Dual-Curved Cold-Plate Integration for Enhanced Liquid-Based Thermal Management of Cylindrical Li-Ion Batteries

Abstract

Liquid-cold-plate-based battery thermal management systems (BTMSs) are widely adopted in new-energy vehicles (NEVs) due to their high heat-transfer efficiency and cost-effectiveness; however, their application to cylindrical batteries is limited by curvature-induced compatibility issues. To address this challenge, a novel dual-curved thermally conductive cold plate (TCCP) integrated with a liquid-based BTMS is proposed, providing an efficient and compact heat-transfer interface for cylindrical battery modules. The thermal behavior of the battery system is comprehensively evaluated under a high discharge rate of 5 C, with particular focus on the effects of the discharge rate, coolant flow speed (CFS), and TCCP structural parameters (including channel diameter, height, and contact angle). The results show that the single-channel dual-curved TCCP maintains the peak temperature and temperature variation below 310.39 and 4.40 K, respectively, at a CFS of 0.09 m/s. Furthermore, an optimized dual-channel TCCP-based BTMS is developed and evaluated against the single-channel design, demonstrating reductions in maximum temperature and temperature variation by 0.17 K and 7.50%, respectively, while simultaneously lowering CFS and weight ratio by 44.40 and 6.67%. Overall, the proposed dual-channel TCCP significantly enhances the thermal management performance and energy efficiency, offering a promising pathway for extending the cycle life and mileage of NEVs.

1. Introduction

The rapid global expansion of NEVs offers a promising solution to mitigate environmental damage and global warming caused by fossil-fuel-based energy use. LIBs have emerged as the primary power source for NEVs compared to other types of rechargeable batteries, owing to their advantages, including high energy density, rapid charging capability, long cycle life, and a lower self-discharge rate. − The ongoing advancement of LIBs continues to improve their application scope and efficiency, making them the cornerstone of new-energy solutions. The key components of the LIB are the anode, cathode, electrolyte, and the separator. Lithium ions travel from the anode via the electrolyte to the cathode, producing electrical energy during the discharge. In contrast, the process switches or reverses during charging, with lithium ions returning to the anode. LIBs come in various geometric models including cylindrical, pouch, and prismatic types. Each model is designed to meet specific requirements and applications based on factors such as safety, cost, and energy density. Cylindrical cell models offer greater structural stability, enhanced durability, and comparatively simpler manufacturing processes than their prismatic and pouch counterparts. ,

Lithium-ion batteries (LIBs) are highly sensitive to temperature fluctuations, with performance, safety, and lifespan critically dependent on maintaining an optimal operating temperature (OOT), typically 15–35 °C, with temperature gradients below 5 °C. ,, During charge and discharge, heat from Joule heating, entropic reactions, side reactions, and mixing can raise cell temperature, risking efficiency loss, accelerated degradation, and safety hazards, including thermal runaway. , Efficient battery thermal management systems (BTMS) are therefore essential to ensure reliability, extend cycle life, and enable safe operation, particularly for NEVs and renewable energy storage. Common BTMS technologies include liquid-based, ,, air-based, − PCM-based, − heat pipe-based, − and hybrid configurations. − Each presents trade-offs: air-based systems are simple, lightweight, and low-cost but limited in heat dissipation; PCM-based systems store heat efficiently but suffer from low thermal conductivity; and heat pipe systems offer passive transfer but incur high cost and design complexity. Effective BTMS design must balance thermal performance, energy efficiency, weight, space, and cost.

Among existing technologies, liquid-based BTMSs have emerged as the most effective and widely adopted solution due to their high heat-transfer coefficient, large contact area, and strong capability to manage high thermal loads. Various coolants, including water, glycol, oils, nanofluids, acetone, and liquid metals, have been used to achieve the desired thermal performance. Compared with air- and PCM-based systems, liquid-based BTMSs offer superior heat dissipation and maintain battery stability under high charge/discharge rates and elevated temperatures. Consequently, it has become the mainstream thermal management strategy for large-scale power batteries in NEVs and is widely implemented by leading manufacturers such as Tesla, BYD, BMW, and Hyundai. ,,,

Ongoing research has advanced liquid-based BTMS, which are generally classified into direct contact cooling (DCC) and indirect contact cooling (ICC) systems. DCC allows direct coolant–battery interaction and offers high TMP, but it poses risks such as leakage and coolant contamination. In contrast, ICC employs an intermediate heat-dissipating component, typically a cold plate, preventing direct contact and enabling the use of a wider range of coolants. Owing to its simplicity, cost-effectiveness, and reliability, ICC is widely adopted in practical applications. However, inadequate cold-plate design may introduce additional thermal resistance and cause temperature nonuniformity. Hence, optimizing cooling structure, compactness, and contact area is essential for improving ICC performance. For instance, Li et al. demonstrated that a liquid-cooled plate with diamond-shaped channels significantly enhanced heat dissipation and reduced power consumption, achieving an effective balance between cooling performance and system efficiency.

Cold-plate-based BTMS for rectangular batteries, such as prismatic and pouch cells, are well-studied and widely implemented. For instance, Hwang et al. employed ANSYS software to investigate the TMP of prismatic LIBs cooled by double cold plates, analyzing the influence of cooling channel designs under various discharge rates. Their results confirmed that optimizing the cold-plate structure significantly enhances BTMS efficiency. Similarly, Mubashir et al. introduced a novel cold-plate design with uniform circular fins for prismatic batteries, demonstrating improved thermal performance by achieving a maximum temperature of 29.87 °C and a temperature difference of 3.52 °C under a 3 C discharge rate. In another study, Wang et al. proposed a butterfly-shaped channel cold plate for a 50 Ah prismatic battery module, successfully maintaining peak temperature and temperature variation below 30.86 and 4.96 °C, respectively, at a 2 C discharge rate with a 5 g/s mass flow rate. Collectively, these studies highlight that optimizing cold-plate geometry and structural parameters can substantially improve heat-transfer efficiency, promote uniform temperature distribution, and minimize both temperature rise and pressure drop in battery modules.

Conversely, the design and application of cold-plate-based systems for cylindrical batteries remain limited due to compatibility challenges associated with their curved surfaces, which hinder efficient thermal contact. This often results in insufficient heat exchange between the cells and cooling plates. To overcome these limitations, researchers have explored specialized cold-plate designs. For example, Wang et al. developed a modular cold-plate-based liquid-cooling system for cylindrical battery modules, employing both numerical simulations and experimental investigations. Their study examined the effects of coolant flow rate and cooling configurations (series versus parallel) on the thermal management performance of the battery module under a 3 C discharge condition. The results revealed that, compared to the series configuration, the parallel cooling mode improved temperature uniformity, whereas increasing the coolant flow rate yielded only marginal reductions in the peak cell temperature. Likewise, Zhao et al. evaluated the performance of serpentine channel cold plates for cylindrical battery packs. By shortening the flow path and enlarging the contact surface area between the channels and battery cells, the optimized design significantly improved the temperature uniformity, as confirmed by numerical simulations.

