The growing demand for electric vehicles has made the thermal management of traction battery packs a critical engineering challenge. As a primary power source, lithium-ion batteries offer high energy density, but they are also prone to overheating during operation. The rate of heat generation inside a traction battery pack depends strongly on the charging and discharging protocol, which affects the temperature uniformity and surface temperature of the cells. Several studies have shown that solid–liquid phase change based cooling is a promising approach because of its high latent heat storage capacity, near-isothermal operating range, and flexibility in material selection. However, the main bottleneck is the low thermal conductivity of phase change materials (PCMs), which limits the heat transfer rate. To overcome this limitation, I proposed to add tree-shaped fins and nanomaterials into the PCM domain. This paper summarizes my research, which combines experiments and numerical simulations to evaluate the heat dissipation performance and temperature uniformity of a traction battery pack cooled by PCM coupled with tree fins.
In the experimental phase, I constructed a test bench using four 26650-format lithium-ion cells connected in series, surrounded by a PCM-filled cavity. I tested several internal fin geometries: a plain cylindrical cartridge, a rectangular fin, and a tree-shaped fractal fin. The tree fin was designed with a branching angle of 90° and four fractal levels. The whole assembly was placed inside a programmable constant-temperature and humidity chamber. I monitored the battery temperature at different locations with K-type thermocouples. The experimental matrix included ambient temperatures of −10 °C, 25 °C, 40 °C and 50 °C, and charging modes of 1C, constant current, and constant-current/constant-voltage (CC-CV). The results showed that the tree fin coupled with PCM not only improved the heat transfer rate but also increased the allowable operating time of the traction battery pack. At an ambient temperature of 25 °C, the tree-fin PCM module decreased the maximum cell temperature by a factor of approximately 0.9 and increased the charging time by 27.5%. At high ambient temperatures (40–50 °C), the PCM module was able to keep the maximum cell temperature below 40 °C even after prolonged operation, whereas the naturally cooled pack quickly exceeded 50 °C. At low temperatures, the PCM module acted as a thermal insulator and slowed down the cooling of the battery, allowing the pack to remain warmer than an unprotected pack. The measured minimum temperature of a battery in a finned PCM housing was 2.4 times higher than that of the natural-convection pack under the same ambient condition.
To better understand the melting front propagation and the transient heat transfer processes, I also performed visualisation experiments using simulated battery cells (cylindrical electric heating rods). The heating rods had the same dimensions as the 26650 cells and were inserted into the same fin structures. I varied the heating power (10 W and 15 W per rod) and the environment temperature (25 °C and 40 °C). A transparent acrylic enclosure allowed me to record the evolution of the solid–liquid interface with a camera. The results revealed that the liquid region first appeared near the fin and well surfaces and then expanded outward and upward. Because of gravity, the melting process was not symmetric in the vertical direction: PCM at the top of the enclosure melted earlier than PCM at the bottom. The temperature distribution inside the PCM domain clearly split into an upper region and a lower region, with the upper region being warmer. The tree-fin module gave the longest operating time before the simulated battery reached the safety limit of 60 °C. Under the condition of 10 W heating and 40 °C ambient temperature, the tree-fin case prolonged the working duration by 54.9% compared with the plain PCM module without fins.
