In the transport sector, the transition toward electric mobility has been driven by environmental regulations and by the necessity of reducing carbon emissions. Central to this transition is the EV battery pack, which must deliver high power and high energy density under a wide range of operating conditions. However, lithium-ion batteries generate heat during charging and discharging, and the resulting temperature rise can cause degradation, reduced capacity and even thermal runaway. Hence, a robust battery thermal management system is indispensable for the safe and efficient operation of an EV battery pack. In this work, I focus on a passive thermal management strategy that combines phase change material (PCM) with tree-shaped fins. My primary objective is to enhance the thermal performance of an EV battery pack while preserving the advantages of PCM, such as high latent heat, near-isothermal phase transition and attractive energy density.
Although PCM offers high heat-absorption capability, its low thermal conductivity severely limits the heat transfer rate between the cells and the PCM. To mitigate this bottleneck, I proposed the insertion of tree-shaped fins inside the PCM container. The tree-shaped branching configuration provides a shorter heat-conduction path and enlarges the effective heat-transfer area without consuming additional pumping power. I also examined the addition of multi-walled carbon nanotubes (MWCNTs) to form a nano-enhanced phase change material (N-PCM). By combining experimental observations and three-dimensional numerical simulations, I systematically studied the influence of fin geometry, number of fins, nanoparticle concentration and operating conditions on the thermal behaviour of the EV battery pack.
1. Heat Generation and Thermal Management Requirements
During normal operation, several heat sources appear inside a lithium-ion cell: reaction heat \(Q_r\), polarization heat \(Q_p\), Joule heat \(Q_j\), and side-reaction heat \(Q_s\). The total rate of heat generation within a cell can be written as
$$
Q_{\text{total}} = Q_r + Q_p + Q_j + Q_s.
$$
The reaction heat is directly connected with the entropy change of the electrochemical reactions. The polarization heat is caused by the deviation from the open-circuit voltage when current flows, while the Joule heat is the irreversible resistive heating. For a typical cell, the polarization and ohmic resistances cause
$$
Q_p = I^2 R_p,
$$
$$
Q_j = I^2 R_j,
$$
where \(I\) is the current, \(R_p\) is the polarization internal resistance and \(R_j\) is the ohmic internal resistance. Because side reactions are generally negligible, the internal heat source is dominated by \(Q_r\), \(Q_p\) and \(Q_j\). In an EV battery pack, the local heat generation rate depends on the charging/discharging protocol. Fast charging, high loads or high ambient temperatures can lead to a severe temperature rise and non-uniform temperature distribution among cells. A suitable thermal management system must therefore keep the maximum cell temperature below the safety limit and improve temperature uniformity throughout the EV battery pack.
2. Experimental Investigation of Fin-Coupled PCM for an EV Battery Pack
2.1 Materials and Fins
I carried out experiments on four series-connected 26650 lithium-ion cells with a nominal capacity of 5 Ah. The cells were placed inside a rectangular organic-glass chamber with internal dimensions of 200 mm × 200 mm × 65 mm. Around the cells, I filled the chamber with a commercial paraffin PCM designated as RT35. The DSC test indicated that RT35 melts between 35.3 °C and 41 °C, and solidifies between 33 °C and 28.3 °C. The measured latent heat was about 170.2 J/g for melting and 161.9 J/g for solidification. These values confirmed that the PCM has excellent potential for the thermal management of an EV battery pack. The thermophysical properties are summarized in Table 1.
| Property | Value |
|---|---|
| Melting onset / end temperature | 35.3 °C / 41 °C |
| Solidification onset / end temperature | 33 °C / 28.3 °C |
| Melting latent heat | 170.2 J/g |
| Solidification latent heat | 161.9 J/g |
| Specific heat capacity | approx. 2.2 kJ/(kg·°C) |
| Thermal conductivity | approx. 0.21 W/(m·°C) |
Three heat-transfer-element configurations were tested: a plain copper/aluminium tube without fins, a rectangular radial fin, and a tree-shaped fin. The tree-shaped fin was inspired by fractal branching structures. Its first branch has length 27.5 mm and thickness 4.0 mm, while successive sub-branches follow a geometric relation. The rectangular fin had a length of 27.4 mm and a thickness of 4.0 mm. All fins were made of aluminium 6061 and were carefully placed in direct contact with the cell surfaces using thermally conductive grease. K-type thermocouples were attached at the positive, negative and middle surfaces of each cell to monitor temperature.
