Multi-Objective Optimization of Thermal and Mechanical Performance of Prismatic Aluminum Shell Lithium Battery Module with Integrated Biomimetic Liquid Cooling Plate

Abstract

Addressing the thermal management challenges of prismatic aluminum shell lithium battery modules in electric vehicles under high-rate charge–discharge conditions, this study proposes a multi-objective optimization design method for integrated biomimetic liquid cooling plates. By integrating various highly efficient heat transfer structures from nature, including fractal-tree-like networks, leaf vein branching systems, and spider web radial distribution, a novel biomimetic liquid cooling plate topology was constructed. A multi-physics coupled numerical model considering electrochemical heat generation, thermal conduction, convective heat transfer, and thermal stress deformation was established. The NSGA-II algorithm was employed to globally optimize 12 design variables including channel geometric parameters, operating conditions, and structural dimensions, achieving collaborative optimization objectives of maximum temperature minimization, temperature uniformity maximization, pressure drop minimization, and structural lightweighting. The weight coefficients for the four optimization objectives were determined through the Analytic Hierarchy Process (AHP) with verified consistency (CR = 0.02 < 0.10), ensuring rational priority allocation aligned with automotive safety standards. The optimization results demonstrated that compared to the initial design, the optimal solution reduced the maximum temperature under 3C discharge conditions by 9.9% to 34.7 °C, decreased the temperature difference by 31.3% to 3.3 °C, lowered the pressure drop by 24.6% to 2150 Pa, reduced structural mass by 4.0%, and decreased maximum stress by 16.7%. Quantitative comparison with single biomimetic structures under identical boundary conditions showed that the integrated design achieved a 3.3% lower maximum temperature and 25.7% better flow uniformity than the best-performing single structure, demonstrating the synergistic advantages of multi-biomimetic integration. These synergistic performance improvements can be attributed to the hierarchical multi-scale architecture where fractal networks provide macro-scale flow distribution, leaf vein branches ensure meso-scale coverage, and spider web radials achieve micro-scale thermal matching. Long-term cycling tests conducted at 1C/1C rate with 25 ± 1 °C ambient temperature showed that the optimized design maintained a capacity retention rate of 92.3% after 1000 charge–discharge cycles, demonstrating excellent durability. The complex biomimetic channel structure can be fabricated using selective laser melting technology with minimum feature sizes below 0.3 mm, indicating promising manufacturing feasibility. The research findings provide theoretical guidance and technical support for the engineering design of high-performance battery thermal management systems.

1. Introduction

With the rapid development of the global electric vehicle industry and the deepening promotion of “dual carbon” goals, lithium-ion batteries, as the core power source of electric vehicles, have become a key technical bottleneck restricting battery pack performance improvement and safe operation. Especially under high-rate charge–discharge conditions, a sharp increase in battery heat generation leads to uneven temperature distribution. When the temperature exceeds the optimal operating range (15–40 °C, with a preferred range of 25–35 °C for optimal performance) or the temperature difference exceeds 5 °C, this not only accelerates battery capacity degradation and cycle life reduction, but may also trigger safety accidents such as thermal runaway in severe cases [1]. Therefore, developing efficient, lightweight battery thermal management systems with excellent thermal–mechanical performance is of great significance for promoting the sustainable development of the new energy vehicle industry.

In recent years, liquid cooling technology has become the mainstream technical approach in the field of battery thermal management due to its excellent heat transfer performance. Research shows that hybrid thermal management systems combining nano-doped phase change materials with liquid cooling can reduce the maximum temperature of cylindrical lithium batteries under 3C discharge rate by 10.35 °C [2]. Cooling plate structures designed based on biomimetic principles show tremendous potential in thermal management performance. The biomimetic cooling plate based on plantain leaf vein channels developed by Tang et al. can reduce pressure drop by 43.55% compared to traditional designs while controlling the maximum temperature below 31.75 °C under 3C discharge conditions [3]. Additionally, multi-objective optimization methods play a key role in balancing thermal and mechanical performance. Dong et al. employed the NSGA-II algorithm combined with response surface methodology to optimize biomimetic lotus leaf channels, achieving comprehensive performance improvements including a 14.898% reduction in maximum temperature difference, 35.786% increase in heat transfer coefficient, and 68.325% reduction in pressure drop [4]. For prismatic aluminum shell battery modules, Park et al. successfully reduced the maximum temperature difference by 14.48% through surrogate model optimization of indirect liquid cooling systems [5].

Recent studies in 2024–2025 have further advanced biomimetic thermal management specifically for prismatic batteries. An et al. proposed a hybrid battery thermal management system with dual bionic cold plates inspired by natural nasturtium veins and honeycomb structures for prismatic lithium batteries under harsh operating conditions [6]. At a discharge rate of 3C and ambient temperature of 40 °C, the system maintained the maximum temperature below 50 °C with a temperature difference of less than 5 °C. Saber et al. presented a comprehensive review of thermal management techniques for prismatic Li-ion batteries, emphasizing that 80% of real-world BTMS samples employ liquid cooling, while emerging technologies such as PCM and hybrid systems offer superior thermal regulation in high-power applications [7]. Furthermore, Banerjee and Nidhu investigated immersion cooling designs with V-shaped fins for high-discharge prismatic cells, achieving maximum temperature reductions of 5K and 9K at 3C and 5C discharge rates, respectively, compared to no-fin configurations [8]. These recent advances demonstrate the growing research focus on prismatic battery thermal management and the effectiveness of biomimetic design approaches.

However, existing research mostly focuses on optimization of single performance indicators or design of specific cooling plate structures, lacking systematic research on collaborative optimization of thermal and mechanical performance for prismatic aluminum shell lithium battery modules with integrated biomimetic liquid cooling plates.

Based on the above research status, this paper proposes a multi-objective optimization design method for prismatic aluminum shell lithium battery modules with integrated biomimetic liquid cooling plates. By constructing a novel liquid cooling plate topology that integrates multiple biomimetic structural features such as fractals, leaf veins, and spider webs, establishing a high-precision simulation model considering thermal–force–flow multi-physics coupling, and employing the NSGA-II algorithm to globally optimize key design variables, including cooling plate channel geometric parameters, coolant flow rate, and inlet temperature, the study aims to simultaneously achieve multi-objective collaboration of maximum temperature minimization, temperature uniformity maximization, pressure drop minimization, and structural lightweighting. The TOPSIS decision-making method is introduced to select the optimal design solution from the Pareto optimal solution set that meets different application scenario requirements. It is expected to control the maximum temperature difference in the battery module within 3.5 °C and achieve a significant pressure drop reduction of 20–30% compared to conventional designs, while improving module structural reliability by more than 15%.

2. Literature Review and Theoretical Foundation

2.1. Research Status of Lithium Battery Module Thermal Management Technology

The heat generation mechanism of lithium-ion batteries during charge–discharge processes includes the following two main parts: reversible entropy change heat generation and irreversible Joule heat. The irreversible heat originates from I²R losses produced by ohmic internal resistance and polarization internal resistance. The heat generation rate increases significantly with a rising discharge rate and ambient temperature. When the battery temperature exceeds the optimal operating range of 15–40 °C or temperature difference exceeds 5 °C, this accelerates capacity degradation and triggers safety hazards [1].

To provide a comprehensive overview of current thermal management technologies,

Table 1. Comparative analysis of different cooling technologies for lithium-ion battery thermal management.

Cooling Technology	Heat Transfer Coefficient (W/m2K)	Temperature Control Range (°C)	Typical Pressure Drop (Pa)	System Complexity	Weight Penalty	Primary Applications
Air cooling	20–100	35–50	<500	Low	Low	Low-power EVs, short-distance driving
Single-phase liquid cooling	500–3000	25–40	1000–5000	Medium	Medium	High-power EVs, mainstream solution
Two-phase immersion cooling	2000–8000	25–35	N/A	High	High	Ultra-fast charging, racing EVs
PCM cooling	50–200 (effective)	30–45	N/A	Low	Medium–High	Thermal buffering, passive systems
Heat pipe cooling	1000–5000	28–38	N/A	Medium	Low	Hybrid systems, localized cooling
Hybrid (Liquid + PCM)	800–2500	25–35	1000–3000	High	High	Premium EVs, extreme conditions

presents a comparative analysis of different cooling approaches for lithium-ion battery systems. As shown in Table 1, each cooling technology has distinct advantages and limitations in terms of heat transfer capability, system complexity, and application scenarios.

Comparative analysis of nine commercial electric vehicle thermal management systems by Maiorino et al. shows that liquid cooling systems have become the dominant technical approach for high-power applications, while air cooling is only suitable for short-distance driving and low-thermal-load conditions [9]. Chen et al. developed a bidirectional symmetrical parallel mini-channel cold plate (PMCP) for large battery packs, demonstrating that the optimized design reduced the average temperature difference and pumping power by at least 76% and 81%, respectively, compared to conventional configurations [10]. The systematic review by Bahrami et al. emphasizes that single cooling methods increasingly struggle to meet the thermal management needs of high-energy-density battery packs, driving the shift toward hybrid active–passive cooling architectures [11]. Based on the comparative analysis in Table 1, liquid cooling technology offers the optimal balance between heat transfer performance, system complexity, and cost-effectiveness for high-power electric vehicle applications, which forms the foundation of the thermal management approach adopted in this study.

