Multi-Objective Optimization on Enhanced Heat Transfer and Pumping Power of Cooling Plate-Based Indirect Cooling System for 6S2P Lithium-Ion Battery Module

Abstract

This study proposes a multi-objective optimization framework for a cooling plate-based indirect liquid cooling system applied to a 6S2P lithium-ion battery module during 3C fast charging. A three-dimensional computational fluid dynamics (CFD) model coupled with the multi-scale multi-domain (MSMD)–Newman–Tiedemann–Gu–Kim (NTGK) battery heat generation model was developed to investigate the system thermal–hydraulic behavior. The numerical model was experimentally validated through single-cell charging tests, with temperature deviations below 5%, confirming its reliability. A systematic parametric analysis was conducted to evaluate the effects of coolant channel number, channel width, channel spacing, and coolant mass flow rate on maximum temperature (T_max), temperature difference (ΔT), and pressure drop (ΔP). The results indicated that increasing the coolant flow rate significantly enhanced thermal performance but caused a substantial increase in hydraulic losses, whereas geometric parameters had comparatively smaller effects. To improve optimization efficiency, 30 design samples were generated using Latin hypercube sampling and used to train ANN surrogate models, which demonstrated high predictive accuracy with test R² values of 0.9931, 0.9960, and 0.9842 for T_max, ΔT, and pumping power (P_pump), respectively. Subsequently, NSGA-II combined with TOPSIS identified the optimal design with a channel width of 6.22 mm, channel spacing of 4.84 mm, and coolant flow rate of 2.55 LPM. Under these conditions, the optimized system achieved a T_max of 30.47 °C, a ΔT of 4.50 °C, and a P_pump of 0.05879 W. The relative deviations between ANN predictions and CFD results were all below 1%, demonstrating the robustness of the proposed optimization framework. These findings provide an effective design methodology for enhancing heat transfer while minimizing pumping power in advanced battery thermal management systems.

1. Introduction

Global climate change and the rapid increase in greenhouse gas emissions pose critical challenges to sustainable development [1,2,3]. The transportation sector is a major contributor to carbon emissions, prompting a global transition toward cleaner energy solutions [4,5,6]. In this context, electric vehicles (EVs) have emerged as a promising alternative to conventional internal combustion engine vehicles, with the potential to significantly reduce emissions and improve energy efficiency [7,8,9]. As the core energy storage component of EVs, lithium-ion batteries (LIBs) have gained widespread adoption owing to their high energy density, long cycle life, and favourable electrochemical performance [10,11,12,13,14].

Despite these advantages, LIBs are highly sensitive to temperature variations during operation, particularly under high load conditions such as fast charging and discharging [15,16,17,18]. To ensure peak performance and safety, LIBs require stable operation within an optimal temperature range of 25–40 °C, with ΔT maintained below 5 °C [19,20,21,22]. Excessive temperature rise can lead to performance degradation, reduced lifespan, and even safety risks such as thermal runaway [23,24,25,26]. Moreover, non-uniform temperature distribution within battery modules can accelerate cell imbalance and capacity fading [27,28,29,30]. In addition to immediate thermal safety concerns, battery lifespan degradation has emerged as a critical challenge for fast charging applications. Elevated temperatures and non-uniform temperature distributions accelerate degradation mechanisms, including lithium plating, solid electrolyte interphase (SEI) growth, and electrode structural deterioration, leading to capacity fading and reduced State of Health (SoH) [31,32]. Recent studies have proposed adaptive battery thermal management strategies based on SoH, dynamically adjusting thermal control parameters, such as coolant flow rate, in response to battery aging [33,34]. These approaches enable more accurate quantification of the relationship between temperature evolution and degradation mechanisms, thereby improving long-term durability. In particular, SoH-aware models provide a theoretical framework for linking thermal behavior with capacity fading, offering significant potential for optimizing dynamic thermal management strategies in LIB systems. In summary, battery lifespan is significantly affected by temperature sensitivity and dynamic fast-charging conditions. By integrating an adaptive flow control strategy based on the SoH, the degradation caused by thermal stress can be further reduced, thereby improving the long-term robustness of the cooling system. Although the present study focuses on thermal–hydraulic optimization, controlling maximum temperature and temperature gradients can be considered key indirect indicators for mitigating long-term degradation. Therefore, the development of an efficient battery thermal management system (BTMS) is essential not only for performance and safety but also for extending battery lifetime [35,36,37,38].

Various BTMS strategies have been proposed in the literature, including air cooling, phase change material (PCM) cooling, heat pipe cooling, and liquid cooling [39,40,41,42]. Air cooling systems are simple and cost-effective but suffer from low heat transfer efficiency, making them less suitable for high-power applications [43,44,45,46]. PCM-based cooling can effectively absorb heat through latent heat storage. However, its limited thermal conductivity and challenges with regeneration limit its performance [47,48,49,50]. Heat pipe systems offer high thermal conductivity and passive operation, but their integration complexity and cost can limit practical implementation [51,52,53,54]. Compared to these methods, liquid cooling systems provide superior heat dissipation capability due to higher heat transfer coefficients, making them particularly suitable for high-performance battery systems [55,56,57,58,59].

Liquid cooling can be broadly classified into direct and indirect cooling methods [60,61,62]. In direct liquid cooling, the coolant is in direct contact with the battery, offering excellent thermal performance [63,64,65]. However, direct liquid cooling poses risks of leakage and material incompatibility issues [66,67,68]. In contrast, indirect liquid cooling, where the coolant flows through cooling plates attached to the battery surface, offers a safer, more reliable solution while maintaining high cooling efficiency [69,70,71]. Therefore, indirect liquid cooling has become a widely adopted approach in practical EV battery systems and is the focus of the present study.

Several studies have investigated the thermal performance of liquid-cooled battery systems with a cooling plate by analysing key design and operating parameters. You et al. investigated the thermal performance of a liquid cooling plate-cooled BTMS for LIBs by analysing the effects of flow rate, channel width, and channel number. Numerical results showed that increasing the coolant flow rate from 2 to 6 LPM reduced the average battery temperature from 53.8 °C to 50.7 °C, while significantly increasing the P_pump from 0.036 to 0.808 W. Additionally, increasing the channel width and the number of channels improved cooling performance and reduced ΔP. Under optimized conditions, a six-channel configuration achieved enhanced temperature uniformity and lower energy consumption. Furthermore, a combined top-and-bottom cooling strategy reduced the average temperature to 35.8 °C, demonstrating substantial improvement in thermal management effectiveness [72]. Similarly, Song et al. investigated the thermal performance of liquid-cooled battery cooling plates using numerical simulations combined with grey correlation analysis. Multiple parameters, including runner structure, plate thickness, inlet temperature, and flow rate, were analyzed. The results showed that serpentine channels provide the best heat dissipation but incur the highest ΔP, while leaf-vein structures achieve a better balance between thermal performance and hydraulic losses. Increasing plate thickness slightly reduces T_max and ΔP, whereas higher flow rates improve cooling but significantly increase ΔP. Optimal performance was obtained at a plate thickness of 4 mm, an inlet temperature of 25 °C, and a flow rate of 0.5 m/s, achieving a T_max of 29.99 °C and a ΔT of 4.97 °C [73].

Building on these parametric studies, recent research has emphasized the importance of flow distribution and structural design. Tang et al. investigated the thermal performance of cooling plates for LIB modules through a validated three-dimensional numerical model. The results demonstrated that the main/side-wall cooling design significantly enhances temperature uniformity, reducing the ΔT from 2.68 °C to 0.68 °C under comparable conditions. Further optimization of the flow channel revealed that a serpentine main channel combined with shortened side-wall channels achieved the best performance by improving coolant distribution, with approximately 81% of the flow directed to the main wall. Under high discharge rates, the optimized structure maintained the ΔT below 5 °C, satisfying thermal safety requirements [74]. Likewise, Ding et al. proposed a cross-flow microchannel cold plate to address non-uniform flow distribution, local hotspots, and high ΔP in BTMSs. An L16 orthogonal experimental design was employed to investigate the effects of coolant type, inlet temperature, and flow velocity. The results showed that lower inlet temperatures and higher flow velocities significantly enhanced cooling performance but increased ΔP. The optimal configuration reduced the heat source temperature by 2.43 °C while decreasing ΔP by approximately 16.3% compared to reference cases. Additionally, a Nusselt number correlation with R² of 0.978 was developed, demonstrating high predictive accuracy for thermal performance [75].

