The rapid development of renewable-energy transportation has placed unprecedented demands on the lithium-ion power systems used in modern vehicles. Among all the components of an electric vehicle, the battery pack is the most performance-limiting and safety-critical subsystem. In particular, the thermal behavior of an electric vehicle battery directly determines its cycle life, charging rate, peak power capability, and overall safety. Excessive temperature rise during high-rate discharge accelerates side reactions, degrades electrode materials, and may trigger catastrophic thermal runaway. On the other hand, low temperatures increase internal resistance and cause lithium plating. Therefore, an effective thermal management system is indispensable for any high-performance electric vehicle battery. Traditional cooling approaches such as air cooling and liquid cooling have been widely studied, but phase change materials (PCMs) offer a unique advantage because they absorb heat passively through latent heat without requiring external energy input. However, the low thermal conductivity of pure PCM limits its practical cooling performance. To address this limitation, I investigate a topology-optimized composite fin structure embedded in a PCM phase-change region, and I evaluate the resulting thermal behavior of an electric vehicle battery system.
In this study, I focus on the design and numerical investigation of a novel phase change cooling structure for an electric vehicle battery. The proposed structure combines aluminium fins and paraffin-based PCM, where the fin layout is obtained by topology optimization rather than by intuitive design. The topology optimization approach allows the fin material to be distributed freely inside the PCM domain so that heat can be transported from the battery surface into the PCM more effectively. I first establish a transient thermal model for both prismatic and cylindrical lithium-ion cells and validate it against experimental data. Then I optimize the fin topology for different fin-to-PCM volume ratios and compare the optimized fin with conventional straight fins. Afterward, I reconstruct the optimized structure into a manufacturable geometry and study its performance under various air-cooling schemes. Finally, I examine the ability of the topology-optimized fin to suppress thermal runaway propagation between adjacent cells. The results show that the proposed structure significantly improves the thermal management capability of an electric vehicle battery.
Thermal Modeling of the Lithium-Ion Battery
I selected two representative lithium-ion cell geometries for this research: a prismatic cell with nominal capacity of 51 Ah and a cylindrical 18650 cell with nominal capacity of 2.6 Ah. Both cells are commonly used in electric vehicle battery packs. The prismatic cell is treated as a homogeneous heat-generating solid with anisotropic thermal conductivity, while the cylindrical cell is also modeled as a homogeneous solid but with orthotropic conductivity oriented along the radial and axial directions. The relevant parameters are summarized in the following table, which provides the basis for all subsequent simulations.
| Parameter | Prismatic cell | Cylindrical cell |
|---|---|---|
| Nominal capacity (Ah) | 51 | 2.6 |
| Dimensions (mm) | 148 × 27 × 91 | R = 18, H = 65 |
| Mass (g) | 816.47 | 47.5 |
| Specific heat (J/(kg·K)) | 1050.31 | 1200 |
| Thermal conductivity (W/(m·K)) | kxy = 14, kz = 1.31 | kxy = 0.2, kz = 37.6 |
| Density (kg/m³) | 2245.3 | 2873.5 |
The heat generation inside a lithium-ion cell is caused by multiple physical processes: ohmic heating due to internal resistance, reversible entropic heating, polarization heat, and exothermic decomposition reactions at elevated temperatures. In normal operation, the total volumetric heat generation rate can be described by the Bernardi equation. For a cell operating under a constant current, the heat generation rate per unit volume is expressed as
$$ q_{\mathrm{gen}} = \frac{I}{V_{\mathrm{cell}}} \left( I R_e – T \frac{\partial U_{\mathrm{ocv}}}{\partial T} \right) $$
where \(I\) is the applied current, \(V_{\mathrm{cell}}\) is the cell volume, \(R_e\) is the total internal resistance, \(T\) is the cell temperature, \(U_{\mathrm{ocv}}\) is the open-circuit voltage, and \(\partial U_{\mathrm{ocv}} / \partial T\) is the entropic heat coefficient. I applied this equation to calculate the heat source for both prismatic and cylindrical cells at discharge rates of 1C, 2C, and 3C. For the prismatic cell, the 3C discharge heat generation rate was fitted by a polynomial function of discharge time in order to capture the transient variation of the source term.