2.2 Experimental Platform and Procedure
The experimental set-up included a battery performance tester, a constant-temperature and humidity chamber, a data acquisition unit, a personal computer and the battery thermal management system itself. I tested three charging protocols: a constant-current 1C charge, a pure constant-current charge and a constant-current-constant-voltage charge. Four environmental temperatures were selected: −10 °C, 25 °C, 40 °C and 50 °C. During each experiment, the chamber was first maintained at 22 °C until the baseline temperature of all thermocouples approached 25 °C. Then the chamber was set to the target temperature, and after stabilisation the charging process was started. The temperature data were recorded until the charge ended.
The measurement uncertainty was estimated by
$$
\frac{\delta T}{T} = \sqrt{\left(\frac{\delta T_{\text{accuracy}}}{T}\right)^2},
$$
using the minimum measured temperature. The result was about 0.4%, far below 5%, confirming the reliability of the experimental data.
2.3 Experimental Results for Different Charging Protocols
Figure 2 (not reproduced here) shows the temperature evolution of the cells in the different systems. The ambient temperature strongly influences the cell temperature. At high ambient temperatures, the cell temperature rises quickly because the cell is exposed to a hot environment and the heat generated by the cell cannot be effectively removed without a thermal management system. When the PCM container is used, the heat produced by the cells is absorbed by the PCM through sensible heating and latent heat. The tree-shaped fin system performs best among all configurations because it spreads the heat more uniformly through the PCM volume.
At an ambient temperature of −10 °C and a 1C charge, the cell without a PCM box reached a minimum temperature of about 8.0 °C, while the cells enclosed in the PCM systems stayed far warmer. For instance, the minimum temperature in the PCM container was 19.2 °C, which is 2.4 times higher than that of the unprotected cell. This indicates that the PCM can serve as a thermal buffer and provide insulation for an EV battery pack in cold climates.
At 25 °C, the tree-fin PCM container reduced the maximum cell temperature to 30.1 °C, which is about 0.9 times the temperature in the unprotected condition. The working time of the cell was also extended by 27.5% with the use of the tree-shaped fin. At 40 °C and 50 °C, the benefits became even more pronounced. For example, at an ambient temperature of 50 °C during a 1C charge, the unprotected cell temperature exceeded 50 °C, which is above the generally accepted safety limit. In contrast, the PCM systems were able to keep the cell temperature below about 40 °C. The results confirm that PCM coupling with tree-shaped fins is particularly beneficial for high-temperature applications of an EV battery pack.
Table 2 summarizes the maximum cell temperature reductions observed in the experiments. The tabulated percentages correspond to the decrease in the maximum temperature relative to the unprotected cell case under the same charging protocol and ambient temperature.
| Charging mode | Ambient temperature (°C) | Best configuration | Maximum temperature reduction / benefit |
|---|---|---|---|
| 1C charge | −10 | Tree-fin PCM | Minimum cell temperature 2.4 times higher than unprotected |
| 1C charge | 25 | Tree-fin PCM | Max temperature ~0.9 times; working time +27.5% |
| 1C charge | 40 | Tree-fin PCM | Max temperature reduction between 20.2% and 22.9% |
| 1C charge | 50 | Tree-fin PCM | Max temperature lower than ~40 °C |
| Constant current | 50 | Tree-fin PCM | Battery temperature 36.8 °C at the end of discharge |
| Constant-current/voltage | 40 | Tree-fin PCM | Cell temperature 34.3 °C |
| Constant-current/voltage | 50 | Tree-fin PCM | Max cell temperature 36.5 °C |
In the cold environment, the charging time in the PCM systems was longer because the phase change material released its stored heat to the cells and thus slowed down heat loss. In addition, the tree-shaped fins acted as heat-distribution pathways, reducing the internal thermal resistance. Therefore, the integration of PCM, fins and optimum phase change temperature can greatly improve the reliability and durability of an EV battery pack in extreme climates.
3. Visualization Experiments with Simulated Battery Cells
3.1 Visualization Platform
To gain deeper insight into the solid–liquid interface evolution and the heat-transfer mechanism, I built a visual test platform using electric heating rods as simulated cells. The rods had the same outer dimensions as 26650 batteries, with a diameter of 26 mm and a height of 65 mm. They were made of 304 stainless steel and filled with magnesium oxide powder to ensure uniform heat flux and good electrical insulation. Four rods were inserted into the same PCM chamber, each connected to an independent DC power supply. The heating power was set to 10 W or 15 W to emulate different levels of heat generation in an EV battery pack.
