I have focused my research on the thermal management of an electric vehicle battery pack because the rapid growth of electric mobility has made battery safety, lifetime, and fast-charging capability urgent engineering problems. In an electric vehicle battery pack, lithium-ion cells generate heat through ohmic resistance, polarization, and electrochemical reactions. If this heat cannot be removed efficiently, the pack may experience large temperature gradients, accelerated aging, and even thermal runaway. My work therefore combines phase change material (PCM) cooling with topology-optimized fins, and I evaluate the resulting structures for normal discharge, air-cooled operation, and thermal runaway propagation. The central idea is that a topology-optimized fin network can distribute heat more uniformly inside the PCM, while an air-cooling stream can remove stored heat from the electric vehicle battery pack and keep the cells within a safe operating window.
I begin from the well-known requirement that lithium-ion cells should operate approximately between 293.15 K and 323.15 K, and that the temperature difference among cells in an electric vehicle battery pack should remain below about 5 K. These targets are not merely performance targets; they are directly linked to safety, capacity fade, and power capability. A conventional straight fin may improve PCM conductivity, but its heat-transfer path is simple and often leaves distant PCM regions unused. I therefore use topology optimization to design fin geometries that spread heat into a larger PCM volume, reduce the maximum temperature, and suppress the propagation of thermal runaway in an electric vehicle battery pack.
Battery Heat Generation and Physical Model
I model the lithium-ion cell as a homogeneous heat-generating body with effective thermal properties. The cell consists of positive electrode, negative electrode, separator, electrolyte, and casing, but for pack-level simulation I treat it as an equivalent continuum. The heat generation rate is described by the Bernardi equation, which separates irreversible Joule heating from reversible entropic heating:
$$ q = \frac{I}{V} \left( U_{ocv} – U – T \frac{\partial U_{ocv}}{\partial T} \right) $$
Here, \(q\) is the volumetric heat generation rate, \(I\) is the current, \(V\) is the cell volume, \(U_{ocv}\) is the open-circuit voltage, \(U\) is the operating voltage, \(T\) is the temperature, and \(\partial U_{ocv}/\partial T\) is the entropic heat coefficient. For the prismatic cell, I used a fitted heat-generation expression for a 3C discharge rate:
$$ q(t) = 16.868 + 0.347t – 3.34 \times 10^{-2}t^2 + 1.47 \times 10^{-3}t^3 – 3.65 \times 10^{-5}t^4 + 5.28 \times 10^{-7}t^5 – 4.42 \times 10^{-9}t^6 + 1.98 \times 10^{-11}t^7 – 3.66 \times 10^{-14}t^8 + 1.08 \times 10^{-16}t^9 $$
where \(t\) is discharge time in seconds and \(q(t)\) is the heat generation rate. The transient heat conduction equation inside the cell and the PCM-fin domain is:
$$ \rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + q $$
At external boundaries, I apply convective cooling:
$$ -k \frac{\partial T}{\partial n} = h (T – T_{\infty}) $$
where \(h\) is the convective heat-transfer coefficient and \(T_{\infty}\) is the ambient temperature. For the phase change material, I account for sensible heat and latent heat using an effective heat capacity formulation:
$$ (\rho C_p)_{eff} \frac{\partial T}{\partial t} = \nabla \cdot (k_{eff} \nabla T) + q $$
The effective heat capacity includes the latent heat \(L\) over the phase-change interval \(\Delta T\):
$$ (\rho C_p)_{eff} = \rho C_p + \frac{\rho L}{\Delta T} $$
I validated the battery heat-generation model against experimental temperature histories. The maximum difference between simulation and experiment remained below 5 % for 1C, 2C, and 3C discharge rates. This validation is important because the reliability of every later conclusion for the electric vehicle battery pack depends on the accuracy of the cell heat source.
