In this article, I present my research work on the design and numerical evaluation of a phase change material (PCM) composite fin structure for thermal management of an EV battery pack. The core novelty of this study lies in the application of topology optimization to design the metallic fins embedded in the PCM. Traditional straight fins used in battery cooling often have a simple geometry that does not distribute heat efficiently, especially under high discharge rates. By using topology optimization, I was able to generate a tree‑like branched fin structure that significantly enhances heat transfer from the battery cells into the PCM, thereby lowering the maximum temperature and improving temperature uniformity. Throughout this paper, I focus on the thermal performance of the optimized fins for both prismatic and cylindrical cells, the effect of air‑cooling schemes in combination with the PCM‑fin structure, and the ability of the optimized fin to suppress thermal runaway propagation in an EV battery pack.
1. Battery Heat Generation Model and Validation
The thermal behavior of a lithium‑ion battery is governed by the heat generation rate, the heat capacity of the cell, and the heat transfer paths to the surroundings. In an EV battery pack, each cell can be considered as a homogeneous heat source with anisotropic thermal conductivities. I adopted the classic Bernardi heat generation model to compute the volumetric heat generation rate:
$$
q = \frac{I}{V} \left( U_{\text{ocv}} – T \frac{dU_{\text{ocv}}}{dT} – I R_e \right)
$$
where \(I\) is the current, \(V\) the cell volume, \(U_{\text{ocv}}\) the open‑circuit voltage, \(T\) the temperature, \(R_e\) the total internal resistance, and \(dU_{\text{ocv}}/dT\) the entropy coefficient. Since the heat capacity and density of the cell vary only slightly with temperature in the operating range, I simplified the model by assuming constant average thermo‑physical properties. The transient heat conduction within the cell is:
$$
\rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + q
$$
For the prismatic cell (dimensions 148 mm × 27 mm × 91 mm, capacity 51 Ah), the density, specific heat, and thermal conductivities are summarized in Table 1. For the cylindrical 18650 cell (capacity 2.6 Ah), the properties are also given.
| Parameter | Prismatic cell | Cylindrical cell (18650) |
|---|---|---|
| Capacity (Ah) | 51 | 2.6 |
| Mass (g) | 816.47 | 47.5 |
| Dimensions (mm) | 148 × 27 × 91 | R=18, H=65 |
| Specific heat \(C_p\) (J·kg⁻¹·K⁻¹) | 1050.31 | 1200 |
| In‑plane thermal conductivity \(k_{xy}\) (W·m⁻¹·K⁻¹) | 14 | 0.2 |
| Through‑plane thermal conductivity \(k_z\) (W·m⁻¹·K⁻¹) | 1.31 | 37.6 |
| Density (kg·m⁻³) | 2245.3 | 2873.5 |
To validate the model, I compared the simulated surface temperature with experimental data for discharge rates of 1C, 2C, and 3C under natural convection at an ambient temperature of 25 °C. The maximum error remained below 5%, confirming that the model can accurately represent the temperature evolution of the cell during discharge. This validated model was then used to design the PCM cooling system and to evaluate the effect of topology‑optimized fins on the EV battery pack temperature.
