In modern transportation, the vehicle traction battery is recognised as the primary power source for electric vehicles because of its high energy density, long cycle life and negligible exhaust emission. However, lithium-ion batteries are susceptible to overheating during aggressive driving, fast charging and high ambient temperature exposure. The heat produced inside a cell, originating from electrochemical reactions, polarisation and ohmic losses, raises the surface temperature and deteriorates temperature uniformity. In severe cases, thermal runaway may occur, leading to catastrophic safety hazards. To address this issue, various thermal management technologies have been developed for vehicle traction battery packs. Among them, solid-liquid phase change material (PCM) based cooling has shown great potential owing to its high latent heat capacity, isothermal phase transition and passive operation. Yet, the low intrinsic thermal conductivity of PCM severely limits the heat transfer rate and prevents the rapid dissipation of heat from the battery surface. Therefore, enhancing the heat conduction and convection inside the PCM is essential for practical vehicle traction battery applications. In this work, I experimentally and numerically investigate a new thermal management structure that utilises tree-shaped fins combined with PCM. The tree-like fractal fin can enlarge the heat transfer area and provide multiple pathways for heat conduction. Additionally, nanomaterials, namely multi-walled carbon nanotubes (MWCNT), are added into PCM to increase its effective thermal conductivity. The combination is intended to simultaneously improve the peak temperature control, temperature uniformity and operating time of vehicle traction battery modules.
The heat generation inside a vehicle traction battery can be expressed through the electrochemical reaction heat \(Q_r\), the polarisation heat \(Q_p\), the Joule heat \(Q_j\) and the side-reaction heat \(Q_s\):
\[
Q_r = \frac{Q}{3600}\cdot F I
\]
\[
Q_p = I^2 R_p
\]
\[
Q_j = I^2 R_j
\]
\[
Q = Q_r + Q_p + Q_j + Q_s
\]
where \(Q\) is the total heat, \(F\) is the Faraday constant, \(I\) is the current, and \(R_p\) and \(R_j\) are polarisation resistance and ohmic resistance, respectively. In normal operation, \(Q_s\) is negligible. The total heat production increases with the square of the current, and therefore high-rate charge/discharge leads to severe temperature rise.
Experimental study on PCM–tree-fin thermal management of vehicle traction battery
In the first part of my research, I constructed an experiment platform with four 26650 lithium-ion cells connected in series. The rated capacity of each cell was 5 Ah, and the maximum open-circuit voltage of the pack was 16.8 V. The battery module was inserted into an organic glass chamber filled with RT35 PCM. The chamber inner dimensions were 200 mm × 200 mm × 65 mm with a wall thickness of 15 mm. The cells were arranged in a 2×2 pattern, and each cell was encircled by either a plain aluminium tube, a rectangular fin tube, or a tree-shaped fin structure. All fins were made of aluminium 6061 with the same total volume. The tree-shaped fins were constructed with four fractal levels, and the branching angle was 90° in the first experiment. For comparison, a rectangular fin with the same total projected length and thickness levels was fabricated, and a plain tube with no fins was used as the baseline heat-transfer sleeve. The front face of the chamber contained four circular holes with a diameter slightly larger than the fin outer diameter, so the cells could slide into the fins with thermal grease between the cell wall and the fin inner surface.
Thermocouples were fixed to three locations on each cell: the positive cap, the negative cap, and the mid-height shell. The assembled BTMS was placed inside a temperature-humidity chamber so that the ambient temperature could be accurately controlled. The charging and discharging protocols were implemented by a battery test system. I performed experiments at ambient temperatures of −10 °C, 25 °C, 40 °C and 50 °C for three charging modes: 1C constant-current charging, constant-current charging, and constant-current/constant-voltage charging. For each condition, I compared four systems: no thermal management, plain-tube PCM box, rectangular-fin PCM box and tree-fin PCM box. To ensure repeatability, the same mass of molten PCM was poured into the chamber before each test, and the initial cell and PCM temperature was equilibrated to about 25 °C.
The uncertainty of the temperature measurements was calculated based on the calibrated thermocouple accuracy; the maximum relative uncertainty was approximately 0.4%, which confirms the reliability of the data.