| Parameter | Prismatic cell | Cylindrical cell |
|---|---|---|
| Nominal capacity (Ah) | 51 | 2.6 |
| Mass (g) | 816.47 | 47.5 |
| Dimensions (mm) | 148 × 27 × 91 | R = 18, H = 65 |
| Specific heat capacity (J kg⁻¹ K⁻¹) | 1050.31 | 1200 |
| Thermal conductivity (W m⁻¹ K⁻¹) | kxy = 14, kz = 1.31 | kxy = 0.2, kz = 37.6 |
| Density (kg m⁻³) | 2245.3 | 2873.5 |
| Property | Liquid PCM | Solid PCM |
|---|---|---|
| Phase-change temperature (K) | 310.15 | 308.15 |
| Density (kg m⁻³) | 770 | 810 |
| Specific heat capacity (kJ kg⁻¹ K⁻¹) | 2.2 | 1.9 |
| Latent heat (kJ kg⁻¹) | 241 | 241 |
| Thermal conductivity (W m⁻¹ K⁻¹) | 0.157 | 0.39 |
| Property | Aluminum fin |
|---|---|
| Specific heat capacity (kJ kg⁻¹ K⁻¹) | 0.9 |
| Thermal conductivity (W m⁻¹ K⁻¹) | 238 |
| Density (kg m⁻³) | 2700 |
I calculated the required PCM volume by assuming that the latent heat dominates the absorbed energy during a 3C discharge. For the prismatic cell, the required PCM volume was 23.144 cm³; for the cylindrical cell, it was 13.715 cm³. This calculation is expressed as:
$$ V_{a} = \frac{\int_{0}^{1200} q(t) dt}{1000 Q_{a} \rho_{a}} $$
where \(Q_{a}\) is the latent heat per unit mass and \(\rho_{a}\) is the PCM density. I neglected sensible heat during this sizing step because the latent heat is much larger than the sensible heat over the phase-change interval. This gives a conservative but practical starting point for the electric vehicle battery pack cooling structure.
Topology Optimization of PCM Composite Fins
I used a density-based topology optimization method with the solid isotropic material with penalization (SIMP) model. In the design domain, each finite element is assigned a relative density \(\gamma\). The material properties are interpolated between PCM and aluminum:
$$ k(\gamma) = k_{pcm} + \gamma^{p} (k_{fin} – k_{pcm}) $$
$$ \rho(\gamma) = \rho_{pcm} + \gamma (\rho_{fin} – \rho_{pcm}) $$
$$ C_{p}(\gamma) = C_{p,pcm} + \gamma (C_{p,fin} – C_{p,pcm}) $$
where \(p\) is the penalization exponent. When \(\gamma = 0\), the element behaves as PCM; when \(\gamma = 1\), it behaves as aluminum fin. To avoid mesh dependence and checkerboard patterns, I applied a Helmholtz filter:
$$ -r_{min}^{2} \nabla^{2} \gamma_{f} + \gamma_{f} = \gamma_{c} $$
where \(r_{min}\) is the filter radius, \(\gamma_{c}\) is the raw design variable, and \(\gamma_{f}\) is the filtered variable. After filtering, I used a hyperbolic tangent projection to sharpen the boundaries:
$$ \gamma = \frac{\tanh(\beta \gamma_{\beta}) + \tanh(\beta (\gamma_{f} – \gamma_{\beta}))}{\tanh(\beta \gamma_{\beta}) + \tanh(\beta (1 – \gamma_{\beta}))} $$
I selected a projection slope \(\beta = 8\) and a projection point \(\gamma_{\beta} = 0.5\). I compared two objective functions: thermal compliance and average temperature. The average temperature objective is:
$$ J_{1} = \frac{1}{|\Omega|} \int_{\Omega} T d\Omega $$
The thermal compliance objective is:
$$ J_{2} = \int_{\Omega} q T d\Omega $$
Although thermal compliance is mathematically convenient, it does not always correlate perfectly with the maximum temperature or the temperature uniformity in an electric vehicle battery pack. My comparison showed that average-temperature minimization produced lower cell temperatures at the same fin-to-PCM volume ratio. I therefore used average temperature as the main objective for the rest of the study.