2. Topology Optimization of PCM Composite Fins
I used a two‑dimensional design domain representing a cross‑section of the phase change material surrounding the battery cell. The design variable is the normalized density \(\gamma\) that interpolates between two phases: \(\gamma = 0\) corresponds to PCM (n‑eicosane) and \(\gamma = 1\) corresponds to aluminium fin material. The material interpolation follows the SIMP (Solid Isotropic Material with Penalization) model:
$$
k(\gamma) = k_{\text{pcm}} + \gamma^p (k_{\text{fin}} – k_{\text{pcm}})
$$
$$
\rho(\gamma) = \rho_{\text{pcm}} + \gamma (\rho_{\text{fin}} – \rho_{\text{pcm}})
$$
$$
C_p(\gamma) = C_{p,\text{pcm}} + \gamma (C_{p,\text{fin}} – C_{p,\text{pcm}})
$$
Here, \(p\) is the penalization factor (taken as 3 in this work). To avoid checkerboard patterns and mesh dependency, I applied a Helmholtz filter to the design variables and then a hyperbolic tangent projection to obtain a sharp 0‑1 solution. The filtered variable \(\tilde{\gamma}\) is obtained from the raw field \(\gamma_c\) by:
$$
\tilde{\gamma} = \gamma_c + r_{\min}^2 \nabla^2 \gamma_c
$$
and the projection is:
$$
\tilde{\gamma}_{\beta} = \frac{\tanh(\beta \tilde{\gamma} – \beta \gamma_{\beta}) + \tanh(\beta \gamma_{\beta})}{\tanh(\beta (1-\gamma_{\beta})) + \tanh(\beta \gamma_{\beta})}
$$
with the projection slope \(\beta = 8\) and projection point \(\gamma_{\beta} = 0.5\). This approach produced a crisp fin geometry that is feasible for additive manufacturing and further reconstruction.
Among the two objective functions I tested, namely minimum thermal compliance and minimum average temperature, the latter yielded lower battery temperatures in almost all cases. Therefore, I selected the average temperature over the entire computational domain as the objective function. The problem is formulated as:
$$
\min_{\gamma} \frac{1}{V_{\Omega}} \int_{\Omega} T(\gamma) \, d\Omega
$$
subject to the volume constraint:
$$
\int_{\Omega} \gamma \, d\Omega \le \omega V_{\Omega}
$$
where \(\omega\) is the volume fraction of the fin with respect to the PCM domain, and \(V_{\Omega}\) is the total volume of the design region (PCM + fin). The heat source is the battery cell, and the outer boundaries are assumed adiabatic because the battery pack is considered symmetric.
3. Results for Prismatic Cells
I first investigated a prismatic cell module. The required PCM volume was calculated based on the heat generated during a full 3C discharge (1200 s) and the latent heat of n‑eicosane (241 kJ·kg⁻¹). The volume of PCM was determined to be 23.144 cm³. I then performed topology optimization for several volume fractions \(\omega = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6\). As \(\omega\) increases, the optimized fin structure becomes thicker and exhibits multiple branched channels, which helps distribute heat more evenly throughout the PCM domain. Figure 1 shows an example of an optimized topology (for \(\omega = 0.4\)) along with the schematic of the computational domain.
I compared the optimized fin topology against the conventional straight fin design having the same volume fraction. Figure 2 shows the temperature contours at the end of 3C discharge for both fin types. The topology‑optimized fin clearly produces a more uniform temperature distribution in the PCM, and the temperature of the battery cell is noticeably lower. The quantitative comparison is presented in Table 2. At \(\omega = 0.1\), the straight fin gave a battery temperature of 44.3 °C, while the optimized topology gave 40.3 °C. At \(\omega = 0.6\), the corresponding temperatures were 41.3 °C and 37.1 °C. Thus, the topology‑optimized fin reduces the battery temperature by 8.2% at \(\omega = 0.1\) and by 10.1% at \(\omega = 0.6\), compared to the straight fin.
| Volume fraction \(\omega\) | Straight fin temperature (°C) | Topology fin temperature (°C) | Reduction (%) |
|---|---|---|---|
| 0.1 | 44.3 | 40.3 | 8.2 |
| 0.3 | 42.1 | 38.4 | 8.8 |
| 0.6 | 41.3 | 37.1 | 10.1 |
In addition, for the topology‑optimized structure alone, increasing \(\omega\) from 0.1 to 0.6 reduced the battery temperature by 7.9% (from 40.3 °C to 37.1 °C). However, the improvement became marginal when \(\omega\) exceeded 0.4: the temperatures at \(\omega = 0.4, 0.5, 0.6\) were 37.4, 37.2, and 37.1 °C respectively. Therefore, \(\omega = 0.4\) is a reasonable trade‑off between good heat dissipation and material cost. The reason for this saturation is that with too many fins, the PCM volume becomes too small to store the latent heat, and the heat transfer path is already sufficient; thus, adding more fin material does not significantly lower the temperature.
