Investigation on Thermal Performance of a Battery Pack Cooled by Refrigerant R134a in Ribbed Cooling Channels

Abstract

This study numerically investigates the thermal performance of a refrigerant-based battery thermal management system (BTMS) under various operating conditions. A validated numerical model is used to examine the effects of cooling channel rib configurations (rib spacing and rib angles) and refrigerant parameters (mass flow rate and saturation temperature) on battery thermal behavior. Additionally, the impact of discharge C-rates is analyzed. The results show that a rib spacing of 11 mm and a rib angle of 60° reduce the maximum battery temperature by 0.8 °C (cooling rate of 2%) and improve temperature uniformity, though at the cost of a 130% increase in pressure drop. Increasing the refrigerant mass flow rate lowers the maximum temperature by up to 10%, but its effect on temperature uniformity diminishes beyond 20 kg/h. A lower saturation temperature enhances cooling but increases internal temperature gradients, while a higher saturation temperature improves uniformity at the expense of a slightly higher maximum temperature. Under high discharge rates (12C), the system’s cooling capacity becomes limited, leading to significant temperature rises. These findings provide insights that can aid in optimizing BTMS design to balance cooling performance, energy efficiency, and temperature uniformity.

1. Introduction

As global energy shortages and environmental pollution become increasingly severe, the overuse of traditional energy sources and their adverse effects on ecological systems are becoming more evident. In response to these challenges, accelerating the transition to sustainable energy sources has become a critical global priority. Electric vehicles (EVs) and hybrid electric vehicles (HEVs) have emerged as effective solutions to decrease dependence on fossil fuels and mitigate greenhouse gas emissions, making them central to green energy policies in many countries [1]. Among various energy storage technologies, lithium-ion batteries have gained prominence as the primary power source for EVs and HEVs due to their high energy density, long lifespan, and low self-discharge rates. Consequently, they have been widely adopted by new energy vehicle manufacturers worldwide. Typically, battery packs are designed by connecting multiple cells in series or parallel to meet varying power demands across different operational scenarios [2]; however, lithium-ion batteries are highly sensitive to temperature fluctuations during operation, particularly under high-load charging and discharging conditions [3]. Internal resistance generates significant heat, leading to temperature variations that can negatively impact battery performance and lifespan [4]. Thus, an efficient battery thermal management system (BTMS) is essential for regulating the temperature of the battery pack, ensuring it operates within the optimal temperature range [5], minimizing temperature imbalances, extending battery life, and improving safety and energy efficiency [6]. Therefore, designing an effective BTMS is crucial for maintaining stable and safe battery operation across various use cases.

At present, BTMS technologies for new energy vehicles primarily include air cooling [7], liquid cooling, phase change materials [8], and refrigerant-based cooling systems [9]. Air cooling systems are simple, cost-effective, and easy to integrate into vehicle design. However, as the energy density of batteries increases, the heat generated during charging and discharging has also grown significantly, making traditional air cooling systems insufficient for meeting the high thermal management demands [10]. As a result, liquid cooling systems are increasingly being used in place of air cooling systems [11]. Liquid cooling research covers a broad spectrum of approaches, with many studies using numerical simulations and experimental techniques to assess cooling performance under various operational conditions [12]. For instance, Shang et al. [13] evaluated cooling performance and pump power consumption through mathematical modeling and numerical analysis, finding that increasing the inlet mass flow rate effectively reduces the maximum battery temperature, though it has limited effects on improving temperature uniformity. Akbarzadeh et al. [14] utilized computational fluid dynamics (CFD) simulations to analyze the effect of parasitic power consumption in BTMSs on battery pack specific energy, demonstrating that liquid cooling systems provide lower temperatures and more uniform temperature distributions under the same power consumption. Wang et al. [15] proposed a hybrid BTMS and found that a dual-sided cold plate design effectively controls the maximum average temperature and temperature differential of battery cells under extreme conditions, keeping them within an optimal range.

Liquid cooling systems are divided into indirect liquid cooling systems and direct liquid cooling systems. Indirect liquid cooling systems are capable of delivering more uniform cooling across battery packs by circulating coolant, which reduces temperature disparities between individual cells, thereby improving overall battery performance and longevity [16]; however, these systems require additional components such as pumps, pipes, and radiators, which increase system complexity and manufacturing costs [17]. Moreover, prolonged use may lead to issues such as coolant leakage, which can degrade performance or cause system failure [18]. Recently, refrigerant-based direct cooling technology has emerged as a promising solution for BTMS design due to its superior heat transfer efficiency [19]. Refrigerant cooling systems offer excellent thermal management performance, particularly under high-power conditions with large temperature gradients, while also providing advantages in terms of size and weight. Shen et al. [20] proposed a refrigerant-based BTMS that effectively regulates battery temperature and enhances energy efficiency in EVs operating under high-speed, high-temperature dynamic conditions. Guo et al. [21] developed a refrigerant-based thermal management system for EVs, achieving significant improvements in temperature control by adding an electronic expansion valve to the refrigerant circuit. Park et al. [22] validated the superior performance of active thermal management systems using refrigerant cooling in combined charge–discharge scenarios through numerical simulations and experimental data, highlighting the respective benefits and drawbacks of active and passive systems under different operational conditions. The most common direct liquid cooling system is immersion cooling. Immersion cooling has emerged as an alternative thermal management solution for high-performance battery systems. This method involves submerging the battery in a thermally conductive liquid, which allows for efficient heat dissipation and uniform temperature distribution [23]. Compared to traditional air and liquid cooling systems, immersion cooling provides better thermal management by directly cooling the battery surface, reducing the risk of hot spots and enhancing overall system performance; however, it also presents challenges around the complexity of the cooling system, the need for specialized coolants, and higher cost [24].

Previous studies indicated that refrigerant-based cooling systems outperform traditional liquid and air cooling systems in terms of thermal management performance; however, these researchers mainly focused on cooling performance at the single-cell or battery module level, primarily considering charging and discharging conditions and refrigerant physical properties. There is still limited research on the thermal performance of refrigerant cooling systems at the battery pack level, especially regarding the effects of refrigerant inlet temperature, mass flow rate, and other boundary conditions on thermal performance. Therefore, the thermal performance of cooling plate with various rib configurations, including rib spacing and rib angle for a HEV battery pack, has been discussed and analyzed in this study. In addition, the influences of refrigerant inlet boundary conditions, including mass flow rate and saturation temperature and battery pack discharge rates on thermal performance, have been considered in the present study. This study uses a commercially available HEV battery pack as a test case. The findings provide valuable insights for the design and implementation of refrigerant-based BTMS in practical engineering applications.