More advanced design approaches have focused on structural and topology optimization of cooling plates. Ren et al. developed a liquid-cooling plate design based on topology optimization and a biomimetic simplification approach to enhance both thermal performance and manufacturability. A two-dimensional topology optimization method was first employed to generate an optimal flow channel configuration, which was subsequently simplified into a bionic cooling plate (BCP) inspired by streamlined natural structures. Numerical simulations demonstrated that both the topology-optimized cooling plate (TCP) and the BCP significantly outperformed conventional straight mini-channel plates. Specifically, within a flow rate range of 300–600 mLPM, the T_max was maintained below 35 °C, while the ΔT was reduced to 1.17–2.35 °C. Furthermore, the optimized designs improved temperature uniformity by over 70% and reduced T_max by approximately 11–12% compared to traditional designs, while maintaining comparable ΔP characteristics [76]. Xie et al. proposed a simplified liquid-cooling structure for large-format LIB modules that employs two liquid-cooling plates. A three-dimensional CFD model was developed to evaluate thermal performance under a 3C discharge condition. Through systematic optimization of inlet velocity, channel width, and plate thickness, the study identified that flow channel configuration plays a critical role in temperature uniformity. In particular, a redesigned dual-inlet, single-outlet channel effectively mitigated edge-overcooling and improved coolant distribution. The optimized configuration achieved a T_max below 31.8 °C and a ΔT of approximately 3.7 °C, while maintaining a lightweight structure [77]. In addition, multi-objective optimization techniques have been increasingly adopted to balance thermal and hydraulic performance. Yang et al. investigated the multi-objective topology optimization of liquid cooling plates for battery thermal management under 5C discharge conditions using a combined RSM-NSGA-II-TOPSIS framework. The study focused on optimizing inlet and outlet configurations to minimize the T_max, the ΔT, and the ΔP. The optimized design reduced the T_max by approximately 0.13–0.22 K compared to conventional layouts and by up to 2.6 K relative to straight-channel designs. In addition, the ΔP decreased by up to 18.75%, while the performance evaluation criteria (PEC) improved by up to 79.4% at higher inlet velocities [78].

Despite the significant progress in cooling plate design and optimization, several limitations remain in the existing literature. First, many studies focus primarily on either geometric parameters or operating conditions independently, without systematically investigating their coupled effects on thermal and hydraulic performance. Second, although multi-objective optimization methods have been applied, the integration of high-fidelity CFD models with data-driven surrogate models, such as artificial neural networks (ANNs), remains relatively limited, particularly for large-scale and complex battery module configurations. Third, most existing works are conducted at the single-cell or simplified module level, with limited consideration of realistic battery pack configurations and high-rate charging scenarios. Notably, while several studies have investigated high discharge rates, thermal behavior under fast charging conditions has received comparatively less attention, despite its increasing importance in practical EV applications. To address these gaps, the present study proposes a comprehensive multi-objective optimization framework for a cooling plate-based indirect liquid cooling system applied to a large-scale 6S2P LIB module under 3C fast charging conditions. A coupled CFD-MSMD-NTGK model is developed and experimentally validated to accurately capture battery heat generation and thermal behavior. Furthermore, an ANN-based surrogate model is constructed to efficiently predict system performance, and a hybrid NSGA-II-TOPSIS approach is employed to simultaneously optimise T_max, ΔT, and P_pump. By systematically considering the combined effects of channel number, channel width, channel spacing, and coolant mass flow rate, this study provides a more comprehensive and practical design methodology for advanced BTMSs. The remainder of this paper is organised as follows. Section 2 describes the model development and numerical methodology, including the battery model, boundary conditions, and experimental validation. Section 3 presents the results and discussion, including parametric analysis and multi-objective optimization results. Finally, Section 4 summarises the study’s key findings and conclusions.

2. Model and Methodology

2.1. Simulation Model

The overall configuration of the BTMS considered in this study is illustrated in Figure 1a. The model consists of a lithium-ion pouch battery module integrated with a cooling plate-based indirect liquid cooling system to enhance heat dissipation during fast charging. The battery module adopts a 6S2P configuration, comprising twelve pouch cells. The 6S2P configuration was selected as it represents a typical module-level arrangement in EV battery systems. In practical EV battery packs, pouch cells are commonly organized in series-parallel configurations to achieve the required voltage and capacity balance. For example, commercial EV battery modules often use a 6S2P configuration, where cells are grouped to improve both energy density and thermal management. This configuration allows the present model to capture realistic thermal interactions between cells while maintaining a manageable computational cost. Each cell has a nominal capacity of 68.0 Ah, with charge and discharge cutoff voltages of 4.10 V and 3.0 V, respectively. The pouch cell used in this study was a commercial large-format LIB with a nickel-cobalt-manganese (NCM) cathode and a graphite anode, which is representative of batteries commonly used in EV applications. The inter-cell spacing is maintained at 5 mm to accommodate the insertion of cooling plates while ensuring compact module design. Each cell is equipped with two electrode tabs, namely the positive and negative tabs, which are electrically connected through busbars to achieve the required series-parallel arrangement. In addition, in the current study, each pouch cell is modeled as a homogenized solid domain with effective thermophysical properties, which represent the combined behavior of the electrode layers, separator, and electrolyte. This approach is widely adopted in battery thermal simulations to reduce computational complexity while preserving the overall heat generation and conduction characteristics of the cell [79,80].

To effectively regulate the module’s thermal behavior, 13 cooling plates are arranged alternately between adjacent battery cells and placed in direct contact with the cell surfaces. This configuration minimizes thermal contact resistance and enhances heat transfer from the battery to the coolant. Coolant is supplied through a coolant distribution plate at the bottom of the module, ensuring uniform flow to each cooling plate. After absorbing heat from the battery surfaces, the coolant is collected by a coolant collection plate positioned at the top and subsequently discharged through the outlet port. The diameters of both the inlet and outlet ports are set to 10 mm, providing a balance between flow distribution uniformity and ΔP. The detailed internal structure of the cooling plates is presented in Figure 1b. Each plate features a series of parallel coolant channels that facilitate convective heat transfer between the coolant and the battery surfaces. The coolant flows upward through these channels, promoting effective heat removal and reducing the likelihood of localized hot spots. In this study, key geometric parameters of the cooling plates, including the number of channels (N), channel width (W), and channel spacing (S), are systematically varied and optimized to achieve a balance between thermal performance and pumping power consumption. The geometric parameters in the numerical model are summarised in

Table 1. The geometric parameters of components employed in the numerical model.

Components	Specifications	Value	Unit
Battery	Length	348.0	mm
	Width	104.0	mm
	Thickness	8.5	mm
Cooling plate	Length	348.0	mm
	Width	104.0	mm
	Thickness	5.0	mm
Coolant channel	Width	2.5, 5.0, 7.5, 10.0, 12.5	mm
	Height	2.0	mm
	Spacing	4.0, 5.0, 6.0, 7.0, 8.0	mm
Inlet/Outlet	Diameter	10.0	mm

.

2.2. Battery Heat Generation Model

The thermal behavior of LIBs during operation is governed by the complex coupling between electrochemical reactions and heat generation. In this study, a multi-scale multi-domain (MSMD) model incorporating the Newman–Tiedemann–Gu–Kim (NTGK) formulation is employed to describe the electro-thermal characteristics of the battery. This approach enables efficient prediction of heat generation while maintaining computational feasibility for module-level simulations [4,19,81].

The governing energy conservation equation accounts for conductive heat transfer and volumetric heat generation within the battery, expressed as [19,81]:

$$\rho C_p{\displaystyle \frac{\partial T}{\partial t}}-\nabla ·(k\nabla T)=q_{gen}$$

(1)

where $\rho$, $C_p$, and $k$ denote density, specific heat capacity, and thermal conductivity, respectively, and $q_{gen}$ represents the total volumetric heat generation rate. In the MSMD framework, heat generation is primarily attributed to electrochemical reactions under normal operating conditions.

The NTGK model characterizes the electrochemical heat generation through the relationship between current density and overpotential. The volumetric current transfer rate is defined as [19,81]:

$$j={\displaystyle \frac{Q_{nominal}}{Q_{ref}Vol}}Y\left[U-V\right]$$

(2)

where $Q_{nominal}$ and $Q_{ref}$ are the nominal and reference capacities, respectively, $Vol$ is the active volume of the cell, $U$ is the open-circuit voltage, $V$ is the terminal voltage, and $Y$ denotes the effective electrical conductivity. The corresponding heat generation rate is expressed as [19,81]:

$$q_{gen}=j\left[U-V-T{\displaystyle \frac{dU}{dT}}\right]$$

(3)

This formulation accounts for both irreversible (ohmic and polarization) heat and reversible entropic heat contributions, enabling accurate prediction of thermal behavior under varying operating conditions.

