In modern electric vehicles, the vehicle traction battery is undoubtedly the most critical subsystem that determines overall performance. Its capability to store and release electrical energy directly governs the driving range, acceleration performance, and lifecycle cost of the vehicle. Among the available battery chemistries, lithium-ion batteries have become the dominant energy storage technology for vehicle traction battery systems due to their high energy density, long cycle life, low self-discharge rate, and negligible memory effect. Nevertheless, the vehicle traction battery is highly sensitive to operating temperature. During high discharge rate operation, a significant amount of heat is generated inside the cells due to irreversible ohmic losses, polarization, and entropic heat generation. Since the battery packs are assembled with high compactness, the heat inside the module is difficult to dissipate promptly. If the accumulated heat cannot be removed effectively, the temperature of the vehicle traction battery will rise rapidly, causing capacity fade, accelerated aging, and even catastrophic thermal runaway in severe cases. In recent years, numerous fire accidents caused by thermal runaway of lithium-ion batteries have raised serious concerns regarding the safety of electric vehicles. Therefore, developing efficient thermal management systems is essential to ensure the safe and stable operation of the vehicle traction battery. In this context, this thesis focuses on the thermal performance of a liquid-cooled cold plate with pin-fin channels for vehicle traction battery thermal management, covering numerical modeling, multi-objective optimization, and experimental validation. A novel hybrid cold plate that integrates straight channels with pin-fin structures was proposed to enhance heat transfer while maintaining acceptable pumping power. The present study systematically investigates the effect of pin-fin geometry, channel height, pin-fin spacing, and coolant mass flow rate on flow and heat transfer characteristics, aiming to provide theoretical guidance for the design of high-efficiency liquid cooling plates for vehicle traction battery modules.
The vehicle traction battery thermal management system must maintain the battery temperature within the optimal range of 293 K to 313 K and ensure good temperature uniformity across all cells. However, with the rapid increase in energy density and the development of fast-charging technology, the heat generation rate of vehicle traction battery modules has risen dramatically. Conventional cooling strategies, such as air cooling, may not provide sufficient heat dissipation capability. Liquid cooling, especially in the form of cold plates, has been widely adopted as the mainstream solution for vehicle traction battery thermal management due to its high heat transfer coefficient, low noise, and controllable energy consumption. The performance of the cold plate is determined primarily by its flow channel structure. Straight channels suffer from developing thick thermal boundary layers along the flow direction, which degrades the convective heat transfer and leads to non-uniform temperature distributions. To overcome this limitation, pin-fin structures have been introduced into the channel to interrupt the boundary layer, induce flow disturbances, and enhance turbulent mixing. In this study, the cooling performance of different pin-fin geometries was first evaluated, followed by multi-objective optimization of the most promising design, and finally, an experimental investigation was carried out to verify the numerical predictions and explore the underlying physics.
Heat generation modeling of the lithium-ion cell
To accurately simulate the thermal behavior of the vehicle traction battery module, the heat generation model of a prismatic lithium-ion battery cell was first established. The cell used in this research is a 100 Ah lithium iron phosphate battery typically employed as a vehicle traction battery. Its geometric dimensions and basic parameters are summarized in the following table.
| Parameter | Value | Unit |
| Nominal capacity | 100 | Ah |
| Voltage window | 2.5 – 3.65 | V |
| Cell dimensions | 160 × 116 × 50 | mm |
| Thermal conductivity | 22.5 / 22.5 / 1.5 | W/(m·K) |
| Cell mass | 1.65 | kg |
| Density | 2050 | kg/m3 |
| Specific heat capacity | 1088.745 | J/(kg·K) |
The heat generated inside a lithium-ion battery consists of four contributions: electrochemical reaction heat \(Q_r\), ohmic heat \(Q_j\), polarization heat \(Q_p\), and side-reaction heat \(Q_s\). The total heat generation rate can be expressed as
\[
Q = Q_r + Q_j + Q_p + Q_s
\]
In normal operating conditions, side-reaction heat can be neglected. For simplicity and engineering applicability, the model proposed by Bernardi is widely employed to calculate the volumetric heat generation rate of a vehicle traction battery. The Bernardi model states:
\[
q = \beta \frac{I}{V_c}\left[(E_0 – U) – T \frac{dE_0}{dT}\right]
\]
where \(I\) is the current, \(V_c\) is the volume of the cell, \(E_0\) and \(U\) denote the open-circuit voltage and terminal voltage, and \(dE_0/dT\) is the temperature coefficient. Since both polarization heat and reaction heat contribute weakly compared with ohmic heat, the simplified form can be written as:
\[
q = \frac{I^2 R_T}{V_c}
\]
where \(R_T\) represents the total internal resistance of the battery. To incorporate the dependence of internal resistance on the state of charge (SOC), discharge experiments were performed at a 1C rate. The measured internal resistance data were fitted as a polynomial function of SOC. The fitted results reveal that the internal resistance changes gently for SOC in the range of 0.2 to 0.8, while severe variation occurs outside this region. Therefore, in the subsequent numerical simulations, the discharge depth of the lithium-ion cell was set to 80%, i.e., the final SOC was 0.2.