2. Numerical Method

2.1. Physical Model

This study utilizes a refrigerant-based battery thermal management system (BTMS) for a commercial hybrid electric vehicle (HEV). The battery pack consists of four modules, each containing 24 lithium-ion cells. The total pack contains 96 cells arranged in a 1P96S configuration, as shown in Figure 1a. In order to effectively remove the heat from battery pack, a cooling plate with microchannels is positioned beneath the battery pack. The refrigerant enters the cooling plate via the inlet pipeline and exits through the outlet pipeline, as illustrated in Figure 1b.

Passive heat transfer enhancement techniques are considered and discussed in this study, particularly examining the impact of the cooling channel structure on thermal performance. The base model features a straight flow channel, equipped with symmetrically arranged ribs on the upper and lower walls, as shown in Figure 1c. These ribs are designed with various angles ranging from 30° to 90° to optimize heat transfer, as depicted in Figure 1d. In addition, rib spacings varying from 2.2 mm to 15.4 mm are considered in the present investigation. The prismatic lithium-ion battery cells employed in this study use an NCM622 cathode and a graphite anode, with a nominal capacity of 5.9 Ah. The key specifications of the battery cells are summarized in

Table 1. Key specifications of the battery cell.

Parameter	Specification
Nominal capacity (Ah)	5.9
Nominal voltage (V)	3.64
Maximum charge voltage (V)	4.1
Minimum discharge voltage (V)	2.7
Dimensions (length × height × width, mm)	123 × 71 × 12.2
Weight (kg)	0.219

.

2.2. Heat Generation Model of Battery

The heat generation model plays a crucial role in simulating the temperature distribution within the battery pack under different charge and discharge conditions, providing a foundation for developing effective thermal management strategies. Battery heat generation models can be broadly classified into two categories: electrochemical thermal models and the Bernardi model. The electrochemical thermal model is detailed and considers the coupling of electrochemical reactions, ion migration, and heat conduction, offering high accuracy in predicting battery heat generation; however, this model requires numerous battery-specific parameters, which are often difficult to obtain, making its application computationally intensive. In contrast, the Bernardi model is a simplified approach that estimates heat generation based on current density during discharge and the thermal properties of battery materials [25]. While less detailed, this model is computationally simpler and only requires a few basic parameters, such as discharge current and ambient temperature, making it more suitable for simulations in this study.

The heat generation calculation formula for the Bernardi model used in this study is as follows:

$$Q=I[(U_{ocv}-U)-T_b{\displaystyle \frac{\partial U_{ocv}}{\partial T_b}}]$$

(1)

where $I$, $U_{ocv}$, $U$, $T_b$ correspond to the current (A), open-circuit voltage (V), terminal voltage (V), and battery temperature (°C) during charging and discharging, respectively, and $\partial U_{ocv}/\partial T_b$ denotes the temperature coefficient. On the right-hand side, both Joule heat and electrochemical reaction heat are included [26]. Given that the electrochemical reaction heat is relatively minor and can be disregarded, the equation is simplified accordingly [27]:

$$Q=I^2{R}_{int}$$

(2)

where $I$ is the current and $R_{int}$ is the internal resistance, which varies with the state of charge (SOC) and is affected by environmental temperature. The dynamic changes in SOC and internal resistance during the charging and discharging cycles directly influence the heat generation rate.

At the same SOC, lower temperatures lead to an increase in the battery’s internal resistance. This is because, as the temperature decreases, the conductivity of the electrolyte is reduced, the electrochemical reaction rate slows down, and certain electrode materials may undergo structural changes or become deactivated at low temperatures. These factors collectively contribute to the degradation of the electrode materials, resulting in a higher internal resistance in the battery. In this study, the open circuit voltage (OCV) of the battery as a function of SOC was obtained through offline OCV tests [28], as shown in Figure 2a. Additionally, the internal resistance of the battery was determined using hybrid pulse power characterization (HPPC) testing [29]. The variation of internal resistance with SOC under different test temperatures is presented in Figure 2b.

The heat generation rate in the battery is dependent not only on time but also on the state of charge (SOC) and the internal resistance of the cell. As shown in Figure 2, the internal resistance of the battery varies with the SOC and is affected by environmental temperatures. This relationship is critical as the internal resistance directly influences the heat generation rate, which is given by Equations (1) and (2). Therefore, the heat generation rate is time-dependent, as both the current and SOC evolve during the charging and discharging processes.

Figure 3 presents the experimentally measured heat generation rate over time. As illustrated, heat generation increases toward the end of discharge, which aligns with the observed temperature trends.

2.3. Governing Equations

The thermal conduction process of the battery pack is quite complex, primarily involving conductive heat transfer between the battery cells and other components (such as endplates, rubber, thermal pads, and cooling plates), as well as convective heat transfer between the battery surface and air. The transient heat conduction equation for the battery pack can be expressed as follows:

$$\rho C_p{\displaystyle \frac{\partial T}{\partial t}}={\lambda }_x{\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\lambda }_y{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}+{\lambda }_z{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}+q_{bat}$$

(3)

where $\rho$ and $C_p$ represent the density and specific heat capacity of the battery components, $T$ is the temperature, $t$ is time, and ${\lambda }_x$, ${\lambda }_y$, ${\lambda }_z$ are the thermal conductivities of the battery cell in the x, y, and z directions, respectively. $q_{bat}$ represents the heat generation rate of the battery cell, which can be calculated using Equation (1).

In automotive air conditioning systems, R134a refrigerant has been widely used in the thermal management systems of both traditional internal combustion engine vehicles and new energy vehicles [30]; however, with growing environmental concerns, new refrigerants, such as R1234yf and CO₂, are increasingly being adopted in recent vehicle models due to their lower global warming potential (GWP) and improved sustainability. In recent years, battery thermal management systems (BTMSs) based on two-phase flow cooling schemes have received significant attention. In this study, R134a is chosen as the coolant due to its established performance in such systems, and its thermophysical properties are shown in

Table 2. Polynomial approximations of thermophysical properties for R134a (adapted from Ref. [32]).

