# Proposing a Hybrid Thermal Management System Based on Phase Change Material/Metal Foam for Lithium-Ion Batteries

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## Abstract

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## 1. Introduction

_{max}) refers to the highest temperature the battery achieves, while maximum temperature difference (ΔT

_{max}) represents the temperature variation between batteries. Recent studies on air-cooling systems have focused on improving traditional structures and suggesting new designs. Airpath design, cell spacing, and pack arrangement are parameters for battery module optimization [8,9]. The key objectives for air-cooling designs are decreased energy consumption and temperature uniformity [10].

_{max}by approximately 60%. In another study, Fan et al. [14] examined air-cooling performance for parallel and crossed battery modules. They discovered that the aligned configuration had the maximum cooling efficiency and temperature uniformity, and the temperature difference was decreased by 12% compared to the crossed configuration. Kirad et al. [15] concluded that the cell distance between the batteries affects the temperature uniformity, and that the transverse distance impacts the cooling performance. Hasan et al. [16] designed a BTMS for electric vehicles using air cooling to reduce operating temperatures and prevent thermal runaway. The simulation results demonstrated that raising the Reynolds number (Re) and the cell spacing can significantly impact the thermal performance and cooling capacity of LIBs. With an Re of 30,000 and cell spacing of 6 mm, the optimal configuration provided improved electrical properties and extended battery life. Rabiei et al. [17] proposed a novel liquid cold plate for the thermal management of prismatic Li-ion batteries. They used wavy microchannels and metal-foam-embedded microchannels to reduce the maximum temperature by 4–6 °C and 14 °C, respectively, compared to straight microchannels. The anode is a critical component of batteries, and its material selection significantly impacts battery safety, charging efficiency, capacity, and overall lifespan [18]. Sha et al. [19] worked to improve the electrochemical performance of Li

_{4}Ti

_{5}O

_{12}(LTO) anode material for lithium-ion batteries. Their results demonstrated that LTO composites are a promising anode material for lithium-ion batteries with a high discharge capacity, stability, and tap density.

_{max}and T

_{max}are below 3 °C and 50 °C, respectively, at rates less than 2C. A numerical analysis was conducted by Verma et al. [24] using capric acid and paraffin wax as the PCM. Their results showed that using PCM reduced battery temperatures by 9 K compared to before. Zhang et al. [25] studied the effect of PCM dosage on battery temperature control in PCM-based BTMSs. They introduced the “Heat ratio” to analyze dosage. The results showed a lower temperature by increasing PCM heat ratio and thermal conductivity. Iasiello et al. [26] conducted a numerical and experimental study on PCM with aluminum foam. Their study showed that porosity significantly impacts the melting process, more than pores per inch (PPI), and foam orientation. Javani et al. [27] recommended a 3D LIB model; the results indicated that battery temperature was reduced by 3 K for a PCM thickness of 12 mm. Also, the temperature distribution for Li-ion cells was enhanced by almost 10% when a 3 mm thick PCM was employed, which was a significant result for the TMS (thermal management system). In another study by Lamrani et al. [28], PCM was investigated as a TMS for LIBs. Results indicated that PCM reduced maximum battery temperatures by up to 3 °C. The simplified model provides a practical tool for battery pack designers to enhance thermal management systems. Bais et al. [29] studied RT-42 to determine the minimum PCM thickness for Li-ion cells to stay below 323 K at 3C. They found a required thickness of 3 mm. Combining air cooling and PCM significantly improved temperature control and maximum temperature in hybrid systems. In hybrid systems based on PCM, the sensible and latent heat capacities play an essential role, while in active systems, they participate in cooling the PCM [30]. Kermani et al. [31] analyzed the thermal efficiency of a battery module, looking at PCM with copper foam and an air-cooling system for prismatic lithium-ion batteries. Compared to natural convection, T

_{max}using the passive, active, and hybrid systems was reduced by 11 °C, 13 °C, and 24 °C, respectively. For the hybrid power train, Yoongi et al. [32] examined the effect of the melting fraction of PCM and flow rate on the thermal performance of an air-cooled and PCM LIB. The proposed BTMS was designed to maintain maximum temperature after the complete melting of the PCM. They could maintain T

_{max}below 49.2 °C at 4C discharge without consuming additional energy. Limited studies have optimized hybrid cooling systems, focusing only on passive or active ones. Under dynamic cycling, Peng Qin et al. [33] proposed a cooling system using air cooling and PCM. They recommended a 5 mm thickness of PCM for optimal cooling, effectively decreasing T

_{max}and ΔT

_{max}at a high charge/discharge rate of 4C.