In the second stage of my work, I performed a systematic numerical study on the tree-shaped fin geometry. The numerical model is based on the enthalpy–porosity method for solid–liquid phase change. I solved the governing equations of continuity, momentum and energy using the finite volume method in Ansys Fluent. The density change in the liquid PCM was accounted for by the Boussinesq approximation. The relevant material properties and boundary conditions were chosen to represent a real traction battery pack cooling system. The governing equations are summarized below:
Continuity:
$$\nabla \cdot \left( \rho \mathbf{u} \right) = 0$$
Momentum:
$$\frac{\partial \left( \rho \mathbf{u} \right)}{\partial t} + \nabla \cdot \left( \rho \mathbf{u} \mathbf{u} \right) = – \nabla p + \nabla \cdot \left( \mu \nabla \mathbf{u} \right) + \rho \mathbf{g} + \mathbf{S}$$
Energy:
$$\frac{\partial \left( \rho h \right)}{\partial t} + \nabla \cdot \left( \rho \mathbf{u} h \right) = \nabla \cdot \left( k \nabla T \right)$$
Here, the enthalpy \(h\) is the sum of the sensible enthalpy and the latent heat related to the liquid fraction \(\gamma\):
$$h = h_{ref} + \int_{T_{ref}}^{T} c_{p} \, dT + \gamma L$$
The source term in the momentum equation is defined by the Carman–Kozeny type equation:
$$\mathbf{S} = – A_{mush} \frac{\left( 1 – \gamma \right)^{2}}{\gamma^{3} + \epsilon} \mathbf{u}$$
with \(A_{mush} = 10^{7}\), \(\epsilon = 0.001\). The liquid fraction \(\gamma\) is given by:
$$\gamma = \begin{cases} 0 & T < T_{solid} \\ \frac{T – T_{solid}}{T_{liquid} – T_{solid}} & T_{solid} \le T \le T_{liquid} \\ 1 & T > T_{liquid} \end{cases}$$
I first validated the numerical model against published experimental and simulation data, and the average deviation was less than 2.8%. I also performed grid and time-step independence tests. A grid size of 0.5 mm and a time step of 0.25 s were chosen to balance computational cost and accuracy. The physical model consists of a cylindrical electric heater (simulating the 26650 lithium-ion cell) with a diameter of 26 mm and a height of 65 mm, surrounded by an annular PCM domain of 65 mm inner diameter and 2 mm shell thickness. The heating rate was set to 10 W per cell, the initial temperature was 25 °C, and the outer surface lost heat to the ambient by natural convection with a coefficient of 10 W/(m²·K).
I designed several tree fins with different fractal levels (2, 3 and 4) and different branch angles (60°, 90°, 120° and 150°). Table 1 describes the geometric parameters of the fins. All fins were made of aluminium 6061 and were designed to occupy the same fin volume so that the comparison was based on the fin shape only.
| Fin type | First-level length (mm) | First-level width (mm) | Number of levels | Branch angle (deg) |
|---|---|---|---|---|
| Rectangular | 27.4 | 4.0 | 1 | — |
| 2-60 | 12.0 | 2.0 | 2 | 60 |
| 2-90 | 12.0 | 2.0 | 2 | 90 |
| 2-120 | 12.0 | 2.0 | 2 | 120 |
| 2-150 | 12.0 | 2.0 | 2 | 150 |
| 3-60 | 9.6 | 1.6 | 3 | 60 |
| 3-90 | 9.6 | 1.6 | 3 | 90 |
| 3-120 | 9.6 | 1.6 | 3 | 120 |
| 3-150 | 9.6 | 1.6 | 3 | 150 |
| 4-60 | 7.7 | 1.3 | 4 | 60 |
| 4-90 | 7.7 | 1.3 | 4 | 90 |
| 4-120 | 7.7 | 1.3 | 4 | 120 |
| 4-150 | 7.7 | 1.3 | 4 | 150 |
The PCM used in the simulations was OP44E with a melting range of 40.6–44.7 °C. Its properties are listed in Table 2 together with the battery and aluminium properties.
| Material | Density (kg/m³) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) | Latent heat (J/kg) |
|---|---|---|---|---|
| OP44E | 700 | 2000 (solid) / 2350 (liquid) | 0.18–0.2 | 240800 |
| Lithium-ion battery | 2007.7 | 837.4 | 32.2 | — |
| Aluminium | 2675 | 903 | 211 | — |
I simulated a total of fifteen fin cases plus a baseline case with no fins and a case with a rectangular fin. Figure 1 shows a representative geometry of the computational domain and fin configuration. During the numerical study, I monitored the average temperatures of the battery and PCM, the battery temperature uniformity, the instantaneous and average velocities of the PCM, and the melting fraction. The stored energy in the PCM is calculated using:
$$Q = \rho V \left[ \int_{T_0}^{T} C_p \, dT + \gamma L \right]$$
The thermal power during complete melting is then:
$$P = \frac{Q}{t_{total}}$$
To compare the convection intensity, I used the time-averaged maximum velocity, defined as:
$$\overline{V}_{max} = \frac{1}{t_{total}} \int_{0}^{t_{total}} V_{max}(t) \, dt$$
Figure 2 presents the simulated average battery temperature and PCM liquid fraction curves for the 4-150 fin case. The results show that, for the same fractal level, increasing the branch angle reduces the average battery temperature and improves temperature uniformity. For the same branch angle, increasing the fractal level also lowers the average battery temperature. The 4-150 geometry (four levels and a 150° branch angle) yielded the lowest battery temperature, with a maximum temperature reduction of 4.5% compared with the no-fin baseline. The melting time for the 4-150 case was 82.5 minutes, which was 11.8% shorter than the baseline’s 93.5 minutes. The average melting speed of the PCM in the 4-150 case was 1.71 times higher than that of the baseline. Meanwhile, the power of the system was increased by 11.2%.