2.2. Design Principles and Application Progress of Biomimetic Liquid Cooling Plates

Biomimetic principles provide revolutionary ideas for cooling plate channel design by mimicking heat and mass transfer structures optimized through billions of years of evolution in nature to enhance cooling performance. The leaf-vein-shaped cooling plate based on topology optimization by Wu et al. reduced the maximum temperature by 0.5–1.4 °C and pressure drop by 92.76% compared to S-shaped and uniform topology cooling plates [12]. Fan et al. found in their fishbone-shaped biomimetic channel research for large-capacity battery packs at a 6C discharge rate that symmetrical fishbone channels combined with a single-inlet dual-outlet design reduced the maximum temperature and temperature difference by 24.16% compared to Z-type straight channels [13]. Spider web structures demonstrate unique advantages in thermal management. The biomimetic spider web channel by Yao et al. controlled the maximum temperature at 29.1 °C with a maximum temperature difference of only 3.8 °C at a 40 °C ambient temperature and 3C discharge rate [14]. Yang et al. developed a honeycomb thermal management system that integrated phase change materials through hexagonal cooling plates and spider-web-inspired microchannels, maintaining battery temperature below 309.15 K while controlling the temperature difference within 3.8K with a pressure drop of only 157.1 Pa [15]. The application of fractal structures further expanded the biomimetic design space. Tang et al.’s fractal cooling plate controlled the maximum temperature and temperature difference within 31.68 °C and 4.15 °C, respectively, at a 4C discharge rate [16]. Wei et al.’s alveolar biomimetic design inspired by biological tissues achieved 0.11% temperature uniformity and a maximum temperature difference of only 1.27 °C through fractal channels and spiral baffles [17]. An et al.’s double-layer leaf vein channel design enabled uniform coolant distribution in the cooling plate, providing a better cooling effect and lower power consumption [18].

While existing biomimetic designs have achieved remarkable performance improvements, each single-structure approach has inherent limitations. Leaf vein designs excel in flow distribution but show moderate pressure drop reduction. Spider web structures provide excellent temperature uniformity but limited heat transfer enhancement at channel intersections. Fractal tree designs offer good scalability but face challenges in covering peripheral regions uniformly. Specifically, compared to An et al.’s double-layer leaf vein design [18] which achieved uniform coolant distribution through parallel vein patterns in a planar configuration, the proposed integrated design in this study differs fundamentally in its hierarchical multi-scale approach. The key distinctions include (1) three-level fractal tree networks following Murray’s law for macro-scale flow management, rather than single-level parallel channels; (2) leaf vein secondary branches integrated with and extending from the fractal system for meso-scale coverage enhancement, rather than a standalone double-layer configuration; and (3) spider web radial distribution creating localized cooling intensification in high-heat-flux zones directly beneath battery cells, a feature absent in pure leaf vein designs. This integration strategy addresses the fundamental limitation that no single biomimetic structure can simultaneously optimize flow distribution uniformity, heat exchange surface coverage, and localized heat transfer enhancement. This synergistic combination enables each biomimetic feature to compensate for the weaknesses of others while amplifying their respective strengths.

2.3. Review of Battery Module Mechanical Performance Research

The mechanical performance of battery modules is directly related to vehicle collision safety and structural reliability. Liquid cooling plates not only undertake thermal management functions, but also need to provide structural support and vibration buffering. The hybrid system of modular liquid cooling plates and negative-Poisson’s-ratio structural laminates developed by Xu et al. enhanced mechanical protection capability while providing thermal management functions. The modular design reduced the coolant heating effect by more than 50%, and the alternating cooling strategy reduced energy consumption by 50% [19]. Aluminum alloy has become the main material for prismatic battery shells and cooling plates due to its excellent thermal conductivity (200–240 W/m·K), lightweight characteristics (density approximately 2700 kg/m³), and good machinability. Morali studied the impact of phase change material thickness on the performance of prismatic lithium-ion battery thermal management systems, finding that appropriate PCM thickness can improve temperature uniformity without significantly increasing system weight [20]. Thermal–mechanical coupling effects are crucial in battery module design. Thermal stress induced by temperature gradients leads to battery expansion deformation and increased contact thermal resistance, thereby affecting heat dissipation performance and forming a vicious cycle. The review by Fayaz et al. points out that most existing research considers thermal design and structural design separately, lacking systematic coupled optimization methods [21]. Therefore, it is necessary to consider both thermal performance and structural strength requirements in optimization design.

2.4. Application of Multi-Objective Optimization Methods in Battery Systems

Multi-objective optimization has become a key method for balancing multiple performance indicators of battery thermal management systems. The NSGA-II algorithm occupies a dominant position in this field due to its excellent global search capability and Pareto frontier generation efficiency. Kumar et al. combined multilayer perceptron neural networks with the cheetah optimizer, gray wolf optimizer, and marine predator algorithm, obtaining optimization solutions with prediction accuracy of R > 0.9999 through the multi-objective salp swarm algorithm and achieving a comprehensive performance with a maximum temperature of 32.3–38 °C, temperature difference of 3.7–5.1 °C, and pressure drop of 15–50 Pa [22]. The combination of the response surface method with NSGA-II significantly improved optimization efficiency. Deng et al. established a validated optimization method using the NSGA-II algorithm for liquid cooling systems, achieving minimization of the maximum temperature and pressure drop while maintaining temperature uniformity [23]. Zhou et al.’s Gaussian process-based surrogate model-assisted design achieved 126% energy efficiency improvement while maintaining battery temperature below 28.4 °C and coolant pressure drop below 3.6 kPa [24]. The latest 2025 heat-pipe-assisted liquid cooling structure optimization research employed orthogonal experiments to identify key parameters, established a Kriging surrogate model, and used NSGA-II combined with the entropy weight TOPSIS method to select the optimal solution from the Pareto frontier [25]. Wang et al. optimized thermal modeling parameters through the particle swarm optimization algorithm combined with the COMSOL numerical model, introducing correction factors related to state of charge to reduce prediction errors to an average of below 0.5 °C [26]. Sun and Peng employed NSGA-II to optimize the vehicle energy storage battery liquid cooling heat dissipation structure, reducing material degradation rate by 42% and corrosion rate by 36% and increasing battery life by 17%, while controlling temperature difference within 5 °C [27]. Ye et al. combined BP neural network prediction with the NSGA-II algorithm, generating Pareto solution sets balancing cooling efficiency and economic performance by optimizing battery spacing, cooling pipe diameter, and inlet velocity [26].

In the present study, the NSGA-II algorithm is employed with specific configurations tailored for the biomimetic cooling plate optimization problem. The algorithm implementation adopts the following key parameters: population size of 100 individuals to ensure adequate diversity in the search space; maximum evolution of 500 generations to guarantee convergence; crossover probability of 0.9 using a simulated binary crossover (SBX) operator with distribution index of 20; and mutation probability of 0.1 using polynomial mutation to maintain exploration capability. An adaptive parameter adjustment strategy is implemented whereby mutation probability is automatically increased to 0.15 when the hypervolume improvement rate falls below 1% for 20 consecutive generations, enhancing global search capability during stagnation periods. The algorithm simultaneously handles 12 design variables organized into the following three categories: channel geometric parameters (main pipe diameter, first-level and second-level branch diameters, branch angle, micro-rib height, and micro-rib spacing), operating conditions (coolant flow rate and inlet temperature), and structural parameters (cooling plate thickness, channel depth, number of annular channels, and number of radial channels). A radial basis function (RBF) neural network surrogate model is constructed using 150 Latin hypercube sampling points to reduce computational cost during optimization iterations, with cross-validation confirming prediction accuracy of R² = 0.976. Detailed implementation procedures, convergence analysis, and Pareto frontier characteristics are presented in Section 4.3.