Chen et al. proposed an innovative cold-plate configuration based on topology optimization to enhance the thermal management efficiency of BTMS for cylindrical battery modules. Three cold-plate designs with varying inlet and outlet configurations were developed to investigate the effects of coolant flow rate, cold-plate thickness, and the number of cold plates. Under a discharge rate of 3C and an inlet flow rate of 2.5 × 10^–6 m³/s, the peak temperature and temperature variation across the battery module were maintained at 30.90 and 4.87 °C, respectively. The results further demonstrated that the TMP of the liquid-based cooling system improved significantly with increases in both cold-plate thickness and number. Similarly, You et al. and Zhao et al. examined the TMP of cold-plate-based cooling strategies for cylindrical lithium-ion batteries under various cooling configurations and operational conditions. Their findings indicated that optimizing the cold-plate structure ensures safe operating temperatures, while higher inlet flow rates markedly enhance TMP and extend battery cycle life. However, although many studies have confirmed that increasing inlet flow rate improves cold-plate performance, excessively high flow rates can negatively impact the overall efficiency of the BTMS. ,,

The aforementioned studies have significantly advanced the development of cold-plate-based BTMSs for cylindrical lithium-ion batteries. Nevertheless, limited attention has been devoted to cold-plate configurations that simultaneously incorporate dual-curved geometries and multichannel coolant pathways specifically designed to conform to cylindrical cell surfaces. Existing cold-plate designs often face challenges associated with limited thermal contact area, nonuniform heat dissipation, and increased cooling requirements under high-rate operating conditions. Although curved cold plates can improve battery-to-cold-plate contact and enhance heat-transfer and multichannel configurations can improve coolant distribution and cooling effectiveness, the combined application of these two design concepts remains largely unexplored. ,

To bridge this research gap, this study proposes a novel dual-curved, dual-channel thermally conductive cold plate (TCCP) for a liquid-cooled BTMS. The novelty of the proposed design lies in the integration of (i) a dual-curved structure that increases the effective thermal contact area between the cold plate and cylindrical battery cells and (ii) a dual-channel flow configuration that enhances coolant distribution while reducing the coolant flow rate required for effective thermal regulation. This integrated design aims to improve heat dissipation, temperature uniformity, and thermal management performance while maintaining a compact and lightweight configuration suitable for new-energy vehicle applications. To evaluate the proposed approach, a lightweight TCCP is first developed and integrated into a liquid-cooled BTMS. Subsequently, numerical simulations are conducted to investigate the effects of the discharge rate, coolant flow speed (CFS), and key structural parameters, including TCCP diameter, height, and thermal contact angle, on the TMP, energy consumption, and system weight. Furthermore, the thermal and hydraulic performance of the proposed dual-channel TCCP configuration is systematically assessed and compared to that of the single-channel TCCP as well as established BTMS solutions documented in the literature. The findings of this study provide new insights into the design and optimization of multichannel cold-plate-based BTMSs for cylindrical LIBs and offer practical guidance for enhancing battery performance, safety, and driving range in NEVs.

2. Battery Model and Numerical Simulation

2.1. Physical Model of the Cylindrical Battery Module with a Cooling System

The battery pack consists of multiple cells assembled to deliver the required energy supply for NEVs. In this study, an adaptable TCCP integrated with a liquid-cooling system is proposed for cylindrical LIBs, engineered to enhance TMP and ensure system reliability. A commercial Panasonic LIB with a rated capacity of 2980 mAh and a nominal voltage of 3.6 V was selected to construct a module comprising 42 cells, arranged in a rectangular 7 × 6 array. The 3D geometry of the battery cells, battery module, and integrated cooling system was developed using SolidWorks. For numerical analysis, a representative computational unit was selected, consisting of a single cylindrical cell surrounded by four TCCPs featuring dual-curved contact interfaces to ensure effective thermal contact.

Figure illustrates the proposed 3D model of the battery module and the liquid-based BTMS integrated with dual-curved TCCPs. It comprises several key components: a battery module made of NCR18650BD cells (Φ18.25 × 65.1 mm), TCCPs, support plates, and top and bottom reservoirs. The NCR18650BD LIB, with dimensions identical to the Panasonic model, was employed, and its key parameters are summarized in Table . The reservoirs, fabricated from lightweight plastic, were specifically designed to minimize system weight. The top reservoir incorporates an inlet through which coolant enters, whereas the bottom reservoir features an outlet for discharging the heated coolant after absorbing thermal energy from the cells. Figure a,b provides an overview of the BTM system, highlighting the contact surfaces between the cells and the TCCPs, essential for effective heat transfer.

1.

3D model of the battery system with liquid-based BTMS coupled to the TCCP: (a) Overall layout of battery module system with TCCPs, (b) battery module comprising multiple cells and TCCPs, (c) battery cell sandwiched between symmetric TCCPs.

1. Specifications of the NCR18650BD Lithium-Ion Battery.

parameters	specifications	unit
height	65.1	mm
diameter	18.25	mm
weight	49.5	g
rated capacity	2980	mAh
nominal voltage	3.6	V
discharge cut-off voltage	2.5	V
charge cut-off voltage	4.2	V
energy density	217	Wh/kg
thickness of cathode	0.138	mm
thickness of anode	0.149	mm
thickness of separator	0.032	mm
thickness of positive tab	0.2	mm
thickness of negative tab	0.25	mm
thickness of outer cover	0.25	mm
electrolyte material	lithium salts and organic carbonates
cathode material	LiNi0.8Co0.15Al0.05O2
anode material	graphite

The TCCPs are manufactured from lightweight aluminum, selected for its strategic benefits, including high thermal conductivity, low density, cost-effectiveness, and ease of fabrication, properties that make it well-suited for efficient heat dissipation while minimizing NEV battery weight. As shown in Figure c, each cell interfaces thermally with four TCCPs, positioned between adjacent cells. Each TCCP incorporates circular channels designed to promote coolant circulation. Coolant enters the TCCP through the top inlet, flows through the mini-channels, and exits via the bottom outlet. Heat generated within the cells is transferred to the TCCPs via thermal conduction and subsequently removed by the circulating coolant through thermal convection. Figure a–c illustrates the dual-curved TCCP design and its conformity with cylindrical batteries. The influence of the TCCP’s structural and geometric parameters, namely height (h), mini-channel diameter (d), and contact (curved surface) angle (α), on the TMP of the battery cooling system is further investigated.

2.

Axonometric view of the (a) single battery cell, (b) dual-curved TCCP’s isometric view, and (c) dual-curved TCCP’s top view with its parameters.

2.2. Battery Thermal Model and Governing Equations

The heat exchange of the flowing fluid and batteries is described through mathematical equations. The continuity, momentum, and energy equations govern the coupled thermal and fluid behaviors of the battery, coolant, and TCCP. The equations governing the coolant can be expressed as follows: ,

The continuity equation of the mass conservation of the cooling fluid:

$$\frac{\partial {\rho }_{\mathrm{w}}}{\partial t}+\nabla ·({\rho }_{\mathrm{w}}\mathrm{\nu ⃗})=0$$ 1

where ρ_w, ∇, and v⃗ represent the density, gradient operator, and the velocity vector of the coolant.

The momentum conservation equation of the cooling fluid:

$$\frac{\partial }{\partial t}({\rho }_{\mathrm{w}}\mathrm{\nu ⃗})+\nabla ({\rho }_{\mathrm{w}}\mathrm{\nu ⃗}·\mathrm{\nu ⃗})=\nabla ·({\mu }_{\mathrm{w}}\nabla \mathrm{\nu ⃗})-\nabla P$$ 2

where μ_w and P denote the dynamic viscosity and static pressure of the coolant.