A key advantage of the NTGK model lies in its ability to derive electrochemical parameters directly from experimental discharge data. Specifically, the open-circuit voltage $U$ and effective conductivity $Y$ are expressed as polynomial functions of the depth of discharge ($DOD$) [19,81]:

$$DOD={\displaystyle \frac{Vol}{3600Q_{nominal}}}{\int }_0^{t}jdt$$

(4)

$$U=\sum _{n=0}^5{a}_n{\left(DOD\right)}^n$$

(5)

$$Y=\sum _{n=0}^5{b}_n{\left(DOD\right)}^n$$

(6)

where $a_n$ and $b_n$ are fitting coefficients obtained from experimental characterization. This semi-empirical approach significantly reduces model complexity while preserving predictive accuracy, making it suitable for large-scale simulations.

It should be noted that, under the normal charging conditions considered in this study, additional heat sources, such as internal short-circuiting and thermal abuse reactions, are neglected. Therefore, the total heat generation is dominated by electrochemical processes, which are sufficiently captured by the NTGK formulation. In general, the MSMD-NTGK model provides a robust, computationally efficient framework for simulating battery heat generation, laying the foundation for subsequent thermal analysis and optimization of the cooling plate-based indirect thermal management system. The NTGK fitting parameters including the $U$ and $Y$ coefficients are summarized in

Table 2. Summary of NTGK correction parameters applied in the simulations.

Coefficient	${\mathit{a}}_{\mathit{n}}$$\mathbf{for} \mathit{U}$$(\mathit{D}\mathit{O}\mathit{D}$)	${\mathit{b}}_{\mathit{n}}$$\mathbf{for} \mathit{Y}$$(\mathit{D}\mathit{O}\mathit{D}$)
$n=0$	4.084909	736.8703
$n=1$	−2.676560	−2175.105
$n=2$	9.211597	15,787.24
$n=3$	−18.00205	−23,290.85
$n=4$	16.01645	−6299.367
$n=5$	−5.338386	24,283.76

.

Assuming the coolant behaves as a steady, incompressible, and constant-property viscous fluid, and that the flow within the cooling channels remains in the laminar regime (Re < 2300), the governing equations, including the conservation equations of mass, momentum, and energy, can be formulated accordingly as follows [73]:

$${\displaystyle \frac{\partial {\rho }_c}{\partial t}}+\nabla \left({\rho }_{c}u\right)=0$$

(7)

$${\rho }_c\left[{\displaystyle \frac{\partial u}{\partial t}}+\left(u·\nabla \right)u\right]=-\nabla p+\mu ({\nabla }^{2}u)$$

(8)

$${\rho }_c{c}_{p,c}{\displaystyle \frac{\partial T_c}{\partial t}}+\nabla ·\left({\rho }_c{c}_{p,c}u{T}_c\right)=\nabla ·\left(k_c\nabla T_c\right)$$

(9)

where ${\rho }_c$,$u$, $\mu$, $p$, $c_{p,c}$, $k_c$ and $T_c$ are the density, velocity, dynamic viscosity, static pressure, specific heat capacity, thermal conductivity and temperature of coolant, respectively.

The temperature difference within the battery module is evaluated as [4,19]:

$$∆T=T_{max, battery}-T_{min,battery}$$

(10)

where $T_{max, battery}$ and $T_{min,battery}$ denote the maximum and minimum temperatures measured among all battery cells, respectively.

The pressure drop (ΔP) across the cooling channels is calculated based on the difference between the inlet and outlet pressures of the coolant [4,19]:

$$∆P_{coolant} =P_{inlet, coolant}-P_{outlet,coolant}$$

(11)

In addition to thermal performance, the hydraulic performance of the cooling system is characterized by the pumping power, which represents the energy required to drive the coolant flow through the channels. It is expressed as [78]:

$$P_{pump}=∆P_{coolant}·A_{in}·u_{in}$$

(12)

where $∆P_{coolant}$ is the pressure drop, $A_{in}$ is the inlet cross-sectional area, and $u_{in}$ is the inlet velocity of the coolant. These parameters collectively quantify the energy consumption associated with the cooling system operation. It should be noted that the pumping power considered in this study represents only the hydraulic energy required to drive the coolant through the cooling plates. In practical battery thermal management systems, additional energy consumption is associated with external components, such as chillers, radiators, and compressors, required to maintain the inlet coolant temperature [82]. Therefore, the present analysis focuses on component-level energy performance, and the reported pumping power does not represent the total energy consumption of the full thermal management system.

2.3. Boundary Conditions

In the present study, ideal thermal contact is assumed between the battery surface and the cooling plate, implying negligible thermal contact resistance. This assumption is reasonable for well-assembled battery modules where sufficient mechanical compression and thermal interface materials are applied to enhance heat transfer. However, it should be noted that, in practical applications, interfacial thermal resistance may exist and could slightly affect the local temperature distribution.

The thermal–hydraulic performance of the battery module and cooling system was numerically investigated using ANSYS Fluent 2025 R2 (Ansys Inc., Canonsburg, PA, USA). Appropriate boundary conditions and assumptions were applied to accurately model the BTMS’s operating conditions. The initial temperature of the battery module and the inlet coolant temperature were both set to 25 °C. The heat generation within the battery was determined under 3C fast charging conditions, representing a high thermal load scenario relevant to practical applications. It should be noted that the present study assumes a constant current (CC) charging condition at 3C to represent a worst-case thermal scenario. In practical applications, battery charging typically follows a constant current-constant voltage (CC-CV) protocol, where the current gradually decreases during the constant voltage phase, thereby reducing heat generation. Therefore, the predicted temperatures in this study may be slightly higher than those under real operating conditions. However, this conservative assumption ensures that the cooling system is evaluated under the most demanding thermal conditions, providing a robust basis for design and optimization. The coolant mass flow rate was varied from 1 to 5 LPM to evaluate its effect on system performance. Within this range, the calculated Reynolds number remains below 2300, indicating that the flow is in the laminar regime. Therefore, a laminar flow model was employed for all simulations. The flow is assumed to be steady-state, which is appropriate for evaluating the average thermal–hydraulic performance of the system during the design stage. This assumption neglects transient effects such as pump-induced flow pulsations and dynamic fluctuations, which may occur in practical applications. The coolant was modelled as water, treated as an incompressible fluid with constant thermophysical properties. The cooling plates were assumed to be made of aluminium, owing to its high thermal conductivity and widespread use in battery thermal management applications. At the inlet, a mass flow rate boundary condition was specified, while a pressure outlet boundary condition was applied at the outlet to ensure stable flow development. In the present study, the thermophysical properties of the battery materials and coolant are assumed to be constant and are evaluated at a reference temperature of 25 °C. This assumption is reasonable within the investigated temperature range, where property variations are relatively small. However, it should be noted that temperature-dependent properties may influence heat transfer behavior across a wider range of operating conditions. The thermophysical properties of the battery, cooling plate, and coolant used in the simulations are summarised in

Table 3. The thermophysical properties of materials employed in the numerical model [81].

Specifications	Aluminum	Copper	Battery	Water
Density (kg/m3)	2719	8978	2505	998.2
Specific heat capacity (J/kg·K)	871	381	960	4182
Thermal conductivity (W/m·K)	202.4	387.6	Normal: 0.566/ Plane: 18.6	0.6
Dynamic viscosity (kg/m·s)	-	-	-	0.001003

. These parameters provide the necessary inputs for accurately capturing the coupled heat transfer and fluid flow behavior within the system.

2.4. Mesh Independence Test

The computational mesh was generated using ANSYS Fluent Meshing 2025 R2 (Ansys Inc., Canonsburg, PA, USA). To ensure adequate spatial resolution for accurately capturing both heat transfer and fluid flow behavior within the battery module, a refined meshing strategy was adopted. Local body sizing was applied to solid regions to enhance resolution in critical areas while controlling the overall cell count. For surface meshing, curvature and proximity size functions were employed to automatically refine regions with high geometric complexity and narrow gaps between adjacent components. Additionally, inflation layers were introduced along solid walls in the fluid domain to accurately resolve near-wall velocity gradients and thermal boundary layers. The volume mesh was constructed using the poly-hexcore method, which combines polyhedral elements near complex geometries with a structured hexcore mesh in the bulk region, thereby improving computational efficiency without compromising accuracy.

To verify the independence of the numerical results from mesh resolution, a mesh-independence study was conducted using five mesh densities. The total cell counts for the tested cases were 566,802 (Case 1), 1,529,228 (Case 2), 2,664,620 (Case 3), 3,330,436 (Case 4), and 4,353,094 (Case 5). The results of this analysis are presented in Figure 2. It is observed that the variation in key performance parameters becomes negligible as the mesh is refined. Specifically, the difference in T_max between Case 4 and Case 5 is only 0.098%, while the deviation in ΔP is 0.15%, indicating that the solution is grid-independent. Considering both numerical accuracy and computational cost, Case 4 was selected as the optimal mesh for all subsequent simulations. The final mesh configuration employed in this study is illustrated in Figure 3, demonstrating the detailed discretization of the battery module and cooling plate system.