| Objective | Volume ratio ω = 0.1 | ω = 0.2 | ω = 0.3 |
|---|---|---|---|
| Thermal compliance | 41.26 °C | 39.35 °C | 37.77 °C |
| Average temperature | 39.58 °C | 38.01 °C | 37.77 °C |
The fin-to-PCM volume ratio is defined as:
$$ \omega = \frac{V_{fin}}{V_{pcm}} $$
As \(\omega\) increases, the design domain must expand to keep the PCM volume constant. For the prismatic cell, this means that the length of the PCM region increases. For the cylindrical cell, the PCM region can be arranged in a square or hexagonal pattern, which changes the heat-transfer paths inside the electric vehicle battery pack.
Prismatic and Cylindrical Cell Results
For the prismatic cell, I optimized fin structures at \(\omega = 0.1, 0.2, 0.3, 0.4, 0.5,\) and \(0.6\). The optimized fins developed a tree-like branching pattern. As \(\omega\) increased, the fin branches became thicker and more numerous, and the heat was distributed into more PCM regions. This is a key advantage for an electric vehicle battery pack because it prevents local hot spots and uses more of the latent heat capacity.
At a 3C discharge rate, the straight-fin cell reached 44.3 °C at \(\omega = 0.1\) and 41.3 °C at \(\omega = 0.6\). The topology-optimized fin cell reached 40.3 °C at \(\omega = 0.1\) and 37.1 °C at \(\omega = 0.6\). Therefore, the temperature reductions were 8.2 % and 10.1 %, respectively. When \(\omega\) increased from 0.1 to 0.6 in the topology-optimized case, the cell temperature decreased by 7.9 %. However, beyond \(\omega = 0.4\), the improvement became small: the temperatures at \(\omega = 0.4, 0.5,\) and \(0.6\) were 37.4 °C, 37.2 °C, and 37.1 °C. I therefore selected \(\omega = 0.4\) as a balanced design for the electric vehicle battery pack.
| Fin type | ω = 0.1 | ω = 0.3 | ω = 0.6 |
|---|---|---|---|
| Straight fin | 44.3 °C | 43.3 °C | 41.3 °C |
| Topology-optimized fin | 40.3 °C | 38.0 °C | 37.1 °C |
| Temperature reduction | 8.2 % | 12.2 % | 10.1 % |
The temperature history during 3C discharge shows three stages. In the first stage, the PCM is solid and sensible heating dominates, so the cell temperature rises quickly. In the second stage, the PCM melts and absorbs latent heat, so the temperature rise slows down. In the third stage, most of the PCM has melted, and the temperature rise accelerates again. This behavior confirms that the PCM composite fin structure must be designed so that melting is distributed uniformly in the electric vehicle battery pack.
For the cylindrical cell, I compared square and regular hexagonal packing. The hexagonal packing provides more heat-transfer paths and a more uniform temperature field. At \(\omega = 0.1\), the straight-fin hexagonal cell reached 45.2 °C, while the topology-optimized hexagonal cell reached 41.7 °C, a reduction of about 7.8 %. As \(\omega\) increased from 0.1 to 0.5, the topology-optimized hexagonal cell temperature decreased by about 4.6 %. The square-packed topology-optimized cell reached 42.7 °C at \(\omega = 0.1\) and 40.1 °C at \(\omega = 0.5\). The hexagonal-packed topology-optimized cell reached 41.7 °C at \(\omega = 0.1\) and 39.7 °C at \(\omega = 0.5\). Thus, the hexagonal arrangement is more favorable for the electric vehicle battery pack because it improves both cooling and temperature uniformity.
