The global shift towards electrified transportation is fundamentally driven by the urgent need to address environmental crises, particularly those stemming from fossil fuel dependence. The heart of any electric vehicle (EV) is its energy storage system, with the lithium-ion battery reigning supreme due to its high energy density, long cycle life, and decreasing cost. Among various chemistries, lithium iron phosphate (LFP) batteries are highly favored for automotive applications owing to their superior thermal stability, safety, and cost-effectiveness. However, the performance, longevity, and safety of any lithium-ion battery are intimately and critically dependent on its operating temperature.
Optimal electrochemical activity and minimal degradation for a lithium-ion battery occur within a narrow temperature window, typically between 20°C and 40°C. Exceeding this range, especially under high discharge rates or in high ambient temperatures, accelerates aging mechanisms and poses severe safety risks, including thermal runaway—a catastrophic failure mode involving fire or explosion. Furthermore, temperature uniformity within a battery pack is equally crucial; a maximum temperature difference (ΔTmax) between cells exceeding 5°C can lead to uneven aging, capacity imbalance, and reduced overall pack life and reliability. Therefore, designing an efficient, reliable, and compact Battery Thermal Management System (BTMS) is paramount for unlocking the full potential of lithium-ion battery technology in demanding automotive applications.
Traditional BTMS approaches include air cooling, liquid cooling, heat pipes, and phase change material (PCM) cooling. Air cooling, while simple, lacks the necessary heat removal capacity for high-power lithium-ion battery packs. Liquid cooling offers high cooling intensity but adds complexity, weight, and potential leakage risks. Passive cooling using PCMs leverages latent heat absorption during phase transition (solid to liquid) to effectively buffer temperature rise and improve uniformity, but its usefulness is limited once the material is fully melted. Consequently, hybrid or composite systems that synergistically combine the strengths of multiple methods have emerged as the most promising solution. This study focuses on the design, parametric analysis, and optimization of a composite BTMS integrating PCM and liquid cooling for a prismatic lithium-ion battery pack, aiming to maintain both peak temperature and temperature differential within safe limits under strenuous operating conditions.
Literature Review on Thermal Management Strategies
Extensive research has been conducted on various BTMS technologies for lithium-ion battery packs. A summary of key approaches, their mechanisms, advantages, and limitations is presented in the table below.
| Cooling Method | Mechanism | Advantages | Disadvantages/Limitations |
|---|---|---|---|
| Air Cooling | Forced convection using air as coolant. | Simple structure, low cost, lightweight. | Low heat capacity and thermal conductivity; poor performance at high C-rates and in high ambient temperatures; large temperature gradients. |
| Liquid Cooling | Circulation of liquid coolant (e.g., water-glycol) through plates or tubes in contact with cells. | High heat transfer coefficient, excellent cooling capacity, good temperature uniformity. | Complex system, risk of leakage, added weight and volume, requires pump power. |
| Phase Change Material (PCM) | Absorbs heat as latent heat during melting at nearly constant temperature. | Passive operation, excellent temperature homogenization, no power consumption. | Limited thermal conductivity; finite heat storage capacity; potential for leakage in liquid state; adds weight and volume. |
| Heat Pipes | Two-phase heat transfer using evaporation and condensation of an internal working fluid. | Very high effective thermal conductivity, passive operation, flexible geometry. | Higher cost, design complexity for integration, limited heat transport distance. |
| Composite/Hybrid Systems | Combination of two or more methods (e.g., PCM + liquid, PCM + fins, liquid + heat pipes). | Leverages strengths and mitigates weaknesses of individual methods; superior performance under extreme conditions. | Increased design complexity, optimization required for multiple parameters. |
Recent studies underscore the effectiveness of composite systems. For instance, research on PCM-air composite systems for cylindrical lithium-ion battery modules demonstrated significant temperature reduction by enhancing PCM conductivity with expanded graphite and optimizing air duct design. Other investigations into prismatic lithium-ion battery packs with PCM and optimized air inlet/outlet configurations achieved remarkable temperature uniformity. Similarly, integrating flat heat pipes with liquid cooling has proven highly effective in maintaining lithium-ion battery temperatures below critical limits under high discharge rates. These works collectively validate the premise that a composite approach, particularly PCM coupled with active liquid cooling, presents a robust solution for managing the thermal behavior of high-power lithium-ion battery packs, which is the focus of this present work.
