Abstract
In this study, I conducted a comprehensive investigation into the single-phase flow and heat transfer characteristics of a novel hybrid cold plate integrating straight channels with pin-fin structures for electric vehicle battery thermal management. My research methodology combined numerical simulation, multi-objective optimization, and experimental validation to systematically evaluate the thermal-hydraulic performance of various pin-fin configurations. Initially, I established a heat generation model for a single lithium-ion battery cell based on experimental data and the Bernardi heat generation rate model, validating its accuracy through temperature rise experiments. Subsequently, I developed a conjugate heat transfer model of the battery-cold plate assembly and compared the performance of straight channels, square pin-fins, circular pin-fins, and triangular pin-fins. My results demonstrated that the circular pin-fin configuration achieved the optimal thermo-hydraulic performance, reducing the maximum temperature by 2.9 K and the temperature difference by 0.7 K compared to conventional straight channel designs at a mass flow rate of 0.03 kg/s. Furthermore, I employed the Optimal Latin Hypercube sampling method and constructed a Kriging surrogate model coupled with the NSGA-II multi-objective optimization algorithm to identify the Pareto-optimal solution set with maximum temperature, temperature uniformity, and pressure drop as optimization objectives. Through sensitivity analysis, I found that channel height was the dominant factor affecting pressure drop with a sensitivity of 44.2%, while mass flow rate exerted the most significant influence on temperature uniformity with a sensitivity of 53%. My optimized model demonstrated a 23.1% improvement in temperature uniformity and a 43.2% reduction in pressure drop compared to the baseline model. Finally, I fabricated the circular pin-fin channel cold plate and constructed a single-phase flow and heat transfer experimental platform to experimentally investigate its flow resistance and heat transfer characteristics. The experimental results revealed that the heating film temperature and thermal resistance decreased gradually with increasing coolant flow rate, providing valuable insights for the practical application of electric vehicle battery thermal management systems.
1. Introduction
Lithium-ion batteries serve as the primary power source in electric vehicles, where they are responsible for the storage and release of electrical energy to drive the traction motor and all auxiliary electronic systems. As a core component of electric vehicle battery systems, the operational capabilities of the vehicle, including its driving range, dynamic performance, and economic efficiency, are directly determined by the battery’s characteristics. However, when subjected to high discharge rates, a significant amount of heat is generated within the electric vehicle battery. This heat cannot be dissipated rapidly from the compact structure of the battery module, predisposing the cells to overheating. Lithium-ion batteries are known to be highly sensitive to temperature, with an optimal operating range of 293-313 K. Elevated temperatures not only lead to a reduction in driving range and a substantial decline in cycle life but can also initiate irreversible side reactions. In severe instances, this thermal runaway may culminate in a vehicle fire, posing a serious threat to occupant safety. Therefore, the implementation of an efficient thermal management system is regarded as essential for ensuring the safe, high-performance, and long-lasting operation of electric vehicle battery systems.
With the continuous increase in battery energy density and capacity, the demands on battery thermal management systems have become increasingly stringent. The mainstream prismatic lithium iron phosphate batteries have achieved an energy density of 220 Wh/kg, while ternary lithium batteries have reached 250 Wh/kg. As energy density continues to rise, the heat generated during operation correspondingly increases, thereby elevating the risk of thermal runaway without effective thermal management measures. Consequently, designing an efficient battery thermal management system represents a critical measure for ensuring the safe, efficient, and long-life operation of electric vehicle battery systems.
2. Heat Generation Model of Single Battery Cell
In my research, I focused on developing an accurate heat generation model as the foundation for subsequent thermal management system analysis. The lithium-ion battery selected for my study is a 100 Ah large-capacity prismatic lithium iron phosphate battery manufactured by CATL. The key parameters of this battery are presented in the following table.