2.5. Research Gaps and Paper Positioning

Comprehensive analysis of existing research reveals that although liquid cooling technology and biomimetic design have achieved significant progress in the battery thermal management field, the following key issues remain to be addressed: Existing biomimetic cooling plate designs mostly focus on mimicking single biological structures, lacking systematic integration research of multiple biomimetic features. The review by Sarvar-Ardeh et al. points out that the application potential of microchannels and small channels in battery thermal management has not been fully exploited [28]. Multi-objective optimization research often focuses on thermal performance indicators, with insufficient attention to collaborative optimization of thermal–mechanical performance. Systematic reviews of design optimization methodologies indicate that most of the literature only focuses on optimization of structural BTMS components [29]. Specialized design research for prismatic aluminum shell battery modules is relatively scarce, not fully utilizing the optimization space brought by their standardized packaging. The latest review of prismatic lithium-ion battery thermal management technology by Saber et al. emphasizes the importance of this research direction [6]. Experimental verification mostly concentrates on ideal working conditions, lacking long-term performance evaluation under real driving cycles. Although the fast-charging thermal analysis of 65 Ah pouch batteries by Adeniran and Park provided experimental validation, it was still limited to specific charging conditions [30]. Additionally, although Mousavi et al. studied hybrid thermal management systems for prismatic batteries, reducing maximum temperature by 16.2 K and pump power by 68%, they did not consider mechanical performance optimization [31]. Kong et al.’s cylindrical battery hybrid thermal management system improved energy density by 13.75% through NSGA-II optimization, but lacked applicability research for prismatic batteries [32]. An et al. optimized the leaf vein structure through NSGA-II, reducing maximum temperature by 0.71 °C under extreme conditions compared to traditional design, but optimization was limited to a single biomimetic structure [33]. Lu et al.’s experimental research on oscillating heat pipe and liquid cooling integration demonstrated that pulsating flow improves OHP stability through periodic enhanced thermal loads, with optimal stability achieved at 38% or 62% duty cycles and 0.03–0.05 Hz frequencies [34]. Their subsequent study found that the hybrid system reduced equivalent thermal resistance by 8.06% and maximum temperature difference by 19.1% [35]. The latest delayed cooling strategy research reduced pumping energy consumption by 73% but did not consider long-term cycling performance [35].

To more intuitively highlight the original contributions of this study,

Table 2. Performance comparison of different biomimetic cooling plate designs under comparable conditions.

Design Type	Maximum Temperature (°C)	Temperature Difference (°C)	Pressure Drop Reduction vs. Traditional (%)	Heat Transfer Enhancement (%)	Reference
Traditional serpentine channel	38.2–42.0	5.0–6.5	Baseline	Baseline	[2]
Single leaf vein channel	35.5–37.0	4.0–4.8	40–50	12–18	[12,18]
Single fishbone channel	36.5–38.0	4.2–5.0	25–35	15–24	[13]
Single spider web channel	29.1–32.0	3.5–4.5	30–40	10–15	[14]
Single fractal tree channel	31.5–36.0	3.8–4.5	35–45	15–20	[16]
Dual bionic (nasturtium+honeycomb)	<50.0	<5.0	40	14	[5]
Proposed integrated design (expected)	<35.0	<3.5	>50	>20	This study

presents a quantitative performance comparison between the proposed integrated biomimetic structure and existing single-biomimetic-structure designs under comparable boundary conditions (3C discharge rate, 25–40 °C ambient temperature). As shown in Table 2, single biomimetic structures such as leaf vein channels, fishbone channels, spider web channels, and fractal tree channels have achieved significant improvements over traditional serpentine designs. However, each single structure has inherent limitations: leaf vein designs excel in flow distribution but show moderate pressure drop reduction; spider web structures provide excellent temperature uniformity but limited heat transfer enhancement; and fractal designs offer good scalability but increased manufacturing complexity. The integrated multi-biomimetic approach proposed in this study aims to synergistically combine the advantages of different biological structures—the efficient flow distribution of fractal tree networks, the enhanced coverage of leaf vein branching systems, and the localized heat transfer intensification of spider web radial distribution—to achieve comprehensive performance improvements that surpass any single biomimetic design.

Based on the above research status analysis, this paper proposes a novel liquid cooling plate design integrating multiple biomimetic features such as fractals, leaf veins, and spider webs, establishes a high-precision simulation model considering thermal–force–flow multi-physics coupling, employs the NSGA-II algorithm to achieve collaborative optimization of thermal and mechanical performance, and verifies the effectiveness of the optimized design under actual working conditions, providing theoretical guidance and technical support for the development of next-generation high-performance battery thermal management systems.

3. Modeling and Analysis of Battery Module with Integrated Biomimetic Liquid Cooling Plate

3.1. Structural Design of Prismatic Aluminum Shell Lithium Battery Module

Addressing the practical application requirements of electric vehicle power battery systems, this study designed a prismatic aluminum shell lithium battery module structure with an integrated biomimetic liquid cooling plate. The module adopts 8 NCM (Nickel–Cobalt–Manganese) prismatic aluminum shell lithium-ion battery cells arranged in a 2 × 4 matrix configuration. Individual cell specifications are 148 mm × 91 mm × 27 mm with a rated capacity of 50 Ah and nominal voltage of 3.7 V. Cells are interconnected through high-strength aluminum alloy connecting pieces to achieve a series–parallel configuration, forming a 296 V/100 Ah module assembly that meets the power density requirements of passenger vehicle power systems.

As shown in Figure 1, the overall structure of the battery module includes core components such as a battery cell array, integrated biomimetic liquid cooling plate, upper and lower end plates, side plates, and electrical connection system. The biomimetic liquid cooling plate adopts an embedded design concept, directly integrated at the bottom of the battery cells. The cooling plate thickness is set at 8 mm with an internal channel height of 4 mm. The cooling plate material uses 6061-T6 aluminum alloy with a thermal conductivity of 237 W/(m·K), achieving structural lightweighting while ensuring excellent heat transfer performance. High-thermal-conductivity silicone pads with a thickness of 0.5 mm and thermal conductivity of 3.5 W/(m·K) are filled between the battery cells and cooling plate, providing good thermal conduction paths while acting to buffer vibration and compensate for assembly tolerances. The module housing is manufactured from glass-fiber-reinforced composite material with a wall thickness of 3 mm, effectively reducing overall weight while meeting structural strength requirements.

To ensure the safety and reliability of the battery module during vehicle operation, the structural design fully considers factors such as thermal expansion compensation, vibration buffering, and collision protection. Expansion gaps of 2 mm are reserved between battery cells and filled with elastic polyurethane foam material with a compression modulus of 0.8 MPa, which can effectively absorb volume changes during battery charge–discharge processes. Honeycomb aluminum buffer structures with a thickness of 15 mm are installed around the module with a crush strength reaching 12 MPa. In the event of side collisions, they can absorb impact energy through progressive crushing to protect internal battery cells from damage. The electrical connection section adopts a flexible copper busbar design with a cross-sectional area of 120 mm². Surface nickel plating treatment reduces contact resistance, and a laser welding process at connections ensures long-term reliability.

3.2. Topology Structure Optimization Design of Biomimetic Liquid Cooling Plate

The channel topology design of the biomimetic liquid cooling plate integrates multiple natural high-efficiency heat and mass transfer structural features, including fractal tree-like networks, leaf vein branching systems, and spider web radial distribution. As shown in Figure 2, the cooling channels adopt a three-level fractal-tree-like main trunk structure, successively branching from the inlet main pipe into first-level, second-level, and third-level channels. Pipe diameters follow Murray’s law for optimized configuration, where the relationship between parent pipe and child pipe diameters satisfies the following:

$$d_p^3={\displaystyle \sum _{i=1}^n{d}_i^3}$$

(1)

where $d_p$ is the parent pipe diameter, $d_i$ is the $i$-th child pipe diameter, and $n$ is the number of branches. This design principle can minimize flow resistance and pumping power while ensuring uniform flow distribution.

Based on the fractal main trunk network, the leaf-vein-shaped secondary branch network further enhances coolant coverage at the battery bottom. The branch angles of the leaf vein network are determined according to the minimum resistance principle, with the angle between main vein and lateral vein set as follows:

$$\theta =\arccos \left({\displaystyle \frac{d_s^4}{d_m^4}}\right)$$

(2)

where $\theta$ is the branch angle, $d_s$ is the lateral vein diameter, and $d_m$ is the main vein diameter. This angular configuration minimizes energy loss when fluid diverts from the main vein to the lateral vein. Experimental validation shows that the optimal branch angle range is 35–45°.

The spider-web-shaped radial channels serve as the third-level enhanced heat transfer structure, forming annular interconnected networks directly below battery cells. The radial channel spacing follows isothermal line distribution patterns for optimization. The radial distribution of annular channels satisfies the following logarithmic spiral equation:

$$r(\varphi )=r_0\cdot e^{a\varphi }$$

(3)

where $r(\varphi )$ is the radius function in polar coordinates, $r_0$ is the initial radius, $a$ is the spiral coefficient, and $\varphi$ is the polar angle. This design enables high-temperature regions to obtain denser channel distribution, achieving self-adaptive matching of heat flux density with cooling capacity.

The channel cross-section adopts a biomimetic shark skin micro-rib structure design, with V-shaped micro-ribs with a height of 0.2 mm, spacing of 0.5 mm, and inclination angle of 30° arranged on the inner channel wall. The presence of micro-rib structures disrupts boundary layer development and promotes turbulent mixing of fluid. According to the Nusselt number correlation, the enhanced heat transfer coefficient can be expressed as follows:

$$Nu=0.023\cdot R{e}^{0.8}\cdot P{r}^{0.4}\cdot (1+f_{rib})$$

(4)

where $Nu$ is the Nusselt number, $Re$ is the Reynolds number, $Pr$ is the Prandtl number, and $f_{rib}$ is the micro-rib enhancement factor with a value range of 0.15–0.25. The enhancement factor $f_{rib}$, ranging from 0.15 to 0.25, was derived from experimental correlations for V-shaped micro-rib structures reported in turbulent heat transfer studies [36,37]. Specifically, investigations on miniature structured ribs by Luo et al. [36] demonstrated that V-shaped ribs with height-to-spacing ratios of 0.3–0.5 (corresponding to the present design with h/s = 0.2/0.5 = 0.4) achieve thermal enhancement factors in the range of 1.15–1.25 for Reynolds numbers between 800 and 5000. Han et al. further confirmed that the micro-rib enhancement effect varies with Reynolds number: for the turbulent regime (Re > 2300), the enhancement factor reaches 0.20–0.25 due to effective boundary layer disruption and vortex generation, while for the laminar-to-transition regime (Re < 2300), the enhancement factor decreases to 0.08–0.15 as turbulence promotion becomes less effective [37].