Experimental results under different charging modes
Figure 2 in the original thesis summarises the cell temperature histories under the 1C charging mode. In the low-temperature environment at −10 °C, the cells without PCM cooling cooled down quickly, and the minimum temperature dropped to 8.0 °C at the end of the test. With the tree-fin PCM box, the lowest cell temperature remained at about 19.2 °C, i.e. roughly 2.4 times higher than that without the PCM system. This demonstrates that the PCM box can effectively protect the vehicle traction battery from severe cold and maintain a warm environment during discharge. At 25 °C, the tree-fin PCM system reduced the maximum cell temperature to about 30.1 °C, corresponding to a 0.9-fold reduction compared with the no-management case. Moreover, the tree-fin box elongated the working time by 27.5% compared to the empty-tube case, because the phase transition absorbed a large amount of heat and delayed the moment when the cell temperature reached the cut-off limit.
At 40 °C and 50 °C ambient temperatures, the cells without PCM overheated severely. In the 50 °C environment, the no-management cell temperature exceeded 50 °C, while all PCM-based systems maintained the maximum temperature below 36 °C. The tree-fin PCM system always produced the lowest maximum temperature. The rectangular fin performed similarly but slightly worse than the tree fin, while the plain-tube PCM box showed the least enhancement among the three PCM configurations. Figure 3 presents the temperature curves under constant-current charging. The trends are close to the 1C case: the tree-fin box provides the lowest end-of-test temperature and the longest discharge time. The temperature curves in the PCM box are smooth and exhibit an initial rapid increase followed by a slow plateau, which is the signature of melting.
The constant-current constant-voltage charging mode resembles practical slow charging and yields the longest charging time among all protocols. During the later constant-voltage stage, the charging current gradually decreases, so the generated heat drops. Hence, the cell temperature in the PCM boxes decreases slowly. Under −10 °C, the tree-fin PCM box kept the cell temperature at 13.2 °C at the end of charging, while the corresponding no-management temperature was far below freezing. At 25 °C, the tree-fin system reduced the maximum temperature to 34.3 °C. At 40 °C, all three PCM boxes performed within a narrow range, but the tree-fin box was still slightly superior. At 50 °C, the no-management cells heated up to nearly 60 °C, whereas the PCM boxes kept the maximum temperature below 36.5 °C. Based on these experiments, I conclude that the tree-fin PCM system is the most effective passive thermal management solution among the tested configurations for a vehicle traction battery under broad operating conditions.
| Ambient temperature (°C) | Charging mode | Max cell temp (Tree-fin, °C) | Working-time enhancement (%) | Temperature-reduction factor |
|---|---|---|---|---|
| −10 | 1C | ~19.2 (end) | – | 2.4× higher minimum temp |
| 25 | 1C | 30.1 | 27.5 | 0.9× |
| 40 | 1C | ~34.5 | ~20–22 | 0.79× |
| 50 | 1C | ~35 | ~17 | 0.7× |
| 25 | Constant-current | ~33 | – | 0.76× |
| 50 | Constant-current | 36.8 | – | 0.75× |
| 25 | Constant-current/constant-voltage | 34.3 | ~2 | 0.73× |
| 50 | Constant-current/constant-voltage | ~36.5 | – | 0.65× |
Visualisation experiment using simulated cell heaters
To better observe the melting behaviour and the temperature field around the fins, I employed four electric heating rods as simulated batteries. Each rod had exactly the same shape as the 26650 cell: 26 mm diameter and 65 mm height. It was made from stainless steel and filled with magnesium oxide powder, providing uniform heat generation and electrical insulation. The heating rods were connected to four individual DC power supplies so that each rod received the same power. I selected heating powers of 10 W and 15 W, and ambient temperatures of 25 °C and 40 °C. The camera was placed in front of the transparent chamber and photographs were recorded every 10 minutes. By applying image processing with MATLAB, the solid and liquid regions of PCM were converted into a binary image, in which the white area represents solid PCM and the black area represents liquid PCM. In addition, the simulated rods were marked with a blue gradient to distinguish them.
