} | rate of dissipation of turbulent kinetic energy |

σ | Stefan–Boltzmann Constant |

σ_{ε} | turbulent Prandtl number for ε_{d} |

φ | angle, deg |

θ | effective utilization coefficient of solar energy |

Subscripts | |

e | electrical |

t | thermal |

air | airflow |

amb | ambient air |

ins | insulation backplane |

pv | photovoltaic panel |

sky | sky |

top | top |

bot | bottom |

ref | reference value at reference conditions |

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**Figure 1.**Schematic of the dual-inlet air-cooled PV/T system: (

**a**) sectional view, (

**b**) three-dimensional model.

**Figure 5.**Comparison of the measured and calculated temperatures in the second PV/T section: (

**a**) top layer, (

**b**) middle layer.

**Figure 7.**The temperature nephogram of 6 cross-sectional area ratios in the longitudinal section of the solar collector.

**Figure 8.**The velocity nephogram of 6 cross-sectional area ratios in the longitudinal section of the solar collector.

**Figure 9.**The averaged outlet temperature and heat exchange amount of 6 cross-sectional area ratios.

**Figure 12.**The temperature nephogram of 7 air passage length ratios in the longitudinal section of the solar collector.

**Figure 13.**The velocity nephogram of 7 air passage length ratios in the longitudinal section of the solar collector.

**Figure 18.**The temperature nephogram obtained at five angles φ in the longitudinal section of the solar collector.

**Figure 19.**The velocity nephogram obtained at five angles φ in the longitudinal section of the solar collector.

Parameters | Symbol | Value |
---|---|---|

Length of the front and back PV module | L | 1 m |

Width of the front and back PV module | W | 0.53 m |

Height of first air channel | H_{1} | 0.045 m |

Height of second air channel | H_{2} | 0.057 m |

Packing factor of the solar cell | F | 0.83 |

Mass flow rate of air | m | 0.0728 kg/s |

Density of air | ρ | 1.205 kg/m^{3} |

Specific heat capacity of air | C | 1.005 kJ/kg·K |

Reference value | η_{ref}, β_{ref}, and T_{ref} | 0.12, 0.0045, and 293 K |

Solar radiation intensity | I | 1040 W/m^{2} |

Absorption coefficient | α | 0.8 |

Speed of air | v | 2 m/s |

Thermal conductivity of air | λ_{air} | 0.0267W/(m·K) |

Condition Name | Height of the Inlet_First (m) | Height of the Inlet_Second (m) | X |
---|---|---|---|

PVT_0 | 0.045 | 0.0081 | 0.847 |

PVT_1 | 0.045 | 0.0153 | 0.746 |

PVT_2 | 0.045 | 0.02025 | 0.690 |

PVT_3 | 0.045 | 0.02475 | 0.645 |

PVT_4 | 0.045 | 0.0351 | 0.562 |

PVT_5 | 0.045 | 0.045 | 0.500 |

Condition Name | Average Temperature of the First PV Panel (°C) | Average Temperature of the Second PV Panel (°C) | Photovoltaic Efficiency |
---|---|---|---|

PVT_0 | 34.1 | 36.7 | 11.17% |

PVT_1 | 34.8 | 35.3 | 11.19% |

PVT_2 | 35 | 34.2 | 11.21% |

PVT_3 | 35.2 | 33.1 | 11.24% |

PVT_4 | 35.5 | 32.6 | 11.24% |

PVT_5 | 35.6 | 31.9 | 11.25% |

Condition Name | Length of the PV Panel_First (m) | Length of the PV Panel_Second (m) | Y |
---|---|---|---|

PVT_6 | 1.244 | 0.667 | 1.865 |

PVT_7 | 1.142 | 0.858 | 1.331 |

PVT_1 | 1 | 1 | 1.000 |

PVT_8 | 0.889 | 1.112 | 0.799 |

PVT_9 | 0.8 | 1.2 | 0.667 |

PVT_10 | 0.728 | 1.273 | 0.571 |

PVT_11 | 0.667 | 1.244 | 0.536 |

Condition Name | Average Temperature of the First PV Panel (°C) | Average Temperature of the Second PV Panel (°C) | Photovoltaic Efficiency |
---|---|---|---|

PVT_6 | 37.4 | 34.8 | 10.62% |

PVT_7 | 35.2 | 35.9 | 11.16% |

PVT_1 | 34.8 | 35.3 | 11.19% |

PVT_8 | 32.8 | 37.1 | 11.18% |

PVT_9 | 32.6 | 37.6 | 11.16% |

PVT_10 | 32.5 | 38.1 | 11.14% |

PVT_11 | 31.8 | 38.3 | 10.64% |

Condition Name | φ |
---|---|

PVT_12 | 0° |

PVT_13 | 1° |

PVT_14 | 2° |

PVT_15 | 3° |

PVT_16 | 4° |

Condition Name | Average Temperature of the First PV Panel (°C) | Average Temperature of the Second PV Panel (°C) | Photovoltaic Efficiency |
---|---|---|---|

PVT_12 | 34.8 | 35.3 | 11.19% |

PVT_13 | 34.4 | 36.4 | 11.17% |

PVT_14 | 34.5 | 36.9 | 11.15% |

PVT_15 | 34.2 | 37.5 | 11.14% |

PVT_16 | 34.6 | 38.2 | 11.11% |

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**MDPI and ACS Style**

Kang, Z.; Lu, Z.; Song, G.; Yao, Q.
A Numerical Study of Dual-Inlet Air-Cooled PV/T Solar Collectors with Various Airflow Channel Configurations. *Sustainability* **2022**, *14*, 9897.
https://doi.org/10.3390/su14169897

**AMA Style**

Kang Z, Lu Z, Song G, Yao Q.
A Numerical Study of Dual-Inlet Air-Cooled PV/T Solar Collectors with Various Airflow Channel Configurations. *Sustainability*. 2022; 14(16):9897.
https://doi.org/10.3390/su14169897

**Chicago/Turabian Style**

Kang, Zhangyang, Zhaoyang Lu, Gangfu Song, and Qiongqiong Yao.
2022. "A Numerical Study of Dual-Inlet Air-Cooled PV/T Solar Collectors with Various Airflow Channel Configurations" *Sustainability* 14, no. 16: 9897.
https://doi.org/10.3390/su14169897