Nine thermocouples were arranged in the PCM region at different heights and radial locations. The temperature of each simulated cell was monitored at three points near the top, middle and bottom. The ambient temperature was controlled at 25 °C or 40 °C. When any of the simulated cells reached 60 °C, which was considered the safety-limit temperature, the test was stopped. Photographs were recorded every 10 min. A MATLAB image-processing routine was then used to convert the photographs into binary images in which the solid PCM regions were white and the liquid regions were black. The fins and the simulated cells were distinguished by coloured markers.
The uncertainty in the electrical heating power can be expressed as
$$
\frac{\delta Q}{Q} = \sqrt{\left(\frac{\delta U}{U}\right)^2 + \left(\frac{\delta I}{I}\right)^2}.
$$
Using the minimum recorded values of voltage and current, the maximum power uncertainty was found to be 1.41%, which is again well below the acceptable 5% threshold.
3.2 Observations of the Melting Interface
The visual results clearly demonstrated three stages of heat transfer inside the PCM: pure conduction at the beginning, followed by natural convection before the melt front moves upward, and finally a combined conduction–convection stage. During the first hour, heat was transferred mainly by conduction from the fins and cylindrical tubes into the solid PCM. A thin liquid layer formed adjacent to each heated surface. As time elapsed, the liquid fraction increased, and the liquid PCM around the upper part of the chamber melted faster because of buoyancy. The hot liquid moved upward and the cold solid near the bottom sank, which established natural convective cells. Adjacent to the top region, the PCM melted earlier than in the lower regions. The temperature at the top was higher and the interface moved more quickly.
For the plain circular-tube configuration, the solid PCM in the central part of the chamber remained almost unchanged after a long time, particularly at the bottom. The rectangular fin improved the melting process because of the larger heat-transfer area. However, the tree-shaped fin was the most effective: it generated a more uniform heating path and allowed the melting front to propagate symmetrically over a wider volume. At some high-power and high-ambient-temperature conditions, the entire PCM was fully melted before the simulated cell reached 60 °C. The liquid-fraction images confirmed that gravity-driven natural convection is the dominant melt-enhancement mechanism after the initial conduction stage.
3.3 PCM Temperature Evolution in Visualization Experiments
Figure (not shown) illustrates the temperature histories for the nine positions inside the PCM chamber. Regardless of the fin type and experimental conditions, the thermocouple readings eventually split into three distinct groups: the upper positions exhibit the highest temperatures, the middle positions follow, and the lower positions have the lowest temperatures. This vertical stratification is caused by the upward movement of the heated liquid PCM. For a given horizontal plane, all thermocouples gave similar values, confirming that buoyancy-driven convection is strong along the vertical direction.
The temperature history of the PCM can be divided into three stages. First, the temperature increases linearly until it reaches the onset melting temperature of about 35.5 °C. In this stage, heat is transferred mostly by conduction. Second, when the PCM begins to melt, the temperature curve rises almost vertically because the liquid fraction increases and natural convection becomes active. Third, once all the PCM around the local thermocouple has melted, the temperature increases at a slower rate because the subsequent heat is used to raise the sensible temperature of the liquid. The tree-fin configurations reach the second and third stages earlier than the rectangular-fin or no-fin cases, which proves that the branching fins accelerate the melting process and reduce the thermal gradient.
3.4 Simulated-Cell Temperature and Working Time
The temperatures of all four simulated cells followed a similar trend during the initial stage. After a few minutes, the cells in the upper portion of the chamber got hotter than those in the lower portion, even though the heating power was identical. The difference is again attributable to the natural convection in the liquid PCM. In the unprotected case, the simulated-cell temperatures reached 60 °C in less than 20 min. With phase change thermal management, the working time was significantly prolonged. The longest working time was always observed in the system with tree-shaped fins.
Under the condition of 25 °C ambient temperature and 10 W heating power, the tree-fin chamber allowed the simulated cells to work for about 823 min before reaching 60 °C. This was approximately 1.3 times the working time in the rectangular-fin chamber and 1.8 times that in the plain-tube PCM chamber. When both the ambient temperature and heating power were increased to 40 °C and 15 W, the simulated-cell working time in the tree-fin system was about 184 min. Compared with the rectangular-fin and plain-tube systems, the extension was about 1.1% and 54.9%, respectively. At 40 °C and 10 W, the working time was approximately 334 min, while the rectangular-fin and plain-tube systems provided 332 min and 160 min, respectively. At 25 °C and 15 W, the tree-fin system prolonged the working time to 286 min, which is 1.1 times longer than the rectangular-fin system and 2.3 times longer than the plain-tube system. Table 3 summarizes the simulated-cell working times for all tested cases.