The transient temperature field in the battery is governed by the heat conduction equation
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + q_{\mathrm{gen}} $$
where \(\rho\), \(c_p\), and \(k\) are the equivalent density, specific heat, and thermal conductivity of the cell. Convection and radiation at the outer surfaces are considered through the boundary conditions. The heat transfer coefficient on the exposed surfaces is set to 10 W/(m²·K), representing natural convection in the surrounding air, while the remaining surfaces are assumed to be adiabatic. Thermal radiation is neglected because its contribution is small compared with conduction and convection in the temperature range of interest.
The PCM used in this thesis is n-eicosane, a paraffin with a melting temperature around 35–37 °C and a high latent heat of 241 kJ/kg. The PCM properties are given in the table below. Since the PCM has very low thermal conductivity in both solid and liquid states, aluminium fins are introduced into the PCM to create a composite structure with enhanced heat transfer capability.
| Property | Solid state | Liquid state |
|---|---|---|
| Phase change temperature (°C) | 35–37 | |
| Density (kg/m³) | 810 | 770 |
| Specific heat (kJ/(kg·K)) | 1.9 | 2.2 |
| Latent heat (kJ/kg) | 241 | |
| Thermal conductivity (W/(m·K)) | 0.39 | 0.157 |
| Aluminium property | Value |
|---|---|
| Density (kg/m³) | 2700 |
| Specific heat (kJ/(kg·K)) | 900 |
| Thermal conductivity (W/(m·K)) | 238 |
Before conducting the performance study, I verified the accuracy of my heat-generation model by comparing the predicted surface temperature with published experimental data for the same battery at different discharge rates. The simulation and experimental temperatures in the ambient environment of 25 °C showed excellent agreement. The maximum relative error over the entire discharge process did not exceed 5 %. This gives me confidence that the model can faithfully reproduce the thermal behavior of an electric vehicle battery and can be used as a reliable foundation for the topology optimization study.
Topology Optimization of Composite PCM-Fin Structures
Topology optimization is a mathematical method that seeks the optimal distribution of material within a prescribed design domain under a given set of loads, constraints, and objective functions. For the thermal management of an electric vehicle battery, the design domain is the region filled with PCM, and the optimized material is aluminium. By changing the local material distribution, I can maximize the heat transfer from the battery surface into the PCM while keeping the volume of the fin material constrained.
I used the density-based method, in which each element in the design domain is assigned a continuous relative density \(\gamma\) between 0 and 1. When \(\gamma = 1\), the element is filled with aluminium fin material; when \(\gamma = 0\), the element is filled with PCM. The intermediate values are penalized to obtain a nearly solid-void design. The material properties are interpolated using the SIMP-like law
$$ k(\gamma) = k_{\mathrm{PCM}} + \gamma \left( k_{\mathrm{fin}} – k_{\mathrm{PCM}} \right) $$
$$ \rho(\gamma) = \rho_{\mathrm{PCM}} + \gamma \left( \rho_{\mathrm{fin}} – \rho_{\mathrm{PCM}} \right) $$
$$ c_p(\gamma) = c_{p,\mathrm{PCM}} + \gamma \left( c_{p,\mathrm{fin}} – c_{p,\mathrm{PCM}} \right) $$
where \(k\), \(\rho\), and \(c_p\) are the interpolated thermal conductivity, density, and specific heat in each element. The subscripts “PCM” and “fin” denote the phase-change material and aluminium, respectively. To avoid mesh dependence and checkerboard patterns, I applied a Helmholtz-type filter to the density field:
$$ \gamma_f – r_{\min}^2 \nabla^2 \gamma_f = \gamma_c $$
where \(r_{\min}\) is the filter radius and \(\gamma_c\) is the unfiltered design variable. In addition, a hyperbolic-tangent projection was applied to reduce gray elements and sharpen the interface between fin and PCM:
$$ \tilde{\gamma} = \frac{\tanh\left(\beta (\gamma_f – \gamma_{\beta})\right) + \tanh(\beta \gamma_{\beta})}{\tanh\left(\beta (1-\gamma_{\beta})\right) + \tanh(\beta \gamma_{\beta})} $$
In my simulations I selected a projection slope of \(\beta = 8\) and a projection point of \(\gamma_{\beta} = 0.5\). This combination produced a clear and manufacturable topology while maintaining numerical stability.
