# Research on the Thermal Characteristics of an 18650 Lithium-Ion Battery Based on an Electrochemical–Thermal Flow Coupling Model

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## Abstract

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## 1. Introduction

_{4}batteries with the P2D model created by COMSOL Multiphysics, finding a 1.9 °C temperature difference between the core and the surface and a 0.9 °C difference between the longitudinal and radial directions. This result was later validated by measurements of LiFePO

_{4}26650 lithium-ion cylindrical cells under different discharge depths [17]. Ghaznavi et al. [18] applied a mathematical approach to conduct a sensitivity study on a lithium–sulfur cell. They focused on the effects of discharge current and positive conductivity over a wide range.

## 2. Establishment of a Lithium-Ion Battery Model

#### 2.1. Basic Electrochemical Model

#### 2.1.1. Conservation of Charge

#### 2.1.2. Conservation of Matter

#### 2.1.3. Electrochemical Reaction Kinetics

#### 2.2. Basic Thermal Model

#### 2.3. An Electrochemical–Thermal Flow Coupling Model

## 3. Model Parameters and Experimental Verification

#### 3.1. Lithium-Ion Battery Model Parameters

#### 3.2. Experimental Verification of Model Validity

## 4. Simulation Results and Analysis

#### 4.1. Results and Analysis of Battery Heat Generation Behavior

#### 4.1.1. Effect of Charge–Discharge Rate on Heat Generation of Battery

#### 4.1.2. Heating Rate of Continuous Charge–Discharge Cycles

#### 4.1.3. Effect of Electrode Thickness on Temperature

#### 4.2. Results and Analysis of Battery Heat Dissipation Behavior

#### 4.2.1. Effect of Inlet Airflow Velocity on Battery Heat Dissipation

#### 4.2.2. Effect of Inlet Flow Area Size on Heat Dissipation

#### 4.2.3. Effect of Airflow Field Direction on Heat Dissipation

## 5. Conclusions

- (1)
- By establishing a three-dimensional electrochemical–thermal current coupling model of the lithium-ion battery, it is convenient and accurate to study the thermal characteristics of the lithium-ion battery, which is more conducive to observing the temperature distribution inside the battery under different working conditions and can obtain results that are difficult to measure by traditional experiments.
- (2)
- The change of charge and discharge rate has a non-linear effect on the temperature of the battery, and the high-rate charge–discharge has a greater effect on the battery temperature. In the condition of short-time continuous charge–discharge cycles, the temperature rise rate is the highest in the first charge–discharge process. After several cycles, the battery temperature is stable. The thickness of battery electrode is directly proportional to the battery capacity and temperature rise.
- (3)
- Increasing the airflow field is of great help to the heat dissipation of the battery. Increasing the inlet airflow velocity can increase the cooling effect of the battery. The greater the inlet velocity, the better the heat dissipation effect. The closer the inlet flow area is to the battery, the better the heat dissipation effect, but the effect on the battery temperature after exceeding one time of the battery radius is not obvious. In the condition of the single airflow field, the cooling effect is best when air enters the positive electrode from the negative electrode of the battery along the axis. In the future, the temperature distribution in the case of battery groups will be studied, and the airflow field will be added to optimize the heat dissipation of battery packs based on the results obtained.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

List of Symbols | |

${\mathrm{a}}_{\mathrm{s}}$ | reaction surface area |

${\mathrm{A}}_{\mathrm{e}}$ | electrode area |

C | ${\mathrm{Li}}^{+}$$\mathrm{concentration}(\mathrm{mol}/{\mathrm{m}}^{3}$) |

D | $\mathrm{diffusion}\mathrm{coefficient}({\mathrm{m}}^{2}/\mathrm{s}$$)$ |

${\mathrm{E}}_{\mathrm{OCV}}$ | $\mathrm{open}\mathrm{circuit}\mathrm{potential}$ |

${\mathrm{E}}_{\mathrm{OCV},\mathrm{ref}}$ | $\mathrm{reference}\mathrm{value}\mathrm{of}\mathrm{open}\mathrm{circuit}\mathrm{voltage}$ |

F | $\mathrm{Faraday}\u2019\mathrm{s}\mathrm{constant}(\mathrm{C}/\mathrm{mol}$$)$ |

$\mathrm{H}$ | convective heat transfer coefficient of the battery |

I | $\mathrm{current}\mathrm{load}\left(\mathrm{A}\right)$ |

${\mathrm{I}}_{\mathrm{pair}}$ | $\mathrm{current}\mathrm{of}\mathrm{a}\mathrm{single}-\mathrm{pair}\mathrm{electrode}\left(\mathrm{A}\right)$ |

${\mathrm{i}}_{0}$ | $\mathrm{exchange}\mathrm{current}\mathrm{density}(\mathrm{A}/{\mathrm{cm}}^{2}$$)$ |

${\mathrm{j}}^{\mathrm{Li}}$ | $\mathrm{current}\mathrm{reaction}\mathrm{density}$ |