| Ambient temperature / heating power | Plain-tube PCM | Rectangular-fin PCM | Tree-fin PCM |
|---|---|---|---|
| 25 °C / 10 W | 457 (approx.) | 633 (approx.) | 823 |
| 25 °C / 15 W | 124 (approx.) | 143 (approx.) | 286 |
| 40 °C / 10 W | 160 | 332 | 334 |
| 40 °C / 15 W | 119 (approx.) | 182 (approx.) | 184 |
The comparison between 40 °C/10 W and 25 °C/15 W shows that the heating power has a stronger effect on the cell working time than the ambient temperature in the tested range. In other words, a high current or high discharge rate is the critical stressor for an EV battery pack. Even in the less favourable cases, the tree-shaped fin continues to outperform other fin geometries, although at high ambient temperature the improvement over the rectangular fin is relatively small.
4. Numerical Study of Tree-Shaped Fin Parameters for an EV Battery Pack
4.1 Physical Model
After demonstrating the thermal superiority of tree-shaped fins in experiments, I used numerical simulations to optimise their structural parameters. The modelled system is a cylindrical unit cell of an EV battery pack consisting of a 26650-format cell, a PCM annulus, an aluminium tree-shaped fin, and an aluminium outer shell. The cell has a diameter \(D_b\) of 26 mm and a height \(H_b\) of 65 mm. The shell has an inner diameter \(D_s\) of 65 mm, and its thickness is 2 mm. The PCM occupies the annular space between the cell and the shell.
The tree-shaped fin was designed with a self-similar fractal pattern. The first branch length is denoted by \(L_1\), and the first branch width is \(b_1\). For the higher levels,
$$
L_i = 0.8 L_{i-1}, \quad i = 2,3,4,
$$
$$
b_i = 0.8 b_{i-1}, \quad i = 2,3,4.
$$
I set \(L_1 = 7\) mm and \(b_1 = 2\) mm. The branching angle \(\beta\) was varied between 60°, 90°, 120° and 150°. The total volume and the total length of all branches were kept constant by adjusting the first-level dimensions, so that all fin configurations contain the same amount of aluminium. In addition to a no-fin baseline and a rectangular fin, which can be regarded as a single-level tree fin, I investigated 12 tree-fin configurations with two, three and four branching levels. Figure 2 in the original thesis shows the geometries; the naming convention used here is level-angle, where “4-150” denotes a four-level fin with a branching angle of 150°.
4.2 Governing Equations and Boundary Conditions
The melting process in the PCM was modelled with the enthalpy-porosity method. The PCM is assumed to be a Newtonian, incompressible fluid. Natural convection in the liquid phase is considered, and the density is treated by the Boussinesq approximation. The governing equations are as follows.
Continuity:
$$
\nabla \cdot (\rho \mathbf{u}) = 0.
$$
Momentum:
$$
\frac{\partial (\rho \mathbf{u})}{\partial t} + \nabla \cdot (\rho \mathbf{u}\mathbf{u}) = -\nabla p + \nabla \cdot (\mu \nabla \mathbf{u}) + \rho \mathbf{g} + \mathbf{S}.
$$
Energy:
$$
\frac{\partial (\rho H)}{\partial t} + \nabla \cdot (\rho \mathbf{u} H) = \nabla \cdot (k \nabla T).
$$
The total enthalpy is the sum of sensible enthalpy \(h\) and latent heat \(\Delta H\):
$$
H = h + \Delta H.
$$
For a PCM with latent heat \(L\) and liquid fraction \(\gamma\),
$$
\Delta H = \gamma L.
$$
The liquid fraction is defined as
$$
\gamma =
\begin{cases}
0, & T < T_{\text{solid}},\\[2pt]
\dfrac{T – T_{\text{solid}}}{T_{\text{liquid}} – T_{\text{solid}}}, & T_{\text{solid}} \le T \le T_{\text{liquid}},\\[6pt]
1, & T > T_{\text{liquid}}.