Figure 4 in the original thesis shows the phase-interface evolution for the plain-tube, rectangular-fin, and tree-fin systems. In all cases, the melted phase first appears adjacent to the heat source surfaces, i.e. the outer tube or the fin branches. The solid-liquid interface propagates outward and upward. The upper region melts faster because buoyancy-driven liquid PCM accumulates there. The melting in the tree-fin box is significantly faster than in the plain-tube box, and slightly faster than in the rectangular-fin box. After 60 minutes, thermal natural convection develops in the melted region; the melt fraction rate accelerates. The lower part of the chamber always remains solid longer. The photograph processing reveals that the phase interface is approximately symmetrical with respect to the vertical axis.
Thermocouples were placed at nine positions inside the PCM chamber and three heights on each heating rod. The measured temperature histories indicate that the PCM temperature always forms three distinct vertical zones: the upper thermocouples show the highest temperatures, the lower thermocouples show the lowest temperatures, and the middle thermocouples lie in between. This confirms that natural convection, driven by gravity, is the dominant heat-transfer mode after the initial melting stage. The temperature of the heating rods increases linearly at first while heat is transferred by pure conduction through the solid PCM. When melting starts, the temperature growth slows dramatically and then forms a plateau. Once all the PCM surrounding a rod is melted, the rod temperature again increases faster. In the tree-fin enclosure, this final rise is gentler and the working time before the safety limit of 60 °C is longest.
For the case of 25 °C and 10 W, the tree-fin box enabled a total operating time of about 823 minutes, while the rectangular-fin box and the plain-tube box achieved only 1.3 times and 1.8 times shorter times, respectively. When the heating power was increased to 15 W while keeping the ambient temperature at 25 °C, the tree-fin box still yielded 286 minutes of operation, that is, about 2.3 times longer than the plain-tube box. At 40 °C and 10 W, the tree-fin box gave 334 minutes, which is almost equal to the rectangular-fin box (332 minutes) and significantly longer than the plain-tube box (160 minutes). Finally, under the harshest condition of 40 °C and 15 W, the tree-fin box produced 184 minutes, outperforming the plain-tube box by 54.9% and outperforming the rectangular-fin box slightly by about 1.1%. These data confirm that the tree-fin structure provides better heat distribution and delayed PCM saturation, which is beneficial for vehicle traction battery cooling under high discharge loads.
| Fin type | 25 °C, 10 W (min) | 25 °C, 15 W (min) | 40 °C, 10 W (min) | 40 °C, 15 W (min) |
|---|---|---|---|---|
| Plain-tube PCM | ~460 | ~124 | 160 | ~119 |
| Rectangular-fin PCM | ~633 | ~260 | 332 | ~182 |
| Tree-fin PCM | 823 | 286 | 334 | 184 |
Numerical investigation: effect of fractal level and branching angle
After demonstrating the advantage of tree-shaped fins experimentally, I performed a detailed three-dimensional numerical study to optimise the tree-fin geometry. I designed thirteen different configurations with fractal levels (2, 3, and 4) and branching angles (60°, 90°, 120°, 150°), in addition to a rectangular fin and no fin. The model geometry is shown in the original thesis. The battery is represented by the same dimensions as the 26650 cell: diameter 26 mm and height 65 mm. The shell is aluminium, and the space between the shell and outer case is filled with OP44E PCM, whose melting range is 40.6 °C–44.7 °C. The battery heat generation is 10 W. The ambient temperature is 25 °C, and natural-convection boundary conditions with a heat-transfer coefficient of 10 W/(m²·K) are set on the outer surface. The numerical formulation uses the enthalpy-porosity method for the solid-liquid phase change.