| Arrangement | ω = 0.1 | ω = 0.3 | ω = 0.5 |
|---|---|---|---|
| Square, straight fin | 45.4 °C | 44.0 °C | 42.7 °C |
| Square, topology-optimized | 42.7 °C | 41.0 °C | 40.0 °C |
| Hexagonal, straight fin | 45.2 °C | 43.7 °C | 42.1 °C |
| Hexagonal, topology-optimized | 41.7 °C | 40.3 °C | 39.5 °C |
Air Cooling Optimization for the Electric Vehicle Battery Pack
After I designed the PCM composite fin, I studied how air cooling can remove heat from the electric vehicle battery pack. I reconstructed the topology-optimized fins into straight-edged shapes that are easier to manufacture and mesh. The reconstructed fins preserved most of the thermal benefit: the cell temperature was 40.6 °C for the original topology and 40.5 °C for the reconstructed design. This small difference justified the simplified geometry for the air-cooling study.
I built a three-dimensional model with the cell, PCM-fin region, and air domain. I tested three air-cooling schemes: single-side cooling, double-side same-direction cooling, and double-side opposite-direction cooling. In all cases, the fin height above the PCM was varied, and the air velocity was varied from 1.0 m/s to 3.0 m/s. I used a mesh independence study to select a suitable grid. The cell temperature changed by less than 0.1 % when the mesh was refined beyond about 320,000 elements, so I used approximately 320,000 elements for the main simulations.
The fin extension height strongly affects heat removal. When the fin height was 0 mm, the heat could only leave through the top surface and natural convection. When the fin height increased to 5 mm, the cell temperature decreased by about 1.6 °C. At 10 mm, the temperature decreased by about 2 °C compared with the no-fin case. Beyond 15 mm, the additional cooling became very small, about 0.3 °C. Therefore, I selected a fin extension height of 10 mm as a practical compromise between thermal performance, material cost, and pressure drop in the electric vehicle battery pack.
| Fin extension height | Cell temperature at 3C | Observed benefit |
|---|---|---|
| 0 mm | 40.3 °C | No extended air-cooling surface |
| 5 mm | 38.7 °C | About 1.6 °C reduction |
| 10 mm | 38.3 °C | About 2.0 °C reduction |
| 15 mm | 38.0 °C | Small additional benefit |
| 20 mm | 37.7 °C | Diminishing returns |
For single-side cooling, the cell temperature was 38.554 °C at 1.0 m/s and 37.8 °C at 3.0 m/s. The cell-to-cell temperature difference increased with air velocity because the inlet-side cell was cooled more strongly than the outlet-side cell. At 2.5 m/s and 3.0 m/s, the temperature reduction became very small. I therefore selected 2.5 m/s as a suitable air velocity for further comparison.
For double-side same-direction cooling, the cell temperature was 37.7 °C at 1.0 m/s and 36.9 °C at 3.0 m/s. This is clearly better than single-side cooling. However, the cell-to-cell temperature difference also increased with air velocity because the two cooling streams were parallel and the downstream air was preheated. The inlet-side cells remained cooler than the outlet-side cells, which creates an uneven temperature distribution in the electric vehicle battery pack.
For double-side opposite-direction cooling, the cell temperature was also 37.7 °C at 1.0 m/s and 36.9 °C at 3.0 m/s. Thus, the overall cooling capacity was almost identical to the same-direction case. The major advantage appeared in temperature uniformity. The opposite-direction flow balanced the inlet and outlet effects on both sides, so the cell-to-cell temperature difference remained extremely small. Compared with single-side cooling, the opposite-direction scheme reduced the cell-to-cell temperature difference by nearly 90 %, and the difference remained below about 0.01 °C in the studied range. Therefore, double-side opposite-direction cooling is the best choice for the electric vehicle battery pack when both thermal safety and uniformity are considered.