\end{cases}
$$
The momentum source term \(\mathbf{S}\) is introduced to dampen the velocity in the solid region:
$$
\mathbf{S} = \frac{A_{\text{mush}}(1-\gamma)^2}{\gamma^3 + \varepsilon} \mathbf{u},
$$
where \(A_{\text{mush}}=10^7\) and \(\varepsilon=0.001\). The Boussinesq approximation gives
$$
\rho = \rho_0 \left[ 1 – \beta_m (T-T_0) \right],
$$
where \(\beta_m\) is the thermal expansion coefficient. The simulations used the PISO algorithm for pressure–velocity coupling, PRESTO for pressure discretization, and second-order upwind schemes for momentum and energy. Convergence was assumed when the residuals dropped below \(10^{-4}\) for continuity, \(10^{-5}\) for momentum and \(10^{-6}\) for energy. The initial temperature was 25 °C. Heat loss from the outer shell to the ambient was modelled with a natural-convection heat-transfer coefficient of \(10\ \mathrm{W/(m^2 K)}\). The volumetric heat-source term corresponding to a cell heat-generation rate of 10 W was applied to the battery domain.
4.3 Thermophysical Properties and Validation
The PCM adopted in the numerical study was OP44E, which melts between 40.6 °C and 44.7 °C. Table 4 lists the material properties used in the simulations.
| Property | OP44E | Battery | Aluminium |
|---|---|---|---|
| Thermal conductivity (W/(m·K)) | 0.18 – 0.2 | 32.2 | 211 |
| Density (kg/m³) | 700 | 2007.7 | 2675 |
| Specific heat (J/(kg·K)) | 2000 – 2350 | 837.4 | 903 |
| Latent heat (J/kg) | 240800 | — | — |
| Melting temperature (°C) | 40.6 – 44.7 | — | — |
| Thermal expansion coefficient (1/K) | 0.00076 | — | — |
| Dynamic viscosity (kg/(m·s)) | 0.005 | — | — |
Before the parametric study, I performed a validation by comparing the model predictions with published experimental data and with another published numerical result. The average absolute deviations were approximately 1.9% and 2.8%, respectively, which is acceptable for this type of simulation. I also conducted grid and time-step sensitivity tests for the 4-150 case. Grid sizes of 0.4, 0.5, 0.6 and 0.7 mm were compared. The maximum relative deviation in liquid fraction from the 0.4 mm solution was 1.27% for the 0.5 mm grid, 2.87% for the 0.6 mm grid and 3.50% for the 0.7 mm grid. Therefore, a grid size of 0.5 mm was selected. Time steps of 0.1, 0.2, 0.25, 0.3 and 0.5 s were compared; the maximum error was below 0.32%. A time step of 0.25 s was chosen for all subsequent simulations.
4.4 Temperature Results for Various Fin Geometries
Figure (not shown in this text) presents the average battery temperature for all 14 configurations. The base case without fins exhibits the highest cell temperature among all systems. Its temperature rises rapidly in the early stage and reaches about 64 °C after 20 min. Once the PCM starts to melt, the cell temperature is stabilised; nevertheless, the unprotected system cannot maintain a sufficiently low temperature. The rectangular fin and all tree-shaped fin configurations significantly reduce the cell temperature. Among them, the 4-150 fin is the most effective, with a maximum average cell temperature of 55.8 °C, compared to 58.4 °C in the base case. Thus, the tree fin reduces the maximum cell temperature by about 4.5%. The rectangular fin provides a reduction of about 2.7%. In general, for the same number of branching levels, a larger branching angle yields a lower average cell temperature. For the same branching angle, a larger number of levels yields a lower temperature because the fin branches cover a larger volume of PCM and create more heat-conduction channels.
The temperature uniformity is a crucial indicator for an EV battery pack. I calculated the temperature-uniformity factor as the difference between the maximum and minimum temperatures over all cells and monitoring points. The 4-150 configuration gives the highest uniformity, with a maximum temperature difference below 1.6 °C. The base case has the worst uniformity. Tree-shaped fins always improve temperature uniformity compared with the rectangular fin and the no-fin tube. The improvements are more pronounced when the branching angle is large and when more branching levels are used.
Temperature contour plots further illustrate the thermal behaviour. At 15 min, the base case already has high battery temperature, while the finned systems have not yet reached the highest scale. At 30–60 min, the temperature around the fin branches progressively increases. Due to gravity, the top part of the PCM melts first and becomes hotter. The melt propagates from the fins and the tube outward and upward. The 4-150 case delays the battery temperature rise more effectively than the other configurations; the cell reaches the highest temperature only after 75 min. These results confirm that a carefully designed tree-shaped fin can provide better thermal protection for an EV battery pack.