2.5. Experimental Validation of the Battery Thermal Model

Experimental investigations were conducted to determine the NTGK model parameters for accurate heat generation prediction and to validate the numerical simulation framework used to assess the battery’s thermal behavior during charging. The overall experimental configuration is illustrated in Figure 4. A TEX60-400 programmable power supply (Toyotech Co., Ltd., Incheon, Republic of Korea) with maximum power of 31.22 kW was employed for battery charging, operating under a three-phase input of 380 V (±10%) and a frequency range of 50–60 Hz. Discharge processes were carried out using a TLF1200 electronic load (Toyotech Co., Ltd., Incheon, Republic of Korea), which supports a maximum power of 1200 W, with an operating voltage range of 1–150 V and a current range of 0–240 A. Voltage and temperature data were continuously recorded using a Graphtec GL840 data acquisition system (GRAPHTEC, Yokohama, Japan) to ensure high-resolution monitoring. All experiments were performed in a temperature-controlled chamber maintained at 25 °C, thereby minimizing environmental variability. The battery was charged at 0.5 C, 1.0 C, 1.5 C, 2.0 C, 2.5 C, and 3.0 C, with an initial voltage of 3.20 V and a charge cutoff voltage of 4.10 V. To capture the battery temperature distribution, nine T-type thermocouples with a measurement range of −220 °C to 400 °C and an accuracy of ±0.1 °C were strategically affixed to the battery surface. Specifically, three thermocouples were positioned near the positive tab, three at the geometric center of the cell, and three near the negative tab. Experimental observations consistently indicated that the region adjacent to the positive tab exhibited the highest temperature during charging. Consequently, this location was selected as the representative point for validating the numerical model.

Figure 5 presents a comparison between the simulated and experimental temperature profiles during charging at rates of 1.0 C, 2.0 C and 3.0 C. The numerical simulation was performed on a single battery cell under natural convection conditions, with a convective heat transfer coefficient of 10 W/m²·K. Both the battery’s initial temperature and the ambient temperature were set to 25 °C. The results demonstrate that the deviations between simulated and measured temperatures remain below 5% throughout the charging process at multiple C-rates. This close agreement confirms the reliability and accuracy of the proposed NTGK-based numerical model. Therefore, the validated model is deemed suitable for subsequent simulations of the 6S2P battery module integrated with a cooling plate-based indirect thermal management system.

3. Results and Discussion

This section presents a comprehensive analysis of the thermal–hydraulic performance of the proposed cooling plate-based indirect liquid cooling system for the 6S2P LIB module under 3C fast charging conditions. First, a single-parameter analysis is conducted to systematically evaluate the effects of key design and operating variables, including the number of coolant channels, channel width, channel spacing, and coolant mass flow rate, on T_max, ΔT, and ΔP. These results provide fundamental insights into the trade-offs between heat transfer enhancement and pumping power consumption. Subsequently, a multi-objective optimization study is performed using an ANN-based surrogate model integrated with NSGA-II and TOPSIS to identify the optimal design configuration. The relationships between design variables and performance metrics are analyzed, and the surrogate model’s predictive capability is validated. Finally, the optimized results are verified through CFD simulations to confirm the effectiveness and reliability of the proposed optimization framework. From a long-term perspective, the thermal–hydraulic trade-off also influences battery degradation, as excessive temperature and non-uniform thermal fields can accelerate aging mechanisms. Therefore, improving both T_max and ΔT is beneficial not only for immediate thermal safety but also for enhancing battery durability. In addition, it should be noted that the thermal results are obtained under a CC charging condition at 3C, which represents a conservative scenario. In practical CC-CV charging, the temperature rise is expected to be slightly lower, particularly during the CV charging stages.

3.1. Analysis of a Single Parameter

The ranges of the design variables were determined based on geometric constraints of the cooling plate structure, engineering feasibility, and relevant literature on liquid-cooled battery thermal management systems. In addition, preliminary sensitivity analyses were conducted to ensure that the selected ranges capture the regions with significant variations in thermal and hydraulic performance. Therefore, these ranges are considered representative of the feasible design space for subsequent analysis and optimization.

3.1.1. Effect of the Number of Coolant Channels

The geometric configuration of coolant channels plays a critical role in determining the thermal–hydraulic performance of cooling plate-based BTMSs. In particular, the number of channels directly influences both the effective heat transfer area and the coolant flow distribution, while simultaneously affecting flow resistance and pumping power. Increasing the number of channels can enhance heat dissipation by enlarging the contact area between the coolant and the cooling plate. However, it may also lead to increased ΔP due to more complex flow paths [72]. Therefore, a systematic investigation of channel number is essential to identify an optimal balance between cooling performance and energy consumption.

In this section, cooling plate configurations with different numbers of channels, namely N = 3, 4, and 5, are analyzed, as illustrated in Figure 6. To ensure a fair comparison, the channel width is kept constant at W = 5 mm for all cases, while only the number of channels is varied. The battery module operates under 3C fast charging, a high heat generation scenario relevant to practical EV applications. The coolant is supplied at an inlet mass flow rate corresponding to 3 LPM, with an initial temperature of 25 °C, ensuring consistent boundary conditions across all configurations. Under these conditions, the influence of channel number on both thermal performance and hydraulic performance is evaluated. This approach enables a comprehensive assessment of how channel design affects the trade-off between enhanced heat transfer and increased pumping power requirements in the cooling plate system.

The influence of the number of coolant channels on the thermal–hydraulic performance of the cooling plate is presented in Figure 7. As the number of channels increases from N = 3 to N = 5, a gradual improvement in thermal performance is observed. Specifically, the T_max decreases from 30.42 °C (N = 3) to 30.11 °C (N = 5), while the ΔT is reduced from 4.47 °C to 4.35 °C, indicating enhanced temperature uniformity within the battery module. This improvement can be attributed to the increased heat transfer area and more uniform coolant distribution associated with a higher number of channels [72,83]. It should be noted that reducing the T_max and ΔT is beneficial not only for immediate thermal safety but also for mitigating long-term degradation effects associated with thermal stress. From a hydraulic perspective, the ΔP exhibits a non-monotonic trend. It increases slightly from 1766.47 Pa (N = 3) to 1775.3 Pa (N = 4) due to the increased flow resistance, but then decreases to 1742.25 Pa (N = 5). This reduction at N = 5 suggests a more favorable flow distribution and reduced localized flow resistance despite the increased number of channels. Considering both thermal and hydraulic performance, the configuration with N = 5 channels achieves the lowest T_max, improved ΔT, and the minimum ΔP among the studied cases. Therefore, N = 5 is identified as the optimal configuration for subsequent analysis, providing the best compromise between enhanced heat transfer and minimized pumping power.

Figure 8 presents the temperature contour plots of the battery module for cooling plate configurations with different numbers of coolant channels. The temperature field is significantly influenced by the channel arrangement. In cases with fewer channels, a relatively larger high-temperature region is concentrated near the battery module’s center, suggesting insufficient heat removal and non-uniform coolant distribution. As the number of channels increases, the high-temperature region gradually diminishes and becomes more uniformly distributed, indicating enhanced heat transfer performance. In particular, the configuration with the most channels exhibits a more homogeneous temperature field, with lower peak temperatures and smoother temperature gradients across the module. This improvement can be attributed to the increased contact area between the coolant and the cooling plate, as well as a more effective flow distribution, which facilitates more uniform heat extraction. Overall, the contour plots clearly demonstrate that increasing the number of coolant channels improves thermal uniformity and reduces thermal hotspots within the battery module.

Figure 9 illustrates the velocity streamlines within the cooling plates for configurations with different numbers of coolant channels. The flow enters through the inlet region, where higher velocities are observed, and then distributes into the parallel channel network. For configurations with fewer channels, the flow distribution appears less uniform, with noticeable variations in streamline density and velocity magnitude among channels, indicating potential flow maldistribution and localized regions of reduced convective heat transfer. As the number of channels increases, the flow becomes more evenly distributed across the entire cooling plate, as evidenced by the more uniform streamline patterns and consistent velocity gradients. Additionally, the higher channel count reduces flow velocity within individual channels by dividing the total flow rate, contributing to a more balanced hydraulic behavior. The smoother flow paths and reduced recirculation zones in configurations with more channels indicate improved flow uniformity and reduced hydraulic losses. In general, the streamline distributions indicate that increasing the number of coolant channels enhances flow uniformity and promotes more effective, stable convective heat transfer within the cooling plate.