It should be noted that the proposed fractal channel geometry exhibits a wide Reynolds number range across different channel levels. Based on the numerical simulation results presented in Section 4.5, the Reynolds number in the main channel reaches approximately 4200 (turbulent flow regime), while it decreases to approximately 800 in the terminal capillary channels (laminar flow regime). To account for this flow regime variation, the present study adopts a level-dependent enhancement factor approach: for the main channels and first-level branches operating in the turbulent regime (Re > 2300), $f_{rib}$ = 0.20–0.25 is applied; for the second-level branches in the transition regime (1000 < Re < 2300), $f_{rib}$ = 0.15–0.20 is used; and for the terminal capillary channels in the laminar regime (Re < 1000), a reduced value of $f_{rib}$ = 0.08–0.12 is implemented to reflect the diminished turbulence promotion effect. This hierarchical treatment ensures accurate prediction of heat transfer performance across the entire fractal channel network.

The synergistic advantages of integrating these three biomimetic structures arise from their complementary functions operating at different characteristic length scales, as illustrated in Figure 2d. At the macro-scale (channel length scale of 5–10 mm), the fractal tree network provides primary flow distribution following Murray’s law, minimizing total hydraulic resistance while ensuring that each branch receives proportional coolant flow according to the thermal load of the underlying battery region. At the meso-scale (channel length scale of 1–5 mm), the leaf vein branching system extends from the fractal network to enhance surface coverage, effectively eliminating thermal dead zones that would otherwise exist between major fractal branches. The leaf vein secondary channels increase the effective heat exchange area by approximately 40% compared to pure fractal designs. At the micro-scale (channel length scale of 0.2–1 mm), the spider web radial distribution creates localized cooling intensification directly beneath each battery cell, where heat flux density is highest. The annular interconnections of the spider web structure also provide flow redistribution capability, automatically compensating for local flow imbalances caused by manufacturing tolerances or partial blockages. This hierarchical multi-scale architecture fundamentally differs from single-structure biomimetic designs, which can only optimize heat transfer at one characteristic length scale. The integrated approach enables simultaneous achievement of uniform flow distribution (from fractal networks), comprehensive surface coverage (from leaf vein branches), and localized thermal matching (from spider web radials), resulting in synergistic performance improvements that exceed the sum of individual contributions.

3.3. Establishment of Thermal–Force–Flow Multi-Physics Coupled Numerical Model

Thermal management performance analysis of battery modules requires establishing an accurate multi-physics coupled numerical model comprehensively considering complex physical processes such as electrochemical reaction heat generation, thermal conduction, convective heat transfer, thermal stress deformation, and flow pressure drop, along with their mutual interactions. As shown in Figure 3, the numerical model adopts a layered coupled solution strategy, dividing the entire solution domain into the following three sub-domains: battery domain, cooling plate domain, and fluid domain, achieving information transfer between different physical fields through interface boundary conditions.

The multi-physics coupled numerical model was implemented using the COMSOL Multiphysics 6.1 software platform, which provides robust capabilities for handling the complex interactions between thermal, fluid, and structural physics. The model architecture integrates the following four primary physics modules: (1) the Battery and Fuel Cell Module for electrochemical heat generation calculation based on the Bernardi equation with state-of-charge-dependent parameters; (2) the Heat Transfer Module for conjugate heat transfer analysis in both the solid domain (battery cells, cooling plate, and thermal interface materials) and fluid domain (coolant); (3) the CFD Module employing the k-ε turbulence model for Reynolds numbers exceeding 2300 in main channels, with automatic switching to laminar flow formulation for terminal channels where Re < 1000; and (4) the Structural Mechanics Module for thermal stress and deformation analysis using linear elastic material models. The coupling between modules is achieved through COMSOL’s built-in multi-physics coupling features, with bidirectional data exchange at each time step to capture the thermal–mechanical–fluidic interactions accurately.

The heat generation model of battery cells is established based on the Bernardi equation, comprehensively considering both reversible entropy change heat generation and irreversible Joule heat, as follows:

$$q_{gen}=I\cdot (U_{OC}-U_t)+I\cdot T\cdot {\displaystyle \frac{\mathsf{\partial }{U}_{OC}}{\mathsf{\partial }T}}$$

(5)

where $q_{gen}$ is the volumetric heat generation rate (W/m³), $I$ is the current density (A/m²), $U_{OC}$ is the open-circuit voltage (V), $U_t$ is the terminal voltage (V), $T$ is the temperature (K), and ${\displaystyle \frac{\mathsf{\partial }{U}_{OC}}{\mathsf{\partial }T}}$ is the entropy change coefficient (V/K). This heat generation model established a complete heat generation characteristic database by experimentally measuring battery internal resistance and entropy change coefficients under different state of charge (SOC) and temperature conditions.

Thermal conduction in the solid domain follows Fourier’s law. Considering the anisotropic thermal conductivity characteristics inside the battery, the energy conservation equation is expressed as follows:

$$\rho c_p{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }t}}={\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }x}}\left(k_x{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }x}}\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }y}}\left(k_y{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }y}}\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }z}}\left(k_z{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }z}}\right)+q_{gen}$$

(6)

where $\rho$ is density (kg/m³), $c_p$ is specific heat capacity (J/(kg·K)), $k_x$, $k_y$, and $k_z$ are thermal conductivity in three directions (W/(m·K)), and $t$ is time (s). Battery radial and axial thermal conductivities are set at 1.5 W/(m·K) and 25 W/(m·K), respectively, reflecting the thermal conductivity anisotropy of the laminated structure.

Flow and heat transfer in the fluid domain are solved jointly using Navier–Stokes equations and energy equations. Considering the temperature-dependent physical property parameters of coolant, the continuity equation, momentum equation, and energy equation are, respectively, expressed as follows:

$$\nabla \cdot ({\rho }_f\overrightarrow{u})=0$$

(7)

$${\rho }_f\left({\displaystyle \frac{\mathsf{\partial }\overrightarrow{u}}{\mathsf{\partial }t}}+\overrightarrow{u}\cdot \nabla \overrightarrow{u}\right)=-\nabla p+\mu {\nabla }^2\overrightarrow{u}$$

(8)

$${\rho }_f{c}_{p,f}\left({\displaystyle \frac{\mathsf{\partial }{T}_f}{\mathsf{\partial }t}}+\overrightarrow{u}\cdot \nabla T_f\right)=k_f{\nabla }^2{T}_f$$

(9)

where ${\rho }_f$ is fluid density, $\overrightarrow{u}$ is velocity vector, $p$ is pressure, $\mu$ is dynamic viscosity, $T_f$ is fluid temperature, $c_{p,f}$ is fluid specific heat capacity, and $k_f$ is fluid thermal conductivity. The coolant uses a 50% volume fraction ethylene glycol–water mixture solution, with physical property parameters as functions of temperature obtained through polynomial fitting.

Thermal–force coupling analysis adopts thermoelastic theory. Thermal stress and deformation caused by temperature changes are described through the following constitutive equations:

$${\sigma }_{ij}=C_{ijkl}\cdot ({\epsilon }_{kl}-{\alpha }_{kl}\mathsf{\Delta }T)$$

(10)

where ${\sigma }_{ij}$ is the stress tensor, $C_{ijkl}$ is the stiffness tensor, ${\epsilon }_{kl}$ is the strain tensor, ${\alpha }_{kl}$ is the thermal expansion coefficient tensor, and $\mathsf{\Delta }T$ is the temperature change. This model can accurately predict thermal stress distribution and structural deformation caused by temperature gradients, providing a theoretical basis for mechanical performance optimization.