Property	Vapor Phase Expression (°C)	Liquid Phase Expression (°C)
Density (kg·m−3)	$\rho$ = −3.0 × 10−7T3 + 9.0T2 − 0.019T + 4.7	$\rho$ = −2.7 × 10−4T3 − 1.0 × 10−5T2 − 3.2T + 1292
Specific heat capacity (J·(kg·°C)−1)	$C_p$ = 3.0 × 10−8T6 − 4.0 × 10−6T5 + 1.7 × 10−4T4 + 0.0029T3 − 0.076T2 + 4.1T + 908	$C_p$ = 2.0 × 10−8T6 − 2.0 × 10−6T5 + 7.0 × 10−5T4 + 0.0018T3 − 0.044T2 + 2.5T + 1348
Thermal conductivity (W·(m·°C)−1)	$k$ = 2.0 × 10−8T3 − 9.0 × 10−7T2 + 7.0 × 10−5T + 0.012	$k$ = −4.0 × 10−9T3 + 4.0 × 10−7T2 − 4.0 × 10−4T + 0.092
Viscosity (kg·(m·s)−1)	$\mu$ = 7.0 × 10−12T3 − 2.0 × 10−10T2 + 4.0 × 10−8T + 1.0 × 10−5	$\mu$ = −1.0 × 10−10T3 + 3.0 × 10−8T2 − 4.0 × 10−6T + 3.0 × 10−4

. The transient volume-of-fluid (VOF) [31] method is employed to simulate the heat transfer and mass transfer processes of R134a in the microchannels of the battery cooling plate.

The VOF method can accurately capture the dynamic behavior of the liquid–gas interface, making it suitable for complex microchannel flows. It also predicts the phase change and heat–mass transfer behavior of the coolant. Similar methods have been used to study the cooling performance of R134a and other refrigerants in microchannels. The continuity equations for the liquid and gas phases are as follows [33]:

$${\displaystyle \frac{\partial {\alpha }_l}{\partial t}}+\nabla \cdot (u{\alpha }_l)=-{\displaystyle \frac{S}{{\rho }_l}}$$

(4)

$$\partial {\alpha }_v{\displaystyle \frac{\partial {\alpha }_v}{\partial t}}+\nabla \cdot (u{\alpha }_v)=-{\displaystyle \frac{S}{{\rho }_v}}$$

(5)

$$\rho ={\alpha }_l{\rho }_l+{\alpha }_v{\rho }_v$$

(6)

$${\alpha }_l+{\alpha }_v=1$$

(7)

where ${\alpha }_l$ and ${\alpha }_v$ represent the volume fractions of the liquid and gas phases, respectively; $\rho$, ${\rho }_l$, and ${\rho }_v$ represent the densities of the mixed phase, liquid phase, and gas phase, respectively; $u$ is the velocity vector; and $S$ represents the source term for liquid-phase evaporation or gas-phase condensation. The momentum conservation equation is as follows [33]:

$${\displaystyle \frac{\partial }{\partial t}}(\rho u)+\nabla \cdot (\rho \overrightarrow{u}\overrightarrow{u})=-\nabla p+\nabla \cdot [\mu (\nabla \overrightarrow{u}+\nabla {\overrightarrow{u}}^T-{\displaystyle \frac{2}{3}}\mu \nabla \cdot \overrightarrow{u}I)]+\rho \mathit{g}+{\mathit{F}}_{\sigma }$$

(8)

where $p$ is the pressure of the working fluid, $\mu$ is the dynamic viscosity, $I$ is the unit matrix, and ${\mathit{F}}_{\sigma }$ is the volumetric force. The energy conservation equation is as follows [33]:

$${\displaystyle \frac{\partial \rho E}{\partial t}}+\nabla \cdot \overrightarrow{u}(\rho E+P)=\nabla \cdot (\lambda \nabla T)+Q$$

(9)

where $E$ is the total energy of the gas-liquid mixture, $\lambda$ is the average thermal conductivity of the mixture, and $Q$ represents the energy source due to liquid-phase evaporation.

In this study, the boiling heat transfer process of R134a refrigerant in the battery cooling plate is modeled using the Rohsenow correlation formula proposed by Chen [34]. This correlation was selected because it is well-suited for the simulation of heat transfer in microchannels, a typical feature of BTMSs. Although Chen’s correlation was originally proposed for vertical channels with fluids like water, methanol, and hydrocarbons, it has also been applied to similar systems involving refrigerants, including R134a, in microchannel heat exchangers. Chen’s model accounts for both single-phase convective heat transfer and two-phase boiling heat transfer, making it appropriate for simulating the boiling process under conditions typical of battery cooling plates. [35]

Various correlations, such as those proposed by Shah, Kandlikar, and Thome, are widely used for predicting boiling heat transfer in microchannels. Chen’s correlation is selected in this study due to its simplicity and suitability for the specific conditions examined, focusing on the overall heat transfer performance of refrigerant-cooled microchannels. This correlation provides a reliable estimation of the heat transfer rate while ensuring both computational efficiency and practical applicability.

This formula assumes that the heat transfer process of the working fluid in microchannels consists mainly of single-phase convective heat transfer and two-phase boiling heat transfer; therefore, the total heat transfer rate $q_t$ can be expressed as follows:

$$q_t=q_c+q_b$$

(10)

where $q_c$ represents the single-phase convective heat transfer rate and $q_b$ represents the two-phase boiling heat transfer rate. The single-phase convective heat transfer rate $q_c$ depends on the following formula:

$$q_c=h_c(T_w-T_l)$$

(11)

where $h_c$ is the convective heat transfer coefficient for the single-phase flow, which can be expressed using the Dittus–Boelter equation:

$$h_c=0.023R{e}^{0.8}P{r}^{0.4}(\lambda /D)$$

(12)

The two-phase boiling heat transfer rate $q_b$ can be expressed as follows:

$$q_b={\mu }_l\sqrt{{\displaystyle \frac{g({\rho }_l-{\rho }_v)}{\sigma }}}{\left({\displaystyle \frac{C_{pl}(T_w-T_s)}{CqrP{r}_l^n}}\right)}^{3.03}$$

(13)

where $r$ is the boiling heat transfer coefficient and $\sigma$ is the surface tension at the liquid–gas interface. Other parameters include the specific heat capacity of the saturated liquid phase $C_{pl}$, wall temperature $T_w$, liquid saturation temperature $T_s$, Prandtl number $P{r}_l$, Prandtl number exponent (default value of 1.73), and the empirical coefficient $C_q$ related to the liquid and surface combination, with values modified based on Ref. [36].