The volume of PCM required to absorb the heat released during a 3C discharge was calculated from the total heat generation. For a discharge duration of 1200 s, the required PCM volume is obtained as
$$ V_{\mathrm{PCM}} = \frac{\displaystyle \int_0^{1200} q(t)\, dt}{\rho_{\mathrm{PCM}} L_{\mathrm{PCM}}} $$
where \(L_{\mathrm{PCM}}\) is the latent heat of the PCM. This calculation yielded a PCM volume of 23.144 cm³ for the prismatic cell and 13.715 cm³ for the cylindrical cell. During the optimization, the PCM volume was kept constant, and the fin volume was varied according to the volume ratio \(\omega = V_{\mathrm{fin}} / V_{\mathrm{PCM}}\).
Choice of Objective Function
I first compared two common objective functions in heat-conduction topology optimization: minimizing thermal compliance and minimizing average temperature. The thermal compliance can be written as
$$ J_1 = \int_{\Omega} q_{\mathrm{gen}} T \, d\Omega $$
while the average temperature is expressed as
$$ J_2 = \frac{1}{V_{\Omega}} \int_{\Omega} T \, d\Omega $$
where \(\Omega\) is the design domain and \(V_{\Omega}\) is its volume. For a fixed heat source, minimizing thermal compliance is equivalent to minimizing a certain weighted average of temperature, but the weighting is not necessarily uniform. In my battery cooling problem, I care most about lowering the peak and average temperature of the electric vehicle battery as uniformly as possible. Therefore, minimizing the average temperature is more appropriate. I optimized the fin structure for volume ratios of 0.1, 0.2, and 0.3 using both objective functions. The resulting temperature fields showed that the average-temperature objective produced consistently lower battery temperatures than the thermal-compliance objective. The difference was largest at small volume ratios and became smaller as the fin volume increased. Based on this comparison, I selected the average-temperature objective for all subsequent optimizations.
Prismatic Battery Results
For the prismatic battery, the PCM region is located between adjacent cells, and the fin topology is optimized in a two-dimensional cross-section representing one repeating spacing. The optimized fin structures at different volume ratios are shown conceptually as tree-like branched shapes. At low volume ratios, the fins are relatively sparse and concentrate near the heat source. As the volume ratio increases, the fins spread into the PCM domain with more branches, creating a more uniform path for heat conduction. This branching behavior is beneficial because it transfers heat from the battery surface to a larger volume of PCM and allows more PCM to participate in the melting process.
I compared the optimized fins with conventional straight fins of the same volume under a 3C discharge condition. The straight-fin design is a simple vertical fin that connects the battery surface to the outer boundary of the PCM region. In contrast, the topology-optimized fin is intentionally disconnected between adjacent batteries, which not only improves heat spreading but also reduces the risk of thermal coupling between neighboring cells. The temperature contours at the end of discharge show that the topologically optimized fin leads to a lower battery temperature and a more uniform temperature distribution in the PCM region. The following table summarizes the final battery temperatures at several volume ratios.
| Volume ratio \(\omega\) | Straight fin (°C) | Topology-optimized fin (°C) | Temperature reduction (%) |
|---|---|---|---|
| 0.1 | 44.3 | 40.3 | 8.2 |
| 0.3 | 42.5 | 38.0 | 10.6 |
| 0.6 | 41.3 | 37.1 | 10.1 |
In addition, I studied the effect of increasing the volume ratio from 0.1 to 0.6 for the topology-optimized fins. The battery temperature decreased monotonically from 40.3 °C to 37.1 °C, corresponding to a 7.9 % reduction. However, the rate of temperature reduction decreased as the volume ratio grew. At volume ratios of 0.4, 0.5, and 0.6, the battery temperatures were 37.4 °C, 37.2 °C, and 37.1 °C, respectively. This indicates that once the fin network is sufficiently developed, additional fin material does not significantly improve the cooling performance. Therefore, a volume ratio of 0.4 offers a good compromise between thermal performance and material cost for the prismatic electric vehicle battery.