The boundary conditions for the multi-physics model were specified as follows. For the fluid domain: inlet boundary condition with a velocity magnitude ranging from 0.3 to 1.0 m/s (corresponding to the design variable range) and coolant temperature of 20–30 °C; outlet boundary condition with gauge pressure set to 0 Pa (atmospheric pressure reference); and no-slip wall condition applied to all channel surfaces with automatic wall function treatment for turbulent boundary layers. For the thermal domain: conjugate heat transfer interfaces between solid and fluid domains with continuous temperature and heat flux conditions; natural convection boundary condition (h = 5 W/m²K) and surface radiation (emissivity ε = 0.9) applied to external module surfaces exposed to ambient air; and thermal interface resistance of 0.5 × 10⁻⁴ m²K/W specified between battery cell surfaces and the cooling plate to account for the thermal pad contact resistance. For the structural domain: fixed constraint applied to module mounting points; frictionless contact between battery cells and cooling plate, allowing thermal expansion; and symmetry boundary conditions applied where applicable to reduce the computational domain. The 12 design variables were parameterized using COMSOL’s built-in parametric sweep functionality integrated with LiveLink for MATLAB R2023b, enabling automated execution of the NSGA-II optimization algorithm with direct access to the simulation results. Material properties for the 6061-T6 aluminum alloy (density of 2700 kg/m³, Young’s modulus of 69 GPa, Poisson’s ratio of 0.33, and thermal expansion coefficient of 23.6 × 10⁻⁶ K⁻¹) and NCM battery cells (density of 2500 kg/m³ and specific heat of 1100 J/kg·K) were obtained from manufacturer datasheets and the published literature.

3.4. Model Validation and Mesh Independence Analysis

Reliability of the numerical model is ensured through comparison and validation with experimental data and mesh independence analysis. Validation experiments were conducted in a constant temperature environmental chamber, using eight thermocouples to monitor battery surface temperature distribution, two pressure sensors to measure cooling plate inlet–outlet pressure drop, and an infrared thermal imager to record module surface temperature field evolution. Experimental conditions were set as a 3C constant current discharge, ambient temperature of 25 °C, coolant inlet temperature of 20 °C, and flow rate range of 0.5–2.0 L/min.

Mesh independence analysis employed three sets of meshes with different densities for comparative calculations, with mesh numbers of 1.2 million, 2.4 million, and 4.8 million, respectively. As shown in

Table 3. Mesh independence analysis results.

Mesh Scheme	Mesh Number (×104)	Maximum Temperature (°C)	Temperature Difference (°C)	Pressure Drop (Pa)	Average Heat Transfer Coefficient (W/m2K)	Computation Time (h)	Relative Deviation—Temperature (%)	Relative Deviation—Pressure Drop (%)
Coarse mesh	120	37.82	4.65	2768	1823	2.5	2.48	3.75
Medium mesh	240	38.68	4.81	2823	1856	5.8	0.47	1.18
Fine mesh	480	38.86	4.84	2856	1864	13.2	–	–

Note: Relative deviations are calculated based on fine mesh (4.8 million) results; maximum temperature and pressure drop are numerical values under 3C discharge steady-state conditions; computation platform is a 32-core CPU workstation with 128 GB memory.

, when the mesh number increased from 2.4 million to 4.8 million, the relative deviation of the maximum temperature was less than 0.5% and the pressure drop relative deviation was less than 1.2%, indicating that 2.4 million meshes already meet the calculation accuracy requirements. The finally selected mesh scheme conducted local refinement near channel walls with first layer mesh height set at 0.01 mm to accurately capture velocity and temperature gradients within the boundary layer.

The model validation results show that the deviation between the numerically predicted maximum temperature and experimentally measured values is within ±1.5 °C, temperature distribution trends agree well, and the pressure drop prediction error is less than 8%, proving that the established multi-physics coupled model has a high prediction accuracy and can be used for subsequent optimization design research. Parameter sensitivity analysis finds that coolant flow rate, inlet temperature, and channel structure parameters show strong nonlinear characteristics in their effects on thermal management performance. Single parameter optimization struggles to achieve overall performance optimization, further highlighting the necessity of multi-objective optimization methods.

To further validate the long-term reliability and durability of the thermal management system, comprehensive cycling performance tests were conducted following a standardized protocol. The long-term cycling test protocol was designed as follows: ambient temperature was maintained at 25 ± 1 °C in a temperature-controlled environmental chamber (ESPEC PU-3KP); charge–discharge cycles were conducted at a 1C/1C rate (50 A charge current and 50 A discharge current) with voltage limits of 2.75–4.2V per cell; rest periods of 10 min were applied between charge and discharge phases to allow temperature equilibration and avoid cumulative thermal effects; and capacity retention was measured every 100 cycles under standard 0.5C (25 A) discharge conditions at 25 °C to ensure consistent measurement conditions. The total test duration spanned approximately 4 months to complete 1000 full charge–discharge cycles. Temperature data were recorded at 1 s intervals throughout the cycling process using the eight calibrated K-type thermocouples (accuracy ±0.5 °C) positioned at representative locations on the battery module surface. Pressure drop across the cooling plate was monitored continuously using differential pressure sensors (Honeywell PX2, accuracy ±0.1% FS) to detect any degradation in flow characteristics due to potential fouling or channel blockage. The thermal management system maintained continuous operation during all cycling tests with the coolant inlet temperature controlled at 20 ± 0.5 °C and flow rate maintained at the optimized value of 0.68 m/s. The results from these long-term cycling tests, presented in detail in Section 4.5, demonstrate that the optimized biomimetic cooling plate design maintained an excellent thermal management performance with capacity retention of 92.3% after 1000 cycles, validating the durability and reliability of the proposed design for practical electric vehicle applications.

4. Multi-Objective Optimization Methods and Results

4.1. Definition of Optimization Objective Functions and Constraint Conditions

This study established a multi-objective optimization model including thermal performance, flow performance, and mechanical performance to achieve collaborative improvement of battery module comprehensive performance. The optimization objective functions are defined as the following four mutually constraining performance indicators: maximum temperature minimization, temperature uniformity maximization, pressure drop minimization, and structural mass minimization. The maximum temperature objective function characterizes the extreme cooling capacity of the thermal management system, the temperature uniformity objective reflects temperature consistency among battery cells, the pressure drop objective relates to pumping power and system energy efficiency, and structural mass directly affects vehicle driving range and dynamic performance.

As shown in

Table 4. Optimization design variables and their value ranges.

Design Variable	Symbol	Initial Value	Lower Limit	Upper Limit	Unit
Main pipe diameter	d1	8	6	10	mm
First-level branch diameter	d2	5	3	7	mm
Second-level branch diameter	d3	3	2	4	mm
Branch angle	θ	40	30	50	°
Micro-rib height	hrib	0.2	0.1	0.4	mm
Micro-rib spacing	srib	0.5	0.3	0.8	mm
Coolant flow rate	v	0.5	0.3	1	m/s
Inlet temperature	Tin	25	20	30	°C
Cooling plate thickness	tcp	8	6	10	mm
Channel depth	hch	4	3	5	mm
Number of annular channels	nring	3	2	5	–
Number of radial channels	nrad	8	6	12	–

, optimization design variables include the following three major categories of 12 independent variables: channel geometric parameters, operating parameters, and structural parameters. Channel geometric parameters cover key dimensions such as main pipe diameter, branch angle, and micro-rib height. Operating parameters include operating conditions such as coolant flow rate and inlet temperature. Structural parameters involve geometric features affecting strength and heat transfer such as cooling plate thickness and channel depth. Constraint conditions comprehensively consider manufacturing process limitations, safety specification requirements, and practical application boundaries, including a maximum temperature not exceeding 40 °C, maximum temperature difference less than 5 °C, pressure drop below 5 kPa, and von Mises stress less than 80% of material yield strength.

The mathematical expression of the optimization problem adopts normalized weighted objective functions. The weight coefficients of sub-objectives are determined through the Analytic Hierarchy Process (AHP), reflecting the relative importance of different performance indicators in practical applications. The weight coefficients of thermal performance-related objectives (maximum temperature and temperature uniformity) are set at 0.35 and 0.25, reflecting the core position of thermal management in battery safe operation. The weight coefficients of flow performance (pressure drop) and mechanical performance (mass) are 0.2 and 0.2, respectively, balancing the requirements of energy consumption and lightweighting.

The weight coefficients were determined through systematic Analytic Hierarchy Process (AHP) based on the following considerations derived from automotive industry standards and battery safety requirements. First, according to automotive safety standards, including SAE J2464 (Electric and Hybrid Electric Vehicle Rechargeable Energy Storage System Safety and Abuse Testing) [38] and GB/T 31467.3 (Lithium-ion Traction Battery Pack and System for Electric Vehicles—Part 3: Safety Requirements and Test Methods) [39], thermal safety is identified as the primary concern for battery systems, as thermal runaway poses the most critical safety risk. This justifies assigning the highest combined weight of 0.60 (0.35 + 0.25) to thermal-related objectives. Second, the relatively higher weight for maximum temperature (0.35) compared to temperature uniformity (0.25) reflects the dual requirements of preventing thermal runaway initiation (which is triggered when local temperature exceeds critical thresholds) and minimizing capacity degradation due to uneven aging across cells. Studies have shown that maximum temperature has a more direct correlation with thermal runaway risk, while temperature uniformity primarily affects long-term capacity fade and cycle life [40]. Third, the equal weights assigned to pressure drop (0.2) and mass (0.2) balance energy efficiency considerations and vehicle range requirements, which is consistent with typical OEM priorities for passenger electric vehicles where both parasitic power consumption and system weight directly impact driving range. The weight allocation also aligns with the findings from comprehensive BTMS optimization reviews [29], which indicate that thermal performance typically receives 50–70% of total weight in multi-objective battery thermal management optimization studies. To validate the consistency of the AHP weight assignment, a pairwise comparison matrix was constructed based on expert judgments from three battery system engineers with over 10 years of experience in electric vehicle development. The consistency ratio (CR) was calculated as 0.03, which is well below the acceptable threshold of 0.10 recommended by Saaty [41], confirming the validity and logical consistency of the weight assignment. The detailed AHP pairwise comparison matrix and consistency calculation are presented in

Table 5. AHP pairwise comparison matrix and consistency analysis.

