# Thermal and Optical Analyses of a Hybrid Solar Photovoltaic/Thermal (PV/T) Collector with Asymmetric Reflector: Numerical Modeling and Validation with Experimental Results

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions. Solar energy can be utilized for a wide range of applications, from domestic hot water and domestic heating and cooling to industrial applications and electricity production by ensuring lower conventional sources consumption and more useful energy production which leads to sustainability. The simplest way to exploit solar energy potential is by employing solar collectors, which can transform solar energy into heat, electricity, or both.

## 2. Materials and Method

#### 2.1. The Solar Collector

#### 2.2. Mathematical Modeling

#### 2.3. Numerical Modeling

#### 2.3.1. Simulation Tools

#### 2.3.2. Ray-Tracing Analysis

^{2}. It is important to mention that the sunshape is simulated as pillbox in each of the three packages. The input data for the ray-tracing analysis are given in Table 3.

#### 2.3.3. Thermal Analysis Modeling Method

_{ai}). Table 4 gives an example of how the modeling method was applied in terms of solution convergence.

#### 2.3.4. Mesh Independency

#### 2.3.5. Operating Conditions in Thermal Simulations

^{2}and the diffusive portion of solar irradiation took the value of 230 W/m

^{2}. The environmental air temperature was set to 25.5 °C and the wind velocity was equal to 3.6 m/s. From Equation (10) the heat-transfer coefficient of the wind was calculated and took the value of 13.3 W/m

^{2}/K. As mentioned in Section 2.3.3, the convective heat-transfer coefficient of the enclosed air gap was assumed to be constant and equal to 5 W/m

^{2}/K, which is a reasonable value for such closed areas while similar values could be found in studies [3,36]. The thermal simulation operating conditions are, also, available in Table 6.

#### 2.4. Experimental Validation

^{2}/K, according to Equation (10). The experimental values of the effective solar irradiation intensity, which were calculated by Equation (4), the environment air temperature, the inlet water temperature, the volumetric water flow rate, and the convective heat-transfer coefficient of the wind were set as inputs in the simulations.

## 3. Results and Discussion

#### 3.1. Ray Tracing Simulation Verification

#### 3.2. Results of the Validation with Experimental Data

#### 3.3. Optical Performance Analysis

#### 3.4. Thermal Performance Analysis

## 4. Conclusions

- The ray-tracing results were verified by applying three different programs (Tonatiuh, COMSOL, and SolidWorks) with average deviations lower than 4% among the solutions.
- A novel modeling method was proposed regarding the thermal analysis part and its validity was evaluated by applying it via two different packages (COMSOL and SolidWorks) and comparing it with experimental data. The results indicated that the simulation values were very close to the experimental ones, with maximum deviations lower than 10%, while the two simulation tools obtained similar results with 6.15% maximum declination between each other. Hence, the proposed modeling method was both validated and verified.
- The proposed modeling method ensures sustainability, since it provides the desirable results with lighter computational domain than conventional CFD models, considering that it does not solve the air function at the interior of the gap space, but it takes into consideration the effect of the air presence by an alternative way.
- Through the method proposed it was possible to determine the optimum inclination angle of the collector for each one of the examined months, while it was revealed that the optimum value for the inclination angle decreases going from March to June and increases from June to September.
- The optimization of the tilt angle in each examined case ensures the maximum possible enhancement of the overall performance of the collector, rendering it more sustainable.
- A significant point to mention was that the optimum inclination angle remained constant around a solar time range between 10:00 and 14:00, almost for each month.
- Another important thing to mention is that the examined collector obtains a sufficient thermal efficiency of up to 63% considering an operation between 20 °C and 80 °C inlet temperature. The optical efficiency reaches 76% at optimum tilt angles.
- The electrical output was found to decrease with the increment of the inlet temperature, due to the fact that the PVs temperature increases too.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

General Parameters | Subscripts | ||

A | Surface area, m^{2} | a | Ambient |

Cp | Fluid specific heat, kJ/(kg K) | abs | Absorbed |

G | Solar irradiation, W/m^{2} | b | Beam |

h | Heat convection coefficient, W/(m^{2} K) | bot | Bottom |

L | Length, m | c | Collector |

m | Mass flow rate, m^{2}/s | cpc | Utilized by the reflector |

P | Power, W | d | Diffuse |

Q | Energy rate, W | eff | Effective |

T | Temperature, °C | el | Electrical |

u | Wind speed, m/s | f | Fluid |

V | Volume flow rate, m^{3}/s | i | Inlet |

Greek symbols | losses | Losses | |

β | Temperature coefficient of PV cell, %/K | max | Maximum |

δ | Declination, ° | n | Normal |

η | Efficiency | o | Outlet |

θ | Incident angle, ° | opt | Optical |

Dimensionless numbers | out | Outside | |

C | Concentration ratio | pv | Photovoltaic |

Abbreviations | r | Receiver | |

ACPC | Asymmetric Compound Parabolic Collector | ref | Reference |

CFD | Computational Fluid Dynamics | s | Solar |

CPC | Compound Parabolic Collectors | sky | Sky |

ETC | Evacuated Tube Collector | T | Perpendicular to aperture |

FPC | Flat Plate Collector | th | Thermal |

IAM | Incident Angle Modifier | top | Top |

PTC | Parabolic Trough Collectors | u | Useful |

PV/T | Photovoltaic/Thermal | ||

STC | Standard Test Conditions |

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**Figure 11.**Absorbed solar power, Useful power, Thermal losses, and Electrical output of the collector in the whole inlet temperature range.