The mass transfer rate at the overheated wall surface due to liquid-phase evaporation can be calculated as follows:

$$S_E=q_b{A}_{W,j}/r{V}_j$$

(14)

where $S_E$ is the mass source term due to liquid-phase evaporation, and $A_{W,j}$ and $V_j$ represent the area and volume of the mesh cells near the wall, respectively. The mass transfer rate for gas-phase condensation in subcooled boiling flow conditions can be expressed as follows:

$$S_C=h_i{A}_i(T_s-T_l)/r$$

(15)

where $S_C$ is the mass source term for gas-phase condensation, and $h_i$ and $A_i$ represent the heat transfer coefficient at the liquid-gas interface and the interfacial area per unit volume, respectively. These parameters can be expressed as follows:

$$h_i={\displaystyle \frac{Nu{\lambda }_l}{D_{bu}}}={\displaystyle \frac{{\lambda }_l}{D_{bu}}}(2+0.6R{e}^{0.5}P{r}^{0.33})$$

(16)

$$A_i=6{\partial }_v/D_{bu}$$

(17)

where $D_{bu}$ is the bubble diameter.

2.4. Boundary Conditions and Mesh Independent Study

In this study, a cooling plate featuring straight channels is positioned beneath the battery pack to provide efficient cooling for the battery cells. Between the battery cells and the cooling plate, a 1 mm thick silicone pad, 0.6 mm thick heating film, and a 1 mm thick aluminum plate are sequentially placed. This arrangement reduces contact thermal resistance and enhances heat transfer efficiency. Additionally, a 1.73 mm thick spacer pad is inserted between the cells to prevent direct contact, which helps to mitigate the risk of short circuits. The elasticity of the spacer pad also absorbs vibrations and shocks during the operation of the EV, thus improving the stability and service life of the battery module. The thermal-physical properties of the components of the battery pack are presented in

Table 3. Thermal properties of battery module components.

Component	Density kg/m3	Specific Heat Capacity J/(kg·K)	Thermal Conductivity W/(m·K)
Battery cell	2150	940	λx = 20, λy = 3, λz = 16
Thermal pad	940	1900	0.42
Cooling plate	2650	870	165
Heater plate	1700	620	0.18
Foam layer	1450	1150	0.35

. The values given in this table are provided by external suppliers based on their proprietary measurements.

For simulations of the direct and indirect cooling of the battery pack with refrigerant, it is crucial to set the boundary conditions accurately to ensure the reliability and precision of the results. Alongside the conventional conditions for the fluid inlet, outlet, and battery heat source, special attention must be paid to factors such as the phase change process of the refrigerant, microchannel wall roughness, and the convective heat transfer coefficient. The phase change process significantly influences heat exchange efficiency, while wall roughness impacts flow characteristics and heat transfer performance. Moreover, the heat transfer coefficient between the refrigerant and the battery surface plays a pivotal role in optimizing cooling performance; thus, carefully selecting and defining boundary conditions is essential for improving simulation accuracy.

Before conducting the numerical simulations, the following assumptions were made: (1) The cooling system consists solely of the cooling plate channels and refrigerant flow; (2) The battery cell heat generation rate is uniformly distributed; (3) The thermal-physical properties of the battery remain constant with temperature; (4) The refrigerant flow within the cooling plate channels is laminar; (5) Radiative heat loss from the battery pack is neglected, and only convective heat transfer with the air is considered.

To ensure the independence of the transient solution, tests were conducted with four different time steps (Δt = 0.1 s, 0.5 s, 1 s, 2 s) under peak cooling load conditions (40 °C ambient temperature). The results showed that, with Δt = 0.5 s, the maximum temperature deviation compared to Δt = 0.5 s was 0.4 °C (approximately 0.8%), while the computational time was reduced by 65%, as shown in Figure 4. Considering the small temperature deviation and significant improvement in computational efficiency, all subsequent simulations were performed with Δt = 0.5 s as the time step.

To ensure the accuracy of the simulation results, a mesh independence analysis was conducted. Five different mesh schemes, with grid counts ranging from 3.4 million to 16.85 million, were computed. The maximum battery temperature and pressure drop in the channel were compared for different grid resolutions, as shown in Figure 5. The results indicate that, as the mesh density increases, the changes in the maximum battery temperature and channel pressure drop become progressively smaller. Notably, when the grid count reached 11.74 million, the calculation results stabilized, with variations remaining within an acceptable error range. This suggests that the chosen mesh meets the mesh independence requirement, and further refinement would have negligible effects on the simulation results. Therefore, a final grid resolution of 11.74 million mesh cells was selected, ensuring accurate representation of the system’s thermal flow characteristics and flow behavior, and confirming the reliability of the simulation.

2.5. Numerical Validation

In this section, the numerical model is validated by comparing the simulation results with experimental data under real operating conditions. The experiments were conducted in a high-temperature environment with a cooling speed of 40 km/h on a 7.2% incline. The ambient temperature was 40 °C, humidity was 40%, and the solar radiation intensity was 950 W/m². The air conditioning system was set to maximum airflow, the lowest temperature, and external circulation in face mode. The refrigerant flow rate entering the battery evaporator was regulated by the expansion valve (EXV) control signal, which provided the necessary boundary conditions for the numerical model. Additionally, the pressure boundary and refrigerant mass flow rate at the EXV outlet were recorded. The details of experimental tests can be found in our previous study in Ref [37] and are not repeated here.

A 3-D numerical model was developed using STAR-CCM+ 2020.3, and the simulation was performed under the specified boundary conditions. The simulation results were compared with experimental measurements. The experimental data used to validate the model were derived from previous work. As illustrated in Figure 6, the temperature profiles of the cell, heater film, and cold plate are compared. While minor discrepancies are observed in the 100–400 s range, the model effectively captures the overall trend. The simulation results closely match the experimental data, with a maximum deviation in battery temperature of only 2 °C.

By comparing the model predictions with experimental measurements, an error analysis was conducted to evaluate the accuracy of the simulation. The maximum battery temperature exhibited good agreement between the experimental and simulated results, with a maximum deviation of 2 °C; however, notable discrepancies were observed for the heater film and cold plate temperatures between 100 s and 400 s, with errors reaching up to 5 °C. These differences may be attributed to rapid temperature fluctuations in the cold plate and heater film during this period, which might not have been fully captured by the transient heat transfer model. Additionally, variations in coolant flow characteristics between the experiment and simulation could have influenced heat transfer intensity. Nevertheless, the model is deemed suitable for system-level predictions, as the observed deviations remain within an acceptable range for the intended application.