Cylindrical Battery Results
For cylindrical cells, I considered two packing arrangements: square array and hexagonal array. The PCM domain around each cylindrical cell can be modeled as a square or a regular hexagon, respectively. The topology optimization was carried out in the hexagonal or square domain while keeping the PCM volume constant at 13.715 cm³. The volume ratio \(\omega\) was varied from 0.1 to 0.5. The optimized fins again show a branched pattern, but the shape adapts to the angular boundary of the design domain. In the hexagonal domain, the fins extend toward the corners, which helps transfer heat to the PCM at the periphery. In the square domain, the fins are more concentrated near the cell and gradually spread outward as the volume ratio increases.
The following table compares the final discharge temperatures at different volume ratios for the two arrangements. At the same volume ratio, the hexagonal arrangement consistently outperforms the square arrangement. For example, at \(\omega = 0.1\), the square topology yields 42.7 °C while the hexagonal topology yields 41.7 °C. At \(\omega = 0.5\), the temperatures are 40.1 °C and 39.7 °C, respectively. The performance improvement of the hexagonal arrangement is attributed to the more uniform distribution of PCM around the cylinder and the reduced corner volumes where heat can stagnate.
| Volume ratio \(\omega\) | Square array topology (°C) | Hexagonal array topology (°C) |
|---|---|---|
| 0.1 | 42.7 | 41.7 |
| 0.2 | 41.6 | 40.8 |
| 0.3 | 40.8 | 40.2 |
| 0.4 | 40.2 | 39.6 |
| 0.5 | 40.1 | 39.7 |
When compared with conventional straight fins at a volume ratio of 0.1, the topology-optimized fins reduce the battery temperature from 45.4 °C to 42.7 °C in the square arrangement, a reduction of about 6 %. In the hexagonal arrangement, the straight fin gives 45.2 °C, while the topology-optimized fin gives 41.7 °C, a reduction of about 7.8 %. At larger volume ratios, the relative benefit of topology-optimized fins becomes smaller, but the optimized structure still yields the lowest temperatures. For the cylindrical electric vehicle battery, a volume ratio of 0.4 is again found to be a suitable design point because further increasing the fin volume does not produce substantial temperature improvement.
Air Cooling Enhancement of the Topology-Optimized Structure
The topology-optimized fin obtained directly from the numerical optimization has an irregular, branching shape that is difficult to manufacture using conventional stamping or extrusion processes. To make the design more practical, I reconstructed the optimized topology into a simplified geometry with straight edges while preserving the essential heat-conduction paths. The reconstructed fin has the same volume fraction and a similar distribution to the original topology, but its boundary is much simpler. I verified that the simplified fin still provides a cooling performance close to the original optimized fin; the reconstructed geometry shows a temperature only about 0.1 °C higher than the original topology. This small penalty is acceptable given the significant improvement in manufacturability.
In the three-dimensional model, I placed a battery module consisting of several prismatic cells, with the composite PCM-fin structure between the cells. The fins extend upward above the PCM region into an air-cooling channel. Air flows through the channel and removes heat directly from the exposed fin surfaces. This hybrid design uses the PCM to absorb transient heat pulses and the air flow to discharge the stored heat continuously, making the system suitable for repeated charge-discharge cycles of an electric vehicle battery.