The conservation equations are as follows:
\[
\nabla\cdot(\rho \mathbf{u})=0
\]
\[
\frac{\partial (\rho \mathbf{u})}{\partial t}+\nabla\cdot(\rho \mathbf{u}\mathbf{u}) = -\nabla p + \nabla\cdot(\mu \nabla \mathbf{u}) + \rho \mathbf{g} + S
\]
\[
\frac{\partial (\rho H)}{\partial t}+\nabla\cdot(\rho \mathbf{u} H)=\nabla\cdot(k \nabla T)
\]
\[
H = h + \Delta H
\]
\[
\Delta H = \gamma L
\]
\[
h = h_{ref} + \int_{T_{ref}}^{T} C_p \, dT
\]
The liquid fraction \(\gamma\) is defined as
\[
\gamma = \begin{cases}
0, & T < T_{solid} \\
\dfrac{T-T_{solid}}{T_{liquid}-T_{solid}}, & T_{solid}\le T\le T_{liquid} \\
1, & T > T_{liquid}
\end{cases}
\]
and the momentum source term is expressed as
\[
S=\frac{(1-\gamma)^2}{\gamma^3+\varepsilon} A_{mush} \mathbf{u}
\]
where \(A_{mush}=10^7\) and \(\varepsilon=0.001\). The Boussinesq approximation is applied for buoyancy:
\[
\rho = \rho_0\left(1-\beta(T-T_m)\right)
\]
I validated the numerical model against previously published experimental and numerical results. The maximum mean absolute deviation was below 2.8%, which proves the reliability of the solver. I also performed a grid-independence and time-step-independence test. Four mesh sizes (0.4, 0.5, 0.6 and 0.7 mm) and five time steps (0.1, 0.2, 0.25, 0.3 and 0.5 s) were checked. A mesh size of 0.5 mm and a time step of 0.25 s were adopted because the corresponding maximum deviations were less than 2.87% and 0.32%, respectively.
Table 5 lists the total melting times for all cases. The base case without fins melted completely at 93.5 minutes. The rectangular-fin case needed 85 minutes. Among the fractal fin configurations, the melting time decreased with both fractal level and branching angle. The case labelled 4-150, i.e. four hierarchical levels and 150° branching angle, gave the shortest melting time of 82.5 minutes, which is an 11.8% reduction compared with the base case. The 4-150 case also resulted in the lowest average battery temperature, 4.5% lower than the no-fin case. The average PCM melting speed of the 4-150 case was 1.71 times that of the base case. Interestingly, the maximum velocity of the PCM was lower in the finned systems because the fins suppress the global circulation; the largest velocity peak, 3.38 mm/s, occurred in the base case. Nevertheless, the average maximum velocity of the PCM in the finned cases was considerably lower because of enhanced local heat transfer.
| Case | Melting time (min) | Battery average max temp (°C) | PCM stored energy (kJ) | Power (W) |
|---|---|---|---|---|
| Base case | 93.5 | 58.4 | 34.1 | 6.07 |
| Rectangular | 85.0 | ~56.8 | 33.7 | 6.60 |
| 2-60 | 85.0 | ~56.9 | 33.7 | 6.61 |
| 2-90 | 85.0 | ~56.7 | 33.7 | 6.62 |
| 2-120 | 85.0 | ~56.6 | 33.7 | 6.62 |
| 2-150 | 85.0 | ~56.5 | 33.7 | 6.61 |
| 3-60 | 85.0 | ~56.7 | 33.7 | 6.61 |
| 3-90 | 84.5 | ~56.5 | 33.7 | 6.64 |
| 3-120 | 84.0 | ~56.2 | 33.6 | 6.70 |
| 3-150 | 83.5 | ~56.0 | 33.5 | 6.69 |
| 4-60 | 84.5 | ~56.7 | 33.7 | 6.64 |
| 4-90 | 83.5 | ~56.5 | 33.6 | 6.71 |
| 4-120 | 83.0 | ~55.9 | 33.5 | 6.74 |
| 4-150 | 82.5 | 55.8 | 33.4 | 6.75 |
The temperature field and liquid-fraction contours in the original numerical results show that at 15 min the PCM melted only near the fins and the battery. At larger times, natural convection becomes visible and intensifies. The top region of the chamber always melts first. The optimised 4-150 fin distributes heat more uniformly over the whole PCM domain, reducing the corner “hot spot” and increasing the effective heat-transfer area. Figure 7 in the original thesis presents the phase interface evolution: after 45 minutes, the 4-150 case exhibits a noticeably smaller remaining solid PCM block than the other configurations, especially at the lower part of the chamber. This behaviour arises from the branching structure, which guides heat radially outward and then along multiple secondary paths, thus enabling a more rapid and symmetric melting front.