4.5 Velocity and Liquid Fraction Analysis
Natural convection in the melting PCM can be characterised by the average velocity and maximum velocity. The average velocity of the PCM is initially zero, then rises after melting begins. The base case reaches a maximum average velocity of about 0.4 mm/s, whereas all finned systems have higher average velocities. During the later melting stage, a second velocity peak appears. This peak originates from the simultaneous melting of the PCM at the bottom region, which creates additional convective cells in both radial and axial directions. The 4-120 case has a maximum average velocity of 0.74 mm/s; the 4-150 case exhibits a slightly smaller value but still much higher than the base case.
In contrast, the maximum velocity of the PCM is higher in the base case because the absence of fins allows free motion of the liquid. The peak maximum velocity in the base case reaches 3.38 mm/s, whereas the 4-150 case gives 3.32 mm/s. However, when averaged over the total melting time, the mean maximum velocity of the 4-150 system is 1.71 times that of the base case. This result indicates that fins suppress the axial movement of the liquid PCM but improve the overall heat-transfer area and the radial natural convection. The use of the branching fins thus accelerates the melting front and enhances the energy-storage rate.
Figure 4-14 in the original thesis shows the liquid-fraction evolution. Up to about 38 min, the base case exhibits a similar or even slightly faster melting rate than the finned systems. After that, the base case falls behind because the layer of liquid PCM becomes thick and its low thermal conductivity limits further heat transfer. At 38 min, the liquid fractions are close to 0.42–0.45. The total melting times are listed in Table 5. The base case requires the longest time of 93.5 min. The 4-150 fin reduces this time to 82.5 min, corresponding to an 11.8% reduction. The rectangular fin requires 85 min.
| Configuration | Total melting time (min) | Average power (W) |
|---|---|---|
| Base case | 93.5 | 6.07 |
| Rectangular | 85.0 | 6.60 |
| 2-60 | 85.0 | 6.61 |
| 2-150 | 85.0 | 6.61 |
| 3-150 | 83.5 | 6.69 |
| 4-90 | 83.0 | 6.71 |
| 4-120 | 83.0 | 6.74 |
| 4-150 | 82.5 | 6.75 |
The liquid-fraction contours reveal that the melting process is symmetric in the radial direction. The solid PCM in the central part tends to remain longer. Eventually, the natural convection accelerates the melting near the top, and the remaining solid melts at the bottom. In the 4-150 configuration, almost all PCM becomes liquid after 75 min, while the other systems still contain a noticeable solid zone. This faster melting is a key factor in preventing the overheating of the cell and in cycling the latent heat capacity more frequently.
4.6 Stored Energy and Power
The energy stored in the PCM was calculated by
$$
Q = \rho V \left[ C_P (T – T_{\text{init}}) + \gamma L \right],
$$
where \(C_P\) is the average of the solid and liquid specific heats. The total stored energy depends mainly on the volume and latent heat of the PCM. Since all fin configurations have the same PCM volume, the total stored energy is nearly identical. The maximum difference between cases is only about 0.6 kJ. The base case stores 34.1 kJ, while the 4-150 case stores 33.4 kJ. The power, which is defined as the stored energy divided by the total melting time, is therefore inversely proportional to the melting time. The base case has the lowest power of 6.07 W, while the 4-150 case achieves 6.75 W, an increase of 11.2%. Table 5 summarises these values for representative configurations.
5. Effect of Fin Number and MWCNT Nano-Particles on an EV Battery Pack
5.1 Nano-Enhanced PCM Formulation
In the final numerical study, I selected the best tree-shaped fin (4 levels, branching angle 150°) and changed the number of fins per cell from one to four. The configurations were labelled as 150°-2, 150°-3 and 150°-4 according to the number of fins around the cell. A rectangular-fin system with four fins was also simulated for comparison. In addition, I dispersed multi-walled carbon nanotubes (MWCNTs) into the PCM with mass fractions of 0%, 3% and 6%. The density and specific heat of the nano-PCM are calculated by mixing rules:
$$
\rho_{N} = \varphi \rho_{\text{MWCNT}} + (1-\varphi)\rho_{\text{PCM}},
$$
$$
(\rho C_P)_{N} = \varphi (\rho C_P)_{\text{MWCNT}} + (1-\varphi)(\rho C_P)_{\text{PCM}}.
$$
The thermal conductivity of the nano-PCM is modelled using the Maxwell–Garnett relation:
$$
k_N = k_{\text{PCM}} \left[ \frac{k_{\text{MWCNT}} + 2k_{\text{PCM}} – 2\varphi(k_{\text{PCM}} – k_{\text{MWCNT}})}{k_{\text{MWCNT}} + 2k_{\text{PCM}} + \varphi(k_{\text{PCM}} – k_{\text{MWCNT}})} \right].