The simulation initially underpredicts the heater film and cold plate temperatures within the first 800 s and subsequently overpredicts them. This discrepancy could result from several factors: First, the transient response at the early stage of the simulation may not fully reflect the actual dynamic behavior of the experimental system, particularly regarding thermal inertia and startup effects; Second, minor variations in boundary conditions, incomplete characterization of fluid properties, and simplifications in model assumptions may contribute to these differences. To improve the model’s accuracy, future work should focus on refining these assumptions and further validating the results with additional experimental data.

2.6. Parameter Definition

Fluid flow can be classified into laminar flow and turbulent flow based on the flow state. The standard for determining the flow regime is typically based on the Reynolds number (Re), which is calculated using the following formula:

$$Re={\displaystyle \frac{\rho vL}{\mu }}$$

(18)

where $v$ is the average velocity of the fluid across the cross-section (m/s) and $L$ is the characteristic length of the cooling channel (m). When the channel cross-section is rectangular, the characteristic length in Equation (18) can be replaced by the hydraulic diameter $D_{eq}$, which is calculated as follows:

$$D_{eq}={\displaystyle \frac{4A}{P}}$$

(19)

where $A$ is the cross-sectional area (m²) and $P$ is the perimeter (m) of the channel. In this study, R134a is used as the refrigerant in the cooling channels. Since the Reynolds number for this refrigerant is less than 1000, the laminar flow model is adopted in this research.

The Nusselt number (Nu) is a dimensionless quantity used in fluid mechanics to describe the thermal performance of a fluid, primarily to assess the relative importance of convective heat transfer versus conductive heat transfer. Specifically, the Nusselt number represents the ratio of convective heat transfer to conductive heat transfer over a unit length, and it is an essential parameter for evaluating the heat transfer performance of fluids. The Nusselt number is calculated using the following formula:

$$Nu={\displaystyle \frac{hl}{k}}$$

(20)

where $h$ is the heat transfer coefficient at the heat exchange wall, $l$ is the characteristic length, and $k$ is the thermal conductivity of the coolant. The calculation formula for $h$ is as follows:

$$h={\displaystyle \frac{q_w}{A_w(T_w-T_{avg})}}$$

(21)

where $q_w$ represents the heat flux on the heat exchange wall surface, $A_w$ denotes the area of the heat exchange wall, $T_w$ is the temperature of the heat exchange wall, and $T_{avg}$ refers to the volume-averaged temperature of the coolant. The calculation formulas for $T_w$ and $T_{avg}$ are as follows:

$$T_w={\displaystyle \frac{{\displaystyle \iint Td{A}_w}}{A_w}}$$

(22)

$$T_{avg}={\displaystyle \frac{T_{inlet}+T_{outlet}}{2}}$$

(23)

where $T_{inlet}$ and $T_{outlet}$ represent the inlet and outlet temperatures of the coolant.

The friction factor $f$ reflects the energy loss caused by viscous resistance in the fluid flow through the channel. The dimensionless value of the friction factor is positively correlated with the pressure drop of the coolant, making it a useful indicator for economic evaluation. The friction factor is calculated as follows:

$$f={\displaystyle \frac{\Delta PL}{\rho v^2}}$$

(24)

where $\Delta P$ is the pressure drop between the inlet and outlet, and $L$ is the length of the flow path.

This study considers both heat transfer performance and economic efficiency, and introduces a thermal performance enhancement factor ($\eta$) to quantify the improvement in heat transfer performance [38]. The calculation of the $\eta$ is as follows:

$$\eta ={\displaystyle \frac{Nu}{N{u}_0}}/({\displaystyle \frac{f}{f_0}}{)}^{\frac{1}{3}}$$

(25)

where $Nu$ and $N{u}_0$ are the Nusselt numbers for the improved and smooth channels, respectively, and $f$ and $f_0$ are the corresponding friction factors. This dimensionless factor represents the improvement in heat transfer performance under the same energy consumption conditions, and it will be used in future research to evaluate the performance improvement of the proposed design compared to the original design.

3. Results and Discussion

3.1. Effect of Rib Spacing in Cooling Channels on Heat Transfer Performance

In a battery pack cooling system, the design of cooling channels plays a crucial role in determining heat conduction and overall heat transfer efficiency. Rib structures are widely employed to enhance heat dissipation, with their configuration significantly influencing fluid flow dynamics and thermal performance. The primary function of ribs is to induce flow disturbances, thereby increasing the contact area between the coolant and the channel walls, which enhances convective heat transfer.

This chapter examines the impact of various rib spacings (2.2 mm, 4.4 mm, 6.6 mm, 11 mm, and 15.4 mm) on the flow characteristics and heat transfer performance of cooling plate channels. A case study with 90° ribs under an inlet mass flow rate of 40 kg/h is presented. The corresponding results are illustrated in Figure 7, where a rib spacing of 0 mm represents a smooth channel for comparison.

The variation in rib spacing affects both heat transfer and flow resistance. As the rib spacing decreases, the contact area between the fluid and the wall increases, which improves heat transfer efficiency. Smaller rib spacings intensify the disturbance caused by the ribs, leading to higher flow disturbance in the fluid and an increased heat transfer coefficient. This results in a higher Nusselt number, indicating improved heat transfer performance; however, this reduction in spacing also increases flow resistance. As the fluid flows through narrower channels, the local pressure loss caused by the ribs rises, resulting in a higher pressure drop and increased energy consumption. While smaller rib spacings enhance heat transfer, excessive reduction in spacing leads to a significant pressure drop, adversely affecting the system’s energy efficiency. Among the tested rib spacings, an 11 mm spacing provides the best balance between heat transfer and pressure drop.

Figure 8 shows temperature contour plots of the battery cross-section for different rib spacings. In the direct cooling mode, the temperature at the inlet of the cooling channel significantly decreases, indicating the strong heat transfer capabilities of the coolant at the inlet; however, as the coolant moves along the channel, its heat transfer capability weakens, resulting in higher battery temperatures at the outlet. Optimizing rib spacing is crucial in regulating this temperature distribution. Smaller spacings (2.2 mm and 4.4 mm) improve fluid disturbance, enhancing the uniformity of the heat transfer along the channel and effectively mitigating temperature rise.

