The imperative for electrification, driven by global decarbonization strategies, has propelled the rapid expansion of the energy storage industry. A core component of this ecosystem is the large-scale EV battery pack, whose safety, longevity, and performance are intrinsically tied to its operating temperature. For lithium-ion batteries, the ideal operational window is typically between 20°C and 40°C, with a maximum temperature difference between individual cells below 5°C. Exceeding these limits, especially surpassing 70°C, risks triggering thermal runaway—a catastrophic failure mode involving fire and explosion. Therefore, developing an efficient, reliable, and energy-conscious Battery Thermal Management System (BTMS) is paramount for the thermal safety and stability of any EV battery pack.
Among various cooling technologies, liquid cooling using cold plates stands out due to its high heat transfer efficiency, compact structure, and cost-effectiveness. The primary mechanism is convective heat transfer, where a coolant circulated by a pump absorbs heat from the battery cells via the cold plate. Since the pump’s energy consumption is directly related to the hydraulic resistance within the cooling channels, an optimal design must achieve excellent cooling performance while minimizing flow resistance. This work focuses on the thermal analysis and hydraulic optimization of a multi-channel serpentine cold plate for a large-capacity EV battery pack.
Mathematical Foundation for Cold Plate Design
The design and analysis of the liquid cooling system for the EV battery pack are grounded in fundamental principles of fluid mechanics and heat transfer. Two core mathematical models govern the system’s behavior: the flow resistance model and the heat transfer equations.
1. Flow Resistance Model
The pressure drop \( \Delta P \) incurred as the coolant flows through the cold plate’s channels is a critical parameter, as it determines the pumping power required. This total resistance comprises two components: frictional (major) losses along straight channel sections and local (minor) losses due to changes in flow direction or cross-section.
Frictional Pressure Drop: Calculated using the Darcy-Weisbach equation:
$$ \Delta P_{\lambda} = \lambda \frac{L}{D_h} \cdot \frac{\rho v^2}{2} $$
where \( \lambda \) is the Darcy friction factor (dependent on flow regime, Reynolds number \( Re \), and channel roughness), \( L \) is the channel length, \( D_h \) is the hydraulic diameter, \( \rho \) is the coolant density, and \( v \) is the average flow velocity.
Local Pressure Drop: Occurs at bends, inlets, outlets, and confluence/divergence zones:
$$ \Delta P_{\zeta} = \zeta \frac{\rho v^2}{2} $$
where \( \zeta \) is the local loss coefficient, which is highly dependent on the specific geometry of the fitting or obstruction.
The total flow resistance for the EV battery pack cold plate is the sum of all frictional and local losses along the flow path:
$$ \Delta P_{total} = \sum \Delta P_{\lambda} + \sum \Delta P_{\zeta} $$
2. Heat Transfer Equations
Heat removal from the EV battery pack involves sequential conduction through the battery cells and cold plate wall, followed by convection to the flowing coolant.
Heat Conduction: Governed by Fourier’s Law, the heat flux through the cold plate wall and battery cells is:
$$ q = -\lambda_s \nabla T $$
where \( q \) is the heat flux vector, \( \lambda_s \) is the thermal conductivity of the solid material (which is anisotropic for battery cells), and \( \nabla T \) is the temperature gradient.
Convective Heat Transfer: The heat transferred from the cold plate’s inner wall to the coolant is described by Newton’s Law of Cooling:
$$ \Phi = h A (T_w – T_f) $$
where \( \Phi \) is the heat transfer rate, \( h \) is the convective heat transfer coefficient, \( A \) is the contact area, \( T_w \) is the wall temperature, and \( T_f \) is the bulk coolant temperature.
The convective coefficient \( h \) is a key parameter calculated from the Nusselt number \( Nu \):
$$ h = \frac{\lambda_l Nu}{D_h} $$
where \( \lambda_l \) is the thermal conductivity of the coolant. For turbulent flow in channels, which is typical for effective cooling, the Gnielinski correlation provides a highly accurate relation for \( Nu \):
$$ Nu = \frac{(f/8)(Re – 1000) Pr}{1 + 12.7(f/8)^{1/2}(Pr^{2/3} – 1)} \left[ 1 + \left( \frac{D_h}{L} \right)^{2/3} \right] $$
Here, \( Pr \) is the Prandtl number of the coolant, and \( f \) is the Darcy friction factor, often calculated using the Konakov formula for smooth tubes under turbulent conditions:
$$ f = (1.8 \log_{10} Re – 1.5)^{-2} $$
The Reynolds number \( Re \) defines the flow regime:
$$ Re = \frac{\rho v D_h}{\mu} $$
where \( \mu \) is the dynamic viscosity of the coolant. An \( Re > 2300 \) generally indicates turbulent flow, which enhances convective heat transfer.