$$
The effective viscosity is
$$
\mu_N = \frac{\mu_{\text{PCM}}}{(1-\varphi)^{2.5}},
$$
while the latent heat is scaled by
$$
(\rho L)_N = (1-\varphi)(\rho L)_{\text{PCM}}.
$$
Table 6 shows the thermophysical properties of MWCNT and the base PCM used in the nano-PCM simulations.
| Property | MWCNT | PCM (OP44E solid / liquid) |
|---|---|---|
| Density (kg/m³) | 1600 | 700 |
| Specific heat (J/(kg·K)) | 796 | 2000 / 2350 |
| Thermal conductivity (W/(m·K)) | 3000 | 0.18 / 0.20 |
| Dynamic viscosity (Pa·s) | — | 0.005 |
| Thermal expansion coefficient (1/K) | 0.000019 | 0.00076 |
| Latent heat (J/kg) | — | 240800 |
5.2 Temperature Behaviour with Nano-PCM and Different Fin Numbers
The average battery temperatures for all nano-PCM cases are shown in Figure (not shown). At zero nanoparticle fraction, the 150°-4 system produces the lowest cell temperature, with a final value of 58.5 °C. The no-fin base case has the highest final temperature of 68.4 °C. Adding 3% or 6% MWCNTs further reduces the temperature. For each fin geometry, increasing the nanoparticle mass fraction from 0% to 6% lowers the maximum cell temperature. The largest decrease occurs in the no-fin system, where the maximum temperature falls from 68.4 °C to 67.2 °C, a reduction by a factor of about 0.98. For the 150°-4 system with 6% nano-PCM, the maximum cell temperature is the lowest among all cases, reaching approximately 57.9 °C. This corresponds to a reduction of 1.18 times compared with the 0%-nanoparticle base case. In other words, using the optimized tree fins together with 6% MWCNT reduces the battery temperature by about 10.5 °C in relative comparison.
The average PCM temperature curves show the expected three-stage behaviour. During the first stage, the PCM acts as a sensible-heat sink, and its temperature rises almost linearly. The slope depends on the effective thermal conductivity. Adding MWCNTs increases the thermal conductivity, leading to a slightly faster temperature increase. During the second stage, the melting plateau is more visible because the latent heat dominates. Finally, the liquid PCM temperature rises again once the melting is complete. At any given time, the 150°-4 case has a lower average PCM temperature than the other configurations, which indicates that the heat absorbed by the PCM is more effectively distributed.
Temperature uniformity is an essential metric for extending the lifetime of an EV battery pack. Figure 5-8 in the original thesis displays the average temperature-uniformity factor for all 15 combinations. The optimum is obtained by the 150°-4 fin with 6% MWCNT, which gives a uniformity factor as low as 0.92. The worst uniformity is found in the no-fin PCM system, with a factor of 2.18. Regardless of fin type, higher nanoparticle concentrations lead to better uniformity, because the enhanced thermal conduction reduces local hotspots.
Temperature contours show that the nanoparticles do not substantially change the melting pattern during the first 45 min. After 75 min, the effect becomes visible: the configurations with higher nanoparticle fractions have much less solid PCM, especially in the lower regions. Among all cases, the 6%-MWCNT case with four tree-shaped fins is the first to complete melting. This synergy between radial fin distribution and improved PCM conductivity is highly beneficial for an EV battery pack subjected to high discharge rates or fast charging.
5.3 Velocity, Melting Time and Energy Storage
The melting rate of the nano-PCM depends on both the fin geometry and the nanoparticle loading. For a given fin configuration, the liquid-fraction curve is steepest when the nanoparticle mass fraction is 6%. Figure (not shown) indicates that the no-fin system has a relatively fast early melting rate, because the liquid can circulate freely without obstacles. However, after about 48 min, the no-fin system falls behind. At 48 min, the liquid fraction in all cases is between 0.56 and 0.63. The total melting time is listed in Table 7. The longest melting time is 93.5 min for the base case without fins or nanoparticles. The shortest melting time is 79 min, obtained with the 150°-4 fin and 6% MWCNT. Thus, adding the optimized tree fins and nanoparticles reduces the total melting time by up to 15.5% relative to the base case.