| Parameter | Value | Unit |
|---|---|---|
| Nominal capacity | 100 | Ah |
| Operating voltage | 2.5-3.65 | V |
| Battery dimensions | 160×116×50 | mm |
| Thermal conductivity (x/y/z) | 22.5/22.5/1.5 | W/(m·K) |
| Battery mass | 1.65 | kg |
| Density | 2050 | kg/m³ |
| Specific heat capacity | 1088.745 | J/(kg·K) |
2.1 Heat Generation Mechanism
The heat generation during the operation of an electric vehicle battery primarily consists of four components: electrochemical reaction heat, internal resistance Joule heat, polarization heat, and side reaction heat. For the purpose of my thermal modeling, I adopted the Bernardi heat generation rate model, which simplifies the calculation while maintaining reasonable accuracy. The volumetric heat generation power is expressed as:
$$q = \beta \frac{I}{V_c} \left[ \left(E_0 – U\right) – T \frac{dE_0}{dT} \right]$$
In this study, I simplified the model by neglecting the reversible electrochemical reaction heat and polarization heat, as they account for a relatively small proportion of the total heat generation. The simplified heat generation formula becomes:
$$q = \frac{I^2 R_T}{V_c}$$
where q represents the volumetric heat generation power, I denotes the current, RT is the battery internal resistance, and Vc is the battery volume. Based on the energy conservation law, the transient heat conduction within the battery is governed by:
$$\rho_b c_b \frac{\partial T}{\partial t} = k_{x,b} \frac{\partial^2 T}{\partial x^2} + k_{y,b} \frac{\partial^2 T}{\partial y^2} + k_{z,b} \frac{\partial^2 T}{\partial z^2} + Q$$
2.2 Determination of Thermophysical Properties
The thermophysical properties of the battery were determined using mass-weighted averaging methods. The specific heat capacity of the battery cell was calculated as follows:
$$c_{cell} = \frac{\sum (\rho_i L_i) c_i}{\sum \rho_i L_i}$$
For the anisotropic thermal conductivity of the battery, I employed different models for different directions. Since the thickness direction consists of multi-layer heterogeneous materials arranged in series, I used the series thermal resistance model:
$$k_{T,x} = \frac{\sum L_i}{\sum L_i / k_{T,i}}$$
For the directions parallel to the lamination plane (y and z directions), where the heat flow path is in parallel, the parallel thermal resistance model was used:
$$k_{T,y} = k_{T,z} = \frac{\sum L_i k_{T,i}}{\sum L_i}$$
2.3 Internal Resistance Fitting and Model Validation
To accurately capture the heat generation characteristics, I measured the battery internal resistance at various states of charge (SOC) under a 1C discharge rate. The internal resistance data was fitted into a polynomial curve, which revealed that the resistance change rate was relatively gradual when the SOC was between 0.2 and 0.8, but increased dramatically outside this range. Based on this finding, my subsequent simulations set the depth of discharge to 80% with a terminal SOC of 0.2.
The transient thermal simulation of the single battery was performed using ANSYS Fluent 2022 R1, where I implemented a user-defined function (UDF) to load the volumetric heat generation power as a heat source. The temperature distribution at the end of discharge showed that the maximum temperature reached 318 K with a surface temperature rise of 15 K and a maximum temperature difference of 12 K under a 1C discharge rate. This result clearly demonstrated the necessity of efficient thermal management for electric vehicle battery systems operating under high-rate discharge conditions.
My validation results showed that the simulation errors at critical nodes were controlled within 5% compared to experimental data, which confirmed the accuracy and reliability of the heat generation model. This established a solid foundation for the subsequent conjugate heat transfer simulations of the battery-cold plate assembly.
3. Numerical Study on Flow and Heat Transfer Characteristics of Pin-Fin Channel Cold Plates
3.1 Physical Model Description
To address the thermal management challenges of high-power battery modules, I designed a liquid cooling system for electric vehicle battery thermal management. The system consisted of 24 battery cells arranged in two columns of twelve cells each, uniformly distributed between cold plates. Thermal silicone pads were filled between adjacent cells and between cells and cold plates to enhance thermal contact. The cold plate dimensions were 655 mm in length, 134 mm in width, and 14 mm in height, with each flow channel being 12 mm wide and 1.5 mm thick. The system employed three cold plates, each equipped with one inlet and two outlets, forming a system with eight cooling channels. As shown in the physical model description, the coolant flows from the central inlet of the cold plate and exits from both ends, a configuration that ensures highly uniform flow distribution. Within each channel, pin-fins were arranged in an aligned configuration to enhance heat transfer. I selected this system as the physical model to investigate the thermo-hydraulic performance of four different channel configurations: straight channel (SC), square pin-fins (S-Pin-fin), circular pin-fins (C-Pin-fin), and triangular pin-fins (T-Pin-fin).