3.1.2. Effect of the Coolant Channel Width

The coolant channel width is a key geometric parameter influencing both the thermal and hydraulic performance of cooling plate-based BTMS. Variations in channel width directly affect the heat transfer area, flow velocity distribution, and hydraulic resistance within the cooling plate. A narrower channel can enhance convective heat transfer due to higher fluid velocity, but may result in a significant increase in ΔP. Conversely, wider channels reduce flow resistance but may weaken heat transfer effectiveness due to lower flow velocity and reduced surface interaction [72]. Therefore, it is essential to systematically investigate the influence of channel width to achieve an optimal balance between cooling efficiency and pumping power consumption. In this section, cooling plate configurations with different channel widths of W = 2.5, 5.0, 7.5, 10.0, and 12.5 mm are examined. To isolate the effect of channel width, all other design parameters are kept constant. Specifically, each cooling plate contains N = 5 channels, with a fixed spacing of S = 5 mm between adjacent channels. The simulations are conducted under consistent operating conditions representative of high thermal load scenarios. The battery module operates at a fast charging rate of 3C, and water is used as the coolant with a mass flow rate of 3 LPM and an inlet temperature of 25 °C. Under these controlled conditions, the impact of channel width on T_max, ΔT, and ΔP is evaluated. This analysis provides insight into how channel geometry influences the trade-off between enhanced heat transfer and hydraulic performance, thereby supporting the identification of an optimal channel width for the cooling plate design.

The influence of coolant channel width on the thermal–hydraulic performance of the cooling plate is illustrated in Figure 10. As channel width increases from 2.5 mm to 12.5 mm, a clear trade-off between thermal performance and hydraulic behavior is observed. Specifically, the T_max increases slightly from 29.95 °C to 30.17 °C, while the ΔT rises from 4.12 °C to 4.43 °C, indicating a gradual deterioration in both cooling effectiveness and temperature uniformity. This trend can be attributed to a reduction in coolant velocity in wider channels at a constant mass flow rate, which weakens convective heat transfer and reduces heat removal from the battery surface [72]. Conversely, the ΔP decreases significantly from 2168.14 Pa at W = 2.5 mm to 1735.31 Pa at W = 12.5 mm. This behavior is expected due to the increase in hydraulic diameter, which lowers flow resistance and frictional losses [73]. In narrower channels, although higher fluid velocities enhance convective heat transfer, they also lead to substantially higher ΔP, increasing pumping power requirements. In summary, the results demonstrate a typical thermal–hydraulic trade-off with narrower channels improving heat transfer at the expense of higher ΔP, while wider channels reduce pumping power but degrade cooling performance. Therefore, optimizing the width of the coolant channel is crucial to ensuring cooling efficiency while minimizing energy consumption.

Figure 11 illustrates the temperature distribution contours of the battery module for cooling plate configurations with varying coolant channel widths. It can be observed that the channel width has a noticeable influence on both the magnitude and spatial distribution of temperature within the module. For narrower channels, the temperature field is relatively uniform, with a smaller high-temperature region concentrated near the battery’s center, indicating effective heat removal due to higher coolant velocity and enhanced convective heat transfer. As the channel width increases, the high-temperature region gradually expands and becomes more pronounced, particularly in the module’s core. This behavior suggests a reduction in heat transfer efficiency associated with lower coolant velocities in wider channels under constant mass flow rate conditions. Furthermore, wider channels exhibit smoother but less effective temperature gradients, indicating diminished thermal interaction between the coolant and the battery surface. Overall, the contour plots demonstrate that narrower channel widths improve thermal uniformity and lower peak temperatures, while wider channels tend to weaken cooling performance despite offering lower hydraulic resistance.

Figure 12 presents the velocity streamline distributions for cooling plate configurations with different coolant channel widths. It can be observed that the channel width significantly affects both the flow distribution and velocity magnitude within the cooling system. In narrower channels, the streamlines are more densely packed, with higher-velocity regions near the inlet and within the channels, indicating accelerated flow due to the reduced hydraulic diameter. This results in stronger convective heat transfer but also reflects increased flow resistance. As the channel width increases, the flow becomes more evenly distributed across the channels, with reduced velocity magnitude as the same mass flow rate is distributed over a larger cross-sectional area. The streamline patterns appear smoother and less concentrated, indicating lower flow resistance and improved hydraulic performance. However, wider channels also exhibit lower flow intensity within individual channels, which may reduce heat transfer effectiveness. In general, the streamlined results indicate that increasing channel width improves flow uniformity and reduces ΔP, but at the expense of lower coolant velocity and potentially diminished thermal performance.

3.1.3. Effect of the Coolant Channel Spacing

The spacing between adjacent coolant channels (S) is an important geometric parameter that significantly influences the thermal–hydraulic performance of cooling plate-based BTMSs. Channel spacing directly affects the distribution of coolant flow, effective heat transfer area, and thermal interaction between neighboring channels. A smaller spacing can enhance heat extraction by increasing the density of cooling channels and improving surface coverage. However, it may also lead to flow interference and increased ΔP. In contrast, larger spacing reduces flow resistance but may result in insufficient cooling coverage and the formation of localized hot spots. Therefore, investigating the effect of channel spacing is essential to achieve an optimal balance between thermal uniformity, cooling efficiency, and pumping power consumption. In this section, cooling plate configurations with different channel spacings of S = 4.0, 5.0, 6.0, 7.0, and 8.0 mm are systematically evaluated. To isolate the influence of this parameter, all other geometric and operating conditions are kept constant. Specifically, each cooling plate has N = 5 coolant channels, with a fixed channel width of W = 12.5 mm. The simulations are conducted under consistent operating conditions representative of high-thermal-load scenarios. The battery module operates at a fast charging rate of 3C, and water is used as the coolant with a volumetric flow rate of 3 LPM and an inlet temperature of 25 °C. Under these controlled conditions, the impact of channel spacing on T_max, ΔT, and ΔP is analyzed. This investigation provides insights into how the spatial arrangement of coolant channels affects the trade-off between enhanced heat transfer and hydraulic performance, thereby guiding the optimal design of cooling plate structures for battery thermal management applications.

The influence of coolant channel spacing on the thermal–hydraulic performance of the cooling plate is presented in Figure 13. As the spacing increases from S = 4 mm to S = 8 mm, only a marginal variation in thermal performance is observed. The T_max remains within a narrow range, increasing slightly from 30.12 °C to 30.24 °C, while the ΔT fluctuates between 4.39 °C and 4.46 °C, indicating that channel spacing has a relatively limited impact on overall temperature uniformity under the investigated conditions. This behavior can be attributed to the fixed number of channels and constant flow rate, which ensure that the overall heat removal capacity is not significantly altered despite changes in channel distribution. In contrast, the ΔP exhibits a nonlinear trend, initially increasing from 1732.33 Pa (S = 4 mm) to 1735.31 Pa (S = 5 mm), then decreasing to 1713.53 Pa (S = 7 mm), and finally increasing again to 1732.07 Pa at S = 8 mm. This variation is associated with the combined effects of flow interaction between adjacent channels and changes in flow passage geometry. At smaller spacing, the proximity of channels may induce stronger flow interference and localized resistance, while moderate spacing improves flow distribution and reduces frictional losses. However, excessively large spacing can lead to less efficient utilization of the cooling surface and slight increases in flow recirculation or uneven distribution. In summary, the results indicate that coolant channel spacing has a secondary influence on thermal performance but a noticeable effect on hydraulic behavior. Therefore, optimizing coolant channel spacing is crucial to ensure stable cooling efficiency and the lowest possible pump energy consumption.

Figure 14 presents the temperature–contour plots of the battery module for cooling plate configurations with varying coolant channel spacing. The overall temperature field remains relatively consistent across all cases, with only minor variations in both peak temperature and spatial distribution. For smaller spacing values, the temperature contours exhibit slightly more uniform coverage across the battery surface, with a relatively compact high-temperature region near the center. As the channel spacing increases, the high-temperature region becomes marginally more dispersed, indicating a slight reduction in local heat removal effectiveness due to increased distance between adjacent cooling channels. However, the differences among all configurations are not pronounced, suggesting that channel spacing has a limited influence on overall thermal performance under the present operating conditions. This can be attributed to the fixed number of channels and constant flow rate, which maintain a similar overall heat transfer capacity regardless of spacing variations. Nonetheless, subtle changes in the contour gradients indicate that moderate spacing promotes a more balanced heat distribution, whereas excessively large spacing may reduce cooling coverage and lead to slightly less uniform temperature fields. In general, the temperature contours confirm that while channel spacing affects local heat transfer characteristics, its impact on global thermal behavior is relatively minor compared to other geometric parameters.