The heat conduction within the vehicle traction battery was described using the energy conservation equation with anisotropic thermal conductivity:
\[
\rho_b c_b \frac{\partial T}{\partial t} = k_{x,b} \frac{\partial^2 T}{\partial x^2} + k_{y,b} \frac{\partial^2 T}{\partial y^2} + k_{z,b} \frac{\partial^2 T}{\partial z^2} + Q
\]
The equivalent specific heat capacity and anisotropic thermal conductivities of the cell were calculated using resistance network models. For the thickness direction, the series thermal resistance model is used:
\[
k_{T,x} = \frac{\sum L_i}{\sum (L_i / k_{T,i})}
\]
For the in-plane directions, the parallel model is expressed as
\[
k_{T,y} = k_{T,z} = \frac{\sum L_i k_{T,i}}{\sum L_i}
\]
The equivalent density of the battery is
\[
\rho_{\text{cell}} = \frac{\sum L_i \rho_i}{\sum L_i}
\]
Since the internal structure of a lithium-ion battery is highly complex, it was simplified as a homogeneous body with a uniform heat source in the simulation model. The positive and negative tabs were neglected, and all thermophysical properties were assumed to be constant.
A finite volume method was applied to solve the transient heat transfer problem of a single cell. The numerical result at the end of 1C discharge in an ambient temperature of 291 K shows that the maximum temperature reaches 318 K, indicating a temperature rise of 15 K above the ambient. Meanwhile, the largest temperature difference within the cell reached 12 K, confirming the necessity of effective cooling. To validate the heat generation model, the predicted temperature rise was compared with experimental data. The comparison shows that the errors at critical time instants are less than 5%, which proves that the thermal model is sufficiently accurate for subsequent conjugate heat transfer analysis of the vehicle traction battery module integrated with liquid cooling cold plates.
Numerical models of pin-fin channel cold plates
A complete thermal management system for a vehicle traction battery module was designed and modeled. The module consists of 24 cells arranged in two rows with 12 cells in each row. Each cell is sandwiched between liquid-cooled cold plates with thermally conductive silicone pads inserted at the interfaces. The dimensions of the cold plate are 655 mm × 134 mm × 14 mm, with a coolant channel width of 12 mm and a channel height of 1.5 mm. The whole system has three cold plates, each configured with one central inlet and two end outlets, resulting in a highly symmetric flow distribution. Pin fins are placed in-line inside each channel to reinforce heat transfer. The cold plate and pin fins are made of aluminum. The physical model is shown in the following table, which summarizes the main geometric parameters of the module.
| Component | Dimension / value | Unit |
| Cell size | 160 × 116 × 50 | mm |
| Cold plate size | 655 × 134 × 14 | mm |
| Channel width | 12 | mm |
| Channel height | 1.5 | mm |
| Pin diameter | 3 | mm |
| Pin spacing | 15 / 19 | mm |
To evaluate the flow and heat transfer performance of different pin-fin geometries, straight channels (SC), square pin-fin channels (S-Pin-fin), circular pin-fin channels (C-Pin-fin), and triangular pin-fin channels (T-Pin-fin) were compared. The coolant is a 50% ethylene glycol-water mixture, whose thermophysical properties are given below.