The thermophysical properties of the materials used in my simulation are summarized in the following table:
| Component | Density (kg/m³) | Specific Heat (J/kg·K) | Thermal Conductivity (W/m·K) | Viscosity (Pa·s) |
|---|---|---|---|---|
| Thermal pad | 2094.96 | 2684 | 4 | / |
| Cold plate (aluminum) | 2719 | 871 | 202.4 | / |
| 50% ethylene glycol | 1065 | 3281 | 0.38 | 0.0069×(T/273)^(-8.3) |
3.2 Governing Equations and Boundary Conditions
The flow and heat transfer processes in my study adhere to the conservation laws of mass, momentum, and energy. For the coolant flow, the continuity, momentum, and energy equations are expressed as follows:
$$\frac{\partial \rho_f}{\partial t} +
abla \cdot (\rho_f \vec{v}) = 0$$
$$\frac{\partial}{\partial t} (\rho_f \vec{v}) +
abla \cdot (\rho_f \vec{v}\vec{v}) = –
abla P$$
$$\frac{\partial}{\partial t} (\rho_f c_f T_f) +
abla \cdot (\rho_f c_f \vec{v} T_f) =
abla \cdot (k_f
abla T_f)$$
For the solid regions, including the thermal pad and cold plate, the energy conservation equation is:
$$\frac{\partial}{\partial t} (\rho_s c_s T_s) =
abla \cdot (k_s
abla T_s)$$
The energy equation for the cold plate is:
$$\frac{\partial}{\partial t} (\rho_c c_c T_c) =
abla \cdot (k_c
abla T_c)$$
In my simulations, I used the laminar flow model for the straight channel configuration, while the standard k-ε turbulence model was selected for the pin-fin channels due to the flow disturbance induced by the pin-fins. The transport equations for the turbulent kinetic energy k and its dissipation rate ε are:
$$\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho u_j k)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k}\right) \frac{\partial k}{\partial x_j} \right] + P_k – \rho \epsilon$$
$$\frac{\partial (\rho \epsilon)}{\partial t} + \frac{\partial (\rho u_j k)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_\epsilon}\right) \frac{\partial \epsilon}{\partial x_j} \right] + C_{\epsilon 1} \frac{\epsilon}{k} P_k – C_{\epsilon 2} \rho \frac{\epsilon^2}{k}$$
where the model constants are Cε1 = 1.44, Cε2 = 1.92, σk = 1.0, and σε = 1.2.
For the boundary conditions, I applied identical heat generation power to each battery cell with a 1C discharge rate and 80% depth of discharge. All surfaces exposed to the environment were set with a convective heat transfer coefficient of 10 W/(m²·K). The inlet employed a mass flow inlet boundary condition, while the outlet used a pressure outlet, with mass flow rates ranging from 0.01 to 0.03 kg/s. The ambient temperature and coolant inlet temperature were maintained at 293 K. Other simulation conditions included treating the coolant as an incompressible fluid, applying no-slip boundary conditions at the walls, and neglecting contact thermal resistance at the interfaces.
3.3 Performance Evaluation Criteria
In evaluating the cooling performance of the electric vehicle battery thermal management system, I employed three primary performance indicators. The heat dissipation performance was evaluated using the maximum temperature:
$$T_{max} = \max\{T_1, T_2, T_3, \cdots, T_n\}$$
The temperature uniformity was assessed using the temperature difference across the center cross-section of the battery module:
$$\Delta T = T_{max-mid} – T_{min-mid}$$
The energy consumption of the cooling system was evaluated using the pressure drop:
$$\Delta P = P_{in} – P_{out}$$
3.4 Mesh Generation and Model Validation
For mesh generation, I employed the Poly-Hexcore grid generation method to achieve a balance between computational accuracy and efficiency. This approach automatically generates high-quality hexahedral cells in the core region while creating polyhedral cells near walls and regions with significant geometric curvature. Through mesh independence verification, I determined that the straight channel model required approximately 12.5 million cells, while the circular pin-fin model required approximately 13.2 million cells for converged results.
To validate my numerical model, I developed an experimental platform and manufactured a circular pin-fin channel cold plate. The comparative analysis of different turbulence models revealed that the Standard k-ε model exhibited the smallest pressure drop deviation with an average error of 7.1%. The subsequent comparison of the average heating surface temperature showed that both the average and maximum errors were within 0.8 K. These results confirmed the reliability of the Standard k-ε model for predicting both the flow resistance and heat transfer characteristics of the pin-fin channel cold plate.
3.5 Comparative Analysis of Different Pin-Fin Configurations
The results of my comparative analysis demonstrated that the maximum temperature of all battery modules decreased with increasing flow rate, with the rate of decrease gradually slowing. Among the different pin-fin configurations, the S-Pin-fin exhibited the best temperature control capability, followed by C-Pin-fin and T-Pin-fin, while the SC configuration, which lacks turbulence enhancement mechanisms, showed the worst performance. At a low flow rate of 0.01 kg/s, the C-Pin-fin configuration reduced the maximum temperature by 1.5 K compared to SC. When the flow rate was increased to 0.02 and 0.03 kg/s, the temperature reductions increased to 2.5 K and 2.9 K, respectively.
The temperature distribution analysis revealed that when the mass flow rate exceeded 0.02 kg/s, the pin-fin channels consistently demonstrated superior temperature uniformity compared to the straight channel. At the maximum flow rate of 0.03 kg/s, the pin-fin channels achieved a temperature difference reduction of 0.7 K compared to the straight channel. The pressure drop analysis revealed that the square pin-fin channel exhibited the highest pressure drop among all pin-fin configurations due to its smallest flow cross-sectional area and greatest turbulence intensity. In contrast, the circular pin-fin configuration demonstrated the best balance between heat transfer performance and pressure drop.