| Fin configuration | 0% MWCNT | 3% MWCNT | 6% MWCNT |
|---|---|---|---|
| No fin | 93.5 | 91 | 88.5 |
| Rectangular (4 fins) | 85 | 83 | 81 |
| 150°-2 | 87 | 85 | 83 |
| 150°-3 | 85 | 83 | 81 |
| 150°-4 | 82.5 | 80.5 | 79 |
The average velocity of the liquid PCM first increases, reaches a peak, then decreases slightly, and later rises again when the bottom PCM melts. The presence of fins confines the fluid motion but also creates additional heated surfaces. The average maximum velocity of the PCM decreases with increasing nanoparticle concentration because the viscosity grows and the nano-PCM becomes more viscous. For instance, the average maximum velocity for the no-fin case is 2.68 mm/s at 0%, 2.55 mm/s at 3% and 2.45 mm/s at 6%. In the 150°-4 case, the corresponding values are 1.36, 1.26 and 1.16 mm/s. Despite the lower velocity, the heat-transfer rate is improved because conduction dominates in the nano-PCM.
The stored energy is lower when the nanoparticle fraction increases because the added nanoparticles replace some PCM mass, thereby reducing the latent-heat capacity. The maximum stored energy is 34.1 kJ for the base case with no nanoparticles, while the 150°-4 fin with 6% MWCNT stores 31.8 kJ. The average power, which equals the stored energy divided by the total melting time, increases as the melting time decreases. The power ranges between 6.07 W for the base case and 6.75 W for the 150°-4 case with 0% nanoparticles. With 6% MWCNT, the power is 6.70 W. Therefore, the presence of nanoparticles slightly reduces the power compared with the pure-PCM tree-fin system, but it still provides an 11.1% increase over the no-fin pure-PCM baseline. Since the paramount goal in an EV battery pack is to keep the cell below its safety temperature, the small penalty in storaged capacity is acceptable in exchange for enhanced thermal conductivity and faster heat absorption.
6. Conclusions and Practical Implications for EV Battery Pack Design
In my research, I combined phase change materials, tree-shaped fins and carbon nanotubes to improve the thermal management of an EV battery pack. The main conclusions can be summarised as follows.
First, the experimental results demonstrate that the tree-shaped fin coupled with PCM offers superior thermal performance compared with rectangular fins and plain tubes. In a cold environment at −10 °C, the PCM container protects the cells and maintains their temperature above freezing, increasing the minimum battery temperature up to 2.4 times relative to an unprotected cell. At an ambient temperature of 25 °C, the tree-fin system lowers the maximum cell temperature by about 10% and extends the charging/discharging time by 27.5%. At high ambient temperatures up to 50 °C, the same system keeps the cell surface temperature below 40 °C, which is a crucial safety margin for an EV battery pack.
Second, the visualisation experiments reveal the fundamental heat-transfer mechanisms. The PCM melts first near the heated surfaces, then expands upward due to buoyancy. The upper zone of the test chamber is always hotter than the lower zone, while cells located at the same height show similar temperatures. The tree-shaped fin accelerates the melting process and prolongs the simulated-cell operating time by up to 54.9% compared with the plain tube. Even at high ambient temperature, the tree-shaped fin retains an advantage.
Third, the numerical optimisation of the fin geometry shows that the fractal level and branching angle both play significant roles. For a fixed branching level, a larger branching angle reduces the battery temperature and improves uniformity. For a fixed branching angle, a larger number of fractal levels yields a more uniform temperature distribution. The optimal configuration in this study is the four-level fin with a branching angle of 150°, which shortens the full-melting time by 11.8%, lowers the average battery temperature by 4.5% and increases the energy-storage power by 11.2% compared with the base case.
Fourth, the use of MWCNT at mass fractions of 3% and 6% further enhances heat conduction in the PCM. Combining 6% MWCNT with the 150°-4 fin leads to the shortest melting time of 79 min, which is a reduction of 15.5% compared to the pure-PCM no-fin case. The battery temperature is reduced by up to a factor of 1.18, and the temperature-uniformity factor is as low as 0.92. Although the latent-heat capacity decreases slightly as the nanoparticle content increases, the improved conductivity and faster melting are more important for controlling the peak temperature in an EV battery pack.
Overall, this work provides a comprehensive experimental and numerical analysis of a novel passive thermal management system for an EV battery pack. Future studies could extend the approach to large-format battery packs, incorporate more complex transient driving cycles, or use topology optimisation to further refine the fin distribution. The combination of phase change material and tree-shaped fins is a promising route for improving the safety, longevity and performance of electric vehicles.