| Material | Density (kg/m3) | Specific heat (J/(kg·K)) | Thermal conductivity (W/(m·K)) | Viscosity (Pa·s) |
| Silicone pad | 2094.96 | 2684 | 4 | / |
| Aluminum cold plate | 2719 | 871 | 202.4 | / |
| 50% ethylene glycol | 1065 | 3281 | 0.38 | 0.0069 × (T/273)-8.3 |
For the coolant flow, the governing equations include the continuity equation, the momentum equation, and the energy equation, as follows:
\[
\frac{\partial \rho_f}{\partial t} + \nabla \cdot (\rho_f \mathbf u)=0
\]
\[
\frac{\partial}{\partial t}(\rho_f \mathbf u) + \nabla \cdot (\rho_f \mathbf u \mathbf u) = -\nabla P
\]
\[
\frac{\partial}{\partial t}(\rho_f c_f T_f) + \nabla \cdot (\rho_f c_f \mathbf u T_f) = \nabla \cdot (k_f \nabla T_f)
\]
The energy conservation equations for the silicone pad and the cold plate are given as
\[
\frac{\partial}{\partial t}(\rho_s c_s T_s) = \nabla \cdot (k_s \nabla T_s)
\]
\[
\frac{\partial}{\partial t}(\rho_c c_c T_c) = \nabla \cdot (k_c \nabla T_c)
\]
The laminar model was used for the straight channels, while the standard \(k-\varepsilon\) turbulence model was selected for pin-fin channels because of the flow separation and vortex generation induced by the pin fins. The transport equations of turbulent kinetic energy \(k\) and dissipation rate \(\varepsilon\) are
\[
\frac{\partial(\rho k)}{\partial t}+\frac{\partial(\rho u_j k)}{\partial x_j}=\frac{\partial}{\partial x_j}\left[\left(\mu+\frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right]+P_k-\rho\varepsilon
\]
\[
\frac{\partial(\rho \varepsilon)}{\partial t}+\frac{\partial(\rho u_j \varepsilon)}{\partial x_j}=\frac{\partial}{\partial x_j}\left[\left(\mu+\frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right]+C_{\varepsilon 1}\frac{\varepsilon}{k}P_k-C_{\varepsilon 2}\rho\frac{\varepsilon^2}{k}
\]
The model constants are \(C_{\varepsilon 1}=1.44\), \(C_{\varepsilon 2}=1.92\), \(\sigma_k=1.0\), and \(\sigma_\varepsilon=1.2\).
At the boundaries, all battery cells were subjected to the same volumetric heat source during a 1C discharge process with 80% depth of discharge. The ambient surfaces were exposed to natural convection with a heat transfer coefficient of \(10\; \mathrm{W/(m^2\cdot K)}\). The inlet boundary condition was set as a mass flow inlet with values ranging from 0.01 kg/s to 0.03 kg/s. The outlet was set as a pressure outlet. The ambient temperature and the coolant inlet temperature were both fixed at 293 K. The SIMPLE algorithm was used for pressure-velocity coupling, and a second-order upwind scheme was adopted for spatial discretization. The convergence criteria required the continuity residual to decrease below \(10^{-6}\) and the energy residual below \(10^{-9}\).
To measure the thermal performance of the cold plates, the maximum temperature \(T_{\max}\) and the temperature difference \(\Delta T\) on the center cross-section of the battery module were selected as indicators. In addition, the pressure drop \(\Delta P\) across the cold plate was used to quantify the energy consumption of the thermal management system:
\[
T_{\max} = \max\{T_1, T_2, T_3, \ldots, T_n\}
\]
\[
\Delta T = T_{\max-\text{mid}} – T_{\min-\text{mid}}
\]
\[
\Delta P = P_{\text{in}} – P_{\text{out}}
\]
Grid independence studies were conducted for both the straight-channel model and the circular pin-fin channel model. It was found that when the grid number reached approximately 12.5 million and 13.2 million respectively, the maximum temperature and pressure drop changed negligibly with further mesh refinement. Therefore, the final CFD models were discretized with approximately 12.5 million and 13.2 million polyhedral-hexahedral core elements. The enhanced wall treatment with pressure gradient effects was enabled to resolve the boundary layer properly.