However, the maximum PCM velocity exhibited an opposite trend: the no-fin case had the largest peak velocity (3.38 mm/s), about 1.02 times that of the 4-150 case, because the fins hindered the natural convection roll. The presence of the tree fins enhanced local conduction and created a more uniform convection pattern, which was beneficial for both melting time and battery temperature uniformity.
Based on these findings, I chose the 4-150 fin for further investigation. In the final numerical study, I varied the number of tree fins (1, 2, 3 and 4 identical fins placed around the battery) and also investigated the addition of multi-walled carbon nanotubes (MWCNTs) into the PCM at mass fractions of 0%, 3% and 6%. The effective thermophysical properties of the resulting nano-enhanced phase change material (N-PCM) were obtained from widely used correlations:
$$\rho_{N-PCM} = \varphi \rho_{MWCNT} + (1-\varphi) \rho_{PCM}$$
$$\rho_{N-PCM} C_{p,N-PCM} = \varphi \rho_{MWCNT} C_{p,MWCNT} + (1-\varphi) \rho_{PCM} C_{p,PCM}$$
$$k_{N-PCM} = k_{PCM} \left[ \frac{k_{MWCNT} + 2k_{PCM} – 2\varphi (k_{PCM} – k_{MWCNT})}{k_{MWCNT} + 2k_{PCM} + \varphi (k_{PCM} – k_{MWCNT})} \right]$$
$$\mu_{N-PCM} = \frac{\mu_{PCM}}{(1-\varphi)^{2.5}}$$
$$\left( \rho L \right)_{N-PCM} = (1-\varphi) (\rho L)_{PCM}$$
Table 3 summarizes the N-PCM cases considered in this phase.
| Fin geometry | Number of fins | MWCNT mass fraction (%) |
|---|---|---|
| No fin | 0 | 0, 3, 6 |
| Rectangular | 4 | 0, 3, 6 |
| Tree 150°-4 | 2 | 0, 3, 6 |
| Tree 150°-4 | 3 | 0, 3, 6 |
| Tree 150°-4 | 4 | 0, 3, 6 |
The inclusion of MWCNTs improved the effective thermal conductivity of the PCM, which accelerated melting and lowered the peak battery temperature. Table 4 lists the computed maximum battery temperature, average battery temperature uniformity, and melting time for all N-PCM cases.
| Case | Battery max temperature (°C) | Average uniformity factor (–) | Melting time (min) |
|---|---|---|---|
| No fin, 0% | 68.4 | 2.18 | 93.5 |
| No fin, 3% | 67.8 | 2.02 | 91.0 |
| No fin, 6% | 67.2 | 1.87 | 88.5 |
| Rectangular, 0% | 60.2 | 1.04 | 85.0 |
| Rectangular, 3% | 59.6 | 0.98 | 83.0 |
| Rectangular, 6% | 59.1 | 0.92 | 81.0 |
| Tree ×2, 0% | 60.4 | 1.42 | 87.0 |
| Tree ×2, 3% | 59.8 | 1.30 | 85.0 |
| Tree ×2, 6% | 59.2 | 1.18 | 83.0 |
| Tree ×3, 0% | 59.0 | 1.17 | 85.0 |
| Tree ×3, 3% | 58.4 | 1.06 | 83.0 |
| Tree ×3, 6% | 57.8 | 0.95 | 81.0 |
| Tree ×4, 0% | 58.5 | 0.96 | 82.5 |
| Tree ×4, 3% | 58.0 | 0.94 | 80.5 |
| Tree ×4, 6% | 57.9 | 0.92 | 79.0 |
It is clear from Table 4 that the beneficial effect of MWCNTs becomes stronger when the number of fins increases. The maximum temperature of the traction battery pack with four tree fins and 6% MWCNTs was only 57.9 °C, which is 18.3% lower than the unprotected baseline. The average battery temperature uniformity factor reached as low as 0.92, meaning that the difference across the cell surface remained below about 2 °C. Moreover, the melting time was reduced from 93.5 min (no fin, no nanoparticle) to 79.0 min, corresponding to a 15.5% shortening. The total stored energy of the PCM at the end of melting was smaller for the highly concentrated N-PCM because the volume fraction of the PCM was reduced by the nanoparticles; nevertheless, the overall power of the system increased by a factor of 1.11 because the melting time decreased more significantly.