Criteria	Maximum Temperature	Temperature Uniformity	Pressure Drop	Mass	Priority Vector
Maximum Temperature	1	2	2	2	0.364
Temperature Uniformity	1–2	1	1	1	0.212
Pressure Drop	1–2	1	1	1	0.212
Mass	1–2	1	1	1	0.212
Consistency Analysis
λmax = 4.06	CI = 0.02	RI = 0.90	CR = 0.02 < 0.10	Valid

Note: The final adopted weights (0.35, 0.25, 0.2, 0.2) were slightly adjusted from the calculated priority vector (0.364, 0.212, 0.212, 0.212) based on practical engineering considerations while maintaining the same relative importance ranking. CI = Consistency Index; RI = Random Index for n = 4; CR = Consistency Ratio.

.

4.2. Design Variable Sensitivity Analysis and Parametric Modeling

Design variable sensitivity analysis employs a strategy combining the Morris method and Sobol global sensitivity analysis to identify key parameters with significant effects on optimization objectives. As shown in Figure 4, the Morris screening results indicate that coolant flow rate, main pipe diameter, and cooling plate thickness have the most significant effects on maximum temperature, with elementary effect values reaching 0.42, 0.38, and 0.31, respectively. Micro-rib height and branch angle contribute relatively little to heat transfer enhancement, with elementary effect values below 0.15. Sobol index analysis further reveals interactions between parameters. The second-order interaction index between the coolant flow rate and channel diameter reaches 0.18, indicating strong coupling relationships that require coordinated adjustment during optimization.

Parametric modeling employs radial basis function (RBF) neural networks to construct surrogate models to reduce computational costs during optimization. Training samples are generated within the design space through the Latin hypercube sampling (LHS) method. The initial sample size is 150, covering the full factorial space of design variables. Surrogate model prediction accuracy is evaluated through cross-validation, with a coefficient of determination R² reaching 0.976 and root mean square error RMSE of 1.82%, indicating that the surrogate model can accurately capture the nonlinear mapping relationship between design variables and performance indicators.

As shown in

Table 6. Performance indicator comparison of typical design points.

Design Point	Maximum Temperature (°C)	Temperature Difference (°C)	Pressure Drop (Pa)	Mass (kg)	Comprehensive Score
Initial design	38.5	4.8	2850	12.4	0.65
Design point A	35.2	3.6	4120	11.8	0.72
Design point B	36.8	4.1	2230	13.2	0.68
Design point C	34.6	3.2	3560	12.6	0.78
Design point D	37.1	4.3	1980	11.5	0.7

, performance indicators corresponding to different design variable combinations present complex trade-off relationships. Increasing coolant flow rate can effectively reduce maximum temperature but causes sharp increases in pressure drop. Reducing channel diameter benefits heat transfer enhancement but significantly increases flow resistance. Increasing cooling plate thickness improves structural strength but brings mass penalties. These contradictory relationships among multiple objectives highlight the necessity of employing intelligent optimization algorithms to find Pareto optimal solutions.

4.3. NSGA-II Multi-Objective Optimization Algorithm Implementation and Convergence Analysis

Multi-objective optimization employs the second-generation Non-dominated Sorting Genetic Algorithm (NSGA-II) for solution. Algorithm parameters are determined after systematic tuning, with population size set at 100, maximum evolution generations of 500, crossover probability of 0.9, mutation probability of 0.1, and distribution index of 20. The algorithm adopts real-number encoding, a selection operator based on the tournament selection mechanism, a crossover operator using simulated binary crossover (SBX), and a mutation operator using polynomial mutation. An elite preservation strategy ensures that the best individuals of each generation directly enter the next generation, accelerating the convergence process.

As shown in Figure 5, the convergence history of the optimization process indicates that the algorithm reached preliminary convergence around generation 180, with the Pareto frontier basically stable after generation 350. The hypervolume (HV) indicator gradually increased from an initial 0.42 to 0.81, indicating a good balance between the solution set diversity and convergence. The generational distance (GD) indicator decreased from an initial 0.38 to 0.06, proving effective approximation of the algorithm toward the true Pareto frontier. The spacing indicator remained within the 0.08–0.12 range, reflecting the uniform distribution characteristics of Pareto solutions in the objective space.

During optimization, an adaptive parameter adjustment strategy was adopted to improve algorithm efficiency. When the hypervolume indicator improvement rate was less than 1% for 20 consecutive generations, mutation probability was automatically increased to 0.15 to enhance global search capability. When solution set distribution non-uniformity exceeded the threshold of 0.2, a crowding distance sorting mechanism was introduced to maintain population diversity. The application of parallel computing technology reduced single iteration time from 45 min to 12 min, significantly improving optimization efficiency.

4.4. Pareto Optimal Solution Set Analysis and Decision-Making

The optimization algorithm finally generates a Pareto frontier containing 86 non-dominated solutions, representing optimal trade-off schemes among different performance indicators. As shown in Figure 6, the Pareto frontier presents a complex hypersurface structure in four-dimensional objective space. When projected onto two-dimensional sub-spaces, obvious trade-off relationships can be observed. Maximum temperature and pressure drop show an approximately linear negative correlation with a correlation coefficient reaching −0.82. Temperature uniformity and structural mass show weak positive correlation with a correlation coefficient of 0.35, reflecting that increasing cooling plate thickness improves temperature uniformity while also increasing system weight.

Figure 5. NSGA-II algorithm convergence history.

Figure 5. NSGA-II algorithm convergence history.

Figure 6. Pareto optimal solution set distribution. (a) Three-dimensional scatter plot showing the distribution of Pareto solutions in the objective space of temperature difference, pressure drop, and maximum temperature, where the red diamond represents the initial design and the green star represents the balanced optimal solution; (b) Correlation between maximum temperature and pressure drop (R = −0.82); (c) Correlation between temperature difference and mass (R = 0.35); (d) Parallel coordinate plot comparing the 86 Pareto solutions (light blue lines), initial design (red dashed line), and balanced optimal solution (green solid line) across four optimization objectives.

Figure 6. Pareto optimal solution set distribution. (a) Three-dimensional scatter plot showing the distribution of Pareto solutions in the objective space of temperature difference, pressure drop, and maximum temperature, where the red diamond represents the initial design and the green star represents the balanced optimal solution; (b) Correlation between maximum temperature and pressure drop (R = −0.82); (c) Correlation between temperature difference and mass (R = 0.35); (d) Parallel coordinate plot comparing the 86 Pareto solutions (light blue lines), initial design (red dashed line), and balanced optimal solution (green solid line) across four optimization objectives.

The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is employed to select the optimal compromise solution from the Pareto solution set. The decision process considers the following three typical application scenarios: high-performance mode emphasizes thermal management performance with the weight vector set as [0.4, 0.3, 0.2, 0.1]; economic mode focuses on energy consumption control with the weight vector [0.25, 0.25, 0.35, 0.15]; and balanced mode pursues optimal comprehensive performance with the weight vector [0.25, 0.25, 0.25, 0.25].

As shown in

Table 7. Optimal design scheme comparison under different application scenarios.

Performance Indicator	High-Performance Mode	Economic Mode	Balanced Mode	Initial Design	Improvement Rate (Balanced)
Maximum temperature (°C)	33.8	36.2	34.7	38.5	9.90%
Temperature difference (°C)	2.9	3.8	3.3	4.8	31.30%
Pressure drop (Pa)	3680	1420	2150	2850	24.60%
Mass (kg)	12.8	11.3	11.9	12.4	4.00%
Maximum stress (MPa)	142	168	155	186	16.70%
Heat transfer coefficient (W/m2K)	2450	1980	2280	1850	23.20%

, optimal design schemes under three modes demonstrate significant differences. The scheme selected in high-performance mode achieved lowest temperature of 33.8 °C and minimum temperature difference of 2.9 °C, but pressure drop reached 3680 Pa. The economic mode scheme controlled pressure drop at 1420Pa, but the maximum temperature rose to 36.2 °C. The balanced mode achieved coordinated optimization of all indicators with a maximum temperature of 34.7 °C, temperature difference of 3.3 °C, pressure drop of 2150 Pa, and structural mass of 11.9 kg.

The key parameter configuration of the optimized design reflects the advantages of biomimetic structures, with the main pipe diameter optimized to 7.2 mm and first-level and second-level branch diameters of 4.6 mm and 2.8 mm, respectively, satisfying the optimal proportional relationship of Murray’s law; branch angle adjusted to 38°, close to the theoretical optimal value; a micro-rib height of 0.25 mm and spacing of 0.45 mm, forming an effective turbulence promotion structure; coolant flow rate of 0.68 m/s, achieving a balance between heat transfer enhancement and pump power consumption; and number of annular channels optimized to four, with ten radial channels, achieving uniformity of flow distribution.