- To Analyze the performance of the BTMS using active and passive cooling techniques under forced air and paraffin/aluminum composite.
- To assess the effect of PCM on the BTMS heat dissipation performance, the thickness of PCM is proposed. A more reasonable optimal PCM for the BTMS is also suggested.
- To prevent thermal runaway, the distance between the cells and the airflow has been studied as factors that contribute to maintaining a uniform temperature distribution in the cells.
- PCM thermal conductivity and phase transition temperature are investigated in detail for paraffin and paraffin/Al foams to determine the battery temperature and PCM utilization.

**Table 1.**Comparison between the current study and recent studies on hybrid cooling in lithium-ion batteries.

Research | Ref. | Year | Elements of Cooling System | Battery Type | C-Rate | ${\mathbf{T}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\left(\mathbf{K}\right)$ | $\u2206{\mathbf{T}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\left(\mathbf{K}\right)$ |
---|---|---|---|---|---|---|---|

Yoongi et al. | [32] | 2017 | PCM + Forced air | Prismatic | 4C | 322.3 | 3.2 |

Qin et al. | [33] | 2019 | PCM + Forced air | Cylindrical | 3C | 289.1 | 1.2 |

Kermani et al. | [31] | 2019 | PCM + Copper foam | Pouchy | 5C | 308.9 | 4.6 |

Zhang et al. | [25] | 2021 | PCM | Prismatic | 5C | 314.5 | 2.5 |

Lamrani et al. | [28] | 2021 | PCM | Cylindrical | 3C | 305.1 | - |

Yang et al. | [34] | 2022 | Forced air | Prismatic | 4C | 324.8 | 2.8 |

Current study | - | - | PCM + Aluminum foam + Forced air | Cylindrical | 5C | 308.1 | 2 |

## 2. Materials and Methods

#### 2.1. Modelling and Governing Equations

- The fluid flow is incompressible, and the flow regime is laminar and turbulent for different fluid velocities.
- Radiative heat transfer is neglected.
- The Boussinesq approximation estimates natural convection due to buoyancy.
- The metal foam is assumed to be isotropic and homogeneous.
- Volume expansion is neglected.

#### 2.1.1. Battery

#### 2.1.2. Coolant

#### 2.1.3. Phase Change Material

#### 2.2. Boundary and Initial Conditions

- The battery cells are fully charged.
- Initially, all module components have a temperature equal to the ambient temperature (24.5 °C).
- The cell heat generated is considered at 5C.
- The convective heat transfer coefficient between the battery and the environment equals 5 (W/m·K).
- The bottom wall of the battery module is thermally insulated.
- This study investigates five different cooling air temperatures (10, 15, 20, 24.5, and 30 °C) to dissipate heat and create suitable working conditions.

## 3. Numerical Method and Mesh Independency

^{−6}, 10

^{−6}, and 10

^{−9}for the continuity, velocity, and energy equations, respectively. The results of a mesh independence study for the average battery temperature distribution are shown in Figure 3. Meshes with varying numbers of elements, i.e., 93, 160, 175, 800, 251, 200, 359, 070, and 462,125, were selected for comparison. The differences between the average temperature values at the designated point is obtained when the mesh elements number was 251,200(less than 1%). Therefore, it was decided that the optimum mesh element number was 251,200, which was sufficient to achieve the desired accuracy while saving computational time. Consequently, this study selected an optimal mesh size for all cases.