I also analyzed the velocity field inside the liquid PCM. The average velocity in the case with four tree fins and 6% MWCNTs reached 0.71 mm/s near the peak, while the time-averaged maximum velocity was only about 1.16 mm/s—much lower than that of the no-fin case (2.68 mm/s). This confirms that the tree fins suppress uncontrolled large-scale natural convection, but they produce a finer and more distributed convective flow that enhances heat transport near the heated surface. The maximum velocity profile for the cases with a small number of fins shows multiple peaks, which is characteristic of re-circulating cells established between the adjacent branches of the fins. These peaks correspond to the periodic increase and break-off of buoyant plumes at the branch ends.
From the experimental and numerical results, I have identified the following key mechanisms responsible for the improved performance of the tree-fin coupled PCM system. First, the tree fins act as extended surfaces that efficiently spread the heat generated by the traction battery pack into the PCM. The branched structure provides long paths without sacrificing much fin volume, so the effective heat conduction area is larger than that of a rectangular fin occupying the same volume. Second, the angled branches create multiple channels that guide the melted liquid upward and allow colder PCM to move downward, promoting natural convection in an organized way. Third, the melting process proceeds faster at the tip of each branch, leading to the formation of a dendritic melting front that travels deeper into the PCM domain. This improves the utilization of the latent heat capacity of the PCM. Fourth, when MWCNTs are added into the PCM, the thermal conductivity of the nanofluid improves while the viscosity increases only slightly; the combined effect is particularly beneficial for a confined space where a large amount of heat must be absorbed quickly during high-rate discharge or fast-charging of a traction battery pack.
To make the above results easy to compare, I have summarized the effect of the tree fins and the nanoparticles in Table 5. The normalized metrics are relative to the baseline case (no fin, no nanocarbon).
| Configuration | Peak battery temperature reduction | Melting time reduction | Power increase | Temperature uniformity improvement |
|---|---|---|---|---|
| Rectangular fin, 0% | 2.7% | 9.1% | 8.7% | 52.3% |
| 4-150 fin, 0% | 4.5% | 11.8% | 11.2% | 56.0% |
| 4-150 fin, 6% | 18.3% | 15.5% | 11.1% | 62.4% |
The table indicates that the combination of tree fins and nanoparticles yields the best overall performance for the thermal management of a traction battery pack. The tree fins provide the primary enhancement by increasing the conductive path and distributing the heat more evenly. The nanoparticles then improve the effective conductivity of the PCM and allow the heat to penetrate the bulk material more quickly. This synergy is particularly important when the battery pack is subjected to high discharge rates, where the instantaneous heat generation exceeds the capability of plain PCM modules.
Throughout my study, I also noted some practical considerations. During the experiments, the PCM volume shrank after solidification, so I had to add liquid PCM in multiple stages to ensure that the enclosure was completely filled. In the visualisation experiments, the solid phase of the PCM sometimes detached from the thermocouple and fell onto the lower fins, leading to a temporary non-symmetric temperature distribution. This behaviour is consistent with the density difference between the solid and liquid phases. In the real traction battery pack, the orientation of the battery pack also plays a role in the natural convection because the gravitational direction is usually fixed. My current model considered gravity perpendicular to the battery axis, which corresponds to a horizontally mounted cylindrical battery. For other orientations, the fin geometry should be optimized accordingly.
In conclusion, my combined experimental and numerical work demonstrates that a tree-shaped fractal fin coupled with a phase change material is an effective passive thermal management solution for a traction battery pack. The tree fin with four levels and a branching angle of 150° provides the lowest battery temperature, the best temperature uniformity, the shortest melting time, and the highest stored-energy power when compared with rectangular fins and the no-fin baseline. Adding MWCNTs to the PCM further improves the performance, especially in systems with four fins. The temperature of the traction battery pack can be kept below 60 °C for a significantly longer period, and under the tested conditions the maximum cell temperature was reduced from roughly 68 °C to below 58 °C. These findings provide useful guidelines for the design of compact, high-performance PCM-based thermal management systems in battery electric vehicles.
Future work should extend this analysis to multi-cell battery modules and packs under realistic drive cycles. The optimization of the tree fin layout, e.g., using fractal dimensions and topology optimisation, could also lead to even better utilisation of the PCM volume. Moreover, the interaction between the fin branches and the natural convection in the liquid phase can be further improved by exploiting non-uniform branch angles or by using fins with varying thickness along the branch direction. The combination of such advanced fin geometries with nano-enhanced PCMs is a promising path for safe and long-lasting traction battery pack operation.