# Experimental and Numerical Investigations of a Thermal Management System Using Phase-Change Materials and Forced-Air Cooling for High-Power Li-Ion Battery Packs

^{1}

^{2}

^{3}

^{*}

*Batteries*)

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

_{batg}${\mathrm{Q}}_{batg}$ is the total battery-generated heat, ${Q}_{pcml}$ is the PCM absorbed energy by latent heat, and ${Q}_{pcms}$ is the PCM absorbed energy by sensible heat. ${Q}_{shell}$ and ${Q}_{bati}$ are the internal energy increments of the shell of the plate and battery, respectively. If the sensible heat of the PCM and the other increments of internal energy are ignored, there will be a certain margin for the calculated PCM usage. Taking battery 1 C discharge as an estimate, the estimation formula is as follows.

^{−1}, m

_{pcm}is mass of PCM, the unit is kg. Theoretically, the PCM can absorb less than 100%, 25%, and 11.1% battery heat generation under 1 C, 2 C, and 3 C discharge conditions.

## 3. Mathematical Modeling

#### 3.1. Model Establishment

_{o}is Joule heat, q

_{p}is polarization heat, R

_{o}is battery ohmic resistance, R

_{p}is polarization resistance, and R is equivalent internal resistance and is a constant in this paper.

_{s}

_{1}and T

_{s}

_{2}are the temperatures on the two sides of the solid–solid wall, respectively, ${\lambda}_{s1}$ and ${\lambda}_{s2}$ are the thermal conductivity of two solid regions, respectively, and $n$is the normal unit vector. (5) is a solid–fluid boundary, and the boundary condition is as follows.

#### 3.2. Model Validation and Uncertainty Analysis

## 4. Results and Discussion

#### 4.1. The Thermal Performance at Different Discharge Rates

#### 4.2. Fin Effect on Cooling System

#### 4.3. PCM Container Heat Transfer Analysis

_{A,}and the other side is T

_{B}.

^{−1}·K

^{−1}, and ${\lambda}_{pcm}=0.29$ W·m

^{−1}·K

^{−1}.The relationship between PCM container effective conduction and the fin volume fraction is illustrated in Figure 10. The effective thermal conductivity increases rapidly at low volume fraction while increasing slowly at high volume fraction zone. Hence, improving the fin volume fraction can enforce PCM container heat transfer. However, the volume fraction of the PCM container and the heat capacity of the phase-change material are contradictory. If the volume fraction is too large in the finite volume, the latent heat capacity of the PCM will be insufficient. When the volume fraction is constant, increasing the number of fins will increase the contact area between the fins and the PCM, so the heat conduction ability of the PCM container can be enhanced.

#### 4.4. Phase-Change Materials PCM Container Coupled with Forced-Air Cooling

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Battery module connection. The numbers in the top figure indicate the battery serial number and the numbers in the bottom figure indicate the PCM container serial number.

**Figure 5.**(

**a**) battery module: (

**a1**) battery module without air-forced cooling, The upper number represents the battery serial number, the lower number represents the PCM container serial number. (

**a2**) battery module with air-forced cooling; (

**b**) heat transfer analysis model; (

**c**) battery module mesh.

**Figure 6.**Model validation results: temperature of simulation and experiments at different discharge rates, (

**a**) 1 C; (

**b**) 2 C; (

**c**) 3 C; (

**d**) Relative errors.

**Figure 7.**Temperature rise curve of non-fins PCM container cooling system at different discharge rates: (

**a**) maximum temperature; (

**b**) average temperature; (

**c**) temperature difference. Simulation result of temperature field diagram of the battery pack with a non-fin PCM container at the discharge time t: (

**d**) 1C, t = 3240 s; (

**e**) 2C, t = 1620 s; (

**f**) 3C, t = 1080 s.

**Figure 8.**Temperature curve of battery pack with a different number of fins and temperature field of a battery pack with PCM containers which have different quantities of fins. (

**a**) maximum temperature; (

**b**) average temperature; (

**c**) temperature difference (

**d**) 3-fin PCM container; (

**e**) 5-fin PCM container; (

**f**) 7-fin PCM container.

**Figure 10.**Relationship between effective thermal conductivity and fin volume fraction of PCM container.

**Figure 11.**Solid volume fraction of PCM distribution in plates with different fins at discharge end (3 C).

**Figure 12.**The temperature rise curve of the PCM container coupling forced-air cooling system (

**a**) maximum temperature; (

**b**) average temperature; (

**c**) temperature difference. Temperature field diagram of PCM container coupled forced-air cooling system (

**d**) 5 m/s; (

**e**) 10 m/s; (

**f**) 15 m/s.

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

Battery type | Lithium iron phosphate |

Voltage (V) | 3.2 |

Capacity (Ah) | 16 |

Size (mm) Density (kg·m ^{−3}) | 103 × 65 × 22 2000 |

Specific heat capacity(J·kg^{−1}·K^{−1}) | 1030 |

Thermal conductivity (x, y, z) (W·m^{−1}·K^{−1}) | 0.37/24/24 |

Equivalent internal resistance (mΩ) | 6 |

Maximum sustained discharge rate | 3 C |

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

Paraffin type | 44# |

Supplier | Sheng bang (China) |

Chemical formula | C_{22}H_{46} |

Thermal conductivity (solid/liquid) (W·m ^{−1}·K^{−1}) | 0.29/0.21 |

Melting point (°C) | 44–46 |

Latent heat (J·kg^{−1}) | 189,000 |

Specific heat capacity (J·kg^{−1}·K^{−1}) | 1770 |

Density (kg·m^{−3}) | 910 |

Errors | Discharge Rates | TMP1 | TMP3 |
---|---|---|---|

MAE | 1 C | 0.44 | 0.46 |

2 C | 0.43 | 0.45 | |

3 C | 0.38 | 0.40 | |

RMSE | 1 C | 0.51 | 0.52 |

2 C | 0.50 | 0.50 | |

3 C | 0.44 | 0.41 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Zhao, S.; Zhou, T.; Wang, H.; Li, S.; Yuan, Y.; Ma, Z.; Wei, J.; Zhao, X.
Experimental and Numerical Investigations of a Thermal Management System Using Phase-Change Materials and Forced-Air Cooling for High-Power Li-Ion Battery Packs. *Batteries* **2023**, *9*, 153.
https://doi.org/10.3390/batteries9030153

**AMA Style**

Zhang Y, Zhao S, Zhou T, Wang H, Li S, Yuan Y, Ma Z, Wei J, Zhao X.
Experimental and Numerical Investigations of a Thermal Management System Using Phase-Change Materials and Forced-Air Cooling for High-Power Li-Ion Battery Packs. *Batteries*. 2023; 9(3):153.
https://doi.org/10.3390/batteries9030153

**Chicago/Turabian Style**

Zhang, Yulong, Shupeng Zhao, Tingbo Zhou, Huizhi Wang, Shen Li, Yongwei Yuan, Zhikai Ma, Jiameng Wei, and Xu Zhao.
2023. "Experimental and Numerical Investigations of a Thermal Management System Using Phase-Change Materials and Forced-Air Cooling for High-Power Li-Ion Battery Packs" *Batteries* 9, no. 3: 153.
https://doi.org/10.3390/batteries9030153