Figure 15 illustrates the velocity streamline distributions for cooling plate configurations with different coolant channel spacings. Overall, the flow patterns remain qualitatively similar across all cases, indicating that channel spacing has a relatively limited influence on the global flow structure under the same inlet conditions. The coolant enters the system with a higher velocity at the inlet region and is subsequently distributed into the parallel channel network, where the flow gradually develops along the channel length. For smaller spacing values, the streamlines appear slightly more concentrated, suggesting stronger interaction between adjacent channels and greater flow interference. As the channel spacing increases, the flow paths become more separated and streamlined, resulting in smoother flow trajectories and slightly more uniform velocity distribution within individual channels. This behavior contributes to reduced localized flow resistance and a more balanced hydraulic performance. However, the differences in streamline patterns among the configurations are not pronounced, which is consistent with the relatively small variation in ΔP observed in the quantitative results. This indicates that, under the present design and operating conditions, channel spacing primarily affects local flow characteristics rather than significantly altering the overall flow distribution. In general, the streamlined results confirm that coolant channel spacing has a modest impact on flow uniformity and hydraulic behavior compared to other geometric parameters such as channel width and number of channels.

3.1.4. Effect of the Mass Flow Rate

The coolant mass flow rate is a critical operating parameter that directly influences the thermal and hydraulic performance of cooling plate-based BTMSs. Variations in flow rate affect the convective heat transfer coefficient, coolant velocity, and overall heat removal capacity. Increasing the flow rate generally enhances heat dissipation by improving convective heat transfer. However, it also increases ΔP and pumping power consumption [4,19,76]. Therefore, it is essential to investigate the effect of mass flow rate to identify an optimal operating condition that balances thermal performance and energy efficiency. In this section, the cooling performance is evaluated for different coolant flow rates of 1.0, 2.0, 3.0, 4.0, and 5.0 LPM. To ensure a consistent comparison, all geometric parameters are kept constant. Specifically, each cooling plate is designed with N = 5 channels, a channel width of W = 12.5 mm, and a channel spacing of S = 7 mm. The simulations are conducted under representative high-thermal-load conditions, with the battery module operating at a fast charging rate of 3C. Water is used as the coolant, with an inlet temperature of 25 °C. Under these controlled conditions, the influence of coolant flow rate on T_max, ΔT, and ΔP is systematically analyzed. This investigation provides insight into the trade-off between enhanced heat transfer at higher flow rates and the associated increase in hydraulic losses, thereby supporting the determination of an optimal flow rate for efficient battery thermal management.

The effect of coolant mass flow rate on the thermal–hydraulic performance of the cooling system is illustrated in Figure 16. As the flow rate increases from 1.0 LPM to 5.0 LPM, a significant improvement in thermal performance is observed. The T_max decreases markedly from 34.85 °C to 29.31 °C, while the ΔT is reduced from 6.66 °C to 3.83 °C, indicating enhanced cooling effectiveness and improved temperature uniformity across the battery module. This trend is primarily due to increased coolant velocity, which enhances the convective heat transfer coefficient and promotes more efficient heat removal from the battery surface [73,76]. However, this improvement in thermal performance is accompanied by a substantial increase in ΔP, which rises sharply from 275.57 Pa at 1.0 LPM to 4350.56 Pa at 5.0 LPM. This behavior is consistent with fluid dynamics principles, in which ΔP increases approximately with the square of the flow velocity due to intensified frictional and inertial effects within the channels [19,73,76]. The non-linear increase in pumping power with mass flow rate is mainly due to the quadratic dependence of pressure drop on flow velocity in the laminar flow regime. It should be noted that the present analysis is based on steady-state assumptions and does not account for transient flow behavior or pump-induced pulsations. In practical systems, such dynamic effects may introduce additional fluctuations in pressure and flow rate. However, their influence on time-averaged thermal performance is generally limited. At lower flow rates, the coolant has insufficient capacity to remove heat effectively, leading to higher temperatures and larger thermal gradients. Conversely, at higher flow rates, although heat transfer is significantly improved, the marginal benefit in temperature reduction diminishes, particularly beyond 3.0–4.0 LPM, while the hydraulic penalty increases rapidly. In summary, the results demonstrate a clear trade-off between thermal performance and pumping power. While higher flow rates provide superior cooling, they incur significantly higher energy consumption. Therefore, optimizing the coolant mass flow rate is particularly important to ensure both cooling efficiency and minimize pump energy consumption.

Figure 17 presents the temperature–contour distribution of the battery module at different coolant mass flow rates. A clear improvement in thermal performance is observed as the flow rate increases. At the lowest flow rate of 1.0 LPM, a pronounced high-temperature region is concentrated in the module’s central area, indicating insufficient heat removal and poor temperature uniformity. As the flow rate increases to 2.0 and 3.0 LPM, the high-temperature region gradually diminishes and shifts to a smaller, localized area, accompanied by a reduction in overall temperature. At higher flow rates of 4.0 and 5.0 LPM, the temperature field becomes significantly more uniform, with the entire module exhibiting lower temperatures. The peak temperature is substantially reduced, and the temperature gradients across the module are smoother, indicating enhanced convective heat transfer and more effective heat dissipation. This improvement is attributed to the increased coolant velocity, which strengthens the convective heat transfer coefficient and promotes more uniform heat extraction from the battery surfaces. In general, the contour plots clearly demonstrate that increasing the coolant mass flow rate effectively suppresses thermal hotspots and improves temperature uniformity, although the incremental benefits become less pronounced at higher flow rates.

Figure 18 illustrates the velocity streamlines within the cooling plates at different coolant mass flow rates. As the flow rate increases, a significant change in velocity magnitude is observed, while the overall flow pattern remains similar. At lower flow rates of 1.0 LPM, the streamlines are relatively sparse and low-velocity, indicating weaker flow intensity and limited convective heat transfer. As the flow rate increases to 2.0 and 3.0 LPM, the streamline density increases, and the velocity magnitude increases, particularly near the inlet and outlet regions, suggesting improved coolant penetration and more effective flow distribution across the channels. At higher flow rates of 4.0 and 5.0 LPM, the velocity within the channels increases substantially, as indicated by the emergence of green to yellow regions near the inlet and along the flow paths. The streamlines become more uniformly distributed throughout the cooling structure, indicating enhanced flow uniformity and reduced stagnant zones. However, the intensified velocity gradients near the inlet also imply increased inertial effects and higher frictional losses, which contribute to the significant rise in ΔP observed in the quantitative results. In general, the streamline patterns demonstrate that increasing the coolant mass flow rate strengthens flow intensity and improves distribution within the cooling channels, thereby enhancing convective heat transfer. Nevertheless, this improvement is accompanied by increased hydraulic resistance, highlighting the inherent trade-off between thermal performance and pumping power.

3.2. Multi-Objective Optimization

Prior to developing the surrogate model, a systematic sampling strategy was used to generate a representative dataset for training and validation. In this study, Latin Hypercube Sampling (LHS) was adopted due to its superior space-filling and uniformity [84]. Unlike conventional random sampling, LHS ensures that each design variable is sampled across its entire range in a stratified manner, thereby providing efficient coverage of the design space with a limited number of samples. This property makes LHS particularly suitable for surrogate modeling and multi-objective optimization problems, where computational cost is a critical concern. The design space is defined by three input parameters, namely coolant channel width (W), coolant channel spacing (S), and coolant mass flow rate (V_in), while the corresponding output responses include T_max, ΔT, and P_pump. The selection of these three design variables is based on their direct influence on the thermal–hydraulic behavior of the cooling plate system. The coolant channel width affects the hydraulic diameter, coolant velocity, convective heat transfer intensity, and flow resistance. The coolant channel spacing determines the spatial distribution of cooling paths and the effective heat transfer coverage over the battery surface. Meanwhile, the coolant mass flow rate directly controls the convective heat transfer coefficient and pressure drop, thereby strongly influencing both cooling performance and pumping power. In the preliminary single-parameter analysis, the number of coolant channels was set to N = 5 to achieve the most favorable balance among T_max, ΔT, and ΔP. Therefore, W, S, and V_in were selected as the key variables for multi-objective optimization to simultaneously improve thermal performance and reduce hydraulic energy consumption. The ranges of the input variables are specified in

Table 4. Design variables and their ranges for Latin Hypercube Sampling (LHS).

Parameter	Range	Units
Coolant channel width (W)	2.5–12.5	mm
Coolant channel spacing (S)	4.0–8.0	mm
Coolant mass flow rate (Vin)	1.0–5.0	LPM

, which defines the feasible design domain for the sampling process. It should be noted that the selected parameter ranges define a bounded design space for the optimization process. While LHS ensures a uniform and space-filling distribution of samples within this domain, it does not strictly guarantee identification of the global optimum. However, the combination of ANN-based surrogate modeling and NSGA-II provides strong global search capability and enables efficient exploration of the design space. Therefore, the obtained optimal solution can be considered a near-global optimum within the defined parameter bounds. Using the LHS method, 30 design cases were generated to ensure adequate representation of the input space. For each sampled design point, CFD simulations were performed to obtain the corresponding thermal and hydraulic performance metrics. The resulting dataset, summarized in

Table 5. LHS-generated design samples and corresponding CFD simulation results for thermal–hydraulic performance.