The equation representing energy conservation in the cooling fluid:

$$\frac{\partial }{\partial t}({\rho }_{\mathrm{w}}{C}_{\mathrm{P},\mathrm{w}}{T}_{\mathrm{w}})+\nabla ·({\rho }_{\mathrm{w}}{C}_{\mathrm{P},\mathrm{w}}{\mathrm{v⃗}T}_{\mathrm{w}})=\nabla ·({\lambda }_{\mathrm{w}}\nabla T_{\mathrm{w}})$$ 3

The governing equations representing the behavior of the TCCP account for the fluid flow through its cooling channels and the heat transfer between the battery and the cold plate, enabling accurate prediction of the system’s thermal performance. The equation governing energy conservation in the TCCP can be described as:

$$\frac{\partial }{\partial t}({\rho }_{\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}}{C}_{\mathrm{P},\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}}{T}_{\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}})=\nabla ·({\lambda }_{\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}}\nabla T_{\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}})$$ 4

where, in eqs () and (4), λ, T, and C _p represent the thermal conductivity, temperature, and specific heat capacity, respectively. The subscripts w and TCCP denote the cooling water and the thermally conductive cold plate, respectively.

The mass of the TCCP can be expressed as:

$$m_{\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}}={\rho }_{\mathrm{T}\mathrm{C}\mathrm{C}\mathrm{P}}·V_{\mathrm{T}}$$ 5

where m _TCCP, and V _T denote mass and total volume of the TCCP, respectively.

The Reynolds number (Re) is expressed as:

$$\mathit{Re}=\frac{\rho v_{\mathrm{f}}·d_{\mathrm{c}}}{\mu }$$ 6

where ρ,v _f, d _c, and μ are the fluid density, flow velocity, diameter of channel, and dynamic viscosity, respectively.

The pumping power (P _p) to drive the fluid flow is given by:

$$\mathit{Pp}=\mathrm{\Delta }P·A_{\mathrm{c}}{v}_{\mathrm{f}}$$ 7

$$\mathrm{\Delta }P=P_{\mathrm{o}\mathrm{u}\mathrm{t}}-P_{\mathrm{i}\mathrm{n}}$$ 8

where ΔP, A _c, P _out, and P _in refer to the pressure drop, inlet channel area, outlet pressure, and inlet pressure, respectively.

The thermal model of the battery is developed based on an energy balance between the internally generated heat and the heat dissipated to the surroundings.

The equation governing energy conservation in the battery

$$\frac{\partial }{\partial t}({\rho }_{\mathrm{b}}{C}_{\mathrm{P},\mathrm{b}}{T}_{\mathrm{b}})=\nabla ·({\lambda }_{\mathrm{b}}\nabla T_{\mathrm{b}})+Q_{\mathrm{g}\mathrm{e}\mathrm{n}}$$ 9

where λ _b is the thermal conductivity of the battery and Q _gen is the heat generation rate of the battery.

During operation, the temperature increase in LIBs is driven by multiple factors, including irreversible electrochemical reactions, entropy (reversible) heat, Joule heating, and interactions with external thermal conditions. − Among these, Joule heating caused by internal resistance scales with the square of the current (I ² R) and can contribute significantly under high-load conditions. To accurately capture the thermal behavior of the battery, this study couples the Newman P2D electrochemical model with the Bernardi et al. (1985) Heat Generation Formulation.

The sum of reversible and irreversible heat contributions gives the total heat generation rate Q _gen in the battery, as expressed in eq ():

$$Q_{\mathrm{g}\mathrm{e}\mathrm{n}}=Q_{\mathrm{r}\mathrm{e}\mathrm{v}}+Q_{\mathrm{i}\mathrm{r}\mathrm{r}}$$ 10

Thus, the battery temperature can be computed by the heat generation rate of the lithium-ion battery, Q _gen, which can be expressed as follows:

$$Q_{\mathrm{g}\mathrm{e}\mathrm{n}}=\frac{I}{V_{\mathrm{b}}}(U_{\mathrm{o}\mathrm{c}\mathrm{v}}-U-T\frac{\partial U_{\mathrm{o}\mathrm{c}\mathrm{v}}}{\partial T})$$ 11

where Q _rev and Q _irr represent the reversible and irreversible heat, respectively. I denote the discharge/charge current of the cell, V _b refers to the volume of the battery cell, U represents the battery’s working voltage, U _ocv refers to the open circuit voltage/potential, T represents the battery temperature, and ∂U _ocv/∂T refers to the temperature coefficient of open circuit voltage. In eq (), the first term (U _ocv–U) represents nonreversible heat (Joule heating), whereas the second term ( $-T\frac{\partial U_{\mathrm{o}\mathrm{c}\mathrm{v}}}{\partial T}$ ) corresponds to reversible heat, which can be either exothermic or endothermic based on the operating conditions.

$$U=U_{\mathrm{o}\mathrm{c}\mathrm{v}}-\mathit{IR}$$ 12

By substituting eq () in eq (), the battery heat generation can be rewritten as: ,

$$Q_{\mathrm{g}\mathrm{e}\mathrm{n}}=\frac{I}{V_{\mathrm{b}}}(\mathit{IR}-T\frac{\partial U_{\mathrm{o}\mathrm{c}\mathrm{v}}}{\partial T})$$ 13

where R is the battery cell’s internal resistance, including the ohmic and polarization resistance.

2.3. Numerical Simulation

This study employed CFD software, ANSYS Workbench Fluent, to study the comprehensive thermal behavior of lithium-ion batteries through 3D numerical computations based on the finite-volume method (FVM). ANSYS Fluent offers two battery modeling approaches: the single-potential empirical battery model (EBM) and the dual-potential multi-scale multi-domain (MSMD) model. , The EBM is computationally efficient but limited to solving a single potential equation, which restricts its ability to capture detailed electrochemical reactions and degradation phenomena, particularly in batteries with complex geometries. In contrast, the MSMD model employs a physics-based, multi-scale framework that couples electrochemical, thermal, and electrical domains, thereby enabling more accurate predictions of battery behavior and performance under realistic operating conditions.

In this study, a dual-potential MSMD model is employed, treating the battery as a continuous medium with directionally dependent (orthotropic) properties such as electrical and thermal conductivity. The Newman P2D electrochemical thermal model is implemented to capture the coupled electrochemical and thermal behavior of the cell. In the simulation, the NCR18650BD cylindrical battery is modeled with positive and negative electrodes, current collectors, a separator, and a central rolled mandrel. To minimize computational expense, the computational domain was confined to a single cell, positioned symmetrically between four TCCPs, as depicted in Figure c. Table presents the thermal and physical properties of the materials used in this study. The Reynolds number corresponding to the CFSs investigated in this study (0.01–0.20 m/s) was calculated to range from approximately 200 to 600. These values lie well within the laminar-flow regime for internal channel flows. Therefore, the coolant flow within the TCCP channels was considered as laminar throughout the scenario, and no turbulence model was applied. This modeling approach is consistent with previously established cooling configurations operating under low-Reynolds-number. Detailed parameter values of the NCR18650BD LIB utilized in the Newman P2D model are provided in Table .