Effect of Fin Extension Height
I first investigated the influence of fin extension height on the cooling performance. The air velocity was fixed at 1.5 m/s, and the fin height above the PCM surface was varied as 0 mm, 5 mm, 10 mm, 15 mm, and 20 mm. The fin height determines the heat-transfer area exposed to air. A larger height increases the contact area and therefore enhances the convective heat transfer. The table below lists the average battery temperatures at the end of a 3C discharge.
| Fin extension height (mm) | Battery temperature (°C) |
|---|---|
| 0 | 40.3 |
| 5 | 38.7 |
| 10 | 38.3 |
| 15 | 38.0 |
| 20 | 37.7 |
The results show that increasing the extension height from 0 mm to 5 mm lowers the battery temperature by about 1.6 °C. A further increase to 10 mm provides another reduction of about 0.4 °C. Beyond 10 mm, the additional temperature reduction becomes small. This behavior occurs because the boundary-layer thermal resistance increases along the fin, and the effective heat transfer per unit area decreases with height. Therefore, I chose 10 mm as the optimal fin extension height because it provides a good balance between enhanced cooling and material usage. In addition, a shorter fin reduces the pressure drop in the air channel and lowers the fan power consumption, which is beneficial for the overall efficiency of the electric vehicle battery thermal management system.
Comparison of Air-Cooling Schemes
I further examined three air-cooling configurations: single-side cooling, double-side cooling with parallel airflow, and double-side cooling with counter airflow. In the single-side scheme, the cooling air flows through a channel on one side of the battery module. In the parallel scheme, two identical air streams enter from the same side and flow through channels on both sides. In the counter scheme, the two air streams enter from opposite sides and move in opposite directions. The fin extension height was fixed at 10 mm, and the airflow rate was varied from 1.0 m/s to 3.0 m/s.
I observed that increasing the air velocity reduces the battery temperature in all three schemes. However, the reduction becomes less significant as the velocity exceeds 2.5 m/s because the thermal resistance inside the fin and the PCM eventually dominates the overall heat transfer. The single-side cooling scheme produces the highest battery temperature and the largest temperature gradient along the flow direction. Parallel double-side cooling gives a lower temperature than single-side cooling because the total heat-transfer area is doubled. Counter double-side cooling has almost the same average temperature as parallel double-side cooling, but it provides a remarkably more uniform temperature distribution. The following table compares the temperature and temperature difference at a representative air velocity of 2.5 m/s.
| Cooling scheme | Battery temperature (°C) | Maximum cell-to-cell temperature difference (°C) |
|---|---|---|
| Single-side | 37.9 | 0.19 |
| Double-side parallel | 37.1 | 0.20 |
| Double-side counter | 37.1 | <0.01 |
The counter-flow configuration is particularly attractive for a large electric vehicle battery pack. In the parallel-flow configuration, the air entering on one side is cold, while the air exiting on the opposite side has already been heated. This creates an inlet-to-outlet temperature gradient. In the counter-flow configuration, both sides have an inlet at opposite ends, so the temperature gradient of one side is compensated by the opposite gradient of the other side. As a result, the cell-to-cell temperature difference is reduced by almost 90 % compared with the single-side scheme. This improvement is highly valuable because thermal uniformity is critical for preventing uneven aging and localized over-discharge in an electric vehicle battery pack.
Thermal Runaway Propagation Suppression
Thermal runaway is one of the most serious safety hazards for an electric vehicle battery. When one cell enters thermal runaway, a large amount of heat is released in a very short time. If this heat is conducted efficiently to neighboring cells, it can trigger a chain reaction that propagates through the entire pack. The fin structure between cells plays a dual role. On the one hand, it is intended to improve cooling during normal operation. On the other hand, if the fins directly connect adjacent cells, they may become a heat bridge that accelerates thermal runaway propagation. Therefore, the design of the inter-cell fin structure must carefully balance normal-operation heat spreading and runaway heat-blocking capability.
I simulated a two-dimensional model of two adjacent cells, one of which is triggered into thermal runaway while the other remains in normal operation. The runaway cell was set to a constant heat generation rate of 136.3 MW/m³ for a duration of 10 seconds, representing the total energy release. The normal cell was operated at a 3C discharge heat source. The initial state of charge was 100 %, and the thermal runaway trigger temperature was set to 150 °C. The simulation was carried out for 500 seconds to capture the transient temperature evolution and the heat propagation from the runaway cell to the normal cell.