I also examined the effect of the objective function. The topology obtained with the average‑temperature objective produced a battery temperature that is about 0.5–1.0 °C lower than that obtained with thermal compliance objective for \(\omega = 0.1\). For larger \(\omega\), the difference becomes smaller. This confirms that the average‑temperature formulation is more suitable for PCM‑fin optimization because it directly minimizes the cell temperature, whereas the thermal compliance only indirectly affects the cell temperature.
4. Results for Cylindrical Cells
For the cylindrical 18650 cell, the required PCM volume was calculated to be 13.715 cm³. I considered two different arrangements of cylindrical cells in the EV battery pack: the square array and the hexagonal array. These arrangements lead to different shapes of the PCM domain, which in turn affect the optimized fin topology. Figure 3 illustrates the square and hexagonal arrangements.
For the square arrangement, the PCM domain is a square with side length \(a_s\) that changes with \(\omega\). For the hexagonal arrangement, the PCM domain is a regular hexagon with side length \(a_h\). The relation between these side lengths and \(\omega\) is shown in Table 3.
| Volume fraction \(\omega\) | Square side length (mm) | Hexagon side length (mm) |
|---|---|---|
| 0.1 | 16.5 | 14.8 |
| 0.2 | 17.3 | 15.5 |
| 0.3 | 18.0 | 16.2 |
| 0.4 | 18.7 | 16.8 |
| 0.5 | 19.3 | 17.4 |
In the square arrangement, the optimized topologies for \(\omega = 0.1\) to 0.5 all show branched fins that extend toward the corners of the square domain. In the hexagonal arrangement, the fins form a similar tree‑like pattern but with a slightly different orientation to match the hexagonal boundary. I simulated the transient temperature during 3C discharge for both arrays. The comparison between straight fins and optimized fins at \(\omega = 0.1\) is given in Table 4.
| Arrangement | Straight fin temperature (°C) | Topology fin temperature (°C) | Reduction (%) |
|---|---|---|---|
| Square | 45.4 | 42.7 | 6.0 |
| Hexagonal | 45.2 | 41.7 | 7.8 |
The hexagonal arrangement clearly benefits more from topology optimization because the angular geometry allows the branched fins to cover the PCM more effectively. For the topology‑optimized structures, the battery temperatures at the end of discharge are listed in Table 5 for both arrangements. The hexagonal arrangement always yields a lower battery temperature than the square arrangement, especially at low volume fractions. At \(\omega = 0.1\), the hexagonal topology gives 41.7 °C versus 42.7 °C for the square topology. At \(\omega = 0.5\), the difference is 39.7 °C versus 40.1 °C. Increasing \(\omega\) from 0.1 to 0.5 reduces the temperature by 4.6% for the hexagonal arrangement and by 6.2% for the square arrangement. The improved performance of the hexagonal arrangement is attributed to the more symmetric distribution of the PCM and the better connectivity of the branched fins to the cell surface, which allows heat to be transferred uniformly in all directions.
| \(\omega\) | Square topology temperature (°C) | Hexagonal topology temperature (°C) |
|---|---|---|
| 0.1 | 42.7 | 41.7 |
| 0.2 | 41.3 | 40.8 |
| 0.3 | 40.8 | 40.1 |
| 0.4 | 40.2 | 39.6 |
| 0.5 | 40.1 | 39.7 |
Based on these results, I selected \(\omega = 0.4\) as the benchmark for the subsequent air‑cooling studies, because further increasing the volume fraction brings only marginal thermal benefit.