I also evaluated the stored energy and power. The energy stored by PCM was calculated using:
\[
Q = \rho V\left(C_p \Delta T + \gamma L\right)
\]
and the average power during melting was:
\[
P = \frac{Q}{t_{melt}}
\]
Owing to the slightly different volume of PCM in each case, the total stored-energy differences are small: 34.1 kJ for the base case and 33.4 kJ for the 4-150 case. However, the shorter melting time in the 4-150 case increases the average power by 11.2% (from 6.07 W to 6.75 W) relative to the base case. This means that the tree-fin structure can absorb heat faster, which is especially important for high-rate charging and demanding driving of a vehicle traction battery.
Numerical study of fin quantity and nano-enhanced PCM
Since the 4-150 tree-fin presented the best overall thermal performance, I then fixed this fin geometry and studied the effect of fin quantity: one fin, two fins, three fins and four fins. For consistency, four tree fins are installed around the cylindrical battery at equally spaced angular positions. For comparison, the rectangular fin arrangement was also simulated. Additionally, I dispersed multi-walled carbon nanotubes (MWCNT) into PCM at three mass fractions: 0%, 3% and 6%. The effective thermophysical properties of the nano-enhanced phase change material (N-PCM) were calculated through the following mixture correlations:
\[
\rho_{N-PCM} = (1-\varphi)\rho_{PCM} + \varphi \rho_{MWCNT}
\]
\[
\rho_{N-PCM} C_{p,N-PCM} = (1-\varphi)(\rho C_p)_{PCM} + \varphi(\rho C_p)_{MWCNT}
\]
\[
k_{N-PCM} = k_{PCM}\left[\frac{k_{MWCNT}+2k_{PCM}-2\varphi(k_{PCM}-k_{MWCNT})}{k_{MWCNT}+2k_{PCM}+\varphi(k_{PCM}-k_{MWCNT})}\right]
\]
\[
(\rho \beta)_{N-PCM} = (1-\varphi)(\rho \beta)_{PCM} + \varphi(\rho \beta)_{MWCNT}
\]
\[
\mu_{N-PCM} = \frac{\mu_{PCM}}{(1-\varphi)^{2.5}}
\]
\[
(\rho L)_{N-PCM} = (1-\varphi)(\rho L)_{PCM}
\]
Here, \(\varphi\) is the mass fraction of MWCNT. The property values used in the simulation are summarised below.
| Property | MWCNT | OP44E (solid/liquid) |
|---|---|---|
| Density, \(\rho\) (kg/m³) | 1600 | 700 |
| Specific heat, \(C_p\) (J/(kg·K)) | 796 | 2000/2350 |
| Thermal conductivity, \(k\) (W/(m·K)) | 3000 | 0.18/0.20 |
| Dynamic viscosity, \(\mu\) (Pa·s) | – | 0.005 |
| Thermal expansion coefficient, \(\beta\) (1/K) | 0.000019 | 0.00076 |
| Latent heat, \(L\) (J/kg) | – | 240800 |
The numerical setup is the same as in the previous chapter. I validated the mesh and time step once more for the configuration with 150°-4 fin and 0% nanoparticles. The maximum temperature deviation was smaller than 0.4% among the selected time steps and below 0.51% for the grid study; therefore, the 0.5 mm grid and 0.25 s time step provide a sufficient accuracy.
Results of the nano-enhanced PCM system
In the first group of simulations, the nano-particle fraction was set to 0%. The four-tree-fin (150°-4) system yielded the lowest cell temperature at the end of melting, about 58.5°C, while the no-fin case reached 68.4°C. The two-tree-fin system gave slightly higher temperatures than the rectangular-fin system, but adding a third or fourth fin improved the performance. When 3% MWCNT was added, the maximum temperature of the 150°-4 system dropped to 58.0°C. With 6%, it was further reduced to 57.9°C. The base case without fins and without nanoparticles reached the highest temperature of 68.4°C. In general, increasing the nano-particle fraction decreases the maximum battery temperature by up to 1.18 times for the best system. A similar trend is observed in the average PCM temperature: the PCM temperature decreases with higher MWCNT content because the added nanoparticles increase the effective thermal conductivity and accelerate heat diffusion. However, the melting time constant reduces because the latent heat capacity per unit volume also decreases slightly.