Figure 9 illustrates the overall temperature distribution of the battery module. The cooling effect of the direct cooling system plays a crucial role in the overall heat transfer performance. With smaller rib spacings, coolant disturbance increases, enhancing overall cooling efficiency and controlling the maximum temperature difference; however, as rib spacing increases to 11 mm and 14.2 mm, the disturbance in the coolant flow decreases, leading to a drop in heat transfer performance and a noticeable temperature increase at the outlet. These results highlight that proper rib spacing design can improve heat transfer performance and balance the temperature distribution within the battery.

Figure 10 displays the velocity contour plots and streamline distributions of the fluid under different rib spacings. Compared to smooth channels, the presence of ribs alters the flow pattern of the coolant. The cross-sectional area of the channel decreases due to the ribs, causing an increase in fluid velocity between the ribs, as shown in the figure. After the coolant passes the ribs, secondary flows are generated due to the geometric structure, causing lateral fluid diffusion and local vortices at the edges of the ribs. These vortices disrupt the thermal boundary layer, allowing the coolant in the mainstream region to directly contact the wall, increasing the temperature gradient and significantly reducing thermal resistance. Furthermore, the enhanced disturbance between flow layers promotes better fluid mixing, intensifying heat exchange and improving the convective heat transfer coefficient, thereby enhancing the heat transfer performance. However, excessively small rib spacings may create local flow dead zones, limiting further improvement in heat transfer and increasing the system’s pressure drop.

3.2. Effect of Rib Angle in Cooling Channels on Heat Transfer Performance

In the previous section, the influence of different rib spacings on the heat transfer performance of cooling plates was examined. This section delves deeper into the mechanism by which variations in rib angle affect thermal performance. Building upon the previous simulation results, a square rib with an 11 mm spacing is selected as the baseline model for this analysis. The effects of different rib angles (30°, 45°, 60°, 75°, and 90°) on the flow characteristics and heat transfer performance of the cooling plate are investigated, the aim being to identify patterns that could optimize rib geometry. The simulation results are presented in Figure 11, where a rib angle of 0° represents a smooth channel for comparison.

It is observed that the arrangement of ribs at different angles significantly increases both the Nusselt number and friction factor compared to a smooth channel. Except for the 30° rib angle, the Nusselt number shows minimal variation for the other rib angles. As the rib angle increases, the friction factor gradually increases as well. Considering both heat transfer performance and pump power consumption, Figure 9 shows that the cooling plate with a 60° rib angle exhibits the highest thermal performance factor, indicating that this rib angle provides the best heat transfer performance under direct cooling conditions.

Figure 12 presents the temperature contour plots of the battery cross-section for different rib angles. The rib angle significantly impacts the temperature distribution across the battery cross-section. Compared to the smooth channel, ribbed cooling plates improve the temperature uniformity of the battery. Rib angles of 45° and 60° result in lower high-temperature regions and more uniform temperature distributions, suggesting better heat transfer performance. These rib angles help in maintaining a more consistent thermal environment within the battery pack.

Figure 13 displays the overall temperature distribution of the battery under the same conditions. It is evident that increasing the rib angle improves heat transfer between the coolant and the battery surface within a certain range; however, when the angle becomes too large (75° or 90°), local high-temperature regions appear inside the cooling plate, leading to decreased overall temperature uniformity. In conclusion, rib angles of 45° and 60° provide better heat transfer performance and more balanced temperature distribution under direct cooling conditions.

Figure 14 shows the velocity contour plots and streamlines of the coolant under different rib angles. Different rib angles significantly affect the flow characteristics and heat transfer performance of the coolant. Smaller angles (30° and 45°) result in ribs that extend over a larger area on the inner wall of the cooling plate. While their ability to disturb the flow is weaker, the larger heat transfer area compensates for the reduced convective heat transfer performance. As the rib angle increases to 60° or higher, the fluid disturbance capability is greatly enhanced, leading to more complex streamline distributions and stronger vortex structures. These vortices effectively disrupt the thermal boundary layer, promoting heat transfer between the coolant and the battery wall; however, when the rib angle reaches 90°, the fluid resistance increases significantly. Despite the higher vortex intensity, the excessive local velocity gradient can cause flow instability, reducing the overall improvement in heat transfer performance.

The ribbed configuration with an 11 mm spacing and a 60° angle, which demonstrates superior thermal performance, was selected for comparison with the smooth channel. The simulation results are presented in

Table 4. Comparison of simulation results for the two configurations.

Structure	Maximum Temperature/°C	Cross-Section Temperature Difference/°C	Pressure Drop/kPa
Smooth channel	45.5	1.89	31.1
Ribbed channel	44.7	1.85	72.9

.

As shown in Table 4, the use of ribbed cooling channels significantly reduces the maximum temperature of the battery pack. Compared to smooth channels, the optimal configuration (with an 11 mm rib spacing and a 60° rib angle) lowers the maximum temperature by approximately 0.8 °C while also improving the cross-sectional temperature difference, indicating a more uniform temperature distribution. However, this configuration increases the pressure drop by approximately 130% compared to smooth channels, leading to higher pump power consumption.

In comparison with reference [39], the ribbed structure in this study led to a 0.8 °C reduction in maximum battery temperature and a decrease in the temperature gradient. In contrast, the reference reported only a 0.3 °C reduction in temperature, accompanied by an increase in the temperature gradient. This discrepancy in performance is primarily attributed to the use of direct refrigerant cooling in our system, which provides superior cooling effectiveness compared to the liquid cooling system employed in the reference. Additionally, significant differences in the cold plate design further contribute to the varying outcomes. Thus, the effectiveness of incorporating ribs into the cooling channels is highly dependent on the specific design of the cold plate.

Under identical operating conditions, the ribbed structure effectively enhances fluid turbulence and heat transfer, thereby improving overall cooling performance. While the ribbed design offers clear advantages in heat dissipation, it inevitably introduces higher flow resistance, resulting in increased energy consumption. In this study, the ribbed configuration with an 11 mm spacing and a 60° angle achieved an efficiency ratio of η = 1.16. This indicates that, despite the increased energy consumption of the ribbed channel, the enhancement in heat transfer performance is sufficient to offset the additional energy cost, leading to a net gain in overall system efficiency.

Additionally, we compared the effects of different rib parameters on system performance. The analysis indicates that a balance must be struck between enhancing cooling effectiveness and minimizing energy consumption during the design process. Future work can further explore the optimization of rib shape, arrangement, or material to improve system performance while reducing energy costs.