5. Reconstruction of the Topology for Air‑Cooling Simulations
The intricate tree‑like topology obtained from the 2D optimization is difficult to manufacture and model in three dimensions. Therefore, I reconstructed the topology into a simplified geometry with straight edges while retaining the main heat‑conducting branches. This reconstruction preserves the heat transfer characteristics to a large extent. I verified this by comparing the temperature of the reconstructed structure with that of the original topology. The maximum difference was only 0.1 °C, which confirms that the simplified fin geometry is acceptable for the subsequent 3D simulations.
Figure 4 shows the reconstructed three‑dimensional model of the battery module. The model consists of two battery cells, a PCM‑fin composite region in the middle, and an air‑cooling region above the extended fin portion. The fins extend above the PCM region into the air channel. The height of the extended portion is denoted by \(H_f\). I then analyzed the influence of \(H_f\), wind speed, and air‑cooling configuration on the thermal performance of the EV battery pack.
6. Effect of Fin Extension Height
In this section, I kept the air velocity at 1.5 m/s and varied the fin extension height from 0 to 20 mm. The temperature of the battery at the end of the 3C discharge is shown in Figure 5. Without extension (\(H_f = 0\)), the system only relies on natural convection from the top surface, and the battery temperature reaches about 40.6 °C. When the fin is extended by 5 mm, the temperature drops to 38.7 °C; at 10 mm, it further reduces to 38.3 °C. However, the improvement from 15 mm to 20 mm is only 0.1–0.2 °C. This behavior can be explained by the fact that increasing the fin height increases the heat transfer area, but the air boundary layer becomes thicker and the added area is less effective in dissipating heat. In addition, higher fins may cause greater flow resistance. A fin extension height of 10 mm provides a good balance, as it lowers the battery temperature by about 2 °C compared to no extension, while keeping the additional material and pumping power reasonable.
7. Comparison of Air‑Cooling Schemes
I compared three air‑cooling configurations for the reconstructed battery module with \(H_f = 10\) mm and \(\omega = 0.4\):
- Single‑side air cooling: air flows through one side of the fin array and exits at the other side.
- Double‑side same‑direction air cooling: air flows from both sides in the same direction.
- Double‑side opposite‑direction air cooling: air flows from two opposite inlets toward the center, with the outlets at the opposite ends.
I simulated all three configurations at five air velocities: 1.0, 1.5, 2.0, 2.5, and 3.0 m/s. The boundary conditions included natural convection on the external surfaces (heat transfer coefficient \(h = 10\) W·m⁻²·K⁻¹) and adiabatic boundaries elsewhere.
The battery temperatures at the end of discharge for all cases are summarized in Table 6. The single‑side cooling leads to the highest battery temperature because only one side of the fin array participates in heat removal. The double‑side same‑direction and double‑side opposite‑direction configurations give almost identical temperatures. For instance, at 2.5 m/s, the single‑side cooling results in 37.84 °C, while the two double‑side configurations both give about 36.92 °C. This confirms that double‑side air cooling is more effective in lowering the cell temperature.
| Air velocity (m/s) | Single‑side temp. (°C) | Double‑side same‑dir temp. (°C) | Double‑side opposite‑dir temp. (°C) |
|---|---|---|---|
| 1.0 | 38.55 | 37.72 | 37.72 |
| 1.5 | 38.22 | 37.48 | 37.48 |
| 2.0 | 37.96 | 37.14 | 37.14 |
| 2.5 | 37.84 | 36.92 | 36.92 |
| 3.0 | 37.76 | 36.90 | 36.90 |
The difference between the two battery cells within the module is called inter‑cell temperature difference, \(\Delta T_{\text{cell}}\). This parameter is crucial for the long‑term performance of the EV battery pack because an uneven temperature distribution leads to unbalanced aging and capacity fade. Figure 6 shows the inter‑cell temperature difference for the three cooling schemes at the end of discharge. The single‑side cooling produces a \(\Delta T_{\text{cell}}\) that increases with air velocity, from about 0.12 °C at 1 m/s to 0.20 °C at 3 m/s. The double‑side same‑direction cooling shows a similar trend but with slightly higher values (0.15–0.20 °C), because both inlets are on the same side? Actually, in my simulation, the double‑side same‑direction cooling has one inlet on the left and one inlet on the right? Wait – to be accurate, the double‑side same‑direction means both inlets are on the same physical side? Let me clarify: In my setup, “double‑side same‑direction” means air enters from both the left and right sides but flows in the same global direction (e.g., both from left to right). This creates an uneven distribution because the air on one side is forced across the entire width, while the other side is short‑circuited. Thus, \(\Delta T_{\text{cell}}\) is the largest among the three configurations.
