The global transition towards sustainable transportation has placed electric vehicles (EVs) at the forefront of automotive innovation. Central to the performance, safety, and longevity of these vehicles is the lithium-ion battery pack. Ensuring these power sources operate within an optimal thermal window is a critical engineering challenge. Effective thermal management systems (TMS) must maintain the operating temperature of a lithium-ion battery pack between 293.15 K and 313.15 K while minimizing the maximum temperature difference within the pack to below 5 K to prevent accelerated degradation, capacity fade, and safety hazards like thermal runaway.
Among various cooling strategies, liquid cooling stands out for its superior heat transfer efficiency and compactness, making it ideal for high-energy-density lithium-ion battery packs. Cold plate-based liquid cooling, where coolant flows through channels embedded in plates contacting the battery modules, is particularly prevalent. The design of the flow channel within these cold plates is paramount. Traditional serpentine channels, while simple, often suffer from significant drawbacks: high pressure drop leading to increased pumping power, and poor temperature uniformity due to continuous coolant heating along its path. As the coolant travels through the long, winding channel, its temperature rises, reducing the local heat transfer coefficient and creating a temperature gradient across the lithium-ion battery pack, with cells near the coolant outlet being significantly warmer.
Recent research efforts have focused on optimizing flow channel geometry to address these issues. Modifications like parallel-serpentine hybrids or topology-optimized “tree-shaped” channels have shown improvements in temperature uniformity or pressure drop, but often at the cost of increased complexity or the other performance metric. The concept of introducing secondary flow channels presents a promising avenue for drastically reducing pressure drop by providing alternative flow paths, though its impact on temperature uniformity can be limited.
This study proposes a novel cold plate design that synergistically combines the pressure-drop-reducing benefit of secondary flows with the heat-transfer-enhancing effect of fluid disturbance. We introduce a Secondary Flow Serpentine Finned Channel (SF-SFC) design. The core innovation lies in integrating straight secondary bypass channels into a traditional serpentine layout and augmenting the latter sections of the main channel with strategically placed fins. The secondary channels lower flow resistance, while the fins disrupt the thermal boundary layer and increase the effective heat transfer area in the downstream regions where the coolant temperature is higher, thereby improving overall temperature uniformity. Through detailed numerical simulation, this work investigates the effects of the secondary flow structure, coolant inlet velocity, and fin height on the thermal and hydraulic performance of the cooling system for a representative lithium-ion battery pack.
Geometry and Numerical Methodology
The lithium-ion battery pack under consideration is constructed from 26650 cylindrical lithium-ion battery cells. For computational efficiency, a representative domain consisting of a single layer of 35 cells (5 rows × 7 columns) is modeled, as shown in the schematic below. The cold plate, with a thickness of 6 mm, is placed beneath this cell layer. The baseline traditional serpentine channel and the proposed optimized designs are machined into this plate with a rectangular cross-section of 4 mm × 4 mm.
The proposed SF-SFC design, as shown in Figure 1(b), modifies the traditional serpentine path (Figure 1(a)) by adding straight secondary channels (2 mm × 2 mm) that branch off at angles from the main channel. Furthermore, small longitudinal fins are added to the walls of the main serpentine channel in its downstream sections to act as turbulence promoters and extended surfaces.
Governing Equations and Material Properties
The flow of coolant (a 50% ethylene glycol-water solution) within the channels is assumed to be incompressible and governed by the standard conservation laws of mass, momentum, and energy. The following equations form the basis of the fluid dynamics and conjugate heat transfer simulation:
Continuity Equation:
$$ \nabla \cdot \vec{v}_c = 0 $$
Navier-Stokes Momentum Equation:
$$ \frac{\partial \vec{v}_c}{\partial t} + (\vec{v}_c \cdot \nabla) \vec{v}_c = -\frac{1}{\rho_c} \nabla p + \nabla \cdot (\mu_c \nabla \vec{v}_c) $$
Energy Equation for the Coolant:
$$ \frac{\partial (\rho_c c_{pc} T_c)}{\partial t} + \nabla \cdot (\rho_c c_{pc} \vec{v}_c T_c) = \nabla \cdot (k_c \nabla T_c) $$
Within the solid domains (the lithium-ion battery cells and the aluminum cold plate), only conductive heat transfer is solved:
$$ \rho_s c_{ps} \frac{\partial T_s}{\partial t} = \nabla \cdot (k_s \nabla T_s) + \dot{q}_{gen} $$
where $\dot{q}_{gen}$ is the volumetric heat generation rate within the lithium-ion battery cell, which is non-zero and time-dependent.