3.6 Heat Transfer Enhancement Mechanism Analysis
Through comprehensive analysis of velocity contours, heat transfer coefficient distributions, vortex structures, and turbulent kinetic energy contours, I revealed the heat transfer enhancement mechanisms of the pin-fin channels. The pin-fin structures induce periodic flow disturbances that continuously interrupt the development of thermal boundary layers, thereby triggering vortex generation and flow separation. This results in significantly enhanced heat transfer coefficients compared to straight channels. In the straight channel, the heat transfer coefficient improvement was confined to the entrance region, as the fully developed flow leads to progressive thickening of the thermal boundary layer and consequent performance deterioration.
For the circular pin-fin configuration, the Q-criterion revealed periodically arranged regular ring-shaped vortices along the flow direction, with high turbulence regions strictly confined to the vortex cores and near-wall shear layers. This configuration achieved efficient utilization of turbulent kinetic energy, minimizing unnecessary turbulent dissipation while continuously disrupting the thermal boundary layer. The square pin-fin configuration generated fragmented vortex structures with high turbulence kinetic energy and heat transfer coefficients, but at the cost of significantly increased pressure drop due to intense vortex breakdown and high turbulent dissipation. The triangular pin-fin configuration exhibited coexistence of front-end separated vortices and tail-end reattachment, providing a moderate balance between heat transfer enhancement and flow resistance.
4. Multi-Objective Optimization of Circular Pin-Fin Channel
4.1 Design Variables and Objective Functions
Based on the preliminary analysis from my previous chapter, I selected the circular pin-fin configuration as the optimal design for further optimization. In the multi-objective optimization process, I first identified the design variables that significantly influence the objective functions. The coolant mass flow rate is a core operational parameter that directly affects the convective heat transfer coefficient. The channel height is a critical structural parameter that influences both flow velocity and pressure drop. The pin-fin spacing determines the frequency of flow disturbance and affects both heat transfer enhancement and flow resistance. The specific ranges of these design variables are presented in the following table:
| Design Variable | Initial Value | Minimum | Maximum |
|---|---|---|---|
| A – Mass flow rate (kg/s) | 0.02 | 0.01 | 0.03 |
| B – Channel height (mm) | 1.5 | 1.5 | 4 |
| C – Pin-fin spacing (mm) | 15 | 4 | 30 |
4.2 Optimal Latin Hypercube Sampling
I employed the Optimal Latin Hypercube Sampling method to obtain sample points within the design space. This method provides excellent space-filling and projective properties, enabling efficient exploration of the design space while ensuring uniform projection distribution across all variable dimensions. I obtained 31 sample points for constructing the surrogate model. The numerical simulation results of these sampling points are shown in the following table:
| No. | A (kg/s) | B (mm) | C (mm) | Tmax (K) | ΔT (K) | ΔP (kPa) |
|---|---|---|---|---|---|---|
| 1 | 0.0260 | 2.16 | 23.6 | 307.2 | 4.4 | 2.2 |
| 2 | 0.0167 | 2.34 | 17.3 | 309.5 | 6.2 | 1.0 |
| 3 | 0.0127 | 1.92 | 22.2 | 311.3 | 7.6 | 0.9 |
| 4 | 0.0293 | 1.76 | 13.8 | 306.7 | 4.1 | 4.2 |
| 5 | 0.0153 | 1.50 | 15.2 | 309.8 | 6.6 | 2.1 |
| 6 | 0.0273 | 2.92 | 11.7 | 307.0 | 4.3 | 1.9 |
| 7 | 0.0140 | 2.66 | 5.4 | 310.5 | 7.0 | 0.8 |
| 8 | 0.0207 | 1.66 | 20.8 | 308.2 | 5.2 | 2.4 |
| 9 | 0.0160 | 3.16 | 14.5 | 309.8 | 6.2 | 0.7 |
| 10 | 0.0193 | 2.00 | 4.0 | 308.5 | 5.6 | 2.3 |
| 11 | 0.0187 | 2.50 | 24.3 | 308.8 | 5.6 | 1.1 |
| 12 | 0.0280 | 3.84 | 7.5 | 306.9 | 4.2 | 1.7 |
| 13 | 0.0120 | 2.84 | 21.5 | 311.8 | 7.7 | 0.5 |
| 14 | 0.0287 | 3.58 | 16.6 | 307.0 | 4.1 | 1.6 |
| 15 | 0.0147 | 4.00 | 11.0 | 310.6 | 6.8 | 0.5 |
| 16 | 0.0213 | 1.58 | 10.3 | 308.0 | 5.1 | 3.3 |
| 17 | 0.0220 | 3.66 | 12.4 | 308.1 | 5.0 | 1.1 |
| 18 | 0.0113 | 3.76 | 18.7 | 312.5 | 8.0 | 0.3 |
| 19 | 0.0173 | 3.50 | 22.9 | 309.4 | 5.9 | 0.7 |
| 20 | 0.0240 | 2.26 | 15.9 | 307.5 | 4.7 | 1.9 |
