# Effective Cooling System for Solar Photovoltaic Cells Using NEPCM Impingement Jets

^{*}

## Abstract

**:**

^{2}. The latent heat shows a slight improvement at the low particle concentration. Increasing the mass flow rate to 0.12 kg/s enhances the PV output power by 17.32%. While the PV performance is shown to be improved over the increment of the number of nozzles, the jet-to-surface spacing of 5.1 mm records a remarkable PV surface temperature reduction to 33.8 °C, which is the ideal operating temperature for the PV panel.

## 1. Introduction

## 2. Physical and Mathematical Model

#### Problem Definition

## 3. Governing Equations

- -
- Continuity equation

- -
- Momentum equation

- -
- Energy equation

- -
- Volume fraction equation

## 4. Thermo-Physical Properties

## 5. Thermal Assessment

## 6. Numerical Setup

## 7. Numerical Validation

## 8. Results and Discussion

^{2}without JIC systems reached 68.5 °C, which resulted in the PV efficiency of 13.3%. Implementing the present JIC system including the NEPCM slurry significantly increases the efficiency to 15.26%. According to the obtained results, at the solar irradiation of 1000 W/m

^{2}, adding 2% of NEPCM particles into pure water of the JIC system reduces the PV temperature from 43 to 41.7 °C under the same operating conditions. Referring to Equation (11), increasing solar irradiation enhances the PV surface temperature leading to a reduction in the PV efficiency [4]. In addition, Figure 3 shows that the PV efficiency is slightly improved by increasing the latent heat of NEPCM particles from 107.1 kJ/kg to 250 kJ/kg, which is consistent with previous studies [34]. The effective specific heat equation in Table 4 confirms the minor effect of the latent heat at lower concentrations. The maximum efficiency of 15.83% is obtained at I = 600 W/m

^{2}.

_{i}is the facet area and i is the number of facets.

^{2}to evaluate the JIC performance. Previous studies [30] demonstrated that increasing the mass flow rate at the jet inlet raises the turbulence kinetic energy, reduces hydrodynamic and thermal boundary layers, and increases heat transfer. In this regard, Figure 4 compares the velocity contours for the minimum and maximum mass flow rates. It can be found that increasing the inlet mass flow rate results in higher velocity magnitudes, a thinner boundary layer, and moving the strong deflected flow toward the wall jet and farther distances from the stagnation points. Therefore, as shown in Figure 5, higher mass flow rates significantly reduce the PV temperature and improve the temperature uniformity. The mean surface temperature significantly decreases as the mass flow rate increases. In addition, according to Equation (12), lower variance values show a more uniform temperature distribution over the PV panels. Hence, increasing the mass flow rate from 0.045 to 0.12 kg/s results in a temperature reduction of 4.2 °C and higher temperature uniformity.

## 9. Conclusions

- While the conventional PV efficiency under the solar irradiation of 1000 W/m
^{2}reached 13.3%, using the NEPCM-JIC system with the mass flow rate of 0.045 kg/s, the jet-to-surface spacing of 30 mm, and 8 active nozzles increased the efficiency to 15.26%. - Using the NEPCM slurry in the JIC system instead of pure water reduced the PV temperature by 1.3 °C under the same conditions.
- Increasing solar irradiation led to higher surface temperature and lower efficiency. The PV efficiency was maximised under irradiation of 600 W/m
^{2}and the latent heat of 250 kJ/kg. - The PV temperature was significantly reduced when the mass flow rate increased. In addition, the temperature uniformity and output power were improved by increasing the mass flow rate.
- Smaller jet-to-surface distances improved the PV output power, and the minimum PV temperature of 33.8 °C was obtained at H = 5.1 mm.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Effect of solar irradiation and latent heat on the PV temperature at c = 2%, ṁ = 0.045 kg/s, N = 8, and H = 30 mm.

**Figure 4.**Comparison of velocity contours between two mass flow rates in the YZ-plane at c = 2%, I = 1000 W/m

^{2}, h

_{sl}= 107.1 kJ/kg, N = 8, and H = 30 mm. (

**a**) ṁ = 0.045 kg/s and (

**b**) ṁ = 0.12 kg/s.

**Figure 5.**Effect of mass flow rates on the PV temperature and its uniformity at c = 2%, I = 1000 W/m

^{2}, h

_{sl}= 107.1 kJ/kg, N = 8, and H = 30 mm.

**Figure 6.**Effect of nozzle-to-surface spacing on the surface temperature and PV efficiency at c = 2%, I = 1000 W/m

^{2}, h

_{sl}= 107.1 kJ/kg, ṁ = 0.12 kg/s, and N = 24.