The numerical model was validated against experiments using a pin-fin cold plate fabricated for verification. The experimental platform consisted of a gear pump, a liquid turbine flowmeter, differential pressure transmitters, a heating film, a DC power supply, an infrared thermal camera, and a data acquisition system. The mass flow rate was varied from 0.01 kg/s to 0.03 kg/s, with a uniform heat flux corresponding to 36 W. Different turbulence models were tested; the standard \(k-\varepsilon\) model yielded the smallest average deviation in pressure drop compared with experimental data, with a mean relative error of 7.1%. The difference between the predicted and measured average heating-surface temperature was consistently below 0.8 K. The acceptable errors confirm that the numerical model is reliable for predicting flow resistance and heat transfer characteristics of pin-fin cold plates. This validation step formed the basis for using the same modeling approach in the parametric studies and multi-objective optimization described in the following sections.
Comparison of flow and heat transfer characteristics among different pin-fin shapes
To identify the optimal pin-fin configuration for vehicle traction battery cooling, the cooling performance of the four geometries was compared at mass flow rates ranging from 0.01 kg/s to 0.03 kg/s. The simulation results show that the maximum temperature of all modules decreases with increasing flow rate, but the decreasing rate gradually slows down. This trend is attributed to the thinning of the thermal boundary layer and the enhancement of convective heat transfer at higher velocity. However, as the temperature difference between the coolant and the cell diminishes, further gains become less pronounced. In the straight channel, where the flow remains laminar, the temperature reduction is relatively limited due to the lack of strong flow disturbance. In contrast, the pin-fin channels effectively promote turbulence and significantly improve thermal performance.
Among the different pin-fin shapes, the square pin-fin channel provides the lowest maximum temperature, followed by circular and triangular pin-fin channels, while the straight channel exhibits the worst thermal performance. At a low mass flow rate of 0.01 kg/s, the circular pin-fin configuration lowers the maximum temperature by 1.5 K compared with the straight channel. As the flow rate increases to 0.02 kg/s and 0.03 kg/s, the temperature reduction increases to 2.5 K and 2.9 K, respectively. This indicates that the advantages of turbulent heat transfer enhancement become more evident at higher flow rates.
In terms of temperature uniformity, for mass flow rates below 0.02 kg/s, the straight channel shows better uniformity than the pin-fin channels because of its relatively uniform laminar velocity profile. When the flow rate exceeds 0.02 kg/s, the pin-fin channels produce superior temperature uniformity. At the highest flow rate of 0.03 kg/s, the pin-fin channels reduce the temperature difference by 0.7 K relative to the straight channel. The cells near the inlet region exhibit significantly enhanced heat dissipation due to the entrance effect, where the thermal boundary layer is thinner and the local heat transfer coefficient is high.
Regarding the pressure drop, the square pin-fin channel produces the highest resistance at the same mass flow rate because of its smallest flow area and strongest turbulence intensity. For instance, at 0.02 kg/s and 0.03 kg/s, the square pin-fin channel increases the pressure drop by 0.6 kPa and 1.2 kPa respectively compared with the circular pin-fin channel. Considering the trade-off between thermal performance and pressure drop, the circular pin-fin channel achieves the best balance among all the investigated geometries. Therefore, the circular pin-fin channel was selected for further optimization and experimental study.
The heat transfer enhancement mechanism of pin-fin channels was further analyzed by inspecting velocity magnitude contours, heat transfer coefficient distributions, vortex structures colored by the Q-criterion, and turbulent kinetic energy contours. In the straight channel, the heat transfer coefficient is improved only in the entrance region; downstream, the fully developed thermal boundary layer thickens along the flow direction, leading to increased thermal resistance and degraded heat transfer. In pin-fin channels, however, periodic flow disturbances caused by pin fins continuously interrupt the development of the boundary layer. Vortex shedding and flow separation induced by the fins considerably enhance convective heat transfer. For the circular pin-fin channel, the Q-criterion reveals periodic, well-organized ring-shaped vortices along the streamwise direction. The high-turbulence regions are confined to the vortex cores and the near-wall shear layer. The high heat transfer region coincides well with the vortex trajectory, resulting in uniform and continuous high-efficiency heat transfer. This configuration achieves the highest utilization of turbulent kinetic energy while minimizing unnecessary dissipation, thus providing the best overall thermal-hydraulic performance. The square pin-fin channel produces fragmented vortical structures and severe turbulent dissipation, which explains its high heat transfer coefficient but excessive pressure drop. Triangular pin-fin channels present a combination of upstream separation vortices and downstream reattachment, with moderate heat transfer enhancement and lower energy loss than square fins.