The temperature uniformity of the battery is a crucial parameter for extending battery life. I calculated the temperature uniformity factor as the difference between the maximum and minimum battery temperatures. The lowest average uniformity (best value) is 0.92, obtained with the 150°-4 system and 6% MWCNT. For 0% nanoparticles, the four-fin system already gives an average uniformity of 0.96; for the two-fin and the rectangular-fin systems the values are about 1.0 and 1.04, respectively. The base no-fin system has an average uniformity factor as high as 2.18, which indicates a serious non-uniform temperature distribution. Therefore, both the tree-fin structure and the nanoparticles jointly improve the thermal homogeneity, which is essential for safe and prolonged operation of a vehicle traction battery.
| Case | 0% MWCNT | 3% MWCNT | 6% MWCNT |
|---|---|---|---|
| Base (no fin) | 2.18 | 1.85 | 1.81 |
| Rectangular | 1.04 | 1.02 | 1.00 |
| 150°-2 | 1.42 | 1.40 | 1.37 |
| 150°-3 | 1.17 | 1.15 | 1.12 |
| 150°-4 | 0.96 | 0.94 | 0.92 |
In terms of the PCM velocity, the average velocity in the four-fin systems is lower than that in the no-fin case because the fins act as flow barriers. Interestingly, the maximum velocity in the system with two fins and 3% MWCNT is about 3.81 mm/s, which is slightly lower than the corresponding value at 0%, equal to 3.88 mm/s. At 6%, the maximum velocity drops to about 3.72 mm/s. Over the whole process, the average maximum velocity decreases with an increase of the MWCNT fraction because the enhanced thermal conductivity reduces the temperature difference that drives the buoyant convection. This observation suggests that in nano-enhanced PCM, the conduction improvement partially replaces the convection contribution to the overall heat transfer. Nevertheless, the overall heat transfer still increases because the thermal conductivity enhancement outweighs the convection suppression.
The liquid fraction curves show that all cases melt completely before the end of simulation, and the complete melting time is reduced when the MWCNT content is raised. For the base case without fins, the melting time is 93.5 min at 0%, 91.0 min at 3%, and 88.5 min at 6%. For the 150°-4 case, the lowest melting time is 79.0 min at 6% MWCNT. This value is 15.5% shorter than the no-fin 0% case, and 4.2% shorter than the same 150°-4 0% case. The rectangular fin and 150°-3 cases exhibit quite similar melting times for a given MWCNT content, indicating that the fin quantity is more important than the detailed shape when the total heat-transfer area is adequate. The three-fin and four-fin configurations exchange overall performance depending on the nano-particle loading, but the four-fin arrangement is consistently better at 6%
| Fin quantity | 0% MWCNT | 3% MWCNT | 6% MWCNT |
|---|---|---|---|
| No fin | 93.5 | 91.0 | 88.5 |
| Rectangular (4 fins) | 85.0 | 83.0 | 81.0 |
| Tree 150°-2 | 87.0 | 85.0 | 83.0 |
| Tree 150°-3 | 85.0 | 83.0 | 81.0 |
| Tree 150°-4 | 82.5 | 80.5 | 79.0 |
From the stored-energy point of view, the phase-change material in the no-fin case stores the largest amount of energy (34.1 kJ at 0%) because the volume fraction of PCM is largest when no fin occupies the space. With the 150°-4 fin and 6% MWCNT, the total PCM stored energy is 31.8 kJ, i.e. 6.7% lower. However, because the melting time is much shorter, the average power of the latter system is higher: 6.75 W compared to 6.07 W, which corresponds to a power increase of 11.2%. The average power values in all simulated cases are summarised in Table 8.
| Fin type | 0% MWCNT | 3% MWCNT | 6% MWCNT |
|---|---|---|---|
| No fin | 6.07 | 6.08 | 6.09 |
| Rectangular | 6.60 | 6.59 | 6.58 |
| 150°-2 | 6.51 | 6.51 | 6.49 |
| 150°-3 | 6.63 | 6.61 | 6.60 |
| 150°-4 | 6.75 | 6.74 | 6.70 |
These results prove that the tree fin with four levels and a branching angle of 150°, combined with a low concentration of MWCNT, creates a highly effective passive thermal management system for a vehicle traction battery. The optimal configuration reduces the peak battery temperature, improves the temperature uniformity, and significantly shortens the PCM melting time. These benefits directly support the safe high-rate operation of modern electric vehicles.