Case	W (mm)	S (mm)	Vin (LPM)	Tmax (°C)	∆T (°C)	Ppump (W)
1	6.05	5.38	1.54	32.31	5.48	0.01521
2	12.05	7.93	4.95	29.34	3.84	0.3481
3	2.54	4	5	28.86	3.43	0.43689
4	12.3	4.09	4.25	29.46	3.94	0.23041
5	2.67	7.86	4.39	29.17	3.58	0.29604
6	11.85	7.94	1.55	32.39	5.67	0.01441
7	2.53	7.99	1.13	34.03	5.89	0.00882
8	12.27	4.46	1.58	32.21	5.66	0.01526
9	7.29	5.97	4.17	29.38	3.79	0.22282
10	7.09	7.99	2.96	30.17	4.32	0.08531
11	12.37	6.32	3.24	30.04	4.33	0.10655
12	2.5	5.36	3.29	29.72	3.97	0.1383
13	7.76	4.07	3.05	30.01	4.26	0.09275
14	7.31	7.24	1.04	34.61	6.37	0.00536
15	2.54	4	1.61	32.04	5.28	0.02161
16	7.43	4.3	4.95	29.06	3.6	0.36249
17	10.88	6.18	1.35	33	5.95	0.01011
18	7.2	7.83	4.73	29.24	3.71	0.32266
19	2.77	5.82	4.99	28.9	3.43	0.42133
20	2.67	7.23	2.75	30.21	4.24	0.08371
21	11.34	5.83	4.84	29.27	3.79	0.33545
22	2.64	6.28	1.15	33.87	5.89	0.00908
23	8.42	4.05	1.23	33.46	6.13	0.00829
24	11.56	7.89	3.35	30	4.28	0.11694
25	8.35	6.5	2.68	30.43	4.53	0.06454
26	4.29	4.11	3.64	29.51	3.87	0.16253
27	9.78	5.26	3.3	29.9	4.2	0.11503
28	5.23	7.09	3.79	29.52	3.85	0.17537
29	9.74	6.89	3.99	29.59	3.99	0.1947
30	11.28	4.13	2.88	30.21	4.45	0.07845

, serves as the foundation for training the ANN-based surrogate model. This data-driven approach enables the efficient approximation of the system behavior and facilitates subsequent multi-objective optimization, as described in the following sections.

3.2.1. Surrogate Modeling Using Artificial Neural Networks (ANN)

To efficiently explore the design space and reduce the computational cost associated with repeated CFD simulations, a surrogate modeling approach based on ANNs is employed. The optimization framework begins with data preprocessing, during which the input design variables and output performance metrics are defined and subsequently split into training and test datasets. All variables are standardized to ensure a zero mean and unit variance, thereby improving the stability and convergence of the learning process. The dataset used to train the ANN model consists of 30 design points generated using LHS, which ensures a uniform, space-filling distribution within the defined design space. The dataset was divided into training and validation subsets: 80% for training and 20% for validation, to assess the model’s predictive capability and generalization performance. Although the dataset is relatively small, the ANN model was selected for its strong ability to capture complex nonlinear relationships between input design variables and output responses. Compared to conventional surrogate models such as linear regression or response surface methods, ANN provides greater flexibility and higher prediction accuracy for nonlinear thermal–hydraulic systems. The high coefficient of determination (R²) and low root mean square error (RMSE) obtained in this study further confirm the reliability of the ANN model. In addition, LHS helps maximize the information content of the limited dataset, thereby improving the robustness of the surrogate model.

To reduce the risk of overfitting, the ANN architecture was kept relatively simple, and excessive hyperparameter tuning was avoided. The dataset was split into training and validation sets to evaluate the model’s generalization capability. In addition, the use of LHS ensures that the limited dataset provides a representative coverage of the design space. The high R² and low RMSE obtained in this study indicate that the model achieves good predictive accuracy without overfitting.

A multi-layer perceptron (MLP) model is adopted as the surrogate model, with separate ANN models constructed for each output variable. The models are trained using the limited-memory BFGS (L-BFGS) optimization algorithm. To enhance prediction robustness and reduce the influence of random initialization, an ensemble learning strategy is implemented, where multiple ANN models with identical hyperparameters but different initial weights are trained, and their averaged predictions are used as the final output.

To further improve model accuracy, Bayesian optimization is employed to determine optimal hyperparameters, including the number of hidden layers, the number of neurons, the activation function, the regularization coefficient, the tolerance, and the maximum iteration number. Model validation is performed using a repeated K-fold cross-validation approach, ensuring reliable generalization and minimizing overfitting. The performance of the surrogate models is evaluated based on the mean and standard deviation of the RMSE across validation folds. In general, the ANN-based surrogate modeling framework provides an accurate and computationally efficient representation of the thermal–hydraulic behavior of the cooling plate system, enabling its integration into subsequent multi-objective optimization procedures [4,11,84,85].

3.2.2. Optimized Results and Validation

To better understand the influence of design variables on the thermal–hydraulic performance of the cooling plate system, a correlation analysis was conducted between the input parameters (X1: coolant channel width, X2: channel spacing, X3: coolant mass flow rate) and the output responses (Y1: T_max, Y2: ΔT, Y3: P_pump), as illustrated in Figure 19. The results reveal that the coolant mass flow rate (X3) has the greatest impact on system performance. Specifically, X3 shows a strong negative correlation with both T_max (Y1: −0.93) and ΔT (Y2: −0.95), indicating that increasing the flow rate effectively reduces peak temperature and improves temperature uniformity. Conversely, X3 is strongly positively correlated with P_pump (Y3: 0.94), reflecting the substantial increase in hydraulic energy consumption associated with higher flow rates. In contrast, the geometric parameters X1 (channel width) and X2 (channel spacing) demonstrate relatively weak correlations with the output variables. Their correlation coefficients with Y1, Y2, and Y3 are all close to zero, suggesting that their influence on system performance is comparatively limited within the investigated parameter range.

Additionally, a strong positive correlation between Y1 and Y2 (0.98) is observed, indicating that configurations with higher T_max tend to exhibit larger ΔT. Meanwhile, both Y1 and Y2 show strong negative correlations with Y3 (−0.79 and −0.84, respectively), highlighting the inherent trade-off between thermal performance and pumping power. In general, the correlation analysis clearly demonstrates that coolant mass flow rate is the dominant factor governing the thermal–hydraulic behavior, while geometric parameters play a secondary role. These findings provide important guidance for the subsequent multi-objective optimization process, where achieving an optimal balance between cooling effectiveness and energy consumption is essential.

The predictive performance of the developed ANN surrogate models is evaluated using the coefficient of determination (R²) and the root mean square error (RMSE), as presented in Figure 20 and Figure 21. The results demonstrate excellent agreement between the predicted and simulated values for all output variables. For the T_max (Y1), the model achieves R² values of 0.9999 for the training set and 0.9931 for the test set, with corresponding RMSE values of 0.0013 and 0.0330, respectively. Similarly, for the ΔT (Y2), the model exhibits high accuracy with R² values of 0.9998 (training) and 0.9960 (testing), and low RMSE values of 0.0114 and 0.0174. For the P_pump (Y3), the model maintains strong predictive capability, with R² values of 0.9996 (training) and 0.9842 (testing), and RMSE values of 0.0024 and 0.0127. Overall, the consistently high R² values and low RMSE values across both training and testing datasets indicate that the ANN models possess excellent fitting accuracy and generalization capability, with no evident overfitting. These results confirm that the developed surrogate models are sufficiently accurate and reliable for subsequent multi-objective optimization analysis.

Figure 22 presents the comparison between the predicted and actual values for the three output variables, namely T_max (Y1), ΔT (Y2), and P_pump (Y3), for both training and testing datasets. The data points for all three outputs are closely aligned along the reference line, indicating excellent agreement between the ANN predictions and the corresponding simulation results. For Y1 and Y2, the predicted values exhibit almost perfect overlap with the actual values across the entire range, with minimal dispersion in both the training and test data. This demonstrates the surrogate model’s strong ability to capture the system’s nonlinear thermal behavior. Similarly, for Y3, although slightly more scatter is observed in the test dataset, the predictions still closely follow the ideal linear trend, confirming the reliability of the hydraulic performance model. In summary, the tight clustering of data points around the diagonal line and the negligible difference between the training and test datasets further confirm the high accuracy, robustness, and generalization ability of the developed ANN models [84,86]. These results are consistent with the previously reported R² and RMSE values, validating the suitability of the surrogate models for subsequent multi-objective optimization.