Mathematical and Geometric Model Formulation
Battery Heat Generation Model
The thermal analysis of a lithium-ion battery begins with accurately characterizing its heat generation. The total heat generated ($Q_{total}$) during operation arises from multiple sources: irreversible heat from electrochemical reaction overpotentials (activation and concentration polarization), reversible entropic heat, and Joule heating due to internal resistance. For engineering modeling purposes, a widely adopted simplified approach treats the lithium-ion battery as a uniform volumetric heat source. The Bernardi model provides a fundamental equation for estimating the volumetric heat generation rate ($\dot{q}$):
$$
\dot{q} = \frac{I}{V} \left( I \cdot R_{internal} – T \cdot \frac{dE_{oc}}{dT} \right)
$$
where $I$ is the discharge current (A), $V$ is the battery volume (m³), $R_{internal}$ is the internal resistance (Ω), $T$ is the absolute temperature (K), and $dE_{oc}/dT$ is the temperature coefficient of the open-circuit voltage (V/K). The term $I \cdot R_{internal}$ represents the irreversible Joule heating, while $T \cdot (dE_{oc}/dT)$ accounts for the reversible entropic heat. For an LFP lithium-ion battery, the entropic coefficient is relatively small, often making the irreversible heat the dominant component, especially at high C-rates.
Phase Change Material (PCM) Model
The heat transfer within the PCM, which involves solid-liquid phase transition, is governed by the energy conservation equation expressed in terms of enthalpy. The governing equation is:
$$
\rho_{PCM} \frac{\partial H_{PCM}}{\partial t} = \nabla \cdot (k_{PCM} \nabla T_{PCM})
$$
where $\rho_{PCM}$ is the density (kg/m³), $H_{PCM}$ is the total enthalpy (J/kg), $k_{PCM}$ is the thermal conductivity (W/m·K), and $T_{PCM}$ is the temperature (K). The total enthalpy $H_{PCM}$ is the sum of sensible heat and latent heat:
$$
H_{PCM} = \int_{T_{ref}}^{T_{PCM}} C_{p,PCM} \, dT + \beta L
$$
Here, $C_{p,PCM}$ is the specific heat capacity (J/kg·K), $L$ is the latent heat of fusion (J/kg), and $\beta$ is the liquid fraction, which varies between 0 (solid) and 1 (liquid). The liquid fraction $\beta$ is defined based on the phase change temperature range ($T_s$, $T_l$):
$$
\beta =
\begin{cases}
0, & T_{PCM} < T_s \\
\frac{T_{PCM} – T_s}{T_l – T_s}, & T_s \leq T_{PCM} \leq T_l \\
1, & T_{PCM} > T_l
\end{cases}
$$
Coolant Flow and Heat Transfer Model
The liquid cooling subsystem involves forced convection. The flow of coolant (ethylene-glycol/water mixture) through the aluminum tubes is governed by the Navier-Stokes equations for momentum and continuity. The convective heat transfer between the tube walls, the PCM, and the coolant is a critical coupling mechanism. The heat transfer rate is described by Newton’s law of cooling:
$$
\dot{Q}_{conv} = h A (T_{wall} – T_{coolant})
$$
where $h$ is the convective heat transfer coefficient (W/m²·K), $A$ is the contact area, $T_{wall}$ is the tube wall temperature, and $T_{coolant}$ is the bulk coolant temperature. The value of $h$ is strongly dependent on the flow regime (laminar or turbulent), which is determined by the Reynolds number ($Re = \rho v D / \mu$).
Geometric Model and Parameters
The physical model comprises a pack of four prismatic LFP lithium-ion battery cells. Key geometric and thermophysical parameters for the battery, PCM, coolant, and aluminum tubes are detailed in the following tables.