| 21 | 0.0300 | 2.76 | 19.4 | 306.7 | 4.0 | 2.1 |
| 22 | 0.0200 | 2.58 | 9.6 | 308.4 | 5.4 | 1.3 |
| 23 | 0.0227 | 3.08 | 18.0 | 307.9 | 4.9 | 1.2 |
| 24 | 0.0267 | 2.08 | 6.8 | 307.0 | 4.3 | 3.1 |
| 25 | 0.0247 | 3.00 | 4.7 | 307.4 | 4.6 | 1.8 |
| 26 | 0.0180 | 3.42 | 6.1 | 309.0 | 5.8 | 0.9 |
| 27 | 0.0107 | 2.42 | 13.1 | 312.7 | 8.4 | 0.5 |
| 28 | 0.0253 | 3.26 | 25.0 | 307.5 | 4.5 | 1.4 |
| 29 | 0.0133 | 1.84 | 8.2 | 310.8 | 7.3 | 1.3 |
| 30 | 0.0233 | 3.92 | 20.1 | 307.9 | 4.8 | 1.1 |
| 31 | 0.0100 | 3.34 | 8.9 | 313.3 | 8.7 | 0.3 |
4.3 Sensitivity and Correlation Analysis
I conducted sensitivity analysis to quantify the contribution of each input parameter’s uncertainty to the uncertainty of the system output responses. The sensitivity index was calculated using the following formula:
$$SA_i = \frac{f_{max}(x_i) – f_{min}(x_i)}{f_{max}(x) – f_{min}(x)} \times 100\%$$
My sensitivity analysis results revealed that among the variables affecting Tmax and ΔT, the coolant mass flow rate was confirmed as the absolutely dominant operating parameter. The sensitivity values of Tmax and ΔT to mass flow rate were 0.996 and 0.988, respectively. For the pressure drop that determines system energy consumption, the channel height demonstrated a sensitivity of 0.442, as its adjustment directly and significantly changes the effective flow cross-sectional area. The pin-fin spacing exhibited minimal influence on pressure drop with a sensitivity of only 0.028.
Through Pearson correlation coefficient analysis, I found that ΔP showed correlation coefficients of -0.70 and -0.67 with Tmax and ΔT, respectively, indicating significant negative correlations. Notably, the correlation coefficient between Tmax and ΔT was 0.99, demonstrating a strong positive correlation. Consequently, I excluded Tmax from the optimization objectives and retained ΔT and ΔP as the final optimization targets to improve optimization efficiency.
4.4 Kriging Surrogate Model
I employed the Kriging surrogate model, which exhibits high fitting accuracy and strong robustness characteristics. The coefficient of determination for evaluating model accuracy is expressed as:
$$R^2 = 1 – \frac{\sum_{i=1}^{n} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i – \bar{y}_i)^2}$$
The cross-validation results demonstrated that the coefficients of determination for ΔP and ΔT were 0.952 and 0.966, respectively, both exceeding the 0.9 threshold and satisfying the application requirements.
4.5 NSGA-II Multi-Objective Optimization
I utilized the Non-dominated Sorting Genetic Algorithm II (NSGA-II) as my optimization algorithm, which is recognized as one of the most widely applied algorithms in the field of multi-objective optimization. The algorithm efficiently identifies and preserves Pareto-optimal solutions through fast non-dominated sorting and elitism preservation strategies. I set the population size and number of generations to 120 and 50, respectively, generating 6000 solutions.
The optimization results revealed a negative correlation between ΔT and ΔP. Notably, when ΔT was maintained at a relatively low level, ΔP could be significantly reduced with only modest sacrifices in ΔT. I selected three optimization models from the Pareto frontier solutions based on their comprehensive evaluation results. The comparison and validation of the optimization results are presented in the following table:
| Model | A (kg/s) | B (mm) | C (mm) | Tmax (K) | ΔT (K) | Error (%) | Improvement (%) | ΔP (kPa) | Error (%) | Improvement (%) |
|---|---|---|---|---|---|---|---|---|---|---|
| Baseline | 0.0200 | 1.50 | 15 | 308.3 | 5.40 | / | / | 3.10 | / | / |
| CFD-1 | 0.0253 | 3.66 | 22 | 307.5 | 4.51 | 0.9% | 16.5% | 1.27 | 1.6% | 59.0% |
| CFD-2 | 0.0285 | 3.14 | 19 | 306.9 | 4.15 | 3.1% | 23.1% | 1.76 | 0.6% | 43.2% |
| CFD-3 | 0.0294 | 2.52 | 18 | 306.7 | 4.07 | 3.4% | 24.6% | 2.30 | 1.7% | 25.8% |
Comprehensively considering heat dissipation performance and cold plate energy consumption, I identified optimization model 2 as the optimal compromise solution. This model demonstrated a 23.1% improvement in temperature uniformity and a 43.2% reduction in pressure drop compared to the baseline model. The corresponding mass flow rate was adjusted to 0.0285 kg/s, channel height increased to 3.14 mm, and pin-fin spacing set to 19 mm.