## 4. Validation of Numerical Model

^{5}was employed [45,46]. The PCM initially starts to melt at a temperature of 22 °C and under conditions where adjacent walls are above the melting point of the fluid at a temperature of 30 °C. During the simulation process, under-relaxation coefficients of 0.3, 0.5, and 0.9 are applied to the pressure, momentum, and liquid fraction relation equations, respectively. Also, validation was conducted with a time step of 0.01 s and 20 iterations per time step. According to Figure 4b, with a maximum deviation of less than 5% from the experimental data, the numerical results of this study are acceptable.

## 5. Results and Discussion

#### 5.1. Effect of Air Inlet Velocity

#### 5.2. The Effect of PCM Thickness

#### 5.3. Effect of Cell Distance

#### 5.4. Impact of Metal Foam

#### 5.5. Effect of Air Inlet Temperature

## 6. Conclusions

- The paraffin/aluminum composite provides better thermal performance than paraffin alone for battery packs, since the high thermal conductivity of paraffin can transfer the heat produced by the batteries to the PCM and surrounding environment. As a result, the temperature distribution becomes more uniform, and the temperature decreases.
- With an increased air temperature, the temperature increases, followed by a decrease in the temperature difference. The proposed system can maintain the uniformity of temperature and the temperature in the optimal range for the battery under a cooling temperature of 10 to 24.5 °C.
- Increasing the thickness of paraffin can affect the efficiency of the BTMS. The proposed system is a paraffin/aluminum composite with a thickness of 3 mm. Increasing the thickness and combining aluminum foam with paraffin improves the capacity for temperature control in the thermal management system and maintains the cell temperature at 35 °C.
- Increasing the inlet air velocity improves temperature control, but the uniformity of the battery pack temperature worsens. Under a discharge rate of 5C and an environment temperature of 24.5 °C, with an inlet speed of 2 m/s, the proposed system can maintain the temperature difference and maximum temperature at 2.04 K and 308 K, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

C: | Discharge rate (C) |

H: | $\mathrm{Enthalpy}\left(\mathrm{k}\mathrm{J}\right)$ |

${\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{f}}$: | $\mathrm{Enthalpy}\mathrm{at}\mathrm{the}\mathrm{reference}\mathrm{point}\left(\mathrm{k}\mathrm{J}\right)$ |

${\mathrm{H}}_{0}$: | $\mathrm{Sensible}\mathrm{enthalpy}\left(\mathrm{k}\mathrm{J}\right)$ |

${\mathrm{Q}}_{\mathrm{g}\mathrm{e}\mathrm{n}}$: | $\mathrm{Heat}\mathrm{generation}\left(\mathrm{W}\right)$ |

${\mathrm{Q}}_{\mathrm{i}\mathrm{r}}$: | $\mathrm{Irreversible}\mathrm{heat}\mathrm{generation}\left(\mathrm{W}\right)$ |

${\mathrm{Q}}_{\mathrm{r}\mathrm{e}}$: | $\mathrm{Reversible}\mathrm{heat}\mathrm{generation}\left(\mathrm{W}\right)$ |

S: | Heat source |

k: | Thermal conductivity (W/m·K) |

${\mathrm{k}}_{\mathrm{a}}$: | Air thermal conductivity (W/m·K) |

K: | Turbulent kinetic energy (m^{2}/s^{2}) |

${\mathrm{P}}_{\mathrm{K}}$: | Turbulence production |

${\mathrm{C}}_{\mathsf{\epsilon}}$: | Empirical parameters |

${\mathrm{C}}_{\mathsf{\mu}}$: | Parameters of the $\mathrm{K}-\mathsf{\epsilon}$ turbulence model |

R: | $\mathrm{Internal}\mathrm{resistance}\left(\mathsf{\Omega}\right)$ |

$\frac{\partial {\mathrm{U}}_{\mathrm{O}\mathrm{C}\mathrm{V}}}{\partial \mathrm{T}}$: | Temperature coefficient of open-circuit voltage (V/K) |