Geometric Model of the EV Battery Pack and Cold Plate
The study focuses on a representative 43 kWh EV battery pack consisting of two modules, each containing 24 prismatic Lithium Iron Phosphate (LFP) cells, for a total of 48 cells. The key parameters for a single cell are summarized in Table 1. Notably, the thermal conductivity is anisotropic due to the layered structure of electrodes and separators.
| Parameter | Value |
|---|---|
| Nominal Capacity | 280 Ah |
| Internal Resistance | 0.22 mΩ |
| Dimensions (x, y, z) | 72 mm × 208 mm × 173 mm |
| Density | 2219 kg/m³ |
| Specific Heat Capacity | 1000 J/(kg·K) |
| Thermal Conductivity (x, y, z) | 2.5, 12, 12 W/(m·K) |
| Max. Continuous Discharge Rate | 1C |
| Heat Generation Rate @ 1C | 17 W per cell |
The EV battery pack model was simplified for computational efficiency, retaining only the essential thermal masses: the 48 tightly packed cells and the bottom-mounted cold plate. Mechanical housing, busbars, and control modules were omitted as their thermal impact is secondary. The cold plate is in full contact with the base of the cell assembly.
A novel parallel serpentine channel design was proposed. Unlike a single serpentine, this design features multiple parallel flow channels connected by enlarged confluence and divergence zones at the ends, forming a continuous “M”-shaped flow path. The inlet and outlet are positioned on the same side for easier plumbing integration within the constrained space of an EV battery pack. Six design variants were created, differing only in the number of parallel channels: 3, 4, 5, 6, 7, and 8. All designs maintain a consistent channel cross-section (20 mm width × 6 mm height) and inlet/outlet diameter (12 mm). The core design variable is thus the number of parallel flow paths \( N \).
Computational Analysis and Cooling Performance
1. Simulation Setup and Mesh Independence
Three-dimensional computational fluid dynamics (CFD) simulations were performed using ANSYS Fluent. The boundary conditions are listed in Table 2. A constant heat generation of 17 W per cell (1C rate) was applied. A coolant (a water-glycol mixture) inlet mass flow rate of 0.05 kg/s and temperature of 25°C was set, with a pressure-outlet condition. Natural convection (5 W/m²·K) was applied to external surfaces. The Realizable k-ε turbulence model was selected as the Reynolds number at the inlet was calculated to be approximately 5273.5, confirming turbulent flow.
| Boundary Condition | Setting |
|---|---|
| Cell Heat Generation | 17 W per cell (1C) |
| Initial Temperature | 25 °C |
| Coolant Inlet | Mass flow inlet, 0.05 kg/s, 25°C |
| Coolant Outlet | Pressure outlet, 0 Pa (gauge) |
| External Walls | Natural convection, h=5 W/(m²·K) |
A Poly-Hexcore meshing scheme was employed to efficiently capture the thin cold plate and small cell tabs. A mesh independence study was conducted, monitoring the maximum temperature of the EV battery pack. The results stabilized beyond 17.97 million elements, which was chosen as the baseline mesh size to ensure accuracy while managing computational cost.
2. Effect of Channel Count on Cooling Performance
All six cold plate designs successfully maintained the EV battery pack temperature within the safe operational limit. The key thermal metrics are compared in Table 3.
| Number of Channels (N) | Max. Pack Temp. T_max (°C) | Avg. Pack Temp. T_avg (°C) | Max. Cell Temp. Difference ΔT_cell (°C) | Total Flow Resistance ΔP (Pa) |
|---|---|---|---|---|
| 3 | 38.58 | 34.29 | 2.12 | 1456.1 |
| 4 | 38.49 | 34.21 | 2.11 | 1271.3 |
| 5 | 38.41 | 34.16 | 2.10 | 1101.0 |
| 6 | 38.37 | 34.13 | 2.10 | 1010.5 |
| 7 | 38.34 | 34.11 | 2.10 | 950.2 |
| 8 | 38.32 | 34.09 | 2.09 | 901.8 |
Analysis of Thermal Performance: The data reveals a surprisingly weak dependence of thermal performance on the number of channels. The maximum temperature spread across all designs is only 0.26°C, and the average temperature spread is 0.20°C. The 3- and 4-channel designs show slightly higher temperatures, likely due to their marginally lower contact area with the pack. As \( N \) increases, the coolant velocity in each channel decreases (for a fixed total flow rate), which tends to reduce the convective coefficient \( h \). However, this is counterbalanced by a more distributed cooling effect and the longer effective perimeter. The net result is a very minor improvement in cooling. Crucially, the maximum temperature difference between any two cells in the EV battery pack remains consistently around 2.1°C for all designs, well below the 5°C safety threshold. This consistency is attributed to the unchanged overall “M” shaped flow path length, which ensures a similar thermal gradient along the pack.