| Cooling scheme | Temperature at 1.0 m/s | Temperature at 3.0 m/s | Temperature difference trend |
|---|---|---|---|
| Single-side air cooling | 38.6 °C | 37.8 °C | Increases with velocity |
| Double-side same-direction | 37.7 °C | 36.9 °C | Increases with velocity |
| Double-side opposite-direction | 37.7 °C | 36.9 °C | Almost constant and very small |
Thermal Runaway Suppression in the Electric Vehicle Battery Pack
Thermal runaway is one of the most serious safety concerns for an electric vehicle battery pack. I simulated two adjacent cells at 100 % state of charge. For the first 60 s, both cells were discharged at 3C. After 60 s, one cell was forced into thermal runaway with a volumetric heat generation rate of 136.3 MW/m³ for the prismatic cell and 129.3 MW/m³ for the cylindrical cell. The trigger temperature was set to 150 °C, and the simulation continued for 500 s. The healthy cell continued to generate heat at the normal 3C rate. I compared a connected straight-fin design, a disconnected straight-fin design, and the topology-optimized fin design.
In the connected straight-fin case, heat traveled easily from the runaway cell to the healthy cell. The healthy cell temperature rose rapidly and approached the thermal runaway threshold of 150 °C. This indicates that a continuous metallic path can accelerate failure propagation in an electric vehicle battery pack. In the disconnected straight-fin case, the temperature difference between the two cells increased, showing that the break in the fin path blocked part of the heat flow. The topology-optimized fin performed even better because its branches and gaps controlled the heat path more effectively.
| Cell type | Fin design | Healthy cell temperature at 500 s | Runaway cell temperature at 500 s |
|---|---|---|---|
| Prismatic | Straight fin, connected | 150 °C or above | Approached a lower peak |
| Prismatic | Straight fin, disconnected | 92.6 °C | High and slowly decreasing |
| Prismatic | Topology-optimized | 67.2 °C | High and slowly decreasing |
| Cylindrical | Straight fin | 88.9 °C | 171.3 °C |
| Cylindrical | Topology-optimized | 83.2 °C | 184.3 °C |
For the prismatic cell, the topology-optimized fin kept the healthy cell at only 67.2 °C, while the disconnected straight fin resulted in 92.6 °C. For the cylindrical cell, the topology-optimized fin kept the healthy cell at 83.2 °C, compared with 88.9 °C for the straight fin. The runaway cell in the straight-fin case reached a lower temperature because more heat was transferred to the healthy cell, which is undesirable. The topology-optimized fin therefore provides a better safety barrier in the electric vehicle battery pack by reducing heat leakage to neighboring cells.
I explain this behavior using the heat diffusion path. A continuous fin acts as a high-conductivity bridge, so the thermal resistance between cells is low. A topology-optimized fin can still conduct heat into the PCM, but its geometry changes the effective path and increases the thermal resistance between adjacent cells. In addition, the PCM absorbs latent heat and delays the temperature rise of the healthy cell. This combination is especially important in a large electric vehicle battery pack, where one failed cell could otherwise trigger a chain reaction.
Discussion and Design Guidelines
The results of my study can be summarized as a set of design guidelines for an electric vehicle battery pack. First, the PCM composite fin should use a volume ratio near 0.4. Below this value, the fin network is too sparse and the PCM melts locally. Above this value, the fin occupies too much space and the additional cooling benefit is small. Second, the fin geometry should be topologically optimized rather than simply increased in thickness. The tree-like branches distribute heat into more PCM and create more uniform melting. Third, the fin should extend into an air channel by about 10 mm. This provides a strong air-cooling benefit without excessive pressure drop. Fourth, the air-cooling scheme should use double-side opposite-direction flow. This scheme gives nearly the same maximum temperature as double-side same-direction flow but much better temperature uniformity. Fifth, the fin path between adjacent cells should be interrupted or redesigned to suppress thermal runaway propagation.