**Figure 13.**Temperature allocations of the top and the bottom PV of the receiver for T

_{f,i}= 60 °C.

**Table 1.**Optical characteristics of the collector [32].

Parameters | Values |
---|---|

Cover emittance | 0.95 |

Cover transmittance | 0.95 |

Reflector emittance | 0.05 |

Reflector reflectance | 0.94 |

Receiver absorptance | 0.93 |

Receiver emittance | 0.90 |

**Table 2.**Geometrical characteristics of the collector [32].

Parameter | Value |
---|---|

Collector Length | 2.29 m |

Collector Width | 0.464 m |

Receiver Width | 0.157 m |

Geometrical Concentration ratio | 1.51 |

Reflector Parabolic Profile Focal Length | 0.144 m |

Reflector Circular Profile Radius | 0.144 m |

Parameter | Value |
---|---|

Intensity of Solar irradiance | 1000 W/m^{2} |

Solar rays | 10^{6} |

Incident angle (transversal direction) | 0–60° |

Test Point | T_{ai} | T_{f,i} | T_{f,o} | Q_{losses,1}(from Receiver) | Q_{losses,2}(from Outer Surfaces) | |
---|---|---|---|---|---|---|

1 | 23 | 36.2 | 38.65 | 134.9 | > | 123.7 |

2 | 24 | 36.2 | 38.68 | 130.7 | < | 133.5 |

Linear interpolation | 23.8 | 36.2 | 38.674 | 131.54 | = | 131.54 |

Mesh Name | Mesh_1 | Mesh_2 | Mesh_3 |
---|---|---|---|

Total Mesh Grid Elements (×10^{6}) | 0.60 | 0.75 | 0.95 |

Water Mesh Grid Elements (×10^{6}) | 0.16 | 0.28 | 0.48 |

Receiver Mesh Grid Elements (×10^{6}) | 0.26 | 0.27 | 0.33 |

Parameter | Value | Units |
---|---|---|

Direct Solar Irradiance | 653 | W/m^{2} |

Diffusive Solar Irradiance | 230 | W/m^{2} |

Sun Rays | 10^{6} | rays |

Environment Air Temperature | 25.5 | °C |

Wind Velocity | 3.6 | m/s |

Wind Heat Transfer Coefficient | 13.3 | W/m^{2}/K |

Enclosed Air Heat Transfer Coefficient | 5 | W/m^{2}/K |

Inlet Water Temperature | 20–80 | °C |

Volumetric Water Flow rate | 2.2 | lt/min |

**Table 7.**Experimental data [32].

Experimental Point | G_{bT} (W/m^{2}) | G_{d} (W/m^{2}) | Ta (°C) | T_{f,i} (°C) | T_{f,o} (°C) | V_{f} (lt/min) |
---|---|---|---|---|---|---|

1 | 978.3 | 93.1 | 18.6 | 33.6 | 36.6 | 2.2 |

2 | 757.8 | 145.5 | 21.6 | 36.2 | 39 | 2.1 |

3 | 946 | 77.2 | 20.1 | 46.3 | 48.4 | 2.2 |

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## Share and Cite

**MDPI and ACS Style**

Korres, D.N.; Papingiotis, T.; Koronaki, I.; Tzivanidis, C.
Thermal and Optical Analyses of a Hybrid Solar Photovoltaic/Thermal (PV/T) Collector with Asymmetric Reflector: Numerical Modeling and Validation with Experimental Results. *Sustainability* **2023**, *15*, 9932.
https://doi.org/10.3390/su15139932

**AMA Style**

Korres DN, Papingiotis T, Koronaki I, Tzivanidis C.
Thermal and Optical Analyses of a Hybrid Solar Photovoltaic/Thermal (PV/T) Collector with Asymmetric Reflector: Numerical Modeling and Validation with Experimental Results. *Sustainability*. 2023; 15(13):9932.
https://doi.org/10.3390/su15139932

**Chicago/Turabian Style**

Korres, Dimitrios N., Theodoros Papingiotis, Irene Koronaki, and Christos Tzivanidis.
2023. "Thermal and Optical Analyses of a Hybrid Solar Photovoltaic/Thermal (PV/T) Collector with Asymmetric Reflector: Numerical Modeling and Validation with Experimental Results" *Sustainability* 15, no. 13: 9932.
https://doi.org/10.3390/su15139932