| Parameter | Value |
|---|---|
| Chemistry | Lithium Iron Phosphate (LFP) |
| Nominal Capacity | 37 Ah |
| Nominal Voltage | 3.7 V |
| Dimensions (L × W × H) | 148 mm × 27 mm × 92 mm |
| Mass | 0.8 kg |
| Internal Resistance | ~0.7 mΩ |
| Volumetric Heat Gen. @ 3C | 32,400 W/m³ |
| Property | Value |
|---|---|
| Base Material | Paraffin Wax + Expanded Graphite (EG) |
| Density ($\rho_{PCM}$) | 900 kg/m³ |
| Specific Heat ($C_{p,PCM}$) | 1200 J/kg·K (average) |
| Thermal Conductivity ($k_{PCM}$) | 5.02 W/m·K (enhanced by EG) |
| Latent Heat of Fusion ($L$) | 120 kJ/kg |
| Phase Change Temperature Range | 33°C – 36°C |
| Component | Parameter | Value |
|---|---|---|
| Coolant (50% EG-Water) | Density | 1075 kg/m³ |
| Specific Heat | 3340 J/kg·K | |
| Dynamic Viscosity | 0.00345 Pa·s | |
| Aluminum Cooling Tube | Outer Diameter | 6 mm |
| Wall Thickness | 0.5 mm | |
| Thermal Conductivity | 202 W/m·K |
The pack assembly involves placing an 8 mm thick layer of the composite PCM between adjacent lithium-ion battery cells. Aluminum cooling tubes are embedded within these PCM layers. The entire assembly is assumed to be insulated from the external environment to focus on the core thermal management performance.
Parametric Simulation Analysis and Optimization
A comprehensive simulation study was conducted using computational fluid dynamics (CFD) software to analyze the thermal performance of the composite PCM-liquid cooling BTMS for the lithium-ion battery pack. The base condition was set as a 3C constant-current discharge (111 A) in a 30°C ambient environment until the battery reached its cutoff voltage. The control variable method was employed to investigate the impact of four key parameters: cooling method, coolant flow direction, PCM thickness, and coolant flow rate. The primary performance metrics are the pack’s maximum temperature ($T_{max}$) and the maximum temperature difference ($\Delta T_{max}$) among the cell surfaces at the end of discharge.
Effect of Cooling Method
The initial analysis compared three fundamental cooling strategies under the 3C discharge: Natural Convection, Pure PCM cooling, and the composite PCM-Liquid cooling. The results starkly highlight the necessity of an advanced BTMS for high-power lithium-ion battery packs.
- Natural Convection: The pack overheated severely, with $T_{max}$ exceeding 58°C, far beyond the safe operating limit for a lithium-ion battery.
- Pure PCM Cooling: The PCM’s latent heat absorption effectively buffered the temperature rise, reducing $T_{max}$ to approximately 42.3°C. However, this still exceeded the optimal 40°C ceiling, and the PCM was nearly fully melted (liquid fraction ~0.75), indicating depletion of its passive cooling capacity.
- Composite PCM-Liquid Cooling: This preliminary composite case (with basic flow settings) successfully maintained $T_{max}$ well within the safe zone, demonstrating the critical role of the active liquid loop in rejecting heat from both the batteries and the PCM, thereby regenerating the PCM’s cooling potential.
This comparison conclusively proves that for a lithium-ion battery pack operating at high C-rates, a passive-only system like PCM is insufficient, and an active component like liquid cooling is essential.
Optimization of Coolant Flow Direction
With the composite system established, the configuration of the liquid cooling circuit was optimized. Three coolant flow direction schemes for the embedded tubes were analyzed:
Scheme A: Parallel flow, all inlets at the bottom, all outlets at the top.
Scheme B: Parallel flow, all inlets at the top, all outlets at the bottom.
Scheme C: Staggered flow, where the inlet and outlet manifolds are arranged such that coolant flows in opposite directions in adjacent PCM layers (e.g., bottom-in/top-out in one layer, top-in/bottom-out in the next).
The performance data for a coolant flow rate of 0.2 L/min is summarized below:
| Flow Scheme | Max. Temp. ($T_{max}$) | Min. Temp. ($T_{min}$) | Max. ΔT ($\Delta T_{max}$) |
|---|---|---|---|
| A (Bottom-In, Top-Out) | 37.30°C | 31.12°C | 6.18°C |
| B (Top-In, Bottom-Out) | 37.90°C | 32.05°C | 5.85°C |
| C (Staggered Flow) | 37.80°C | 32.71°C | 5.09°C |
While Scheme A yielded the lowest $T_{max}$, its temperature uniformity was the poorest ($\Delta T_{max}=6.18°C > 5°C$). Scheme C (staggered flow) produced the best temperature uniformity, bringing $\Delta T_{max}$ closest to the sub-5°C target. The staggered configuration promotes a more balanced heat extraction from different regions of the pack, counteracting the natural thermal stratification that occurs in parallel flow schemes. Since temperature uniformity is often harder to improve than lowering peak temperature (which can be addressed by increasing flow rate), Scheme C was selected as the optimal flow direction.