Multi-objective optimization of circular pin-fin channel cold plates
The circular pin-fin channel was chosen for further optimization because of its superior balanced thermal-hydraulic performance. The design variables considered in the optimization include the coolant mass flow rate \(A\), the channel height \(B\), and the pin-fin spacing \(C\). These three parameters directly affect both the heat transfer and pumping power of the cold plate. The ranges of these variables are given in the following table.
| Design variable | Baseline | Minimum | Maximum | Unit |
| Mass flow rate \(A\) | 0.02 | 0.01 | 0.03 | kg/s |
| Channel height \(B\) | 1.5 | 1.5 | 4 | mm |
| Pin spacing \(C\) | 15 | 4 | 30 | mm |
Because CFD simulations of the vehicle traction battery module are computationally expensive, the optimal Latin hypercube sampling method was used to generate 31 sample points distributed uniformly over the design space. Each sample point was evaluated using the validated CFD model at a 1C discharge rate. The results were used to construct a Kriging surrogate model that maps the design variables to the thermal and hydraulic performance indicators. The surrogate model allows rapid fitness evaluation during optimization without additional costly CFD runs.
Sensitivity analysis was performed to quantify the influence of each design variable on the objective functions. The sensitivity index is calculated as
\[
SA_i = \frac{f_{\max}(x_i) – f_{\min}(x_i)}{f_{\max}(x) – f_{\min}(x)} \times 100\%
\]
The sensitivity results reveal that the mass flow rate has a dominant effect on both the maximum temperature and the temperature difference. The sensitivity values of \(T_{\max}\) and \(\Delta T\) to mass flow rate are as high as 0.996 and 0.988, respectively. For the pressure drop, the channel height is the dominant factor, with a sensitivity value of 0.442. This is because the channel height directly changes the cross-sectional area of the flow passage, thereby strongly influencing the flow velocity and both friction and local resistances. The pin-fin spacing, however, has a negligible effect on the pressure drop, with a sensitivity of only 0.028.
Correlation analysis was also carried out among the optimization objectives. The Pearson correlation coefficient between \(T_{\max}\) and \(\Delta T\) was found to be 0.99, indicating extremely strong positive correlation. Therefore, \(T_{\max}\) was removed from the objective set to reduce redundancy and improve optimization efficiency. The final two objectives retained were the temperature difference \(\Delta T\) and the pressure drop \(\Delta P\).
The Kriging model was validated by cross-validation. The coefficients of determination for \(\Delta P\) and \(\Delta T\) are 0.952 and 0.966, respectively. Both values exceed 0.9, demonstrating the high prediction accuracy of the surrogate model.
The NSGA-II algorithm was then used to perform the multi-objective optimization. The population size and generation number were set to 120 and 50, yielding 6000 candidate solutions. After screening the results within the feasible objective range, the Pareto front was extracted. The scatter plot of \(\Delta T\) versus \(\Delta P\) illustrates a clear trade-off between the two objectives: when \(\Delta T\) is maintained at a low level, a small sacrifice in temperature uniformity can lead to a significant reduction in pressure drop. Three representative models were selected from the Pareto front and validated using full CFD simulations. The comparison between surrogate predictions and CFD results shows that all errors are below 3.4%, confirming the accuracy and reliability of the optimization methodology. The following table summarizes the baseline model and the representative optimal models.
| Model | \(A\) (kg/s) | \(B\) (mm) | \(C\) (mm) | \(\Delta T\) (K) | \(\Delta P\) (kPa) | \(T_{\max}\) (K) |
| Baseline | 0.0200 | 1.50 | 15 | 5.40 | 3.10 | 308.3 |
| Opt-1 | 0.0253 | 3.66 | 22 | 4.47 | 1.25 | 307.5 |
| Opt-2 | 0.0285 | 3.14 | 19 | 4.15 | 1.76 | 306.9 |
| Opt-3 | 0.0294 | 2.52 | 18 | 4.07 | 2.34 | 306.7 |
Among these models, Opt-2 was considered the best compromise because it reduces the temperature difference by 23.1% relative to the baseline while reducing the pressure drop by 43.2%. The optimized mass flow rate is 0.0285 kg/s, the channel height is 3.14 mm, and the pin-fin spacing is 19 mm. This configuration achieves the best balance between thermal performance and energy consumption of the vehicle traction battery thermal management system.