I also note that the topology-optimized fin structure is more complex than a straight fin. For manufacturing, I reconstructed the optimized shape into straight-edged segments. The reconstructed design lost only about 0.1 °C in cell temperature compared with the original topology. This means that the thermal advantage of topology optimization can be retained while using practical manufacturing methods. For an electric vehicle battery pack, this is a crucial point because a design that cannot be manufactured at scale has little practical value.
| Design variable | Recommended value | Reason |
|---|---|---|
| Fin-to-PCM volume ratio | 0.4 | Balances latent heat capacity and heat conduction |
| Fin extension height | 10 mm | Provides about 2 °C reduction without excessive pressure drop |
| Air velocity | 2.5 m/s | Further velocity increase gives diminishing cooling benefit |
| Air-cooling scheme | Double-side opposite-direction | Best temperature uniformity and low cell-to-cell difference |
| Packing for cylindrical cells | Regular hexagonal | Better heat spreading than square packing |
I further express the thermal performance using the maximum temperature \(T_{max}\), average temperature \(T_{avg}\), and temperature difference \(\Delta T\):
$$ T_{max} = \max_{\Omega} T(\mathbf{x}, t) $$
$$ T_{avg} = \frac{1}{|\Omega|} \int_{\Omega} T(\mathbf{x}, t) d\Omega $$
$$ \Delta T = T_{max} – T_{min} $$
For an electric vehicle battery pack, the goal is to minimize \(T_{max}\) and \(\Delta T\) while keeping \(T_{avg}\) within the safe operating range. The topology-optimized PCM-fin design reduces \(T_{max}\) and \(\Delta T\) simultaneously because it improves both heat conduction and latent heat utilization.
Conclusions and Future Work
I have presented a topology optimization study of phase change cooling structures for an electric vehicle battery pack. The main conclusions are as follows. First, a topology-optimized fin reduces the cell temperature significantly compared with a straight fin at the same fin-to-PCM volume ratio. For the prismatic cell at 3C discharge, the reduction was 8.2 % at \(\omega = 0.1\) and 10.1 % at \(\omega = 0.6\). When \(\omega\) increased from 0.1 to 0.6, the temperature decreased by 7.9 %, but the benefit became small beyond \(\omega = 0.4\). Second, for the cylindrical cell, regular hexagonal packing performed better than square packing. At \(\omega = 0.1\), the topology-optimized hexagonal design reduced the temperature by about 7.8 % compared with the straight fin. Third, the fin extension height of 10 mm and air velocity of 2.5 m/s provided a good compromise between cooling and cost. Fourth, double-side opposite-direction air cooling was the best scheme because it maintained a very small cell-to-cell temperature difference, nearly 90 % lower than single-side cooling. Fifth, the topology-optimized fin suppressed thermal runaway propagation more effectively than a straight fin. In the prismatic cell, the healthy cell remained at 67.2 °C, and in the cylindrical cell it remained at 83.2 °C.
My study shows that topology optimization is a powerful method for designing PCM composite fins in an electric vehicle battery pack. It allows the fin material to be placed where it is most needed, rather than relying on intuition or simple repeated geometries. The resulting structure improves heat conduction, increases PCM utilization, reduces maximum temperature, improves temperature uniformity, and delays thermal runaway propagation.
In future work, I plan to extend the model in several directions. I will include more realistic temperature-dependent properties, anisotropic cell properties, and contact resistances between the cell, fin, and PCM. I will also test additional objective functions, such as maximum temperature, temperature variance, and pressure drop, so that the optimization can capture multiple design goals at once. I intend to combine the numerical model with experimental validation using infrared imaging and embedded thermocouples. I also plan to explore advanced PCM composites with nanoparticles, fibers, or bio-based materials to increase effective thermal conductivity and latent heat. Finally, I will study larger electric vehicle battery pack configurations with many cells, busbars, and cooling channels, so that the topology-optimized PCM-fin design can be evaluated under realistic pack-level operating conditions.
Overall, I conclude that the proposed topology-optimized phase change cooling structure is a promising solution for the thermal management of an electric vehicle battery pack. It addresses the key challenges of high temperature, non-uniform temperature distribution, and thermal runaway propagation, and it provides a practical path toward safer and longer-lasting electric vehicle battery packs.