The thermal properties of the lithium-ion battery cell (modeled as an anisotropic cylinder) and the coolant are critical inputs. These are summarized in Table 1.
| Component | Density, $\rho$ (kg/m³) | Specific Heat, $c_p$ (J/(kg·K)) | Thermal Conductivity, $k$ (W/(m·K)) |
|---|---|---|---|
| Lithium-Ion Battery (26650) | 1760 | 1108 | $k_{radial}=3.91$, $k_{axial}=23.0$ |
| Coolant (50% EG-Water) | 1071 | 3300 | 0.384 |
Heat Generation Model and Boundary Conditions
The heat generation within the lithium-ion battery during operation is a function of its state of charge and current. For this study, a 1C charge-discharge cycle is simulated. The transient volumetric heat generation rate $\dot{q}_{gen}(t)$ is derived from experimental measurements and implemented via a User-Defined Function (UDF). Key data points for the single-cell heat generation power and the corresponding volumetric rate are listed in Table 2.
| Cycle Phase | Time (s) | Single-Cell Heat Gen. (W) | Volumetric Source, $\dot{q}_{gen}$ (W/m³) |
|---|---|---|---|
| Discharge | 0 | 0.277 | 6581 |
| 360 | 0.257 | 7450 | |
| 720 | 0.196 | 5682 | |
| 1080 | 0.154 | 4464 | |
| 1440 | 0.185 | 5363 | |
| 1800 | 0.168 | 4870 | |
| 2160 | 0.289 | 8378 | |
| Charge | 2160 | 0.465 | 13481 |
| 2520 | 0.566 | 16409 | |
| 2880 | 0.623 | 18062 | |
| 3240 | 0.293 | 8495 | |
| 3600 | 0.513 | 14873 | |
| 3960 | 0.426 | 12350 | |
| 4320 | 0.395 | 11452 |
The numerical setup employs the following boundary conditions:
- Coolant Inlet: Specified velocity inlet with a constant temperature of $T_{in} = 293.15$ K.
- Coolant Outlet: Pressure outlet (gauge pressure = 0 Pa).
- Channel Walls: No-slip condition and coupled thermal boundary for conjugate heat transfer.
- External Battery Pack Surfaces: Convective heat transfer to ambient air at 293.15 K with a heat transfer coefficient of $h = 5$ W/(m²·K).
The SIMPLE algorithm is used for pressure-velocity coupling. Second-order upwind schemes are employed for spatial discretization of momentum and energy equations to ensure accuracy. A time step of 1 s is used for the transient simulation of the 4320-second cycle, verified through a time-step independence study. Similarly, a mesh independence study was conducted, confirming that a mesh size of approximately 420,000 elements provides grid-independent solutions for the key parameters: the maximum temperature $T_{max}$ and the maximum temperature difference $\Delta T_{max} = T_{max} – T_{min}$ of the lithium-ion battery pack, and the pressure drop $\Delta P$ across the cold plate.
Results and Discussion
Performance of the Secondary Flow Serpentine (SF-S) Channel
The initial evaluation compares the traditional serpentine (TS) channel against the secondary flow serpentine (SF-S) channel (without fins) at a coolant inlet velocity of 0.05 m/s. The thermal and hydraulic performance metrics at the end of the charge-discharge cycle are critical for assessing the lithium-ion battery pack’s state.
The temporal evolution of the battery pack’s $T_{max}$ and $\Delta T_{max}$ is shown in Figure 2. The SF-S channel demonstrates a clear advantage in temperature uniformity. At t=4320 s, the TS channel results in a $T_{max}$ of 304.77 K and a $\Delta T_{max}$ of 4.49 K. In contrast, the SF-S channel reduces these values to 304.53 K and 4.08 K, respectively. The reduction in $\Delta T_{max}$ by 0.41 K is significant for lithium-ion battery pack longevity. This improvement stems from the secondary channels, which allow cooler fluid from upstream to mix into and replenish the warmer downstream sections of the main serpentine path, leading to a more uniform cooling capacity across the plate surface.