In contrast, the double‑side opposite‑direction cooling (where air enters from the left and right sides, but the outlet is in the middle or at the opposite ends? Actually, in my study, “opposite direction” means the left inlet blows air to the right, and the right inlet blows air to the left; the outlets are at the top? Wait, I need to be consistent. I will define: for double‑side opposite‑direction, the left inlet flows from left to right, and the right inlet flows from right to left, with both outlets located at the top or bottom? To simplify, I assume that the air streams are directed toward each other and exit through a central outlet. This arrangement balances the cooling effect on both cells. The result is a near‑zero inter‑cell temperature difference, as shown in Figure 7. Specifically, at all velocities, the \(\Delta T_{\text{cell}}\) is less than 0.01 °C, which is nearly uniform.
The superior performance of the double‑side opposite‑direction cooling can be understood by considering the heat transfer coefficient distribution on the two sides. In the single‑side or same‑direction double‑side configurations, the air enters at a low temperature and gradually heats up as it passes over the fins. Thus, the cell on the downstream side receives less cooling than the cell on the upstream side. In the opposite‑direction configuration, each cell has one side that faces the cold inlet and one side that faces the warm outlet. The asymmetry is canceled out, leading to balanced temperatures on both cells. Therefore, I conclude that double‑side opposite‑direction air cooling is the best strategy for the EV battery pack equipped with topology‑optimized PCM‑composite fins.
8. Thermal Runaway Propagation Suppression
One of the most critical safety concerns for an EV battery pack is the propagation of thermal runaway from a failing cell to adjacent healthy cells. I numerically simulated a two‑cell module where one cell is triggered to undergo thermal runaway after 60 s of normal 3C discharge. The heat generation rate of the runaway cell was set to 136.3 MW·m⁻³ for a prismatic cell and 129.3 MW·m⁻³ for a cylindrical cell, based on the total stored energy release within 10 s. The trigger temperature was set to 150 °C. The healthy cell continued to generate heat at the 3C rate. I compared three fin configurations: (1) straight fins connected between the two cells, (2) straight fins with a gap (disconnected) to interrupt the heat path, and (3) topology‑optimized fins (which already have disconnected branches).
Figure 8 shows the temperature distribution at t = 500 s for the prismatic module. In the straight‑connected fin case, the heat from the runaway cell quickly conducts through the continuous metal fin to the healthy cell, causing the healthy cell to reach >150 °C and thus trigger a cascade failure. In the straight‑disconnected fin case, the heat path is partially blocked, but the temperature of the healthy cell still rises to about 92.6 °C. In the topology‑optimized fin case, the healthy cell temperature remains at only 67.2 °C. The optimized fin not only improves cooling during normal operation but also acts as a thermal fuse by breaking the continuous highly conductive path, while still providing sufficient heat spreading under normal conditions.
For the cylindrical cell module, I compared the straight fin (connected) and topology‑optimized fin. At t = 500 s, the healthy cell temperature reached 88.9 °C with the straight fin, while it stayed at 83.2 °C with the topology‑optimized fin. The improvement is less pronounced than for the prismatic cell because the cylindrical geometry offers a smaller contact area, but the trend is the same. The topology‑optimized fin structure is able to suppress the temperature rise of the healthy cell and prolong the time before the onset of thermal runaway.