2. Thermo-Physical Properties of the NCR18650BD, TCCP, and the Cooling Fluid ,

	thermo-physical properties	density	heat capacity	thermal conductivity	viscosity
materials	measuring unit	kgm–3	Jkg–1K–1	Wm–1K–1	Pa·s
battery		2900	1000	3.9
positive tab		2719	871	202.4
negative tab		8978	381	387.6
TCCP		2719	871	202.4
water		998.2	4182	0.6	0.001003

3. Electrochemical Parameters for the P2D Model Simulation of the NCR18650BD .

	value			unit
parameters	cathode		anode	separator
thickness	138	149	32	μm
particle diameter	16	25		μm
max. solid lithium-ion (Li+) conc.	22,860	26,390		mol/m3
stoichiometry at 0% SOC	0.99	0.005
stoichiometry at 100% SOC	0.17	0.5635
initial solid Li+ conc.	3886.20	14,870.76		mol/m3
initial electrolyte Li+ conc.	2000	2000	2000	mol/m3
volume fraction of electrolyte (ϵs)	0.444	0.357	1
filler fraction (ϵf)	0.259	0.172
electrical conductivity (σ)	3.8	100		S/m
Bruggeman tortuosity exponent (β)	1.5	1.5	1.5
reference diffusivity (D)	1.00 × 10–13	3.90 × 10–14		m2/s
reference rate constant	2.07 × 10–11	2.07 × 10–11		m2.5/mol0.5 s
transfer coefficient at anode (αα)	0.5	0.5
transfer coefficient at cathode (αc)	0.5	0.5
electrolyte diffusivity for cathode (D e)	7.50 × 10–11			m2/s
transference no. of Li+ for cathode (t+)	0.363

^aConc.: concentration; max.: maximum.

A transient model is employed to capture the unsteady heat generation behavior of the battery. A pressure-based solver is selected to compute battery parameters and evaluate their influence on the system’s TMP. To achieve accurate pressure-velocity coupling, the SIMPLE algorithm is applied. Spatial discretization is performed using least-squares cell-based for gradients, second-order for pressure, and second-order upwind schemes for momentum and energy. All governing equations are solved iteratively, with under-relaxation factors of 0.7 for momentum, 0.3 for pressure, and 1.0 for energy. A second-order implicit scheme is used for the transient formulation to ensure numerical stability and reliable convergence. The simulation is executed with a time-step size of 1 s, a maximum of 20 iterations per time step, and convergence criteria of 10^–5 for continuity and 10^–6 for velocity and energy equations.

2.4. Boundary Conditions and Modeling Assumptions

In the current study, the fluid inlet was specified as a velocity-inlet boundary condition, while the channel outlet was defined as a pressure outlet with a gauge pressure of 0 Pa. The inlet coolant temperature and ambient temperature were both set to 298.15 K. To reduce computational complexity while maintaining the essential heat-transfer characteristics of the BTMS, the interface between the cylindrical battery cell and the TCCP was modeled as a thermally coupled wall. Ideal thermal contact was assumed; therefore, thermal contact resistance at the battery–TCCP interface was neglected. Moreover, radiative heat transfer was not considered in the present study. These assumptions are widely adopted in numerical studies of liquid-based BTMSs and are considered reasonable for systems operating within the temperature range investigated in this work, where heat transfer is mainly governed by conduction and convection. The interfaces between the TCCP and the coolant were also defined as thermally coupled walls to enable conjugate heat transfer between the solid and fluid domains. A no-slip boundary condition was imposed at all fluid–solid interfaces, consistent with conventional liquid-cooling applications. The external surface of the battery cell was subjected to natural convection with a heat-transfer coefficient of 5 W/m²K. All remaining walls of the cooling system were assumed to be adiabatic.

2.5. Grid Independence Evaluation

A grid independence study was conducted to ensure the reliability of the numerical simulations and to identify an appropriate mesh resolution. The evaluation was performed using a TCCP configuration with a contact angle of 60°, a height of 65 mm, and a diameter of 1.7 mm, under boundary conditions of an inlet temperature of 298.15 K, a discharge rate of 2 C, and a coolant flow velocity of 0.01 m/s. The maximum battery temperature was selected as the evaluation metric. The computational domain was discretized using a hybrid mesh of tetrahedral and hexahedral elements, with local edge refinement applied in both fluid and solid regions to enhance accuracy near critical interfaces, as shown in Figure a.

3.

(a) Computational grid model structure. (b) Mesh number independence test.

Six mesh sizes ranging from 8,85,028 885,028 to 2 3,44,476 2,344,476 elements were examined. As illustrated in Figure b, increasing the grid size from 8,85,028 885,028 to 12,21,276 1,221,276 elements reduced the maximum battery temperature from 308.720 to 308.396 K, corresponding to a relative deviation of 0.105%. When the grid size exceeded 13,11,373 1,311,373 elements, the relative deviation fell below 0.0302%, indicating mesh-independent results. Consequently, a mesh with 13,11,373 1,311,373 elements was selected as an optimal compromise between the computational cost and accuracy. The minimum orthogonal quality and maximum skewness of the selected mesh were 0.3066 and 0.7464, respectively, confirming an adequate mesh quality for reliable simulations.

2.6. Numerical Model Validation

In this section, experimental validation is conducted to rigorously evaluate the accuracy and predictive capability of the developed battery heat generation model and the numerical model for the dual-curved, TCCP-based BTMS. The battery heat generation model is first validated by comparing its predictions with previously published experimental data reported by Akula and Balaji under identical operating conditions. The experiments were performed on a single NCR18650 cylindrical LIB discharged at rates of 0.5, 1, and 2 C at an ambient temperature of 24 °C. The material properties adopted in the numerical simulations are summarized in Tables and . During the experiments, five thermistors were uniformly attached to the battery surface, and the average of their readings was used to represent the mean battery temperature. Figure a–c compares the simulated and experimental results, highlighting a close alignment. The battery peak temperature error and the mean temperature error are within 1.7 and 0.85 K, respectively.

4.

Validation of battery heat generation on various discharge rates (a–c), validation of the numerical model for battery cooling (d).

Furthermore, the reliability of the numerical model for the dual-curved, TCCP-based BTMS is validated using experimental data reported by Zhang et al. As shown in Figure d, the maximum temperature deviation does not exceed 1.67 K, indicating a close correspondence between the numerical predictions and experimental measurements. This agreement further confirms the accuracy, reliability, and predictive capability of the developed numerical model, supporting its suitability for subsequent parametric and performance analyses.

3. Results and Discussion

This study presents a dual-curved, dual-channeled TCCP integrated with a liquid-based BTMS for cylindrical LIBs, targeting enhanced TMP under a 5 C discharge rate. This section evaluates the influence of the discharge C-rate, CFS, and TCCP structural parameters on the thermal regulation of the BTMS. The cooling performances of single-channel and dual-channel TCCP configurations are comparatively analyzed. The overall system performance is evaluated in terms of the maximum temperature, temperature difference, and pressure drop.

3.1. Impacts of Discharge C-Rates

In this section, the influence of discharge C-rates on the battery temperature and the TMP of the proposed cooling system is investigated by simulating four cases ranging from 2 to 5 C in 1 C increments, as illustrated in Figure . The simulations were conducted at six different CFS, ranging from 0.01 to 0.2 m/s, using a TCCP with a diameter (d) of 1.7 mm. The height (h) and thermal contact angle (α) of the TCCP were set to 65 mm and 52°, respectively.

5.

Effect of various discharge C-rates on the battery temperatures: (a) Maximum temperature. (b) Temperature variation.