4.6 Thermal Resistance Analysis
I analyzed the thermal resistance of the optimized cold plate design as a crucial evaluation parameter. The total thermal resistance was decomposed into three components: convective thermal resistance, enthalpy change thermal resistance, and conductive thermal resistance. These components are calculated as follows:
$$R_{conv} = \frac{T_{ave} – T_{liq}}{q}$$
$$R_{heat} = \frac{T_{out} – T_{in}}{q}$$
$$R_{cond} = \frac{L_b}{k_s \cdot A_{cont}}$$
$$R_{total} = R_{conv} + R_{heat} + R_{cond}$$
My results demonstrated that the optimized circular pin-fin cold plate significantly reduced the total thermal resistance compared to the straight channel cold plate, with reductions of 14% and 16% at mass flow rates of 0.02 and 0.03 kg/s, respectively. These improvements were primarily attributed to the significantly lower convective thermal resistance, while the differences in enthalpy change and conductive thermal resistance were negligible.
4.7 Effective Heat Transfer Enhancement Factor
The effective heat transfer enhancement factor is a crucial indicator for evaluating the comprehensive performance of enhanced heat transfer techniques. I employed this factor to assess the balance between heat transfer enhancement and flow resistance penalty:
$$p_f = \frac{Nu/Nu_0}{(\Delta P / \Delta P_0)^{1/3}}$$
The Nusselt number is defined as follows:
$$Nu = \frac{h_{ave} D_h}{k_{liq}}$$
My analysis revealed that the optimized circular pin-fin cold plate exhibited the highest Nusselt number (Nu) and effective heat transfer enhancement factor (pf) values among all configurations at the same mass flow rate. At a mass flow rate of 0.02 kg/s, the Nu was more than 6 times higher than that of the straight channel, with the pf improved by 7 times. Compared to the baseline model, the Nu increased by 33.9% and the pf increased by 97.5%. At 0.03 kg/s, the Nu increased by 43.7% and the pf increased by 87.7% compared to the original circular pin-fin configuration.
4.8 Cooling Efficiency Factor
I introduced the cooling efficiency factor to evaluate the comprehensive energy efficiency of the cooling system. This factor is calculated using the following formulas:
$$Q(t)_{liq} = c \cdot m \cdot \Delta T$$
$$Q(t)_{cell} = \int_{t_0}^{t_1} I^2 R(t) dt$$
$$\eta = \frac{Q(t)_{liq} / t}{\Delta P \cdot q_v}$$
My results demonstrated that the optimized circular pin-fin cold plate significantly improved the cooling efficiency factor. At a mass flow rate of 0.02 kg/s, the maximum cooling efficiency factor reached 15,452, while maintaining the lowest pressure drop. In comparison, the baseline circular pin-fin configuration achieved a maximum cooling efficiency factor of only 4,875 at the same flow rate, while the straight channel achieved 7,250. Although all configurations showed a decrease in cooling efficiency factor with increasing flow rate, the optimized model maintained the highest values throughout, confirming its superior comprehensive thermal-hydraulic performance.
5. Experimental Study on the Thermal Performance of Circular Pin-Fin Channel Cold Plate
5.1 Channel Height Optimization
Before proceeding to the experimental study, I investigated the influence of channel height on the thermo-hydraulic performance of the cold plate. The channel height directly affects the cold plate thickness during manufacturing, and excessive channel heights would increase the space occupied by the thermal management system in the electric vehicle battery pack. My analysis revealed that at a mass flow rate of 0.0285 kg/s, the maximum battery temperature gradually increased with increasing channel height, with an overall variation of only 0.3 K. Meanwhile, the pressure drop decreased as the channel height increased. Notably, when the channel height increased from 1 mm to 1.5 mm, the pressure drop decreased by 7.7 kPa, representing a 59.2% reduction. However, further increases in channel height resulted in diminishing pressure drop reductions.
Based on this comprehensive analysis, I determined that the channel height of 1.5 mm exhibited superior thermo-hydraulic performance while maintaining structural compactness. Therefore, I selected this channel height for the circular pin-fin channel design, designated as C-Pin-fin (BCS), for manufacturing and subsequent experimental investigations.