Analysis of Hydraulic Performance: In contrast to the thermal results, flow resistance shows a strong and clear trend: it decreases monotonically with increasing channel count \( N \). The resistance drops by over 550 Pa (38%) from the 3-channel to the 8-channel design. This is a direct consequence of fluid dynamics. For a constant total volumetric flow rate \( Q_{total} \), the flow velocity \( v_n \) in each of the \( N \) parallel channels is:
$$ v_n = \frac{Q_{total}}{N \cdot A_c} $$
where \( A_c \) is the cross-sectional area of one channel. Since pressure drop is proportional to the square of velocity (\( \Delta P \propto v^2 \)) in both frictional and local loss terms, reducing \( v_n \) by increasing \( N \) leads to a significant reduction in \( \Delta P \). Therefore, adding more channels is an effective strategy for lowering the pumping power requirement of the EV battery pack cooling system.
3. Effect of Coolant Flow Rate
Using the 5-channel design as a baseline, the impact of the coolant mass flow rate \( \dot{m} \) was investigated. The results in Table 4 demonstrate a fundamental trade-off: higher flow rates improve cooling at the expense of increased flow resistance and pump power.
| Mass Flow Rate \( \dot{m} \) (kg/s) | Max. Pack Temp. T_max (°C) | Flow Resistance ΔP (Pa) | Estimated Pumping Power \( \dot{W}_p \propto \dot{m} \Delta P / \rho \) |
|---|---|---|---|
| 0.03 | 39.82 | ~410 | Low |
| 0.05 | 38.41 | 1101 | Medium |
| 0.07 | 37.45 | ~2100 | High |
| 0.10 | 36.32 | ~4200 | Very High |
The flow rate of 0.05 kg/s was selected as the optimal operating point, balancing good thermal performance (T_max < 39°C) against a reasonable flow resistance for the EV battery pack system.
4. Thermal Field Analysis for the 5-Channel Design
The temperature distribution within the EV battery pack cooled by the 5-channel plate shows the highest temperatures in the upper region of the pack, farthest from the cold plate. This is expected as heat conducts downward through the cells. The temperature on the cold plate surface exhibits a clear serpentine pattern, mirroring the flow path, with the outlet side being warmer than the inlet side by approximately 3.8°C. Velocity streamlines revealed significant vortices and high-velocity regions in the confluence/divergence zones at the ends of the cold plate. These zones were identified as major contributors to the local pressure drop \( \Delta P_{\zeta} \), presenting a clear opportunity for hydraulic optimization.
Multi-Objective Optimization for Reduced Flow Resistance
Based on the comprehensive analysis, the 5-channel design was selected for further optimization. It offered a favorable compromise: excellent thermal performance (T_max ~38.4°C, ΔT_cell ~2.1°C), significantly lower flow resistance than designs with fewer channels, and lower manufacturing complexity than designs with more channels. The optimization goal was to minimize the flow resistance \( \Delta P \) (Objective \( Y_2 \)) while constraining the cooling performance, measured by the average coolant outlet temperature \( T_{out,avg} \) (Constraint \( Y_1 \)), to be no worse than the baseline design (approximately 29.5°C).
1. Design of Experiments (DOE) and Variables
The geometric features targeted for optimization were the dimensions of the confluence/divergence zones at the ends of the cold plate, where flow recirculation was observed. To simplify the problem, symmetry was assumed along the x and y axes. This reduced the number of independent geometric design variables to six (X1 to X6), representing specific gap widths within these zones, as defined in Table 5.
| Variable | Description (Gap Width) | Lower Bound (mm) | Upper Bound (mm) |
|---|---|---|---|
| X1 | Lateral gap between outer channel and plate edge | 20 | 60 |
| X2 | Gap between outer channel and first inner channel | 20 | 60 |
| X3 | Gap between first and second inner channels | 20 | 60 |
| X4 | Gap between second inner channel and central channel | 20 | 60 |
| X5 | Longitudinal gap in the first serpentine turn | 20 | 60 |
| X6 | Longitudinal gap in the second serpentine turn | 20 | 60 |
A space-filling Latin Hypercube Sampling (LHS) method was used to generate 43 sample points within the design space. A simplified CFD model, replacing the full EV battery pack with a constant heat flux boundary condition on the cold plate top surface, was used to evaluate \( Y_1 \) and \( Y_2 \) for each sample, creating a training database for the surrogate model.