Optimization of Phase Change Material Thickness
The thickness of the PCM layer is a critical design parameter trading off cooling performance against pack volume and weight. Simulations were run for PCM thicknesses of 6 mm, 8 mm, 10 mm, and 12 mm within the composite system (with staggered flow). The results illustrate a non-linear relationship.
The average and maximum temperatures of the lithium-ion battery pack decrease as PCM thickness increases from 6 mm to 8 mm, due to the greater latent heat storage capacity. However, the marginal benefit diminishes significantly for thicknesses beyond 8 mm. The temperature reduction from 10 mm to 12 mm is minimal. This saturation effect occurs because the primary thermal resistance shifts from the PCM conduction to the convective resistance at the coolant interface. Furthermore, a thicker PCM substantially increases the pack’s volume and mass, reducing the overall energy density—a critical metric for EVs. Therefore, an 8 mm PCM thickness was identified as the optimal compromise, providing substantial cooling benefit without excessive penalization of system size and weight.
Optimization of Coolant Flow Rate
The coolant flow rate directly influences the convective heat transfer coefficient $h$ and the coolant’s temperature rise. Its impact on pack $T_{max}$ and $\Delta T_{max}$ was analyzed over a range from 0.2 L/min to 1.2 L/min.
| Flow Rate (L/min) | Max. Temp. ($T_{max}$) | Max. ΔT ($\Delta T_{max}$) |
|---|---|---|
| 0.2 | 37.80°C | 5.09°C |
| 0.4 | 36.52°C | 4.55°C |
| 0.6 | 36.00°C | 4.02°C |
| 0.8 | 35.62°C | 3.78°C |
| 1.0 | 35.32°C | 3.61°C |
| 1.2 | 35.17°C | 3.51°C |
The data reveals a clear law of diminishing returns. Increasing the flow rate from 0.2 to 0.6 L/min yields a significant improvement: $T_{max}$ drops by 1.8°C and $\Delta T_{max}$ drops by 1.07°C. However, doubling the flow rate again from 0.6 to 1.2 L/min results in a mere 0.83°C reduction in $T_{max}$ and a 0.51°C reduction in $\Delta T_{max}$. This marginal gain comes at a steep cost: the pumping power required to drive the coolant scales approximately with the cube of the flow rate ($P_{pump} \propto \dot{V}^3$), drastically reducing system efficiency. Consequently, a flow rate of 0.6 L/min was selected as the optimal point, as it achieves the performance targets ($T_{max} < 40°C$, $\Delta T_{max} < 5°C$) with high energy efficiency, leaving the PCM with residual latent heat capacity for additional thermal load.
Optimal Composite System Performance
The integrated optimal configuration for the lithium-ion battery pack BTMS is defined as: Composite PCM-Liquid Cooling, with Staggered Coolant Flow Direction, 8 mm PCM thickness, and a Coolant Flow Rate of 0.6 L/min.
Under the 3C discharge condition at 30°C ambient, this optimal system delivers exemplary thermal performance:
- Maximum Pack Temperature ($T_{max}$): 36.00°C
- Minimum Pack Temperature ($T_{min}$): 31.98°C
- Maximum Temperature Difference ($\Delta T_{max}$): 4.02°C
Both key metrics are well within the stringent requirements for lithium-ion battery operation ($T_{max} \leq 40°C$, $\Delta T_{max} \leq 5°C$). Furthermore, analysis of the PCM state reveals a liquid fraction ($\beta$) of approximately 0.56 at the end of discharge. This confirms that the PCM is only halfway through its latent heat capacity, providing a substantial safety buffer. This residual capacity allows the system to handle transient peak loads, higher ambient temperatures, or partial pump failure, significantly enhancing the thermal safety and reliability of the lithium-ion battery pack.