To further evaluate the optimized design, thermal resistance decomposition was performed. The total thermal resistance consists of the convective resistance \(R_\text{conv}\), the heat capacity resistance \(R_\text{heat}\), and the conductive resistance \(R_\text{cond}\):
\[
R_\text{conv} = \frac{T_{\text{ave}} – T_{\text{liq}}}{q}
\]
\[
R_\text{heat} = \frac{T_{\text{out}} – T_{\text{in}}}{q}
\]
\[
R_\text{cond} = \frac{L_b}{k_s A_{\text{cont}}}
\]
\[
R_\text{total} = R_\text{conv} + R_\text{heat} + R_\text{cond}
\]
The results show that at both mass flow rates of 0.02 kg/s and 0.03 kg/s, the optimized circular pin-fin configuration (C-Pin-fin (Opt)) reduces the total thermal resistance by 14% and 16% respectively, compared with the straight-channel cold plate. This reduction is mainly attributed to the improvement in convective thermal resistance. The differences in heat capacity and conductive resistance are negligible. Compared with the baseline circular pin-fin model, the optimized model shows a slight increase in thermal resistance due to a reduced number of fins and enlarged channel height. However, this increase is negligible, while the pressure drop is significantly reduced.
The effective heat transfer enhancement factor \(p_f\) is a comprehensive index that compares the improvement in heat transfer with the increase in flow resistance. It is defined as
\[
p_f = \frac{Nu/Nu_0}{(\Delta P / \Delta P_0)^{1/3}}
\]
The Nusselt number \(Nu\) is evaluated as
\[
Nu = \frac{h_{\text{ave}} D_h}{k_{\text{liq}}}
\]
At a mass flow rate of 0.02 kg/s, the optimized circular pin-fin channel achieves a Nusselt number more than six times higher than that of the straight channel, while the enhancement factor is improved by a factor of 7. Compared with the baseline pin-fin model, the optimized design improves \(Nu\) by 33.9% and \(p_f\) by 97.5%. When the flow rate increases to 0.03 kg/s, the improvement in \(Nu\) is 43.7% and in \(p_f\) is 87.7%. This demonstrates that the optimized pin-fin cold plate provides a superior combination of heat transfer enhancement and manageable pressure loss. Although the Nusselt number increases with higher flow rate, the enhancement factor decreases slightly due to the more severe pressure drop penalty.
The cooling efficiency factor \(\eta\) was introduced to quantify the energy efficiency of the thermal management system:
\[
Q_{\text{liq}}(t) = c_p \, m \, \Delta T_{\text{coolant}}
\]
\[
Q_{\text{cell}}(t) = \int_{t_0}^{t_1} I^2 R(t) \, dt
\]
\[
\eta = \frac{Q_{\text{liq}}(t)/t}{\Delta P \, q_v}
\]
The optimized circular pin-fin cold plate achieves a maximum cooling efficiency factor of 15,452 at 0.02 kg/s, which is much higher than that of the baseline pin-fin model (4,875) and the straight channel (7,250). Although the cooling efficiency factor of all configurations decreases with increasing flow rate, the optimized model retains the highest value, confirming its excellent comprehensive thermal-hydraulic performance for vehicle traction battery applications.
Experimental study of circular pin-fin channel cold plates
Before manufacturing the cold plate, the effect of channel height was further investigated. The channel height is a key structural parameter that determines both the hydraulic performance and the overall thickness of the cold plate. For compact vehicle traction battery modules, the cold plate thickness must be minimized while maintaining sufficient cooling performance. The simulation results show that when the channel height increases from 1 mm to 4 mm at a fixed mass flow rate of 0.0285 kg/s, the maximum battery temperature rises only slightly, by about 0.3 K. At the same time, the pressure drop decreases with increasing channel height. Notably, when the channel height is increased from 1 mm to 1.5 mm, the pressure drop is reduced by 7.7 kPa, corresponding to a 59.2% decrease. Further increases in channel height result in much smaller pressure drop reductions. Considering both thermal performance and structural compactness, a channel height of 1.5 mm was identified as the optimal choice, designated as C-Pin-fin (BCS).