3.3. Effect of Different Discharge C-Rates on Battery Heat Transfer

Hybrid Electric Vehicles (HEVs) typically require lithium-ion batteries with high power density, characterized by high instantaneous output power and relatively small energy capacity. The selected battery pack in this study has a maximum output power of 60 kW and a capacity of 2.1 kWh. Under extreme operating conditions, the maximum allowable discharge rate (C-rate) can reach up to 30 C. Based on the findings in the previous two subsections regarding the effects of different rib arrangements, the rib spacing of 11 mm and 60° arrangement, which demonstrated relatively better thermal performance, is selected for further analysis. The cooling conditions are set as follows: the cooling plate inlet mass flow rate is 20 kg/h, with refrigerant R134a at an initial temperature of 6 °C, corresponding to a saturation pressure of 0.36 MPa and a vapor quality of 0.2. Both the ambient temperature and initial temperature of the battery pack are set to 40 °C to simulate high-temperature operating conditions typical of vehicle usage.

Figure 15a shows the variation in the maximum and minimum temperatures of the battery pack at different discharge rates. As the discharge rate increases, the battery discharge time decreases, and the temperature rises towards the end of the discharge cycle. For discharge rates below 8 C, the temperature at the end of the discharge cycle decreases significantly compared to the initial temperature. This indicates that the cooling system effectively manages thermal accumulation under these conditions. However, when the discharge rate exceeds 8 C, the battery temperature continues to rise relative to the initial temperature, suggesting that the cooling system is unable to fully dissipate the heat generated under high-rate discharge conditions. For instance, at a discharge rate of 12 C, the maximum temperature at the end of discharge reaches 43 °C, a significant increase from the initial 40 °C, indicating insufficient cooling performance at extreme discharge rates. Furthermore, temperature variation is faster at the beginning and end of the discharge cycle, while it stabilizes during the middle phase. This behavior can be attributed to the nonlinear relationship between the battery’s internal resistance and its state of charge (SOC), which results in higher heat generation at both low and high SOCs.

Figure 15b illustrates the temperature difference within the battery pack at different discharge rates. When the discharge rate is below 8 C, the temperature difference decreases with an increase in the discharge rate; however, for discharge rates above 8 C, the temperature difference increases, which is indicative of the heat transfer characteristics within the battery pack under varying discharge rates.

Figure 16 presents the temperature distribution within the battery cross-section under different discharge rates. When the discharge rate is below 8 C, the maximum temperature difference primarily occurs near the module endplates. This suggests that the batteries near the endplates are not sufficiently cooled due to limitations in the heat transfer structure. For discharge rates above 8 C, heat generation increases significantly due to higher discharge currents, resulting in a higher battery temperature at the end of the discharge compared to the initial temperature. The maximum temperature difference occurs near the outlet, away from the coolant inlet, highlighting the uneven heat transfer characteristics of the cooling system at high discharge rates.

Figure 17 shows the variation in pressure drop within the cooling plate at different discharge rates. The ribbed channel structure with a rib spacing of 11 mm and a rib angle of 60° significantly impacts the flow and heat transfer performance of the cooling system. At higher discharge rates, more heat is generated, which increases the evaporation of the liquid-phase refrigerant, leading to a higher vapor-phase refrigerant ratio. The flow of vapor results in higher fluid resistance. Additionally, the ribbed structure enhances flow disturbance, which improves heat transfer but also increases pressure drop. Particularly at discharge rates of 10 C and above, the pressure drop increases significantly due to the heightened fluid resistance in the ribbed channels, further exacerbating the overall pressure drop.

The results suggest that higher discharge rates lead to an increase in the maximum battery temperature and temperature differences within the battery pack, indicating that the cooling system struggles to manage heat generation effectively under high-rate discharge conditions. While ribbed cooling plates improve heat transfer performance, they also contribute to higher pressure drops, especially at elevated discharge rates. This analysis emphasizes the importance of optimizing both the thermal management system and cooling plate design to handle the thermal challenges associated with high discharge rates in HEV battery packs.

3.4. Effect of Different Refrigerant Mass Flow Rate on Battery Heat Transfer

The mass flow rate of refrigerant in the battery cooling plate is a key factor influencing the performance of the battery thermal management system (BTMS), significantly affecting the thermal behavior of the battery pack. In engineering practice, BTMSs typically adjust the refrigerant mass flow rate dynamically, often by controlling the compressor speed or expansion valve opening to match the fluctuating thermal load of the battery pack. Consequently, understanding the impact of refrigerant mass flow rate on the heat transfer performance of ribbed cooling plates is crucial. This study investigates the effect of refrigerant mass flow rates ranging from 5 kg/h to 40 kg/h on the thermal performance of a ribbed channel cooling plate with an 11 mm rib spacing and a 60° rib angle. Simulations were performed under fixed conditions, including a discharge rate of 12 C, an inlet refrigerant temperature of 6 °C, a vapor quality of 0.2, and both ambient and initial battery temperatures set to 40 °C.

Figure 18 depicts the variations in both the maximum and minimum temperatures of the battery pack as a function of discharge time, considering different refrigerant mass flow rates. As shown in Figure 18a, increasing the mass flow rate leads to a substantial reduction in the maximum temperature of the battery pack. This reduction is mainly due to the enhanced flow disturbance of the refrigerant in the ribbed channel, which improves heat transfer, while the refrigerant’s latent heat from vaporization effectively absorbs the heat generated by the battery pack at higher mass flow rates. At lower mass flow rates (e.g., 5 kg/h), the cooling capacity is insufficient, resulting in a peak temperature of 46.3 °C at the end of discharge, indicating inadequate heat dissipation. However, once the mass flow rate exceeds 10 kg/h, the maximum temperature remains below 45 °C, suggesting a significant improvement in cooling efficiency.

Figure 18b shows the trend of the minimum temperature of the battery pack. As the mass flow rate increases, the minimum temperature steadily decreases. Between 25 s and 70 s, higher flow rates result in a higher minimum temperature compared to lower rates. This occurs because, at higher flow rates, much of the refrigerant remains in the liquid phase near the inlet, weakening the local evaporation effect and initially hindering heat transfer. Conversely, at lower flow rates, the refrigerant has more time to undergo phase change inside the cooling plate, improving local heat transfer performance early in the process.