Figure a,b shows the battery peak temperature and temperature variation, respectively, at various discharge rates. As the discharge rate increases, the peak temperature increases significantly. At a CFS of 0.2 m/s, the battery peak temperature under a 5 C discharge is 9.75 K higher than that under a 2 C discharge. This behavior is primarily attributed to a substantial increase in internal heat generation and the resulting rise in battery temperature, which is mostly associated with the irreversible heat generation rate and leads to a notably higher thermal load at higher discharge rates. Consequently, the heat generation rate exceeds the cooling system’s dissipation rate, causing thermal accumulation to challenge the cooling system.

Figure b further shows that the temperature variation across the battery increases with higher discharge rates. At a CFS of 0.2 m/s, the temperature variation rises by 2.57 K when the discharge rate increases from 2 to 5 C, indicating a deterioration in thermal uniformity and an increase in the thermal gradients within the battery cell. These effects can be attributed to the nonuniform distribution of generated heat and poor heat conduction within the battery under high-rate operating conditions, thereby making heat accumulation more pronounced and resulting in higher peak temperatures and greater temperature variation within the battery. These results show that higher discharge rates degrade the battery temperature and uniformity, underscoring the need for effective BTMS under high-power conditions to ensure safe, reliable operation within recommended temperature limits and suppress thermal gradients.

However, increasing the CFS effectively mitigated this thermal effect. For instance, when a CFS of 0.01 m/s is used, increasing the discharge rate from 2 to 5 C results in a 16.6 % increase in peak battery temperature (from 307.82 to 358.92 K). In contrast, at a CFS of 0.2 m/s, the same increase in discharge rate causes only a 3.25 % rise in peak temperature (from 299.94 to 309.69 K). Thus, this demonstrates that higher CFS substantially enhances the heat removal capability of the TCCP-based BTMS. The improved thermal performance at higher CFSs can be attributed to the increased convective heat transfer between the coolant and TCCP. Overall, higher discharge rates increase battery heat generation; however, appropriate coolant flow management can significantly mitigate these effects. Thus, balancing operating conditions with the cooling capacity is essential for optimal thermal conditions, safety, and battery longevity.

3.2. Effects of the Coolant Flow Speed (CFS)

As shown in Figure a in Section , during a discharge rate of 5 C, the battery temperature increases significantly, accompanied by a highly nonuniform thermal distribution within the cell. Such thermal nonuniformity can adversely affect overall battery performance, including efficiency, lifespan, and safety. Therefore, the subsequent sections present additional simulations conducted at the same high discharge rate (5 C) under varying operational scenarios to further investigate these effects and assess the potential mitigation strategies.

This section examines the impact of CFS on the performance of a liquid-based cooling system integrated with dual-curved TCCPs. The simulations were conducted at nine different CFS values to quantify the trade-offs between thermal regulation, energy efficiency, and operational feasibility. The various CFS values employed in the simulation are listed in Table . In these simulations, other TCCP parameters, including diameter, contact surface angle, and height, were set to 2 mm, 60°, and 65 mm, respectively. The system performance was assessed based on peak temperature, temperature variation, and pressure drop. Figure a,b illustrates how the maximum temperature, temperature variation, and pressure drop respond to varying CFSs. As depicted in Figure a, the peak battery temperature decreases with increasing CFS. At a CFS of 0.01 m/s, the peak temperature and temperature variation are 333.69 and 31.39 K, respectively. Increasing the CFS to 0.2 m/s reduces the peak temperature and temperature variation to 307.87 and 2.01 K, respectively. Consequently, the peak temperature and temperature variation decrease by 7.74 and 93.6%, respectively, when the CFS increases from 0.01 to 0.2 m/s.

4. Peak Temperature, Temperature Variation, and Pressure Loss under Various CFFS Values.

CFS (m/s)	maximum temperature T max (K)	temperature difference ΔT (K)	pressure drop ΔP (Pa)
0.01	333.69	31.39	5.2
0.04	315.01	9.59	20.8
0.05	313.4	7.75	26
0.06	312.33	6.51	31.2
0.07	311.53	5.61	36.4
0.08	310.91	4.93	41.6
0.09	310.39	4.4	46.8
0.1	310	3.97	52
0.2	307.87	2.01	104

6.

Influences of the CFS on the battery: (a) Maximum temperature and temperature variation. (b) Pressure drop.

The peak battery temperature can be maintained within a safe range (below 40 °C) when a CFFS of 0.07 m/s is employed. However, the temperature difference does not meet the battery-safe condition. When the CFS reaches 0.09 m/s or higher, the maximum temperature is maintained below 310.39 K, and the temperature variation is controlled to below 4.4 K. This ensures that the optimal limits for both peak temperature and temperature variation of the battery are met. Thus, increasing the CFS significantly enhances the TMP of the liquid-cold-plate-based BTMS. Apart from this, the pressure drop increased significantly with CFS. It can be demonstrated from Figure b that the highest temperature and temperature variation of the battery fall within the optimal range for the BTMS at both CFS of 0.09 and 0.2 m/s. However, the pressure drop at 0.2 m/s is more than double that at 0.09 m/s, which significantly affects cooling efficiency. Excessively increased CFS are not cost-effective, as they require high-power consumption to cool the battery system.

Hence, to design an efficient TMS, the optimal CFS should be determined on the basis of a balanced consideration of energy consumption, TMP, and the overall efficiency of the BTMS. The results demonstrate that the proposed dual-curved TCCP-based cooling system effectively regulates battery operating temperatures while maintaining low coolant flow rates, making it an energy efficient solution. Accordingly, a CFS of 0.09 m/s was adopted for further simulations in this study.

3.3. Impacts of the Height (h) of the TCCP

In this section, the CFS, diameter, and contact surface angle are specified as 0.09 m/s, 2 mm, and 60°, respectively. The influence of height (h) on the TMP of TCCP is subsequently analyzed. Figure presents a schematic diagram designed to assess the impact of the thermal contact height on the TMP of the TCCP. The TCCP heights of 55, 58, 60, 63, and 65 mm are assigned for the investigations. The height of the TCCP in a liquid-based cooling system for a cylindrical battery significantly influences its TMP. Increasing the TCCP height enhances the contact surface area between the batteries and cooling plates, thereby improving both conductive and convective heat transfer. This larger surface area allows for more effective heat removal from the battery to the coolant fluid, remarkably enhancing the TMP of the TCCP-based cooling system. The results of peak temperature and temperature variation at the end of the 5 C discharging for various contact surface height values are shown in Figure . The TCCP height is reduced on the inlet side because the working temperature in that region is lower than at the outlet.

7.

Schematic of the contact surface height of the TCCP.

8.

Influence of the TCCP height on the peak temperature and temperature variation.

As shown in Figure , increasing the TCCP height leads to a reduction in the maximum temperature. Specifically, when the height increases from 55 to 65 mm, the maximum temperature decreases by 3.5 % (from 321.68 to 310.39 K). Table provides a detailed comparison of BTMS performance across varying TCCP heights. The temperature difference initially decreases with height but later shows a slight rise as the height continues to increase. The minimum temperature variation of 4.33 K is observed at a height of 55 mm. Figure illustrates the corresponding temperature distributions for different heights.