5.2 Experimental Model Fabrication
For the fabrication of the cold plate, I evaluated two manufacturing approaches: subtractive manufacturing utilizing CNC milling, and additive manufacturing based on selective laser melting. After comprehensive consideration of the large dimensions, manufacturing cost, surface quality requirements, and processing precision, I selected subtractive manufacturing using CNC machining. The C-Pin-fin (BCS) cold plate dimensions are presented in the following table:
| Component | Length×Width×Height (mm) | Inlet/Outlet Diameter (mm) | Channel Height (mm) | Pin-Fin Spacing (mm) | Pin-Fin Diameter (mm) |
|---|---|---|---|---|---|
| C-Pin-fin (BCS) | 732×191×12 | 6 | 1.5 | 19 | 3 |
To conserve experimental resources, I employed four heating films to replace the actual battery cells as heat sources for the cold plate experiments. The heating film dimensions were 150 mm × 116 mm each, uniformly attached to the cold plate surface. I used automotive antifreeze (50% ethylene glycol aqueous solution) as the coolant and conducted a series of thermo-hydraulic performance tests.
5.3 Experimental Platform and Procedure
I constructed a closed-loop experimental platform to investigate the flow and heat transfer characteristics of the circular pin-fin channel cold plate. The experimental system consisted of a constant temperature water bath with storage tank, gear pump, filter, mass flow meter, pressure transmitters, heating films, DC power supply, infrared thermal imager, data acquisition system, and computer. The accuracies and ranges of the main experimental equipment are summarized as follows:
| Equipment | Accuracy/Range |
|---|---|
| Multi-channel DC power supply | 0-200 W |
| Infrared thermal imager | ±2% (-20-2000 °C) |
| Liquid turbine flow meter | ±0.5% (0-10 L/min) |
| Constant temperature water bath | ±0.75% (-20-100 °C) |
| Temperature sensor | ±1% (-100-280 °C) |
| Inlet pressure transmitter | ±0.5% (0-500 kPa) |
| Outlet pressure transmitter | ±0.5% (0-130 kPa) |
The flow resistance experiment involved measuring the pressure drop across the cold plate as a function of flow rate without energizing the heating films. I regulated the coolant flow rate to predetermined setpoints and recorded pressure data after stabilization was achieved. For the heat transfer performance experiment, I set the heating film input power levels to 200 W, 280 W, 360 W, and 440 W in sequence, and at each power level, adjusted the coolant flow rate through the preset operating points. Thermal equilibrium was considered achieved when the temperature fluctuation remained below 0.5 K for five consecutive minutes.
5.4 Uncertainty Analysis
To ensure the scientific rigor and methodological soundness of my research, I conducted a systematic uncertainty analysis. The relative uncertainties of the directly measured parameters are calculated as follows. For the T-type thermocouples with a measurement error of 0.5 °C and the lowest measured liquid temperature of 20 °C:
$$\xi_{T_{in}} = \xi_{T_{out}} = \frac{0.5}{20} \times 100\% = 2.5\%$$
For the pressure transmitters with different ranges used at the inlet and outlet:
$$\xi_{P_{in}} = \frac{500}{103.2} \times 0.5\% = 2.4\%$$
$$\xi_{P_{out}} = \frac{130}{102.3} \times 0.5\% = 0.6\%$$
Based on the error propagation theory, the relative uncertainties of the derived parameters were calculated using:
$$\delta R = \sqrt{\sum_{i} \left(\frac{\partial R}{\partial v_i} \delta v_i\right)^2}$$
$$\xi_R = \frac{\delta R}{R}$$
The maximum relative errors of the experimental parameters are summarized in the following table:
| Experimental Parameter | Maximum Relative Error |
|---|---|
| Inlet pressure Pin | 2.4% |
| Outlet pressure Pout | 0.6% |
| Volumetric flow rate V | 2.5% |
| Mass flow rate m | 2.5% |
| Inlet/outlet water temperature Tin, Tout | 1.6% |
| Pressure drop ΔP | 2.5% |
| Heating film heat flux q | 3.1% |
| Thermal resistance R | 3.6% |
5.5 Experimental Results and Discussion
My experimental results on the pressure drop characteristics revealed that the pressure drop showed a continuously increasing trend with increasing flow rate, with distinctly different growth rates in different flow rate ranges. In the low flow rate region, the boundary layers were thicker with good flow attachment around the pin-fins, and the flow loss was primarily attributed to surface friction, resulting in a gentle pressure drop rise. As the flow rate increased to the medium range, inertial effects strengthened, with expanding wake regions behind the pin-fins and initial flow separation phenomena, causing faster pressure drop growth. At high flow rates, inertial effects completely dominated the flow, with dramatic expansion of wake regions and intensified turbulent mixing, leading to rapid pressure drop increases accompanied by potentially periodic vortex shedding.