${\mathrm{U}}_{\mathrm{O}\mathrm{C}\mathrm{V}}$: | Open-circuit voltage (V) |

$\mathrm{U}$: | Battery voltage (V) |

I: | Cell charge/discharge current (A) |

m: | Mass (kg) |

${\mathrm{m}}_{\mathrm{b}}$: | Battery mass (kg) |

L: | Characteristic length |

$\mathrm{v}$: | Volume (m^{3}) |

${\mathrm{v}}_{\mathrm{b}}$: | Battery volume (m^{3}) |

${\mathrm{C}}_{\mathrm{p}}$: | Specific heat capacity (J/kg·K) |

${\mathrm{C}}_{\mathrm{p}\mathrm{b}}$: | Battery specific heat capacity (J/kg·K) |

${\mathrm{C}}_{\mathrm{p}\mathrm{a}}$: | Air specific heat capacity (J/kg·K) |

T: | Temperature (K) |

${\mathrm{T}}_{\mathrm{a}}$: | Air temperature (K) |

${\mathrm{T}}_{\mathrm{L}}$: | Melting temperature (K) |

${\mathrm{T}}_{\mathrm{S}}$: | Solidus temperature (K) |

${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$: | Maximum temperature (K) |

${\u2206\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$: | Maximum temperature difference (K) |

t: | Time (s) |

V: | Velocity (m/s) |

Re: | Reynolds number |

Greek symbols | |

$\mathsf{\beta}$: | Melting fraction of phase change material |

$\mathsf{\gamma}$: | $\mathrm{Specific}\mathrm{enthalpy}\mathrm{of}\mathrm{phase}\mathrm{change}\mathrm{material}\left(\frac{\mathrm{k}\mathrm{J}}{\mathrm{k}\mathrm{g}}\right)$ |

$\mathsf{\rho}$: | $\mathrm{Density}(\frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^{3}}$) |

${\mathsf{\rho}}_{\mathrm{b}}$: | $\mathrm{Battery}\mathrm{density}(\frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^{3}}$) |

${\mathsf{\rho}}_{\mathrm{a}}$: | $\mathrm{Air}\mathrm{density}(\frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^{3}}$) |

$\mathsf{\mu}$: | Viscosity (kg·m/S) |

${\mathsf{\mu}}_{\mathrm{a}}$: | Air viscosity (kg·m/S) |

${\mathsf{\mu}}_{\mathrm{T}}$: | Turbulent viscosity coefficient |

ε: | Turbulent dissipation rate |

$\mathsf{\sigma}$: | $\mathrm{Inverse}\mathrm{effective}\mathrm{Prandtl}\mathrm{numbers}\mathrm{of}\mathrm{K}$$\mathrm{and}\mathsf{\epsilon}$ |

Abbreviations | |

BTMS: | Battery thermal management system |

PCM: | Phase change materials |

SOC: | State of charge |

PPI: | Pores per inch |

LIB: | Lithium-ion battery |

TMS: | Thermal management system |

CFD: | Computational fluid dynamics |

UDF: | User-defined function |

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**Figure 1.**(

**a**) Geometry and (

**b**) schematic of LIB pack with the phase change material cooling system and cooling fan.

**Figure 2.**Mesh distribution across the battery and fluid domains: (

**a**) battery grid, (

**b**) PCM module grid, (

**c**) BTMS grid.

**Figure 5.**(

**a**) Influence of inlet velocity on T

_{max}. (

**b**) Comparison of ΔT

_{max}at different inlet velocities.