The pressure distribution within the channels, depicted in Figure 3, reveals the primary hydraulic benefit. The SF-S channel exhibits a markedly lower and more uniform pressure field. The introduction of parallel flow paths reduces the flow resistance in any single channel segment. Upon reaching steady flow conditions, the pressure drop for the SF-S channel is approximately 16.08% lower than that of the TS channel. This reduction directly translates to lower pumping power requirements for the thermal management system, enhancing overall system efficiency for the lithium-ion battery pack cooling.
| Channel Design | Battery $T_{max}$ (K) | Battery $\Delta T_{max}$ (K) | Cold Plate $\Delta P$ (Pa) | $\Delta T_{max}$ Reduction | $\Delta P$ Reduction |
|---|---|---|---|---|---|
| Traditional Serpentine (TS) | 304.77 | 4.49 | $\Delta P_{TS}$ | — | — |
| Secondary Flow Serpentine (SF-S) | 304.53 | 4.08 | 0.8392 $\times \Delta P_{TS}$ | 0.41 K | 16.08% |
Effect of Coolant Inlet Velocity
The influence of coolant inlet velocity ($v_{in}$) on the performance of the SF-S channel was investigated. As expected, higher flow rates improve cooling performance due to increased convective heat transfer coefficients. The relationship can be partially understood by considering the Nusselt number correlation for developing flow in channels, where $Nu \propto Re^{m}Pr^{n}$, and the convective heat transfer coefficient $h_{conv} \propto Nu$.
Simulations were conducted for $v_{in}$ = 0.05, 0.10, and 0.15 m/s. The results, summarized in Table 4 and plotted in Figure 4, show a consistent trend: both $T_{max}$ and $\Delta T_{max}$ decrease with increasing velocity. Increasing $v_{in}$ from 0.05 m/s to 0.15 m/s reduced $T_{max}$ by 3.25 K (from 304.53 K to 301.28 K) and $\Delta T_{max}$ by 1.63 K (from 4.10 K to 2.47 K). The higher flow rate not only removes heat more effectively but also mitigates the streamwise temperature rise of the coolant, leading to better uniformity. However, this enhancement comes at the cost of a significantly increased pressure drop, which scales approximately with the square of the velocity ($\Delta P \propto v_{in}^2$ for turbulent flow, and a strong function of $v_{in}$ even in laminar/transitional regimes).
| Inlet Velocity, $v_{in}$ (m/s) | Battery $T_{max}$ (K) | Battery $\Delta T_{max}$ (K) | Relative $\Delta P$ Trend |
|---|---|---|---|
| 0.05 | 304.53 | 4.10 | 1.0 (Baseline) |
| 0.10 | 302.65 | 3.12 | ~3.8 x |
| 0.15 | 301.28 | 2.47 | ~8.2 x |
Enhancement with Finned Disturbance: The SF-SFC Design
To further improve temperature uniformity without incurring a large pressure drop penalty, the Secondary Flow Serpentine Finned Channel (SF-SFC) was proposed. Longitudinal fins of height $H_f$ = 0.2 mm were added to the walls of the main serpentine channel in its downstream section. These fins serve a dual purpose: they increase the effective heat transfer area $A_{eff}$, and they disrupt the hydrodynamic and thermal boundary layers, promoting local mixing and enhancing heat transfer. The local enhancement can be conceptualized by an increased heat flux: $\dot{q}” = h_{local} (T_{wall} – T_{coolant})$, where $h_{local}$ is increased due to disturbance.
At $v_{in}$ = 0.05 m/s, the addition of these fins yielded a remarkable improvement. As shown in Figure 5, the $\Delta T_{max}$ for the lithium-ion battery pack cooled by the SF-SFC design was 0.55 K lower than that cooled by the baseline SF-S design (without fins). Crucially, as seen in Figure 6, the pressure drop of the SF-SFC channel was marginally lower than that of the SF-S channel at the same flow rate (e.g., ~50.62 Pa lower at 0.15 m/s). This counter-intuitive result can be attributed to the fin orientation (aligned with the flow), which may streamline the flow in the channel corners and reduce viscous drag in certain regions, offsetting the added friction from the fin surfaces. This demonstrates that the SF-SFC design achieves superior temperature uniformity for the lithium-ion battery pack without increasing, and even slightly decreasing, the required pumping power—a highly desirable outcome.