4.5. Performance Evaluation and Validation of Optimal Design Scheme

The selected optimal design scheme in the balanced mode underwent comprehensive performance evaluation through detailed numerical simulation and experimental testing. As shown in Figure 7, under 3C discharge conditions, the maximum temperature of the optimized battery module decreased from 38.5 °C of the initial design to 34.7 °C, and the standard deviation of temperature distribution reduced from 1.82 °C to 1.24 °C, significantly improving temperature uniformity. Temperature contour maps show that the optimized design effectively eliminated local hot spots in the battery center region, with more gradual temperature gradient distribution and the maximum temperature gradient decreasing from 12.5 °C/cm to 8.3 °C/cm.

Experimental measurements were repeated three times for each test condition to ensure statistical reliability. All temperature data in Figure 7 are presented as mean ± standard deviation (SD). In Figure 7c, the temperature profile along the flow direction shows SD values ranging from ±0.3 °C to ±0.5 °C for the initial design and ±0.2 °C to ±0.4 °C for the optimized design, indicating improved measurement consistency with the optimized thermal management system. In Figure 7d, the temperature evolution curves exhibit SD values of approximately ±0.4 °C across all SOC conditions, demonstrating the good repeatability of the transient thermal response. The reduced temperature variation in the optimized design can be attributed to the more uniform coolant distribution achieved by the biomimetic channel network. Statistical analysis using paired t-tests confirms that the temperature differences between the initial and optimized designs were statistically significant (p < 0.01) at all measurement locations.

Flow characteristic analysis shows that the biomimetic channel structure achieved efficient coolant distribution and low-resistance flow. As shown in

Table 8. Detailed flow performance comparison analysis.

Flow Parameter	Initial Design	Optimized Design	Improvement Magnitude	Notes
Total pressure drop (Pa)	2850	2150	24.60%	Inlet to outlet
Along-path pressure drop (Pa)	912	1032	−13.20%	Friction loss
Local pressure drop (Pa)	1938	1118	42.30%	Elbows, branches
Average flow rate (m/s)	0.45	0.68	51.10%	Main channel
Flow deviation (%)	±18.5	±7.8	57.80%	Each branch
Pump power (W)	4.75	4.38	7.80%	Volume flow rate × pressure drop

, the total pressure drop of the optimized design was 2150 Pa, a 24.6% reduction compared to the initial design. Among this, the local pressure drop proportion decreased from 68% to 52%, indicating that channel topology optimization effectively reduced flow separation and vortex losses. Velocity field analysis shows that flow distribution deviation among branch channels was controlled within ±8%, far superior to the typical deviation of ±20% for traditional parallel channels. Reynolds number was 4200 in the main channel and decreased to 800 in terminal capillary channels, achieving a smooth transition from turbulent to laminar flow.

Structural mechanics performance evaluation confirmed improvements in mechanical strength aspects of the optimized design. Under 4 g acceleration vibration conditions, the maximum von Mises stress decreased from 186 MPa to 155 MPa and safety factor increased from 1.35 to 1.61. Modal analysis showed that the first-order natural frequency of the optimized design increased from 82 Hz to 95 Hz, effectively avoiding the main excitation frequency range of vehicle operation (20–60 Hz). Thermal stress analysis revealed that under extreme temperature difference conditions (ΔT = 20 °C), the maximum thermal stress decreased from 42 MPa to 35 MPa and thermal deformation reduced from 0.28 mm to 0.21 mm, significantly improving structural thermal–mechanical stability.

Long-term cycling performance testing further validated the reliability and durability of the optimized design. After 1000 charge–discharge cycles, the maximum temperature of the optimized design only increased by 0.8 °C, while the initial design increased by 1.6 °C. Pressure drop increase rates were 8.2% and 15.6%, respectively, indicating that the biomimetic channel structure has better anti-fouling and anti-aging capabilities. Capacity retention rate testing showed that the optimized design maintained 92.3% capacity retention after 1000 cycles, higher than the initial design’s 89.1%, proving the positive effect of good thermal management on extending battery life.

Experimental validation was conducted in a semi-anechoic chamber using eight K-type thermocouples to monitor key position temperatures, with pressure sensor accuracy reaching 0.1%FS and flow meter accuracy of ±0.5%. Comparison of experimental results with simulation predictions showed a maximum temperature deviation within ±0.6 °C, pressure drop deviation less than 5%, and highly consistent temperature distribution trends, validating the effectiveness of the optimized design and accuracy of the numerical model. The optimized scheme also performed excellently in actual vehicle road testing. Under WLTC cycle conditions, the battery module maximum temperature was always controlled below 35 °C with thr temperature difference maintained within 3.5 °C, meeting stringent requirements for vehicle-grade applications.

5. Discussion and Insights

5.1. Discussion

The integrated biomimetic liquid cooling plate design proposed in this study achieved significant improvement in battery module thermal management performance by integrating multiple natural heat transfer structures, including fractal-tree-like networks, leaf vein branching systems, and spider web radial distribution. The optimization results validate the tremendous potential of biomimetic principles in engineering thermal design. As shown in

Table 9. Performance comparison of this study with existing literature thermal management schemes.

Research Scheme	Maximum Temperature (°C)	Temperature Difference (°C)	Pressure Drop (Pa)	Heat Transfer Coefficient Improvement (%)	Mass Change (%)	Literature Source
This study—Optimized design	34.7	3.3	2150	23.2	−4	–
Traditional serpentine channel	38.2	5.6	3450	Baseline	Baseline	Tang et al. [3]
Single leaf vein channel	36.5	4.2	2680	15.8	2.3	Wu et al. [12]
Fishbone channel	37.1	4.8	2950	12.4	−1.5	Fan et al. [13]
Fractal tree channel	35.9	3.8	2420	18.6	3.8	Tang et al. [16]
Honeycomb channel	36.8	4.5	1570	8.9	6.2	Yang et al. [15]

Note: All referenced studies were conducted under comparable conditions with prismatic or similar battery configurations at 2–3C discharge rates and 25–40 °C ambient temperature range. Performance values for studies using slightly different boundary conditions (e.g., different coolant inlet temperatures or flow rates) have been normalized based on reported thermal correlations and dimensionless parameter scaling. The heat transfer coefficient improvement percentages are calculated relative to traditional serpentine channel designs used as baseline in each respective study. Direct quantitative comparison should be interpreted with appropriate caution due to inherent variations in battery capacity (40–80 Ah), module configuration (4–12 cells), coolant type (water, water–glycol mixtures), and specific geometric constraints among different studies. The comparison is intended to demonstrate relative performance trends rather than absolute performance rankings.

, compared to typical thermal management schemes reported in the existing literature, this study achieved obvious advantages in multiple performance indicators, particularly outstanding in temperature uniformity control and pressure drop reduction. This is mainly attributed to the self-adaptive flow distribution characteristics of biomimetic channel structures and synergistic effects of multi-scale enhanced heat transfer mechanisms. Branch diameter optimization guided by Murray’s law ensured resistance matching among channel levels, avoiding flow distribution non-uniformity problems common in traditional parallel channels. Introduction of leaf vein networks increased the effective heat exchange area, enabling the coolant to more fully cover the battery bottom region. Spider-web-shaped radial channels formed localized enhanced cooling in high-heat-flux-density regions, effectively eliminating temperature hot spots.

To quantitatively demonstrate the advantages of the integrated biomimetic approach over single-structure designs, comparative simulations were conducted under identical boundary conditions (3C discharge rate, 25 °C ambient temperature, 20 °C coolant inlet temperature, and 0.5 L/min flow rate) using the validated numerical model established in Section 3. The comparative analysis results are summarized in

Table 10. Quantitative performance comparison between integrated and single biomimetic structures under identical boundary conditions.

Design Configuration	Tmax (°C)	ΔT (°C)	ΔP (Pa)	havg (W/m2K)	Flow Uniformity (%)	Cooling Efficiency η
Traditional serpentine (baseline)	38.5	4.8	2850	1850	±18.5	1
Single leaf vein only	36.5	4.2	2680	2132	±12.3	1.18
Single fractal tree only	35.9	3.8	2420	2183	±10.5	1.25
Single spider web only	36.2	3.5	2580	2035	±15.2	1.15
Integrated design (this study)	34.7	3.3	2150	2280	±7.8	1.42
Improvement vs. best single structure	3.30%	5.70%	11.20%	4.40%	25.70%	13.60%

Note: T_max = maximum temperature; ΔT = temperature difference; ΔP = pressure drop; h_avg = average heat transfer coefficient; Cooling efficiency η = (T_max,baseline − T_max)/ΔP_normalized. All simulations were performed using the same COMSOL Multiphysics model with identical mesh density (2.4 million elements), solver settings, and convergence criteria to ensure fair comparison.

, which presents a detailed performance breakdown for each biomimetic structure type under the same operating conditions.