5. Comparison of the TMP of the TCCP under Different Parameters.

diameter (d) (mm)	height (h) (mm)	contact angle (°)	CFS (m/s)	T max (K)	ΔT (K)
1.7	65	60	0.09	311.93	6
2	65	60	0.09	310.39	4.4
2.5	65	60	0.09	309.97	2.87
3	65	60	0.09	308.88	2
2	65	40	0.09	312.94	4.73
2	65	52	0.09	311.7	4.5
2	65	60	0.09	310.39	4.4
2	65	70	0.09	310.1	4.26
2	65	80	0.09	309.68	4.11
2	55	60	0.09	321.68	4.52
2	58	60	0.09	317.02	4.33
2	60	60	0.09	313.93	4.35
2	63	60	0.09	310.47	4.38
2	65	60	0.09	310.39	4.4

9.

Temperature contour of the battery surface and temperature distribution for different TCCP height values.

As discussed, reducing TCCP height from the inlet side increases the maximum temperature at the battery’s inlet but decreases the temperature variation across the cell. However, when the height is too short, the battery surface cannot effectively dissipate heat due to inadequate contact with the TCCP, resulting in higher maximum temperatures, degraded thermal performance, and potential capacity loss. At greater heights (63 and 65 mm), the maximum temperature shifts to the bottom of the battery, whereas at intermediate heights (58 and 60 mm), it exceeds the optimal threshold, causing the hottest point to move to the top of the cell. To maintain the battery’s peak temperature within the required limit of 40 °C, the TCCP height should be no less than 63 mm. These results indicate that increasing TCCP height enhances the TMP of liquid-based mini-channel systems integrated with TCCPs.

Table further compares BTMS performance across TCCP height and other key structural parameters, including channel diameter and thermal contact angle. The findings underscore the critical role of these parameters in determining the peak temperature and thermal uniformity, offering practical guidance for optimizing TCCP design to achieve scalable and efficient thermal management of cylindrical LIBs in NEVs under real-world conditions. Nevertheless, the TCCP height must be carefully optimized, as excessive height increases system weight, which can negatively impact cooling efficiency. Therefore, selecting a moderate height is crucial to striking a balance among heat dissipation, structural feasibility, and overall system efficiency. On the basis of these considerations, a TCCP height of 65 mm is adopted for further analysis in this study.

3.4. Effects of the Contact Surface Angle (α) of the TCCP

In this section, the CFS is defined as 0.09 m/s, the height as 65 mm, and the diameter as 2 mm. The influence of the contact surface angle on the TMP of the TCCP is subsequently examined. The selected curvature angles for evaluation are 40, 52, 60, 70, and 80°. Figure presents the simulated results for the peak temperature and temperature variation under these different angles. The contact angle of the TCCP exerts a critical effect on the TMP of liquid-based BTMS integrated with TCCP in cylindrical LIBs, as it increases the contact area between the TCCP and battery cells, thereby reducing temperature rise. This enhancement in the heat-transfer interface results in improved cooling performance. The simulation results demonstrate that both the maximum temperature and temperature variation decrease with increasing contact angle, as shown in Figure . Specifically, when the curvature angle increases, the cooling fluid flows are distributed more uniformly across the battery surface. As the surface contact angle increased from 40 to 80°, the peak temperature decreased by 1.04% (312.94 to 309.68 K), while the temperature variation decreased by 17.34% (4.73 to 3.91 K). Table provides a detailed comparison of BTMS performance across varying TCCP contact angle. Overall, increasing the TCCP curvature significantly improves the TMP of the proposed cooling system by lowering both the battery operating temperature and temperature variation. The improved performance is primarily attributed to the optimized conformity between the TCCP and the cylindrical battery surface, which increases the effective heat-transfer area and reduces interfacial thermal resistance. Consequently, heat generated within the battery can be conducted efficiently to the cooling system, resulting in enhanced heat dissipation and a more-uniform temperature distribution. However, a higher curvature angle also substantially increases the weight of the TCCP, underscoring the necessity of careful design to balance effective cooling performance with energy consumption. Based on these considerations, a curvature angle of 60° was selected for subsequent simulations.

10.

Influence of the contact angle on the maximum temperature and temperature variation.

3.5. Impacts of the Channel Diameter (d) of the TCCP

In this section, values of 0.09 m/s, 65 mm, and 60° are assigned to the CFS, height, and contact surface angle, respectively. Consequently, the impact of diameter on the TMP of TCCP is explored. The TCCP channel diameter of 1.7, 2, 2.5, and 3 mm are taken for the evaluation. Figure presents the simulation results for peak temperature and temperature variation at different diameter. In the proposed BTM system, enlarging the channel diameter enhances thermal energy transfer between the batteries and the TCCP. The enhanced performance can be attributed to the larger heat-transfer surface area available coolant flow within the TCCP channels, reduced hydraulic resistance, and mitigation of the pressure-drop penalty. Furthermore, a larger channel diameter promotes more effective convective cooling and improves temperature uniformity across the battery module. Consequently, both peak temperature and temperature variation are reduced, as shown in Figure a. In addition, the pressure drop is significantly reduced, as illustrated in Figure b, indicating improved thermal-hydraulic performance of the proposed BTMS.

11.

Influence of the TCCP channel diameter on (a) the peak temperature and temperature variation. (b) Pressure drop.

In contrast, smaller channel diameters restrict coolant flow, leading to an increased pressure drop. This also causes higher maximum temperatures and greater temperature nonuniformity, both of which adversely affect overall battery performance due to a reduced heat-transfer interface. Table provides a detailed comparison of BTMS performance across varying TCCP channel diameters. When the TCCP diameter is increased from 1.7 to 3 mm, the maximum temperature decreases by 1%, the temperature variation across the battery is reduced by 66.67%, and the pressure-drop penalty is mitigated by 68.05%. At a diameter of 2 mm, the peak temperature and temperature variation are effectively controlled at 310.39 and 4.4 K, respectively. This ensures that the battery remains within the OOT range, demonstrating that the proposed liquid-based BTMS integrated with the TCCP represents a promising strategy to enhance the TMP of LIBs. However, structural strength requirements and economic considerations limit excessive increases or decreases in diameter. Therefore, determining the appropriate TCCP diameter is critical for optimizing the TMP of the liquid-based cooling system, balancing factors such as the heat-transfer efficiency, pressure loss, temperature uniformity, and structural integrity. A TCCP diameter of 2 mm keeps the maximum temperature and thermal variation within optimal limits, hence making it the chosen parameter for further simulations.

3.6. Dual-Channel TCCP and Its Impact on Battery Cooling Efficiency

In this section, a dual-curved, dual-channel TCCP is integrated into a liquid-based cooling system, and its impact on battery cooling efficiency is comparatively evaluated. Figure a,b presents the configurations of the dual-channel TCCP and the corresponding BTMS integrated with the battery. The TCCP diameter, height, and contact angle are fixed at 2 mm, 65 mm, and 60°, respectively. The effect of channel number on TMP is examined at a 5 C discharge rate under CFS ranging from 0.04 to 0.08 m/s, as shown in Figure a. The dual-curved, dual-channel TCCP enhances thermal regulation by optimizing coolant flow distribution and increasing the effective thermal contact area, thereby reducing thermal resistance, a key factor governing BTMS performance. In contrast, high thermal resistance exacerbates heat accumulation, increases energy consumption, and accelerates battery degradation, posing safety risks. By minimizing temperature gradients, the proposed design promotes a more-uniform temperature distribution across the battery module, as illustrated in Figure c, thereby improving overall performance and cycle life.