A dedicated experimental setup was designed and constructed to test the manufactured circular pin-fin channel cold plate. The cold plate was fabricated by CNC machining, with dimensions of 732 mm × 191 mm × 12 mm. The channel height is 1.5 mm, the pin diameter is 3 mm, and the pin spacing is 19 mm. The inlet and outlet diameters are 6 mm. The experimental loop consists of a gear pump, a liquid turbine flowmeter, a thermostatic water bath, differential pressure transmitters, T-type thermocouples, an infrared thermal camera, a DC power supply, and a data acquisition system. Four heating films were attached to the cold plate surface to simulate the heat generated by the vehicle traction battery cells. The total heating power was set to 200 W, 280 W, 360 W, and 440 W under different test conditions. The coolant was 50% ethylene glycol-water mixture, and the inlet temperature was maintained at 293 K. The mass flow rate was varied from 0.005 kg/s to 0.03 kg/s.
The experimental system was first used to validate the CFD model of the C-Pin-fin (BCS) configuration. The comparison between simulation and experimental results shows that the maximum relative error of pressure drop is less than 8%, while the maximum error in average surface temperature is 1.2 K. These small deviations confirm the reliability of the numerical model in predicting the flow and heat transfer behavior of the optimized cold plate.
The flow resistance experiment was conducted without activating the heating films. The pressure drop across the cold plate was recorded as a function of coolant flow rate. The results show that \(\Delta P\) increases continuously as the flow rate increases. The growth rate is strongly nonlinear. In the low flow rate region, the pressure drop increases slowly because the flow is dominated by viscous forces and the boundary layer remains attached to the pin surfaces. As the flow rate increases, flow separation appears behind the pin fins, and form drag gradually dominates the total pressure loss. In the high flow rate region, vortex shedding and strong turbulent mixing cause a sharp increase in pressure drop. Despite the higher flow resistance at elevated flow rates, the pressure drop of the C-Pin-fin (BCS) cold plate remains within an acceptable range for practical vehicle traction battery thermal management.
In the heat transfer experiments, the infrared thermal camera was used to record the temperature distribution on the heating film surface. The infrared images clearly indicate that the temperature gradually increases along the coolant flow direction. The coolant temperature rises as it absorbs heat along the channel, reducing the local temperature difference between the fluid and the wall. Therefore, the heating film temperature near the inlet area is the lowest, while higher temperatures appear in the downstream region. The temperature difference between different heaters is consistent with the entrance effect: the heater located closer to the inlet exhibits a lower temperature than the heater located downstream due to the higher local heat transfer coefficient near the entrance. This phenomenon reinforces the conclusion that the thermal boundary layer development is the main cause of temperature non-uniformity in straight and even pin-fin channels.
The influence of heat flux and flow rate on the heating film temperature was analyzed. Under a constant flow rate, the surface temperature increases with increasing heat flux because more resistive heat is generated while the heat removal capacity of the coolant remains relatively unchanged. Under a constant heat flux, the surface temperature decreases as the flow rate increases. A higher flow rate intensifies fluid disturbance, increases the convective heat transfer coefficient, and decreases the thickness of the thermal boundary layer, thus improving heat dissipation. By comparing the measured temperatures of different heaters, it is observed that the heater adjacent to the inlet always has a lower temperature than the heater further downstream under all test conditions. This observation agrees well with the infrared thermal images and confirms favorable consistency of the experimental results.
In addition, the thermal resistance and pump power consumption of the cold plate were evaluated. With increasing flow rate, the pump power grows exponentially due to the combined effect of increasing flow rate and pressure drop. At the same time, the thermal resistance gradually decreases because the higher flow rate enhances convective heat transfer and thins the thermal boundary layer. The thermal resistance also decreases when the heating power increases. This trend is caused by the variation of coolant thermophysical properties with temperature. As the heating power rises, the coolant viscosity decreases, and the thermal conductivity and heat transfer coefficient improve, enhancing the heat transfer capability. Nevertheless, the reduction of thermal resistance gradually diminishes and eventually stabilizes when the heat flux reaches a high level, as the improvement in thermophysical properties gradually saturates. Therefore, in practical vehicle traction battery thermal management systems, care should be taken to balance the pump power consumption and the thermal resistance. Increasing the coolant flow rate excessively in pursuit of a marginal thermal resistance reduction can lead to unacceptable energy penalties.