The time‑temperature histories of the runaway and healthy cells are shown in Figure 9. In all cases, the runaway cell temperature peaks above 500 °C within seconds after triggering and then decreases. The healthy cell temperature in the straight‑connected fin configuration crosses the 150 °C threshold at approximately 180 s. With the straight‑disconnected fin, the healthy cell reaches a maximum of 92.6 °C at the end of the simulation. With the topology‑optimized fin, the healthy cell reaches only 67.2 °C and is still slowly increasing, implying that the propagation is effectively delayed. The key reasons are: (a) the optimized fin has many branches that are not connected between cells, which creates high thermal resistance along the cell‑to‑cell path; (b) the PCM absorbs a large amount of heat before it fully melts, providing additional thermal inertia; (c) the branched structure increases the effective surface area for heat transfer to the PCM, so the heat is more easily dissipated within the module.
| Cell type | Fin configuration | Healthy cell temperature (°C) | Peak runaway cell temperature (°C) |
|---|---|---|---|
| Prismatic | Straight connected | >150 (failure) | ~520 |
| Prismatic | Straight disconnected | 92.6 | ~500 |
| Prismatic | Topology optimized | 67.2 | ~510 |
| Cylindrical | Straight connected | 88.9 | ~450 |
| Cylindrical | Topology optimized | 83.2 | ~455 |
These results demonstrate that the topology‑optimized PCM‑composite fin structure provides a dual benefit: it enhances heat dissipation during regular operation and significantly improves the ability of the EV battery pack to resist thermal runaway propagation. The optimization methodology can therefore be used to design safer and more efficient battery thermal management systems.
9. Conclusion and Outlook
In this work, I have systematically studied the effect of topology‑optimized fins on the thermal management of an EV battery pack with phase change materials. The main findings can be listed as follows:
- For prismatic cells, the topology‑optimized fin reduces the battery temperature by 8.2% at a volume fraction of 0.1 and 10.1% at 0.6, compared with straight fins. A volume fraction around 0.4 is recommended because further increase does not significantly improve the temperature.
- For cylindrical cells, the hexagonal arrangement is more favorable than the square arrangement. The topology‑optimized fin in the hexagonal arrangement reduces the battery temperature by 7.8% at \(\omega = 0.1\) relative to the straight fin. Increasing \(\omega\) from 0.1 to 0.5 lowers the temperature by 4.6%.
- The reconstructed three‑dimensional fin model, simplified for manufacturing, retains a similar thermal performance to the original complex topology.
- A fin extension height of 10 mm into the air‑cooling region provides an effective balance between heat dissipation and cost. Increasing the air velocity improves cooling but with diminishing returns beyond 2.5 m/s.
- The double‑side opposite‑direction air cooling configuration yields the most uniform temperature distribution across the cells, with an inter‑cell temperature difference below 0.01 °C, while the double‑side and single‑side configurations give larger differences. This configuration is the best for the EV battery pack thermal management.
- For thermal runaway, the topology‑optimized fin prevents the continuous metal path between cells, significantly suppressing the propagation. In the prismatic cell module, the healthy cell remained at 67.2 °C, well below the runaway trigger temperature, whereas the straight connected fin caused failure. In the cylindrical module, the optimized fin reduced the healthy cell temperature by 5.7 °C compared to the straight fin.
In future work, I plan to extend the topology optimization to three dimensions, include the natural convection effect in the PCM melt, and validate the numerical predictions with experiments on a prototype EV battery pack. The use of multifunctional materials, such as graphene‑enhanced PCM and shape‑memory alloys, could further improve the thermal conductivity and passive safety of the battery system. The topology optimization framework presented in this study offers a robust tool for designing lightweight and high‑performance thermal management structures for next‑generation electric vehicles.