**Figure 7.**Temperature distribution contour at various cell spacings: (

**a**) 21 mm spacing, (

**b**) 23 mm spacing, (

**c**) 25 mm spacing.

**Figure 10.**Contour plot of cooled battery pack temperature distribution by the PCM: (

**a**) Paraffin, (

**b**) paraffin/aluminum composite.

**Figure 11.**Contour plot of the melting fraction of phase change material up to 700 s: (

**a**) Paraffin, (

**b**) paraffin/aluminum composite.

Properties | Value |
---|---|

Density (kg/m^{3}) | 2700 |

Thermal conductivity (radial) (W/m·K) | 0.2 |

Thermal conductivity (axial) (W/m·K) | 31.15 |

Specific heat capacity (J/kg·K) | 1726 |

Height (mm) | 65 |

Diameter (mm) | 18 |

Nominal capacity (mAh) | 3000 |

Charging voltage (V) | 4.20 |

Nominal voltage (V) | 3.6 |

Lifecycles (cycles) | 300 @0.5C to 80% |

Discharge end voltage (V) | 2.5 |

Weight (g) | 45.50 |

Max. continuous discharge current (A) | 15 |

Properties | Aluminum [36] | Air [37] | Paraffin RT27 [38] | RT27—Metal Foam Composite [36] |
---|---|---|---|---|

Specific heat capacity (J/kg·K) | 910 | 1005 | 2500 | 1195.68 |

Thermal conductivity (W/m·K) | 237 | 0.0267 | 0.2 | 4.49 |

Latent heat (kJ/kg) | - | - | 179 | - |

Density (kg/m^{3}) | 2800 | 1.165 | 870 at 299 K 781.5 at 301 K 750 at 343 K | 1005 (Solid) 902 (Liquid) |

Viscosity (kg·m/S) | - | 1.86 × 10^{−5} | −1.137439E − 8T^{3} + 1.178188E − 5T^{2}–0.004111388T + 0.4857203 | - |

Solidus temperature (K) | - | - | 297.65 | - |

Melting temperature (K) | - | - | 300.15 | 300.15 |

**Table 4.**Polynomial modeling of equivalent internal resistance (R) at different temperatures [40].

Polynomial Fitting of Equivalent Internal Resistance (R) | Temperature (K) |
---|---|

58 − 355 × SOC + 1898 × SOC^{2} − 5121 × SOC^{3} + 7376 × SOC^{4} − 5374 × SOC^{5} + 1559 × SOC^{6} | 333 |

58 − 355 × SOC + 1898 × SOC^{2} − 5121 × SOC^{3} + 7376 × SOC^{4} − 5374 × SOC^{5} + 1559 × SOC^{6} | 323 |

66 − 382 × SOC + 1962 × SOC^{2} − 5181 × SOC^{3} + 7378 × SOC^{4} − 5365 × SOC^{5} + 1559 × SOC^{6} | 313 |

107 − 793 × SOC + 4036 × SOC^{2} − 10,514 × SOC^{3} + 14,700 × SOC^{4} − 10,480 × SOC^{5} + 2989 × SOC^{6} | 303 |

166 − 1334 × SOC + 6559 × SOC^{2} − 16,531 × SOC^{3} + 22,391 × SOC^{4} − 15,496 × SOC^{5} + 4301 × SOC^{6} | 293 |

Velocity (m/s) | Reynolds |
---|---|

0 | 0 |

0.5 | 1403.4 |

1.5 | 4210.2 |

2 | 5613.6 |

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## Share and Cite

**MDPI and ACS Style**

Saeedipour, S.; Gharehghani, A.; Ahbabi Saray, J.; Andwari, A.M.; Mikulski, M.
Proposing a Hybrid Thermal Management System Based on Phase Change Material/Metal Foam for Lithium-Ion Batteries. *World Electr. Veh. J.* **2023**, *14*, 240.
https://doi.org/10.3390/wevj14090240

**AMA Style**

Saeedipour S, Gharehghani A, Ahbabi Saray J, Andwari AM, Mikulski M.
Proposing a Hybrid Thermal Management System Based on Phase Change Material/Metal Foam for Lithium-Ion Batteries. *World Electric Vehicle Journal*. 2023; 14(9):240.
https://doi.org/10.3390/wevj14090240

**Chicago/Turabian Style**

Saeedipour, Soheil, Ayat Gharehghani, Jabraeil Ahbabi Saray, Amin Mahmoudzadeh Andwari, and Maciej Mikulski.
2023. "Proposing a Hybrid Thermal Management System Based on Phase Change Material/Metal Foam for Lithium-Ion Batteries" *World Electric Vehicle Journal* 14, no. 9: 240.
https://doi.org/10.3390/wevj14090240