12.

Schematic diagram of (a) dual-channeled TCCP, (b) battery cell sandwiched with the dual-channel TCCP, (c) temperature contour of battery surface and temperature distribution for dual-channeled TCCP.

13.

Dual-channel TCCP performance on (a) the maximum temperature and thermal variation. (b) Comparison of simulation results of Nusselt number against analytical correlation.

Figure a Dual-channel TCCP-based BTMS can maintain the battery’s maximum temperature below 310.22 K and the temperature variation below 4.07 K, even at a low CFS of 0.05 m/s. As is evident from the figure, increasing the number of channels from single to double noticeably improves the TMP of the TCCP-based cooling system. As discussed in Section , the single-channel TCCP achieves acceptable operating temperature and temperature uniformity only when the CFS exceeds 0.08 m/s. In contrast, the dual-channel TCCP attains comparable thermal performance at a lower CFS of 0.05 m/s, corresponding to a 44.4% reduction in the required CFS. Thus, the dual-channel TCCP structure reduces the battery’s peak temperature and temperature variation by 0.17 K and 7.5%, respectively, compared with the single-channel design.

Furthermore, dimensionless parameters, including the Reynolds number and Nusselt number, are analyzed to evaluate the thermal performance of the proposed dual-curved, dual-channel TCCP-based liquid-cooled BTMS. The Nusselt number of the coolant can be defined using Sieder-Tate model, expressed as:

$$\mathit{Nu}=1.86{\left(\mathit{RePr}\frac{d_{\mathrm{C}}}{L}\right)}^{1/3}{\left(\frac{{\mu }_{\mathrm{r}}}{{\mu }_{\mathrm{w}}}\right)}^{0.14}$$ 14

where (Pr) is Prandtl number of the coolant, (d _c) is the channel diameter, (L) is the channel length, (μ_r) is the dynamic viscosity of the coolant at reference temperature, (μ_w) dynamic viscosity at channel wall temperature, and (Re) is the Reynold number defined by the eq ().

Figure b Comparison of simulation Nusselt numbers with analytical results from developing laminar-flow correlation under various Reynolds numbers. As indicated from the figure, the increasing trend of the Nusselt number with an increase of the Reynolds number highlights improved convective heat transfer between the coolant and TCCP walls. This enhancement is attributed to the increased coolant flow rate, which enhances the heat-transfer coefficient and hence strengthens the cooling capability of the proposed BTMS. Moreover, the simulation results are consistent with the analytical correlation, with an average relative error of 4.92%. This close correspondence validates the numerical model and confirms its reliability to predict the convective heat-transfer characteristics of the dual-channel TCCP-based liquid-cooled BTMS.

In general, the improved TMP can be attributed to the enhanced heat-transfer characteristics of the dual-channel TCCP. The additional channel promotes a more even coolant flow distribution across the cell surface, thereby minimizing localized heat accumulation and reducing the hotspot formation. Additionally, the increased channel number expands the effective heat exchange area between the coolant and the TCCP, which decreases the overall thermal resistance and facilitates more efficient heat removal from the battery cells. Consequently, heat is dissipated effectively, resulting in lower peak temperatures and an improved temperature uniformity throughout the battery system. Operating the BTMS at a lower coolant flow rate also benefits from an energy-efficiency perspective, as it reduces the pumping power required by the cooling system while maintaining effective thermal regulation. However, the number of channels cannot be increased indefinitely because of structural constraints, manufacturing complexity, and space limitations within the battery module. Therefore, identifying an appropriate channel configuration is essential for achieving an optimal balance among thermal performance, system compactness, and energy consumption.

Figure a,b further compares the maximum temperature and temperature variation obtained with the single- and dual-channel TCCP configurations. The results clearly demonstrate the importance of channel optimization in enhancing the TMP of the liquid-cooled BTMSs. By maintaining battery temperatures within the desired operating range and reducing temperature nonuniformity, the dual-channel TCCP contributes to improved battery safety, performance, and durability. The reduction in thermal gradients suppresses hotspot formation and may help extend the battery cycle life while simultaneously lowering cooling energy requirements. Overall, these findings highlight the importance of channel design optimization in developing high-performance BTMSs for cylindrical lithium-ion batteries used in real-world NEVs.

14.

Comparison of the performance of single-channel TCCP and dual-channel TCCP in terms of (a) maximum temperature and (b) temperature variation.

3.7. Comparative Assessment of the Proposed System with Existing BTMS Technologies

To validate the performance of the novel dual-curved TCCP with dual channels, a comparison is made against a previously published similar method. ,, The comparison focuses on the following key parameters, including maximum temperature, temperature variation, the weight ratio of the TCCP, and the temperature uniformity index (TUI). The weight ratio is defined as the ratio of the TCCP weight to the total weight of the battery system, serving as an indicator of structural efficiency. The TUI is used to assess the level of thermal homogeneity and the uniformity of temperature distribution across the battery system. The following equation defines it:

$$\mathrm{T}\mathrm{U}\mathrm{I}=1-\frac{\mathrm{\Delta }T}{T_{\max }}$$ 15

where TUI stands for temperature uniformity index, ΔT is the temperature variation across the system, and T _max denotes the maximum battery temperature. A higher TUI value indicates better temperature uniformity and more effective thermal management performance.

Figure a,b compares the maximum temperature and temperature variation obtained in the present dual-channel TCCP scheme with those reported in a previously published study by Lai et al. Both studies investigate liquid-based cold-plate cooling applied to battery modules composed of 18,650-type lithium-ion cells. In ref , each battery cell is positioned between three cold plates with straight channels, and the cooling performance is evaluated at an ambient temperature of 300 K and a discharge rate of 5 C. The maximum temperature and temperature variation reported in ref are 312.22 and 4.806 K, respectively. In contrast, the present study yields lower values of 310.22 K for the maximum temperature and 4.07 K for the temperature variation. Compared with the results of ref , the present study model reduces the maximum temperature by 0.64% and the temperature variation by 15.31%. These results indicate that the proposed design achieves improved thermal regulation and enhanced temperature uniformity compared to previously reported cold-plate-based BTMS configurations.

15.

Comparison of the present study (dual-channel TCCP scheme) with ref according to (a) maximum temperature and (b) temperature variation.

Figure a,b presents a comparison of the TMP of the proposed design with other cooling schemes reported in refs , . As demonstrated in Figure a, the TUI of the dual-curved, single-channel TCCP is reduced by 1.73% compared to solutions reported in refs , . Upon introducing a dual-channel design to the TCCP, the TUI of the dual-curved, dual-channel TCCP is further reduced by 2.77% relative to earlier studies and by 1.02% compared to the single-channel TCCP. These results indicate that the proposed model achieves a more-uniform temperature distribution. Furthermore, the weight ratio of the single-channel TCCP is 16.94% lower than that of other schemes presented in refs , , as depicted in Figure b. With the dual-channel implementation, the weight ratio of the optimized scheme is further decreased by 22.48 and 6.67% compared to the prior solutions and the single-channel TCCP configuration, respectively.

16.

Comparison of different schemes based on (a) temperature uniformity index and (b) the weight ratio.