Figure 19 illustrates the temperature difference and pressure drop variations across the battery pack and cooling plate at different refrigerant mass flow rates. As shown in Figure 19a, the temperature difference decreases as the mass flow rate increases. For mass flow rates above 10 kg/h, the temperature difference remains below 2.1 °C, indicating that the cooling plate’s heat transfer performance is sufficient for even cooling of the battery module. At a low mass flow rate of 5 kg/h, however, the temperature difference reaches up to 4.4 °C, possibly due to incomplete evaporation of the refrigerant, which leads to overheating at the outlet and a reduction in heat transfer performance due to single-phase convective heat transfer in certain regions. Figure 19b shows that the pressure drop increases with the rising refrigerant mass flow rate, primarily due to the ribbed channel’s flow disturbance enhancement, which also raises fluid resistance. The maximum pressure drop within the tested range can reach 105 kPa. While the ribbed channel is effective in improving heat transfer, the associated pressure drop requires balancing energy consumption with heat dissipation efficiency in cooling system design.

Figure 20 presents the temperature distribution across the battery cross-section for different refrigerant mass flow rates. It is evident that, as the mass flow rate increases, the temperature distribution becomes more uniform, with a significant reduction in high-temperature regions. At a low mass flow rate of 5 kg/h, hotspots appear within the battery and the temperature gradient is steep; however, at higher flow rates (40 kg/h), the temperature distribution evens out, with the hotspots nearly vanishing, except near the outlet region. This observation suggests that higher refrigerant flow rates improve cooling efficiency, suppress hotspot formation, and enhance the overall thermal performance of the battery pack.

3.5. Effect of Different Refrigerant Saturation Temperature on Battery Heat Transfer

The saturation temperature of the refrigerant plays a crucial role in determining the thermal performance of the battery pack, significantly influencing both heat transfer efficiency and pressure drop in the cooling system. In this study, the refrigerant saturation temperature was varied from 3 °C to 20 °C, corresponding to saturation pressures ranging from 0.33 MPa to 0.57 MPa, simulating realistic operational conditions. The refrigerant mass flow rate was maintained at 20 kg/h with a vapor quality of 0.2. The battery pack underwent discharge at a 12 C discharge rate, with both the initial and ambient temperatures set to 40 °C.

Figure 21 shows the variation of the maximum and minimum temperatures of the battery pack with discharge time under different refrigerant saturation temperatures. It is evident that a lower saturation temperature significantly improves the cooling effect. This is because a lower saturation temperature increases the temperature difference between the cooling plate and the battery pack, thereby enhancing the heat transfer capability of the refrigerant. However, while higher saturation temperatures slightly weaken the cooling performance, they significantly improve the temperature uniformity of the battery pack, further reducing the temperature difference between battery cells.

Figure 22 shows the effect of refrigerant saturation temperature on the temperature difference within the battery pack and the pressure drop across the cooling plate. As the saturation temperature increases, the temperature difference within the battery pack gradually diminishes. This trend occurs because higher saturation temperatures lower the temperature differential between the cooling plate and the battery pack, thereby weakening the heat transfer driving force but improving the temperature uniformity across the pack. Additionally, an increase in saturation temperature notably reduces the pressure drop within the cooling plate. This can be explained by the fact that higher saturation temperatures reduce the proportion of liquid-phase refrigerant transitioning to the gas phase, which decreases the gas-phase mass fraction and consequently lowers flow resistance. The ribbed channel structure used in this study, with a rib spacing of 11 mm and a 60° rib angle, enhances turbulent mixing compared to smooth channels, improving heat transfer efficiency. However, this benefit comes at the cost of a higher pressure drop, which becomes more prominent at lower saturation temperatures.

Figure 23 presents the temperature contour plots of the battery cross-section for various refrigerant saturation temperatures. As observed, a decrease in the refrigerant saturation temperature leads to a significant reduction in the overall temperature of the battery pack, especially in high-temperature regions. This suggests that lower saturation temperatures significantly improve heat transfer efficiency by enhancing the temperature differential between the cooling plate and the battery, thereby reducing the formation of high-temperature zones. In contrast, although higher saturation temperatures result in a slightly elevated overall temperature, they improve the uniformity of the temperature distribution, indicating that higher saturation temperatures contribute to a more balanced temperature profile between the individual battery cells.

4. Conclusions

This research examines the thermal performance of a battery thermal management system (BTMS), utilizing refrigerant cooling under various operating conditions. By analyzing cooling channels with different rib configurations, the effects of rib spacing, rib angle, refrigerant mass flow rate, and saturation temperature on the cooling performance were explored. Additionally, the study investigated the impact of different discharge rates on the thermal behavior of the battery. The findings offer valuable insights for optimizing both the design of cooling channels and operating parameters of the BTMS. The main conclusions of the study are as follows:

(1) The simulation results indicate that both rib spacing and rib angle have a significant impact on the heat transfer enhancement and pressure drop of the cooling channel. Among all the tested configurations, the design with a 11 mm rib spacing and a 60° rib angle reduced the maximum battery temperature by approximately 0.8 °C (a cooling rate of about 2%), while improving temperature uniformity. However, this design also resulted in a pressure drop approximately 130% higher than that of the smooth channel. The overall thermal performance factor reached 1.16, indicating that, after balancing energy consumption and cooling effectiveness, this configuration offers a clear advantage.

(2) At lower discharge rates, the BTMS provides sufficient cooling capacity, resulting in a smaller internal temperature difference within the battery pack. However, at high discharge rates (such as 12 C), the heat generation rate increases sharply, causing both the maximum temperature and the temperature gradient to rise significantly, indicating that the cooling capacity of the system is limited under high thermal load conditions.

(3) As the mass flow rate increases, the maximum temperature of the battery pack decreases significantly. For example, when the flow rate increases from 5 kg/h to 40 kg/h, the maximum temperature decreases by approximately 10%. However, beyond a flow rate of 20 kg/h, the improvement in temperature uniformity tends to level off, suggesting the existence of an optimal flow rate range that balances energy efficiency and cooling performance.

(4) A lower saturation temperature increases the temperature difference between the refrigerant and the battery, thereby improving cooling efficiency, with the maximum temperature reducing by up to 7%. However, at lower saturation temperatures, the internal temperature gradient of the battery increases. Conversely, a higher saturation temperature, while improving temperature uniformity, leads to a slight increase in the maximum temperature.

In conclusion, this study provides valuable theoretical insights into the design and optimization of refrigerant-cooled BTMSs for electric vehicle battery packs. It addresses the challenges associated with high heat loads during discharge while considering the need for maintaining temperature uniformity across the battery pack. Future work will focus on exploring transient operating conditions in real driving scenarios.