2. Surrogate Modeling and Optimization Algorithm
A Response Surface Methodology (RSM) model, specifically a quadratic polynomial with cross terms, was constructed to approximate the relationship between the design variables (X1-X6) and the responses (Y1, Y2). The accuracy of the surrogate models was verified using the coefficient of determination \( R^2 \):
$$ R^2 = 1 – \frac{\sum_{i=1}^{n} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i – \bar{y})^2} $$
where \( y_i \) is the actual CFD result for sample \( i \), \( \hat{y}_i \) is the surrogate model prediction, and \( \bar{y} \) is the mean of the actual results. The models for \( Y_1 \) and \( Y_2 \) achieved \( R^2 \) values of 0.91064 and 0.98779, respectively, indicating excellent fit, particularly for the primary objective \( \Delta P \).
The Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed to perform the multi-objective optimization on the surrogate models. NSGA-II is well-suited for this task as it efficiently handles non-linear problems, maintains population diversity, and converges to a Pareto-optimal front. The crowding distance calculation, a key component of NSGA-II for preserving diversity, is given by:
$$ I_{distance} = \sum_{k=1}^{m} \frac{|z_k(i+1) – z_k(i-1)|}{z_k^{max} – z_k^{min}}, \quad (2 \leq i \leq n-1) $$
where \( z_k(i) \) is the value of the \( k \)-th objective for the \( i \)-th solution in the sorted front.
3. Optimization Results and Validation
The optimization process yielded an optimal geometry defined by the variable set: X1=54 mm, X2=44 mm, X3=52 mm, X4=52 mm, X5=56 mm, X6=60 mm. The surrogate model predicted a flow resistance \( Y_2 \) of 590.9 Pa for this configuration while meeting the outlet temperature constraint \( Y_1 \leq 29.5^\circ C \).
This optimized design was then modeled in full detail and simulated with the complete EV battery pack CFD model to validate the predictions. The results are summarized in Table 6 and compared against the baseline 5-channel design.
| Performance Metric | Baseline 5-Channel | Optimized 5-Channel | Change |
|---|---|---|---|
| Flow Resistance \( \Delta P \) (Pa) | 1101.0 | 640.6 | -41.8% |
| Avg. Coolant Outlet Temp. \( T_{out,avg} \) (°C) | ~29.5 | ~29.4 | Negligible |
| EV Battery Pack Max. Temp. \( T_{max} \) (°C) | 38.41 | 38.40 | Negligible |
| EV Battery Pack Max. Cell ΔT (°C) | 2.10 | 2.10 | None |
The validation confirmed the optimization’s success. The flow resistance was reduced dramatically by 41.8%, from 1101 Pa to 640.6 Pa (a discrepancy of only 7.8% from the surrogate prediction, which is acceptable in engineering design). Crucially, this significant hydraulic improvement was achieved without compromising the thermal management of the EV battery pack. The maximum pack temperature and cell-to-cell temperature uniformity remained virtually identical to the baseline. Flow field analysis of the optimized plate showed a much more uniform velocity distribution and a significant reduction in the size and intensity of vortices within the reshaped confluence/divergence zones, directly explaining the lower pressure drop.
Conclusion
This study presents a systematic approach to the design and optimization of a liquid cold plate for thermal management of a large-scale EV battery pack. The analysis of a multi-channel parallel serpentine design led to several key conclusions:
1. For the specific EV battery pack configuration and operating condition (1C discharge), the number of parallel flow channels \( N \) has a minimal impact on the overall cooling performance. All designs from 3 to 8 channels maintained the maximum pack temperature below 39°C and cell temperature differences around 2.1°C. The primary thermal constraint is the total cold plate contact area and the fixed “M”-shaped flow path length, not the subdivision into parallel channels.
2. In contrast, hydraulic performance is strongly influenced by \( N \). Flow resistance decreases substantially as \( N \) increases, due to the reduced flow velocity in each channel (\( v_n \propto 1/N \)) and the resulting quadratic reduction in pressure drop (\( \Delta P \propto v_n^2 \)). This presents a direct pathway to lower pumping power consumption for the EV battery pack cooling system.
3. The 5-channel design was selected as the optimal baseline, balancing good thermal performance, significantly lower flow resistance than fewer-channel designs, and manageable manufacturing complexity compared to designs with more channels.
4. A formal optimization framework using DOE, RSM surrogate modeling, and the NSGA-II algorithm was successfully applied to minimize the flow resistance. By intelligently reshaping the confluence/divergence zones at the cold plate ends, the flow resistance was reduced by 41.8% (from 1101 Pa to 640.6 Pa) without any detriment to the thermal performance of the EV battery pack. This optimization directly translates to lower energy consumption by the cooling system pump, enhancing the overall efficiency of the EV battery pack.
This work demonstrates that for large EV battery pack applications, a well-designed serpentine cold plate can provide excellent temperature uniformity. The primary focus for system efficiency gains should be on hydraulic optimization to reduce flow resistance, as thermal performance is often sufficient with a relatively simple channel layout. The proposed methodology and design insights are valuable for engineers developing efficient and reliable thermal management solutions for next-generation energy storage systems.