I compared three inter-cell configuration cases: straight connected fins, straight disconnected fins, and topology-optimized fins. The volume ratio was 0.4 for all cases. The temperature contours after 500 seconds show that the straight connected fins create a strong thermal bridge; the normal cell quickly approaches the critical temperature and eventually exceeds 150 °C. In contrast, the straight disconnected fins and the topology-optimized fins both provide better blocking of heat propagation. However, the topology-optimized fins are more effective than the straight disconnected fins because their branched geometry distributes heat over a larger volume of PCM and dissipates a portion of the heat through localized melting, thereby delaying the temperature rise of the normal cell.
| Configuration | Normal cell temperature after 500 s (°C) |
|---|---|
| Straight connected fins (prismatic) | >150 (thermal runaway) |
| Straight disconnected fins (prismatic) | 92.6 |
| Topology-optimized fins (prismatic) | 67.2 |
| Straight fins (cylindrical) | 88.9 |
| Topology-optimized fins (cylindrical) | 83.2 |
In the prismatic cell case, the topology-optimized fin structure keeps the normal cell temperature at 67.2 °C, which is far below the thermal runaway threshold. This is 25.4 °C lower than the straight disconnected fin case. This dramatic improvement is due to the fact that the topology-optimized fin is divided into multiple branches that are not directly connected from one cell to another. The heat entering the fin network must travel through a longer path and is partially absorbed by the PCM before it reaches the adjacent cell. In addition, the branched structure increases the effective surface area for heat exchange with the PCM, allowing more latent heat to be activated during the early stage of thermal propagation.
For the cylindrical cell arrangement, the topology-optimized fin also shows a clear benefit. The normal cell temperature under topology-optimized fins is 83.2 °C, compared with 88.9 °C for the straight fin design. Although the improvement is not as large as in the prismatic case, the topology-optimized fin still reduces the potential for thermal runaway propagation and provides additional safety margin for the electric vehicle battery pack. These results demonstrate that topology optimization can be used not only to enhance steady-state cooling but also to improve the abuse tolerance and safety of an electric vehicle battery.
Conclusions
In this thesis, I have presented a systematic numerical study of a phase change cooling structure with topology-optimized fins for an electric vehicle battery. I first established and validated a transient thermal model for prismatic and cylindrical lithium-ion cells. Then I applied density-based topology optimization to design the fin layout inside the PCM region. The average-temperature objective produced lower battery temperatures than thermal compliance, and the optimized fins exhibited a branched, tree-like geometry that substantially improved heat spreading compared with conventional straight fins.
For the prismatic electric vehicle battery, my topology-optimized fins reduced the discharge-end temperature by 8.2 % at a volume ratio of 0.1 and by 10.1 % at a volume ratio of 0.6 relative to straight fins. Increasing the volume ratio from 0.1 to 0.6 lowered the battery temperature by 7.9 %, but the marginal benefit declined significantly after a volume ratio of 0.4. For the cylindrical electric vehicle battery, the hexagonal cell arrangement performed better than the square arrangement. The topology-optimized fin in the hexagonal arrangement reduced the temperature by 7.8 % compared with straight fins at a volume ratio of 0.1.
I also investigated the integration of the topology-optimized PCM-fin structure with air cooling. A fin extension height of 10 mm provided the best trade-off between thermal performance and cost. Among the three air-cooling schemes, double-side counter-flow cooling was the most effective because it lowered the overall temperature while maintaining an extremely uniform temperature distribution, with a cell-to-cell temperature difference below 0.01 °C. Finally, I evaluated the ability of the proposed fin structure to suppress thermal runaway propagation. The topology-optimized fins significantly reduced the temperature of the neighboring normal cell relative to straight fin configurations. In the prismatic cell case, the normal cell temperature was only 67.2 °C, far below the 150 °C critical limit. These findings confirm that topology optimization offers a powerful and versatile approach for designing high-performance, safe, and manufacturable thermal management structures for electric vehicle battery packs.