In addition, the thermal performance of the proposed dual-channel TCCP-based configuration is evaluated against several representative BTMS technologies, including liquid-immersion cooling, air cooling, heat-pipe-based cooling, and air–PCM (hybrid) systems. Table summarizes the thermal performance of the proposed configuration and previously reported BTMS approaches. As indicated in Table , the proposed configuration achieves effective temperature regulation and improved temperature uniformity while operating at a relatively low coolant flow rate, suggesting lower hydraulic resistance and pumping-power requirements as discussed earlier. Among the studies considered, Luo et al. achieved the lowest maximum battery temperature using a composite vapor chamber–heat pipe (CVC–HP) configuration. Although the reported maximum temperature is 1.21 K lower than that of the present study, the system operated at a higher CFS (4.55 m/s), which may incur greater pumping-power requirements. Nevertheless, the proposed system demonstrates competitive overall thermal performance compared with other BTMS designs. For example, compared with the hybrid air–PCM system investigated by Singh et al., the proposed configuration reduces maximum temperature by 14.78 K and decreases temperature difference by 32.28% under the same 5 C discharge condition, despite operating at a lower CFS (0.05 m/s). These results demonstrate that the proposed BTMS can effectively balance temperature control and temperature uniformity while maintaining low coolant demand. The comparative analysis further supports the suitability of the proposed design as an efficient thermal management solution for lithium-ion batteries in NEVs.

6. Comparative Performance Analysis of the Proposed Approach and Existing BTMS Methods .

		operating conditions			thermal performance
studies	BTMS strategies	C-rate	Tamb (K)	CFS	T max (K)	ΔT (K)
Luo et al.	liquid-immersion	3	298.15	70 mL/min	312.87	4.90
Zeng et al.	air-cooled	12	308.15	100 m3/h	312.65	3.57
Luo et al.	CVC-HP	40,000 W/m3	298.15	4.55 m/s	309.01
Singh et al.	air-PCM	5	298.15	0.1 m/s	325	6.01
current study	liquid (dual-channel)	5	298.15	0.05 m/s	310.22	4.07
current study	liquid (dual-channel)	5	308.15	0.08 m/s	312.66	3.39

^aCVC-HP: Composite vapor chamber-heat pipe; CFS: Coolant flow speed; PCM: Phase change material; Tamb: Ambient temperature; T _max: Maximum temperature; ΔT: Temperature difference.

4. Conclusions

A dual-curved, adaptable TCCP integrated with a liquid-based BTMS is proposed for cylindrical LIBs to maintain thermal conditions within safe limits and enhance the battery TMP in NEVs. The Newman P2D model is used to analyze the thermal behavior of a module of 18,650 cells under a 5 C discharge. A compact dual-curved TCCP is designed to improve heat dissipation, and the effects of the discharge rate, CFS, and TCCP structural parameters, including diameter, height, and contact angle, on BTMS performance are systematically evaluated. Finally, a dual-curved, dual-channel TCCP is developed, and its cooling efficiency is compared to that of the single-channel design.

The major conclusions are presented as follows:

• (1)The dual-curved adaptable TCCP structure coupled to the liquid-based BTMS demonstrated effective thermal management by maintaining cell temperatures within the optimum operational range. The study results indicate that the battery’s peak temperature and temperature variation can be controlled below 310.39 and 4.4 K, respectively, at a CFS of 0.09 m/s.
• (2)An increase in the CFS value significantly improved the TMP of the battery system. However, increases beyond the optimal range yield diminishing benefits and a proportional increase in power consumption, thereby reducing practical viability. The findings revealed that when the CFS exceeds 0.08 m/s, both the peak temperature and temperature nonuniformity can be maintained within safe operating thresholds. However, increasing the CFS to 0.2 m/s introduces a trade-off between an enhanced cooling performance and a substantially higher pressure-drop penalty.
• (3)Evaluation of the TCCP structural parameters indicates that a moderate reduction in TCCP height decreases temperature variation and system weight, albeit with a slight increase in maximum temperature, whereas excessive reduction in TCCP height diminishing the thermal regulation capability and causes the peak temperature to exceed acceptable limits. Increasing the TCCP diameter significantly improves TMP. Specifically, increasing the diameter from 1.7 to 3 mm leads to a notable reduction in peak temperature, temperature difference, and pressure drop of 1, 66.67, and 68.05%, respectively. A larger surface contact angle further lowers both the peak temperature and temperature difference, but increases system weight. Based on these trade-offs, the optimal TCCP configuration in this study comprises a height of 65 mm, a diameter of 2 mm, and a contact angle of 60°.
• (4)Compared with the single-channel TCCP-based liquid BTMS, the dual-channel TCCP configuration exhibits a superior TMP. The optimized dual-curved, dual-channel TCCP maintains a maximum temperature of 310.22 K and a temperature difference of 4.07 K at a low CFS of 0.05 m/s, which is within safe operating limits for LIBs. The improved thermal performance is attributed to the enhanced heat-transfer capability of the dual-channel TCCP, driven by more-uniform coolant flow distribution and an increased heat exchange area, while lowering the pressure drop. Notably, the temperature uniformity achieved at the single-cell level is comparable to that of a full-battery module.

This study proposes a dual-curved TCCP integrated with a liquid-based BTMS, providing a compact and efficient heat-transfer interface for high-rate battery cooling. While the analysis is performed at the single-cell level, the flexible design and compatibility with advanced manufacturing techniques indicate a strong potential for scalability to module-level applications. Future research should incorporate machine-learning-assisted multiobjective optimization to balance key performance metrics, including temperature uniformity, pressure drop, and system weight, thereby further enhancing BTMS performance. Overall, this work offers valuable insights and a practical reference for the development of advanced cold-plate-based liquid BTMSs in NEVs.

Glossary

Nomenclature

h

height (mm)

d

diameter (mm)

P

pressure (Pa)

ΔP

pressure drop (Pa)

v⃗

velocity (V)

I

charge/discharge current (A)

T

temperature (K)

ΔT

temperature difference (K)

C _p

specific heat capacity (J·kg^–1K^–1)

Q

heat generation rate of the battery (Wm^–3)

D

reference diffusivity (m²/s)

De

electrolyte diffusivity for cathode (m²/s)

U

voltage (V)

V _b

volume of the battery (mm³)

R

internal resistance (Ω)

Glossary

Symbols

ρ

density (kgm^–3)

α

contact surface angle (°)

μ

dynamic viscosity (kg/(m·s))

∇

gradient operator

Δ

change in variable

λ

thermal conductivity (Wm^–1K^–1)

ϵf

filler fraction

ϵs

volume fraction of electrolyte

β

bruggeman tortuosity exponent

αα

transfer coefficient at the anode

αc

transfer coefficient at the cathode

σ

electrical conductivity (S/m)

Glossary

Subscripts

b

battery

w

water

gen

generation

rev

reversible

irr

irreversible

ocv

open circuit voltage

max

maximum

Glossary

Acronyms

TCCP

thermally conductive cold plate

BTMS

battery thermal management system

NEVs

new-energy vehicles

P2D

Pseudo-two-dimensional

DCC

direct contact cooling

ICC

indirect contact cooling

CFS

coolant flow speed

LIB

lithium-ion battery

OOT

optimal operating temperature

PCM

phase change materials

TMP

thermal management performance

EVs

electric vehicles

MSMD

multiscale multidomain

OTP

optimum thermal performance

TUI

temperature uniformity index

The authors declare no competing financial interest.