In the heat transfer performance experiments, I observed from the infrared thermal imaging that the heating film surface temperature exhibited a progressively increasing trend along the coolant flow direction. This phenomenon was attributed to the coolant absorbing heat as it flowed through the cold plate channels, causing its temperature to gradually increase along the flow path. At the coolant inlet region, the fluid temperature was lower, creating a larger temperature difference with the heating film and resulting in stronger heat transfer driving potential. Consequently, the heating film temperature was relatively low in this region. As the coolant absorbed heat along the flow direction, the temperature difference between the fluid and wall gradually decreased, leading to reduced local heat transfer capability and progressively higher heating film temperatures downstream.
My analysis of the heating film temperature variations with heat flux at different flow rates revealed that at constant volume flow rates, the heating film temperature increased with increasing heat flux. This occurred because the greater heat flux generated more resistive heat in the heating film while the coolant’s heat removal capacity remained relatively fixed. Conversely, at constant heat flux, the heating film temperature decreased with increasing flow rate, as the enhanced flow velocity increased the convective heat transfer coefficient, enabling more effective heat removal.
The comparison between Heater1 and Heater2 temperatures demonstrated that Heater2, which was closer to the cold plate inlet region, consistently exhibited lower temperatures than Heater1 located downstream. This temperature difference was attributed to the entrance effect, where the thermal boundary layer had not yet fully developed near the inlet, resulting in thinner boundary layers and higher local convective heat transfer coefficients.
The thermal resistance and pump power analysis revealed that as the coolant flow rate increased, the pump power exhibited exponential growth due to the combined effects of increased flow rate and pressure drop. Simultaneously, the thermal resistance of the cold plate decreased as the enhanced flow disturbance increased the convective heat transfer coefficient and thinned the thermal boundary layer. Furthermore, the thermal resistance showed a decreasing trend with increasing heating film power, although the decreasing rate gradually diminished due to the saturation of thermophysical property changes and heat transfer enhancement effects. This pattern suggests that in practical applications, a comprehensive trade-off between pump power consumption and thermal resistance should be considered to avoid excessive energy penalty for marginal thermal resistance improvements.
6. Conclusions
In this study, I conducted a comprehensive investigation into the single-phase flow and heat transfer characteristics of pin-fin channel cold plates for electric vehicle battery thermal management systems using a combination of numerical simulation, multi-objective optimization, and experimental validation. My main conclusions are as follows:
(1) All pin-fin channel cold plates demonstrated superior heat dissipation performance compared to the straight channel, with the circular pin-fin configuration achieving the optimal balance between heat transfer performance and energy consumption. At a mass flow rate of 0.03 kg/s, the circular pin-fin configuration reduced the maximum temperature by 2.9 K and the temperature difference by 0.7 K compared to the straight channel. The heat transfer enhancement mechanism analysis revealed that the pin-fin structures induce periodic flow disturbances, disrupt thermal boundary layer development, and generate vortices and flow separation, with the circular pin-fins forming regular ring-shaped vortex structures that achieve efficient utilization of turbulent kinetic energy.
(2) My multi-objective optimization approach, combining the Kriging surrogate model with the NSGA-II algorithm, successfully identified optimal design parameters. The sensitivity analysis showed that mass flow rate dominated temperature control (sensitivity of 0.996 for Tmax) while channel height dominated pressure drop (sensitivity of 44.2%). The optimized circular pin-fin cold plate with a mass flow rate of 0.0285 kg/s, channel height of 3.14 mm, and pin-fin spacing of 19 mm achieved a 23.1% improvement in temperature uniformity and a 43.2% reduction in pressure drop compared to the baseline model.
(3) The comprehensive performance evaluation confirmed the superiority of the optimized design. The optimized model achieved a thermal resistance reduction of 14-16% compared to the straight channel, a 6-fold improvement in Nusselt number, and a 7-fold improvement in effective heat transfer enhancement factor at 0.02 kg/s. The cooling efficiency factor reached 15,452, significantly higher than both the baseline model (4,875) and straight channel (7,250), demonstrating efficient heat transfer at minimal energy cost.
(4) The experimental study validated the numerical model accuracy with pressure drop prediction errors within 8% and average temperature errors within 1.2 K. The channel height of 1.5 mm was identified as the optimal parameter balancing performance and structural compactness, achieving a 59.2% pressure drop reduction compared to the 1 mm design with negligible temperature variation. The experimental results confirmed that heating film temperature and thermal resistance decreased with increasing coolant flow rate, while the cooling efficiency factor exhibited complex behavior reflecting the need for balanced optimization between thermal performance and energy consumption in practical electric vehicle battery thermal management applications. These findings provide valuable insights and reference for the design of high-efficiency liquid cooling systems for electric vehicle battery packs and contribute to the advancement of battery thermal management technology for next-generation electric vehicles.