${\mathrm{k}}_{\mathrm{i}}$ | $\mathrm{reaction}\mathrm{rate}$ |

L | $\mathrm{thickness}\mathrm{of}\mathrm{the}\mathrm{electrode}(\mathsf{\mu}\mathrm{m}$$)$ |

Q | $\mathrm{heat}\mathrm{generation}\left(\mathrm{W}\right)$ |

${\mathrm{Q}}_{\mathrm{ohm}}$ | ohmic heat |

${\mathrm{Q}}_{\mathrm{rea}}$ | reaction heat |

${\mathrm{Q}}_{\mathrm{act}}$ | active polarization heat |

${\mathrm{Q}}_{\mathrm{conv}}$ | heat dissipation rate |

$\mathrm{r}$ | $\mathrm{radial}\mathrm{coordinate}\mathrm{in}\mathrm{spherical}\mathrm{particle}(\mathsf{\mu}\mathrm{m}$$)$ |

${\mathrm{r}}_{\mathrm{p}}$ | $\mathrm{radius}\mathrm{of}\mathrm{active}\mathrm{substance}$ |

T | temperature (°C) |

${\mathrm{T}}_{\mathrm{amb}}$ | $\mathrm{ambient}\mathrm{temperature}$ |

${\mathrm{T}}_{\mathrm{sol}}$ | $\mathrm{temperature}\mathrm{solved}\mathrm{by}\mathrm{solid}\mathrm{thermal}\mathrm{model}$ |

t | $\mathrm{time}\left(\mathrm{s}\right)$ |

${\mathrm{t}}_{+}$ | $\mathrm{transference}\mathrm{coefficient}$ |

Greek Letters | |

${\mathsf{\alpha}}_{\mathrm{a}}$ | $\mathrm{transfer}\mathrm{coefficients}\mathrm{of}\mathrm{positive}\mathrm{poles}$ |

${\mathsf{\alpha}}_{\mathrm{c}}$ | $\mathrm{transfer}\mathrm{coefficients}\mathrm{of}\mathrm{negative}\mathrm{poles}$ |

${\mathsf{\epsilon}}_{\mathrm{s}}$ | $\mathrm{volume}\mathrm{fraction}\mathrm{of}\mathrm{the}\mathrm{active}\mathrm{material}$ |

${\mathsf{\epsilon}}_{\mathrm{f}}$ | $\mathrm{volume}\mathrm{fraction}\mathrm{of}\mathrm{the}\mathrm{filling}\mathrm{material}$ |

$\mathsf{\eta}$ | $\mathrm{overpotential}\left(\mathrm{V}\right)$ |

$\mathsf{\kappa}$ | $\mathrm{ionic}\mathrm{conductivity}(\mathrm{S}/\mathrm{m}$$)$ |

${\mathsf{\kappa}}_{\mathrm{D}}^{\mathrm{eff}}$ | $\mathrm{diffusion}\mathrm{conductivity}(\mathrm{S}/\mathrm{m}$$)$ |

$\mathsf{\lambda}$ | $\mathrm{thermal}\mathrm{conductivity}\mathrm{of}\mathrm{the}\mathrm{battery}\mathrm{shell}$ |

${\mathsf{\rho}}_{\mathrm{i}}$ | density |

${\mathsf{\sigma}}^{\mathrm{eff}}$ | $\mathrm{solid}-\mathrm{phase}\mathrm{effective}\mathrm{conductivity}$ |

${\mathsf{\sigma}}_{\mathrm{cc}}$ | $\mathrm{current}\mathrm{collector}\mathrm{conductivity}$ |

${\mathsf{\varphi}}_{\mathrm{s}}$ | $\mathrm{solid}-\mathrm{phase}\mathrm{potential}\left(\mathrm{V}\right)$ |

${\mathsf{\varphi}}_{\mathrm{cc}}$ | $\mathrm{current}\mathrm{collector}\mathrm{potential}\left(\mathrm{V}\right)$ |

${\mathsf{\varphi}}_{\mathrm{e}}$ | $\mathrm{electrolyte}\mathrm{potential}\left(\mathrm{V}\right)$ |

Subscripts/Superscripts | |

$\mathrm{cc}$ | current collector |

$\mathrm{e}$ | electrolyte |

$\mathrm{f}$ | filler |

$\mathrm{eff}$ | effective |

$\mathrm{s}$ | solid |

$\mathrm{neg}$ | negative |

$\mathrm{pos}$ | positive |

surf | surface |

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**Figure 8.**Internal temperature distribution of batteries with different rates. (