Flow behaviour and phase distribution
The visualisation of the velocity field in the numerical simulations reveals that the presence of the tree-shaped fin breaks the large-scale natural-convection cell into several smaller circulation regions between adjacent branches. Although these smaller cells reduce the peak velocity, they increase the local mixing and temperature uniformity. The liquid-fraction contours indicate that melting starts from the battery surface and advances through the fin arms toward the outer domain. The top part of the PCM chamber melts first due to buoyancy. The lower part melts later, especially when the fins are short and the conduction path to the bottom is longer. In the case with four 150° fins, the branching structure reaches a large radial extent and therefore covers the bottom region more effectively. Consequently, the remaining solid PCM at the bottom is reduced.
The N-PCM with 6% MWCNT has a higher thermal diffusivity, so the heat from the battery reaches the fin tips faster. The melting interface is more planar and less affected by convection in the high-conductivity case. On the one hand, this leads to a more uniform melting and avoids hot spots. On the other hand, the nano-particles increase the effective viscosity and suppress the buoyancy-induced circulation. Therefore, the design of a nano-enhanced PCM system must balance conduction enhancement and convection suppression. In the specific geometry studied in this work, the six-per-cent addition is beneficial because the improvement in heat conduction overrides the reduction in natural convection, resulting in an overall shorter melting time and lower cell temperature.
Conclusions
Through a systematic combination of experiments and three-dimensional numerical simulations, I evaluated the thermal performance of phase-change material coupled with tree-shaped fins for the thermal management of vehicle traction battery. The following conclusions are drawn.
First, the experimental tests with four 26650 cells show that the tree-fin PCM box outperforms both the rectangular-fin and the plain-tube PCM boxes under all tested ambient temperatures and charging modes. In the low-temperature environment of −10 °C, the PCM box maintains the battery temperature much higher than the unmanaged case, demonstrating a heat-insulation effect. In the normal/high-temperature environment, the tree-fin system reduces the maximum cell temperature by a factor of up to 0.9 and increases the working time by up to 27.5%. At 50 °C ambient, the tree-fin PCM system keeps the cell temperature below 36.5 °C.
Second, the visualisation experiments, performed with heating rods at powers of 10 W and 15 W and ambient temperatures of 25 °C and 40 °C, reveal that the PCM melts first near the heat source and then propagates upward. The upper region of the chamber always melts faster than the lower region. The tree-fin enclosure significantly delays the temperature rise of the simulated battery; the maximum working-time enhancement over the plain-tube PCM system amounts to 54.9% under 40 °C and 15 W. This confirms that the tree-fin structure provides a more effective heat path and promotes natural convection in the liquid PCM.
Third, the numerical optimisation of the fractal level and branching angle shows that increasing the branching angle and fractal level improves the system performance. The case with four fractal levels and a 150° branching angle (denoted as 4-150) gives the shortest melting time of 82.5 min, which is 11.8% shorter than the no-fin case. It also lowers the average battery temperature by 4.5%, increases the average melting speed by 1.71 times, and increases the average thermal power by 11.2%.
Fourth, using this optimal fin geometry, I studied the effect of fin quantity and MWCNT mass fraction. The four-fin construction, together with 6% MWCNT, gives the best overall performance: the battery maximum temperature is reduced by 1.18 times compared to the no-fin and no-nano PCM case, the complete melting time is shortened to 79 min, and the average battery temperature-uniformity factor is as low as 0.92. The nano-particles improve the effective thermal conductivity and thus accelerate the heat transfer, although they modestly suppress the natural-convection velocity. The power of the optimal system is 1.11 times higher than that of the baseline system.
In conclusion, the proposed combination of tree-shaped fractal fins and MWCNT-enhanced phase-change material is a promising approach for the thermal management of vehicle traction battery, particularly for high-rate operations in electric vehicles. The tree-shaped fins increase the heat-exchange surface and create small convection cells that homogenise the temperature, while the MWCNT improve the PCM thermal conductivity. These enhancements help to keep the battery temperature within the safe range and to prolong the service life of the pack. Future work should focus on the design of the fin layout and the compatibility of nano-particles with other types of phase-change materials under realistic driving cycles, and eventually on full-scale battery-pack integration.