| Channel Design | Battery $\Delta T_{max}$ (K) | Cold Plate $\Delta P$ (Pa) | Improvement vs. SF-S |
|---|---|---|---|
| SF-S (No Fins) | 4.08 | $\Delta P_{SF-S}$ | — |
| SF-SFC (With Fins) | 3.53 | < $\Delta P_{SF-S}$ | $\Delta T_{max}$↓ 0.55 K, $\Delta P$↓ |
Parametric Study on Fin Height
An optimal fin height must balance the enhancement in heat transfer against the increase in flow resistance. A parametric study was conducted with fin heights $H_f$ ranging from 0.2 mm to 0.6 mm at $v_{in}$ = 0.05 m/s. The results are summarized in Table 6 and plotted in Figures 7 and 8.
The thermal performance ($T_{max}$ and $\Delta T_{max}$) shows a phenomenon of diminishing returns. Increasing $H_f$ from 0.2 mm to 0.6 mm produces negligible further reduction in battery temperatures. The initial fins effectively disrupt the boundary layer and add surface area, but further height increases do not proportionally enhance the heat transfer rate, as the fin efficiency may decrease and the flow blockage becomes more dominant.
In contrast, the hydraulic penalty is severe and nearly linear. The pressure drop increases by approximately 47.54% when $H_f$ is increased from 0.2 mm to 0.6 mm. This is because the increased fin height reduces the effective flow area $A_{flow}$, significantly increasing the flow velocity between fins and the associated frictional losses, described by $\Delta P \propto f (L/D_h) (\rho v^2/2)$, where $D_h$ decreases. Therefore, the optimal fin height is identified as $H_f = 0.2$ mm, which delivers the majority of the thermal benefit with a minimal pressure drop increase compared to the unfinned SF-S design.
| Fin Height, $H_f$ (mm) | Battery $T_{max}$ (K) | Battery $\Delta T_{max}$ (K) | Normalized $\Delta P$ (H_f=0.2mm = 1.0) | Performance Assessment |
|---|---|---|---|---|
| 0.2 | ~304.3 | 3.53 | 1.00 | Optimal |
| 0.4 | ~304.2 | ~3.50 | ~1.25 | Marginal thermal gain, significant $\Delta P$ increase |
| 0.6 | ~304.2 | ~3.48 | ~1.475 | Negligible thermal gain, large $\Delta P$ penalty |
Conclusion
This study successfully designed and numerically evaluated an optimized cold plate structure for thermal management of lithium-ion battery packs. The proposed Secondary Flow Serpentine Finned Channel (SF-SFC) effectively addresses the key limitations of traditional serpentine channels: high pressure drop and poor temperature uniformity. The integration of secondary bypass channels and strategically placed, low-height fins creates a synergistic effect. The secondary flows redistribute the coolant, lowering flow resistance and providing cooler fluid to downstream sections, while the fins enhance local heat transfer in these warmer regions by disturbing the boundary layer and increasing surface area.
The key findings from this investigation are:
- The Secondary Flow Serpentine (SF-S) channel alone improves upon the traditional design, reducing the maximum temperature difference in the lithium-ion battery pack by 0.41 K and the system pressure drop by 16.08% at an inlet velocity of 0.05 m/s.
- Coolant inlet velocity is a strong driver of thermal performance for the lithium-ion battery pack; increasing it from 0.05 m/s to 0.15 m/s with the SF-S channel reduced the maximum temperature by 3.25 K and the maximum temperature difference by 1.63 K, albeit with a large increase in pressure drop.
- The addition of 0.2 mm high fins to create the SF-SFC design provided a further significant improvement in temperature uniformity, lowering $\Delta T_{max}$ by an additional 0.55 K compared to the SF-S design, without increasing the pressure drop.
- A parametric study on fin height established that a height of 0.2 mm is optimal, as larger fins (up to 0.6 mm) yielded negligible thermal benefits but incurred a substantial pressure drop increase of 47.54%.
In summary, the SF-SFC design presents a compelling solution for advanced thermal management systems. It demonstrates that through intelligent geometric integration of secondary flows and minimal surface modifications, it is possible to simultaneously enhance the temperature uniformity of a lithium-ion battery pack and reduce the energy consumption of the cooling system. This approach offers valuable insights for the design of efficient and compact cooling plates for high-performance electric vehicle battery packs and other energy storage applications utilizing lithium-ion battery technology.