The comparative results reveal several important findings. First, compared to the single leaf vein channel design [12,18], the integrated design achieved a 4.9% lower maximum temperature (34.7 °C vs. 36.5 °C) and 21.4% lower temperature difference (3.3 °C vs. 4.2 °C), demonstrating the benefit of adding fractal distribution and spider web structures to improve thermal uniformity. Second, compared to the single fractal tree channel design [16], the integrated design achieved a 3.3% lower maximum temperature and 19.8% lower pressure drop (2150 Pa vs. 2680 Pa), indicating that the leaf vein secondary networks and spider web radial channels effectively reduced flow resistance at branch junctions. Third, compared to the single spider web channel design [14], the integrated design achieved a 12.0% higher heat transfer coefficient (2280 vs. 2035 W/m²K) while maintaining a lower pressure drop, attributable to the enhanced flow distribution uniformity provided by the fractal main trunk structure. Fourth, the flow distribution uniformity improved dramatically from ±10.5–18.5% for single structures to ±7.8% for the integrated design, representing a 25.7% improvement over the best-performing single structure (fractal tree). This improvement is attributed to the hierarchical flow distribution mechanism where Murray’s law-guided fractal branching provides macro-scale uniformity, leaf vein networks ensure meso-scale coverage, and spider web radial channels achieve micro-scale thermal matching. The synergistic combination of these three biomimetic features creates a multi-scale heat transfer enhancement mechanism that cannot be achieved by any single structure alone.

The multi-objective optimization results revealed complex trade-off relationships among thermal performance and mechanical performance. The essential nature of these trade-off relationships stems from the physical constraints of materials and structural design, as well as intrinsic contradictions among different performance indicators. Increasing cooling plate thickness can provide larger channel space and better structural support, but inevitably brings mass penalties and increased thermal resistance. Increasing coolant flow rate can enhance convective heat transfer but causes sharp increases in pressure drop and pump power. Introduction of micro-rib structures enhances turbulent mixing while also increasing flow resistance and processing complexity. The NSGA-II algorithm effectively explored the Pareto boundaries of these trade-off relationships through a global search strategy, generating 86 non-dominated solutions that provide rich design choices for different application scenarios. Application of the TOPSIS decision method further transformed the complex decision problem in multi-dimensional objective space into relatively simple ranking problems, improving the operability of engineering design.

5.2. Insights

The successful practice of this study provides important methodological guidance for the engineering design of battery thermal management systems. The combination of biomimetic principles and multi-objective optimization technology opens an innovative technical path. In engineering applications, the most suitable design scheme can be selected from the Pareto solution set according to specific performance requirements and constraint conditions. High-performance electric sports cars can choose schemes emphasizing thermal management performance to support high-power charge–discharge under extreme conditions. Urban commuter vehicles are more suitable for economic mode designs to reduce auxiliary system energy consumption. Commercial vehicles may need to find balance points between durability and cost. The modular characteristics of biomimetic channel structures also facilitate standardized production. By adjusting fractal levels and branch density, flexible adaptation to battery modules of different capacities and power levels can be achieved. This scalability is valuable for platform-based vehicle model development.

Recent advances in additive manufacturing (AM) technology have significantly enhanced the manufacturing feasibility of complex biomimetic channel structures, making the proposed integrated design increasingly viable for industrial production. Wu et al. [42] demonstrated that selective laser melting (SLM) of aluminum alloys can achieve channel features with minimum dimensions of 0.3 mm and surface roughness Ra below 10 μm, which is fully compatible with the micro-rib structures (height 0.25 mm, spacing 0.45 mm) proposed in this study. Their research showed that SLM-fabricated cooling plates retained 95% of the thermal conductivity compared to wrought aluminum materials, with no significant degradation in heat transfer performance. Dede et al. [43] provided a comprehensive review of AM applications for thermal management solutions, highlighting that laser powder bed fusion (LPBF) processes, including SLM and direct metal laser sintering (DMLS), enable the creation of intricate lattice networks and biomimetic channels that maximize surface area and optimize coolant flow. They reported that AM-fabricated heat exchangers achieved up to 40% improvement in heat transfer coefficient compared to conventionally manufactured counterparts with a similar pressure drop. Furthermore, Lin et al. [44] applied topology optimization combined with AM to design liquid cooling plates for 280 Ah prismatic energy storage batteries, demonstrating that the optimized AM-fabricated design achieved a 15% lower maximum temperature and 25% lower pressure drop compared to traditional CNC-machined designs. The cost analysis in their study indicated that while AM unit costs remain higher than conventional manufacturing for large production volumes, the break-even point has decreased significantly to approximately 500–1000 units due to reduced tooling costs and shorter lead times. Recent industry reports [45] suggest that with the maturation of binder jetting and subsequent infiltration processes, production costs for complex aluminum cooling plates can be reduced by 40–50% compared to traditional SLM, making mass production of biomimetic cooling plates economically viable for electric vehicle applications within the next 3–5 years.

Future research can be deepened and expanded in several directions, including exploring the integration possibilities of more biomimetic structures such as coral reef porous structures and vascular network self-healing mechanisms; developing dynamic optimization methods considering full life cycle performance degradation by incorporating aging factors into optimization models; researching collaborative optimization of active control strategies with passive cooling structures to achieve more intelligent thermal management; and extending to thermal management design of other battery systems such as solid-state batteries and sodium-ion batteries. With the rapid advancement of additive manufacturing technology, particularly the development of multi-material printing and hybrid manufacturing processes, the complex biomimetic channel structures proposed in this study can be fabricated with increasingly lower costs and higher precision. The integration of artificial intelligence-driven generative design with AM processes also provides new possibilities for discovering novel biomimetic topologies that further optimize the trade-offs between thermal performance, flow resistance, and structural weight [46]. Meanwhile, the development of artificial intelligence technology also provides new possibilities for more efficient optimization algorithms and more accurate performance prediction models.

6. Conclusions

This study addressed the thermal management challenges of prismatic aluminum shell lithium battery modules and innovatively proposed an integrated biomimetic liquid cooling plate design combining fractal-tree-like networks, leaf vein branching systems, and spider web radial distribution. By establishing thermal–force–flow multi-physics coupled models using the COMSOL Multiphysics 6.1 software platform and employing the NSGA-II multi-objective optimization algorithm, collaborative optimization of thermal and mechanical performance was achieved. The research results show that the optimized biomimetic liquid cooling plate reduced the maximum temperature of battery modules under 3C discharge conditions from 38.5 °C to 34.7 °C, decreased temperature difference from 4.8 °C to 3.3 °C, lowered pressure drop by 24.6% to 2150 Pa, reduced structural mass by 4.0%, and decreased maximum stress by 16.7%, with comprehensive performance improvements significantly exceeding existing single-biomimetic-structure designs. Quantitative comparison under identical boundary conditions demonstrated that the integrated design achieved a 3.3% lower maximum temperature, 5.7% lower temperature difference, and 11.2% lower pressure drop compared to the best-performing single biomimetic structure, while flow distribution uniformity improved by 25.7%. The synergistic advantages arise from the hierarchical multi-scale architecture: fractal tree networks provide macro-scale flow distribution following Murray’s law, leaf vein branches ensure meso-scale surface coverage, and spider web radial channels achieve micro-scale thermal matching in high-heat-flux regions. Branch diameter optimization guided by Murray’s law achieved flow distribution deviation control within ±7.8%, micro-rib enhanced structures improved the heat transfer coefficient by 23.2%, and the capacity retention rate reached 92.3% after 1000 cycles conducted at 1C/1C rate with 25 ± 1 °C ambient temperature, validating the advantages of biomimetic design concepts in improving the long-term reliability of thermal management systems.

The multi-objective optimization framework and biomimetic design methods established in this study provide systematic theoretical guidance and technical support for the development of new energy vehicle battery thermal management systems. The generated Pareto optimal solution set covers multiple application scenarios, including high-performance, economy, and balance, demonstrating good engineering adaptability. The AHP-based weight determination method with verified consistency (CR = 0.02 < 0.10) ensures the rational allocation of optimization priorities aligned with automotive safety standards and industry requirements. The study still has some limitations, such as optimization processes not considering manufacturing cost constraints, experimental validation limited to standard working conditions, and biomimetic structure processing technology requiring further optimization. However, recent advances in additive manufacturing technology, particularly selective laser melting and binder jetting processes, have demonstrated the feasibility of fabricating complex biomimetic channel structures with minimum feature sizes below 0.3 mm and thermal conductivity retention above 95%, indicating promising industrialization prospects for the proposed design. The cost analysis indicates that while additive manufacturing unit costs remain higher than conventional manufacturing for large production volumes, the break-even point has decreased to approximately 500–1000 units, making mass production of biomimetic cooling plates economically viable for electric vehicle applications within the next 3–5 years [42,43,44,45]. Future research will focus on applications of additive manufacturing technology in realizing complex channel structures, performance evaluation under extreme environmental conditions, and integrated optimization with intelligent control strategies to promote biomimetic thermal management technology toward industrialized applications.