The multi-objective optimization of the cooling plate design was performed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to simultaneously minimize the T_max, ΔT, and P_pump. To identify the most suitable solution from the obtained Pareto front, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed as the decision-making method. The optimal design parameters selected by TOPSIS are summarized in

Table 6. Optimal design parameters and corresponding performance metrics obtained from NSGA-II-TOPSIS optimization.

	W (mm)	S (mm)	Vin (LPM)	Tmax (°C)	∆T (°C)	Ppump (W)
Predicted values	6.22	4.84	2.55	30.47	4.50	0.05879

. The results indicate that the optimal configuration corresponds to a coolant channel width (W) of 6.22 mm, channel spacing (S) of 4.84 mm, and coolant mass flow rate (V_in) of 2.55 LPM. Under these conditions, the system achieves a T_max of 30.47 °C and a ΔT of 4.50 °C, while maintaining a relatively low P_pump of 0.05879 W. These results demonstrate that the optimized design effectively balances thermal performance and hydraulic efficiency. Compared to single-parameter optimization, the multi-objective approach provides a more comprehensive solution by accounting for the trade-off between heat dissipation and energy consumption. The selected optimal point lies close to the ideal solution in the objective space, confirming the effectiveness of the combined NSGA-II-TOPSIS framework in identifying high-performance cooling plate configurations for LIB thermal management. Therefore, the identified optimal solution is considered representative of a near-global optimum within the defined design space.

Although NSGA-II has been widely adopted in recent multi-objective thermal management studies [87,88], the advantage of the present optimization framework lies in its integration with an experimentally validated CFD-MSMD-NTGK model and ANN-based surrogate modeling. Compared with direct CFD-based optimization, the ANN surrogate model significantly reduces computational cost while preserving the nonlinear relationship between design variables and thermal–hydraulic responses. Moreover, the NSGA-II algorithm generates a diverse Pareto front for simultaneously minimizing T_max, ΔT, and P_pump, while TOPSIS provides a systematic decision-making procedure to identify the most balanced solution. Therefore, the proposed ANN-NSGA-II-TOPSIS framework offers an efficient and practical optimization strategy for cooling plate design under 3C fast charging conditions.

To validate the accuracy of the proposed ANN-based surrogate model and the optimization framework, the optimal results predicted by the NSGA-II-TOPSIS approach were compared with the corresponding CFD simulation results, as shown in

Table 7. Comparison between ANN predictions and CFD simulation results with relative deviations.

Performance Metrics	Prediction Value	Calculation Value	Relative Deviation (%)
Tmax (°C)	30.47	30.46	0.033
∆T (°C)	4.50	4.51	0.22
Ppump (W)	0.05879	0.05830	0.83

. The comparison shows an excellent agreement between the predicted and calculated values for all performance metrics. Specifically, the model-predicted T_max is 30.47 °C, while the simulated value is 30.46 °C, resulting in a negligible relative deviation of 0.033%. Similarly, for the ΔT, the predicted and simulated values are 4.50 °C and 4.51 °C, respectively, with a small deviation of 0.22%. For the P_pump, the predicted value of 0.05879 W closely matches the simulated value of 0.05830 W, with a relative deviation of 0.83%. In general, all deviations are below 1%, indicating that the surrogate model provides highly accurate predictions of both thermal and hydraulic performance. These results confirm the reliability and robustness of the developed ANN model and demonstrate the effectiveness of the combined optimization approach in identifying optimal design parameters with high confidence.

To further evaluate the effectiveness of the optimization, the optimized design is compared with a representative initial configuration used in the parametric analysis. The initial design corresponds to a typical baseline case with moderate geometric and operating parameters of W = 12.5 mm, S = 7 mm, and V_in = 3 LPM. As shown in

Table 8. Comparison of thermal–hydraulic performance before and after optimization.

	Baseline Design	Optimized Design	Change (%)
Tmax (°C)	30.23	30.47	$\uparrow$ 0.79%
∆T (°C)	4.46	4.50	$\uparrow$ 0.89%
Ppump (W)	0.08567	0.05879	$\downarrow$ 31.38%

Note: $\uparrow$ and $\downarrow$ indicate increases and decreases relative to the baseline design, respectively.

, the optimized design significantly reduces pumping power while maintaining nearly unchanged thermal performance. Specifically, compared to the baseline, the optimized configuration results in only marginal increases in T_max of 0.79% and ΔT of 0.89%, while significantly reducing the pumping power by up to 31.38%. The slight increases in T_max and ΔT are negligible compared to the substantial energy savings, indicating that the proposed optimization achieves an effective balance between thermal management and energy efficiency. This result demonstrates the practical applicability of the proposed optimization framework for real-world BTMSs, where energy efficiency is a critical design consideration. The improvement can be attributed to the combined effects of geometric and operating parameter adjustments. The optimized channel width provides a balanced hydraulic diameter, enhancing convective heat transfer while avoiding excessive flow resistance. Meanwhile, the adjusted channel spacing improves the spatial distribution of coolant flow, resulting in more uniform heat removal across the battery surface. In addition, the optimized coolant mass flow rate enhances the convective heat transfer coefficient while effectively limiting the rapid increase in pressure drop associated with higher flow rates. Overall, the optimized design achieves a more favorable thermal–hydraulic trade-off by significantly reducing hydraulic losses while minimizing thermal performance compromise. This demonstrates the effectiveness of the proposed ANN-based NSGA-II-TOPSIS optimization framework in identifying a well-balanced design within the defined parameter space.

From a system-level perspective, minimizing pumping power alone does not fully capture the overall energy efficiency of the battery thermal management system. The integration of cooling plates with external thermal control units, such as chillers or radiators, increases energy consumption and depends on the thermal load and system configuration. Therefore, the optimization results presented in this study should be interpreted as component-level improvements, which provide a foundation for further system-level optimization.

4. Conclusions

In this study, a comprehensive multi-objective optimization framework was developed to enhance the thermal–hydraulic performance of a cooling plate-based indirect liquid cooling system for a 6S2P LIB module under 3C fast charging conditions. A coupled CFD-MSMD-NTGK model was established and experimentally validated, demonstrating good agreement with measured data and confirming the numerical approach’s reliability.

A detailed parametric analysis revealed that the coolant mass flow rate is the dominant factor affecting system performance. Increasing the flow rate significantly reduced the T_max and ΔT but resulted in a substantial increase in ΔP and P_pump. In contrast, geometric parameters such as channel number, channel width, and channel spacing exhibited comparatively smaller but still notable effects. Among these, increasing the number of channels improved both thermal performance and flow uniformity, while channel width showed a clear trade-off between heat transfer enhancement and hydraulic losses. Channel spacing was found to have a relatively minor influence on thermal performance but affected ΔP behavior.

To efficiently explore the design space, Latin hypercube sampling was employed to generate training data for ANN-based surrogate models. The developed ANN models demonstrated excellent predictive capability, with high R² values and low RMSE across all performance metrics. Subsequently, a hybrid NSGA-II-TOPSIS optimization approach was applied to identify the optimal design configuration. The optimal solution was obtained with a coolant channel width of 6.22 mm, a channel spacing of 4.84 mm, and a coolant mass flow rate of 2.55 LPM. Under these conditions, the system achieved a T_max of 30.47 °C, a ΔT of 4.50 °C, and a P_pump of 0.05879 W, satisfying both thermal safety requirements and energy efficiency criteria.

Furthermore, validation of the optimized results showed that the deviations between ANN predictions and CFD simulations were all below 1%, confirming the robustness and accuracy of the proposed optimization framework. Overall, this study demonstrates that integrating CFD simulation, experimental validation, surrogate modelling, and multi-objective optimization provides an effective and practical methodology for the design of advanced BTMSs. Although the present study focuses on thermal–hydraulic optimization, the obtained improvements in maximum temperature and temperature uniformity are directly related to reducing thermal-induced degradation mechanisms. Battery lifespan is significantly affected by temperature sensitivity and dynamic fast-charging conditions. By integrating an adaptive flow control strategy based on SoH, the degradation caused by thermal stress can be further reduced, thereby improving the long-term robustness of the BTMS. In future work, the proposed framework can be extended by incorporating electrochemical aging models and SoH-based adaptive thermal management strategies. In particular, coupling thermal–hydraulic optimization with SoH-aware dynamic flow control could enable real-time adjustment of coolant flow rates to mitigate degradation under varying operating conditions, thereby enhancing battery lifespan and overall system efficiency. In addition, it should be noted that the present study evaluates energy consumption based on component-level pumping power. A comprehensive assessment of total energy consumption would require including auxiliary systems such as chillers, radiators, and compressors. Future work will focus on integrating the proposed cooling plate design with system-level thermal management models to evaluate overall vehicle energy efficiency and thermal–electric coupling effects.