The experimental results provide important guidance for the practical design of liquid-cooled cold plates for vehicle traction battery thermal management. The use of circular pin fins in a parallel-channel cold plate effectively enhances heat transfer while maintaining acceptable pressure drop, making it a promising candidate for high-power-density battery modules.
Conclusion
This study systematically investigated the single-phase flow and heat transfer characteristics of pin-fin channel cold plates for vehicle traction battery thermal management. A combination of numerical simulation, multi-objective optimization, and experimental validation was adopted. The main conclusions are as follows:
(1) A heat generation model of a prismatic lithium-ion cell was established based on experimental discharge data and the Bernardi heat generation rate model. The simulation results agree well with experimental measurements, with errors less than 5%. This provides an accurate thermal load model for subsequent conjugate heat transfer simulations of a vehicle traction battery module integrated with liquid cooling plates.
(2) The comparison of different channel configurations reveals that pin-fin channels significantly improve the cooling performance compared to straight channels. Among square, circular, and triangular pin-fin configurations, the circular pin-fin channel demonstrates the best balance between heat transfer enhancement and pressure drop. At a mass flow rate of 0.03 kg/s, it reduces the maximum temperature by 2.9 K and the temperature difference by 0.7 K relative to the straight channel. The mechanism of heat transfer enhancement is attributed to periodic flow disturbances, boundary layer interruption, and vortex induction by pin fins. Circular pin fins generate organized ring-like vortices, leading to high utilization of turbulent kinetic energy and excellent overall performance.
(3) Multi-objective optimization was carried out using a Kriging surrogate model and the NSGA-II algorithm. Sensitivity analysis shows that the mass flow rate is the dominant factor affecting \(T_{\max}\) and \(\Delta T\), while the channel height is the primary factor determining \(\Delta P\). Correlation analysis reveals strong positive correlation between \(T_{\max}\) and \(\Delta T\). The optimized model achieves a 23.1% reduction in temperature difference and a 43.2% reduction in pressure drop compared with the baseline design. Thermal resistance analysis shows a 14–16% reduction relative to the straight channel. The effective heat transfer enhancement factor of the optimized model is improved by up to 97.5% over the baseline. The maximum cooling efficiency factor reaches 15,452, demonstrating the remarkable energy efficiency of the optimized cold plate for vehicle traction battery applications.
(4) Experimental studies confirmed the accuracy of the numerical model and revealed the effects of flow rate and heating power on cold plate performance. The temperature of the heating film decreases with increasing flow rate and increases with increasing heat flux. The experimental data also reveal a nonlinear pressure drop growth pattern, which results from the local flow separation and vortex dynamics around pin fins. Thermal resistance decreases with increasing heating power but eventually approaches a stable value. Moreover, a higher flow rate always leads to an exponential growth of pump power, so both thermal performance and energy consumption must be considered when choosing the optimum operating condition for vehicle traction battery thermal management systems.
In summary, the proposed circular pin-fin channel cold plate offers a promising solution for efficient and energy-saving thermal management of high-power vehicle traction battery modules.
Outlook
Several aspects deserve further investigation in the future. First, the battery heat generation model can be extended to consider non-uniform heat generation distributions and dynamic electrochemical-thermal coupling to improve the fidelity of simulations. Second, the performance of the pin-fin cold plate under extreme operating temperatures and different discharge rates, including fast-charging scenarios, should be tested to broaden its applicability. Third, the current study uses heating films to simulate battery heat sources; future experiments should be conducted with real vehicle traction battery cells to validate the cooling performance under realistic charge-discharge cycles. Finally, advanced optimization methods such as topology optimization and machine learning-based design can be introduced to further enhance the thermal-hydraulic performance and compactness of cold plates for next-generation vehicle traction battery systems.