Glass | PV Cells | Tedlar | Substrate | |
---|---|---|---|---|

Thickness, t, (mm) | 4 | 0.3 | 0.5 | 0.5 |

Thermal conductivity, k, (W/mk) | 1 | 148 | 0.033 | 202 |

Specific heat capacity, C_{p}, (J/kg·K) | 500 | 677 | 1250 | 903 |

Density, ρ, (kg/m^{3}) | 2450 | 2330 | 1200 | 2702 |

Absorptivity, α | 0.05 | 0.9 | 0.128 | - |

Transmissivity, τ | 0.92 | 0.09 | - | - |

Emissivity, ε | 0.85 | - | - | - |

**Table 2.**Thermophysical properties of water and NEPCM [20].

Materials | ρ (kg/m^{3}) | k (W/m·K) | C_{p} (J/(K·kg)) |
---|---|---|---|

Water | 997 | 0.61 | 4180 |

Octadecane (core) | 850 | 0.34 | 1800 |

Polystyrene (shell) | 1260 | 0.21 | 2130 |

Parameter | Variation Range | |
---|---|---|

Solar irradiation (W/m^{2}) | I | 600–1000 |

Latent heat (kJ/kg) | h_{sl} | 107.1–250 |

Inlet mass flow rate (kg/s) | ṁ | 0.045–0.12 |

Number of nozzles | N | 8–24 |

Jet-to-surface spacing (mm) | H | 5.1–55 |

**Table 4.**Correlations for modelling effective physical properties [27].

Properties | Correlation | ||
---|---|---|---|

Density | ${\rho}_{slurry}=c{\rho}_{p}+\left(1-c\right){\rho}_{w}$ where c is the volumetric concentration of particles. | ||

Dynamic viscosity | ${\mu}_{slurry}={\left(1-c-1.16{c}^{2}\right)}^{-2.5}{\mu}_{w}$ | ||

Thermal conductivity | ${k}_{slurry}={k}_{b}\left(1+BcP{e}_{p}^{m}\right)$ ${k}_{b}={k}_{w}\left({k}_{p}+2{k}_{w}+2\left({k}_{p}-{k}_{w}\right)c\right)/\left({k}_{p}+2{k}_{w}-\left({k}_{p}-w\right)c\right)$ | ||

$\{\begin{array}{c}B=3,m=1.5,P{e}_{p}0.67\\ B=1.8,m=0.18,0.67P{e}_{p}250\\ B=3,m=\frac{1}{11},P{e}_{p}250\end{array}$ | and | $P{e}_{p}=\frac{e{d}_{p}^{2}}{{\alpha}_{bf}}$ | |

where $e$ and $\alpha $ are the shear rate magnitude and thermal diffusivity, respectively [27]. | |||

Specific heat capacity | ${C}_{p,slurry}=\left(1-{c}_{m}\right){C}_{p,w}+{c}_{m}{C}_{p,p}+{c}_{m}{\rm Y}\left[\left\{\frac{\pi}{2}\left(\frac{{h}_{sl}}{{T}_{MR}}-{C}_{p,p}\right)\mathrm{sin}\pi \left[\frac{\left(T-{T}_{s}\right)}{{T}_{MR}}\right]\right\}\right]$$,{\rm Y}$= 0 or 1 where ${c}_{m}$ is the mass concentration of particles. ${h}_{sl}$ is the latent heat, ${T}_{s}$ is the solidus temperature, and ${T}_{MR}$ is the melting range. |

**Table 5.**Effect of mass flow rate on economic factors at c = 2%, I = 1000 W/m

^{2}, h

_{sl}= 107.1 kJ/kg, N = 8, and H = 30 mm.

ṁ (kg/s) | %P(max)increase |
---|---|

0.045 | 14.99 |

0.07 | 16.01 |

0.095 | 16.76 |

0.12 | 17.32 |

**Table 6.**Effect of number of IJs on the PV temperature and PV efficiency at c = 2%, I = 1000 W/m

^{2}, h

_{sl}= 107.1 kJ/kg, ṁ = 0.12 kg/s, and H = 30 mm.

Nozzle No. | T_{PV} (°C) | ${\mathit{\eta}}_{\mathit{P}\mathit{V}}$ |
---|---|---|

8 | 37.55 | 15.56 |

12 | 34.88 | 15.76 |

16 | 34.77 | 15.77 |

20 | 34.75 | 15.78 |

24 | 34.31 | 15.81 |

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**MDPI and ACS Style**

Mohammadpour, J.; Salehi, F.; Lee, A.
Effective Cooling System for Solar Photovoltaic Cells Using NEPCM Impingement Jets. *Thermo* **2022**, *2*, 383-393.
https://doi.org/10.3390/thermo2040026

**AMA Style**

Mohammadpour J, Salehi F, Lee A.
Effective Cooling System for Solar Photovoltaic Cells Using NEPCM Impingement Jets. *Thermo*. 2022; 2(4):383-393.
https://doi.org/10.3390/thermo2040026

**Chicago/Turabian Style**

Mohammadpour, Javad, Fatemeh Salehi, and Ann Lee.
2022. "Effective Cooling System for Solar Photovoltaic Cells Using NEPCM Impingement Jets" *Thermo* 2, no. 4: 383-393.
https://doi.org/10.3390/thermo2040026