Discussion and Mechanism Analysis
The superior performance of the optimized composite system stems from the synergistic interaction between the PCM and the liquid cooling, effectively managing the heat generated by the lithium-ion battery.
1. Dual-Phase Heat Absorption and Rejection: During operation, heat from the lithium-ion battery first conducts into the surrounding PCM. The PCM acts as a thermal capacitor, absorbing a large amount of heat as latent heat at nearly constant temperature. This process effectively flattens the temperature rise curve of the battery and homogenizes temperatures across the pack. Simultaneously, the embedded liquid cooling tubes act as a heat sink embedded within this thermal buffer. They actively remove heat from the PCM, preventing it from becoming saturated and effectively “recharging” its solid state by solidifying the material near the tubes. This continuous cycle—PCM absorbs heat from the battery, liquid coolant removes heat from the PCM—creates a stable thermal equilibrium.
2. Role of Staggered Flow in Uniformity: The staggered flow configuration is key to achieving the low $\Delta T_{max}$. In a parallel flow scheme, the coolant temperature increases along the flow path, leading to a warmer outlet region and a cooler inlet region. This creates a steady-state temperature gradient in the pack aligned with the flow direction. Staggering the flow forces adjacent cells to experience opposing coolant temperature gradients, which counterbalance each other and result in a more uniform average heat extraction across the entire lithium-ion battery pack.
3. Analysis of Marginal Effects: The observed diminishing returns for both PCM thickness and coolant flow rate are classic examples of system-level thermal resistance analysis. The total thermal resistance from the battery core to the coolant has several components in series: conduction through the battery and PCM, and convection at the coolant interface.
$$ R_{total} \approx R_{cond,batt} + R_{cond,PCM} + R_{conv} $$
Initially, increasing PCM thickness reduces $R_{cond,PCM}$, and increasing flow rate reduces $R_{conv}$. However, after a certain point, one resistance becomes dominant. For thick PCM, $R_{conv}$ becomes the limiting factor; for high flow rates, $R_{cond,PCM}$ (or even $R_{cond,batt}$) becomes dominant. Further increasing the parameter affecting the non-dominant resistance yields minimal overall improvement in heat transfer, explaining the saturation in performance gains.
4. Safety and Reliability Implications: The final liquid fraction of 0.56 is a critical safety metric. It indicates the system is not operating at its limit. This headroom is vital for real-world scenarios where a lithium-ion battery might face consecutive high-power demands, cooling system degradation, or unexpectedly high ambient temperatures. The composite system’s inherent redundancy—both latent heat storage and active cooling—makes it far more robust than single-mode systems.
Conclusion and Future Perspectives
This study systematically designed, analyzed, and optimized a composite Phase Change Material and liquid cooling thermal management system for a prismatic lithium-ion battery pack. Through detailed numerical simulation and parametric studies, several key conclusions were reached:
- A composite PCM-liquid cooling strategy is essential for maintaining the thermal safety of high-power lithium-ion battery packs under strenuous operating conditions (e.g., 3C discharge, 30°C ambient), where passive or single-mode active systems fail.
- The configuration of the active cooling subsystem is crucial for temperature uniformity. A staggered coolant flow direction was identified as optimal for minimizing the maximum temperature difference within the lithium-ion battery pack.
- An 8 mm thickness for the composite PCM (paraffin/expanded graphite) was determined to be the optimal balance, providing significant latent heat benefits without excessively penalizing the pack’s volume and weight.
- An optimal coolant flow rate of 0.6 L/min was selected, achieving the target thermal performance ($T_{max}=36.00°C$, $\Delta T_{max}=4.02°C$) with high energy efficiency, avoiding the steep penalty of pumping power associated with higher flow rates.
- The final optimized system maintained a PCM liquid fraction of 0.56, demonstrating substantial residual cooling capacity and enhanced safety headroom for the lithium-ion battery pack.
This research provides a validated framework and specific design guidelines for developing high-performance BTMS for electric vehicles. Future work should focus on experimental validation of the simulation results, investigation of the system’s performance under dynamic driving cycles and fast-charging scenarios, and lifecycle analysis considering the long-term stability of the PCM and its interaction with the lithium-ion battery over thousands of cycles. Furthermore, multi-objective optimization incorporating weight, volume, cost, and control strategy would be a valuable next step for practical engineering implementation.