**a**) 0.5 C charge–discharge rates; (

**b**) 1 C charge–discharge rates; (

**c**) 2 C charge–discharge rates; (

**d**) 4 C charge–discharge rates.

**Figure 14.**Internal temperature distribution of batteries at different air velocity and inlet flow area size.

**Figure 15.**Comparison of heat dissipation capacity in airflow field direction. (

**a**) radial X airflow field direction; (

**b**) radial Z airflow field direction; (

**c**) radial −Z airflow field direction; (

**d**) axial–radial coupling airflow field direction.

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

Capacity (Ah) | 2.9 |

Operating nominal voltage (V) | 3.7 |

Charging cutoff voltage (V) | 4.2 |

Discharge cutoff voltage (V) | 2.5 |

Positive electrode material | $\mathrm{Li}\left[\mathrm{NiCoAl}\right]{\mathrm{O}}_{2}$ |

Negative electrode material | ${\mathrm{Li}}_{\mathrm{x}}{\mathrm{C}}_{6}\mathrm{MCMB}$ |

Electrolyte | ${\mathrm{LiPF}}_{6}/\mathrm{EC}:\mathrm{EMC}\left(3:7\right)$ |

Diameter (mm) | $18.5\pm 0.2$ |

Height (mm) | $64.5\pm 0.5$ |

Parameter | Positive Electrode [31,32] | Separator [33] | Negative Electrode [34,35] |
---|---|---|---|

$\mathrm{Particle}\mathrm{radius}\mathrm{r}(\mathsf{\mu}\mathrm{m}$) | 0.25 | 2.5 | |

Volume fraction of active substances | 0.42 | 0.384 | |

Electrolyte volume fraction [23] | 0.41 | 0.37 | 0.444 |

$\mathrm{Electrolyte}\mathrm{initial}\mathrm{concentration}(\mathrm{mol}/{\mathrm{m}}^{3}$) [23] | 1200 | ||

$\mathrm{Maximum}\mathrm{lithium}-\mathrm{ion}\mathrm{concentration}(\mathrm{mol}/{\mathrm{m}}^{3}$) | 48,000 | 31,507 | |

$\mathrm{Specific}\mathrm{heat}\mathrm{capacity}(\mathrm{J}/\left(\mathrm{kg}\xb7\mathrm{K}\right)$) | 700 | 1978.2 | 1437.4 |

$\mathrm{Thermal}\mathrm{conductivity}(\mathrm{W}/\left(\mathrm{m}\xb7\mathrm{K}\right)$) | 5 | 0.334 | 1.04 |

$\mathrm{Diffusivity}({\mathrm{m}}^{2}/$s) [36] | $1.5\times {10}^{-15}$ | ||

$\mathrm{Electrode}\mathrm{thickness}(\mathsf{\mu}\mathrm{m}$) | 40 | 30 | 55 |

$\mathbf{Positive}\mathbf{Electrode}\mathbf{Thickness}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathbf{Negative}\mathbf{Electrode}\mathbf{Thickness}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathbf{Capacity}(\mathbf{A}\mathbf{h}/{\mathbf{m}}^{2})$ | Average Temperature Rise (K) | Maximum Temperature Rise (K) |
---|---|---|---|---|

40 | 55.00 | 16.210 | 7.780 | 7.969 |

45 | 61.88 | 18.236 | 8.801 | 9.015 |

50 | 68.75 | 20.262 | 9.819 | 10.058 |

55 | 75.63 | 22.288 | 10.880 | 11.147 |

60 | 82.50 | 24.314 | 11.962 | 12.257 |

65 | 89.38 | 26.345 | 13.063 | 13.388 |

70 | 96.25 | 28.367 | 14.160 | 14.514 |

Airflow Field Direction | Average Temperature Rise (K) | Maximum Temperature Rise (K) | Average Temperature Drop (K) | Heat Dissipation Efficiency |
---|---|---|---|---|

No flow field | 22.913 | 22.950 | 0 | 0 |

Radial X | 2.934 | 3.154 | 19.979 | 0.872 |

Axial Z | 2.425 | 2.873 | 20.488 | 0.894 |

Axial −Z | 2.948 | 3.370 | 19.965 | 0.871 |

Axis-diameter coupling | 1.701 | 2.051 | 21.212 | 0.926 |

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**MDPI and ACS Style**

Liu, G.; Zhang, L.
Research on the Thermal Characteristics of an 18650 Lithium-Ion Battery Based on an Electrochemical–Thermal Flow Coupling Model. *World Electr. Veh. J.* **2021**, *12*, 250.
https://doi.org/10.3390/wevj12040250

**AMA Style**

Liu G, Zhang L.
Research on the Thermal Characteristics of an 18650 Lithium-Ion Battery Based on an Electrochemical–Thermal Flow Coupling Model. *World Electric Vehicle Journal*. 2021; 12(4):250.
https://doi.org/10.3390/wevj12040250

**Chicago/Turabian Style**

Liu, Guanchen, and Lijun Zhang.
2021. "Research on the Thermal Characteristics of an 18650 Lithium-Ion Battery Based on an Electrochemical–Thermal Flow Coupling Model" *World Electric Vehicle Journal* 12, no. 4: 250.
https://doi.org/10.3390/wevj12040250