Fin structure and liquid cooling to enhance heat transfer of composite phase change materials in battery thermal management system

In order to improve the performance of a battery thermal management system (BTMS) based on phase change material (PCM), expanded graphite (EG) is added to paraffin to form composite PCM (CPCM), and embedded aluminum fins are coupled with liquid cooling to enhance heat transfer. A heat generation model for lithium‐ion batteries (LIBs) is established and verified by experiments. The cooling performances of four BTMS designs were simulated. The effects of the thermal characteristics of LIBs were investigated at various velocities and directions of coolant flow as well as EG fractions in CPCMs. The simulation results indicate that Design IV shows a good cooling effect at a coolant flow rate of 0.06 m s−1 and an EG fraction of 12 wt%. Under ambient temperatures of 26°C, 35°C and 40°C, the maximum battery temperatures are 28.14°C, 37.15°C and 42.09°C, respectively, and the maximum temperature difference over the battery module is 1.88°C, 1.89°C and 1.92°C, respectively. The charge‐discharge cycle performances of the four BTMS designs were further investigated. In Design IV, the maximum temperature and the maximum temperature difference in the battery module remain unchanged during five cycles under 1, 2 and 3 C discharge rates. The new BTMS has significantly improved the secondary heat storage problem of PCMs and the temperature uniformity of LIBs. The fin structure combined with liquid cooling is efficient in enhancing the heat transfer of CPCM for battery thermal management.


| INTRODUCTION
As a power battery, lithium-ion batteries (LIBs) have become the fastest-growing secondary battery with the continuous development of electric vehicles (EVs).LIBs have high energy density and long service life. 1 However, the lifespan, performance and safety of LIBs are primarily affected by operation temperature. 2The best temperature range for the LIB is 25 C to 40 C, 3 and the allowable discharge temperature ranges from À20 C to 60 C, 4 which means that the maximum operating temperature of LIBs (T max ) should be lower than 60 C. 5 To avoid any possible short circuit inside a battery cell, the battery pack's temperature should be uniform, and the maximum difference of temperatures inside the battery pack (ΔT max ) should not exceed 5 C. 6 The battery life reduces by about 60 days per degree of temperature increase when the battery pack works from 30 C to 40 C. 7 Lithium plating can quickly occur inside the cell when the battery charges at a temperature lower than 0 C. Its charge-discharge capacity and cycle performance will deteriorate rapidly. 8,91][12] In low-latitude areas, the ground temperature can reach above 50 C in summer, which brings severe challenges to the regular operation of battery thermal management system (BTMS).In addition, major manufacturers are developing LIBs with high battery energy density to increase the range of EVs.An increase in battery number within a limited volume and energy density increases the workload of BTMS.Thus, a thermal management system with excellent cooling performance is important to ensure the LIBs pack works stably. 105][26][27][28][29][30] Air cooling includes natural and forced convection, and the latter has better heat transfer efficiency.Air cooling may cause uneven temperature distribution in a battery pack compared to liquid cooling.Forced convection air cooling has a simple structure and low cost, so it is currently a common solution for BTMS by major manufacturers. 11,12][15][16] As a passive cooling strategy, 23 heat pipe cooling uses the evaporation and condensation of an internal working fluid to achieve enhanced heat transfer.However, the heat pipe is relatively expensive and its effectiveness is affected by the vehicle's attitude.Combining heat pipes with other cooling systems is necessary to improve BTMS performance. 21,22iquid cooling has a higher heat transfer rate than air cooling and has a more compact structure and convenient layout, 18 which was used by Tesla and others to achieve good results. 19The coolant can be in the way of direct or indirect contact with batteries. 20Direct contact liquid cooling brings an excellent cooling effect but a higher risk of liquid leakage.In the indirect contact method, the coolant flows in the channel and does not contact directly to batteries.The heat generated in batteries is transferred to the coolant through the channel wall and brought to the environment by convection.Therefore, a good structure design of liquid cooling channels is essential to significantly reduce the risk of leakage.
The PCM cooling strategy is one of the most promising alternatives to traditional battery thermal management technologies. 24PCMs such as paraffin wax can absorb heat during their phase change processes.However, its low thermal conductivity makes it impossible to diffuse heat to the external environment in time.The most common method to have a higher thermal conductivity of PCM is to add EG 25 or metal foam 29 to form a composite PCM (CPCM) or add a metallic component to the PCM as a thermal conductive framework. 26,27,30here are still some shortcomings in practical applications when adopting PCM as the primary cooling strategy for battery packs.First, due to the low thermal conductivity of PCM, the heat absorbed in PCM is not easy to transfer to the external environment.Second, to accommodate more batteries, the battery pack structure is highly integrated, resulting in a limited PCM volume, which cannot effectively increase the temperature uniformity in the battery pack.Third, when all the latent heat of PCM is exhausted, the battery pack will suffer from the effects of heat storage saturation and poor secondary heat dissipation of PCM under the continuous high temperature environment.This condition will re-magnify the effects during constant charge and discharge cycles and increase the risk of thermal runaway.
A comprehensive BTMS based on PCM and an active cooling scheme is widely proposed to improve the heat dissipation of battery packs.Bai et al 31 proposed a BTMS by adding liquid cooling into PCM and simulated the effects of cell distance, cooling plate length, coolant flow rate and direction, and PCM melting temperature at 2C discharge rate and 27 C ambient temperature.Results show that liquid cooling helps to lower the maximum temperature and PCM helps to reach temperature uniformity in the battery module.The BTMS based on the combination of PCM and liquid cooling was designed to improve the temperature uniformity of large-scale battery packs at high temperature discharge. 32The thermal performance of the system was verified experimentally and numerically.The results show that too low a coolant temperature would increase the temperature difference of the battery pack, and the higher inlet water temperature was given priority.Compared with the traditional heat dissipation scheme, this structure could ensure that the temperature difference between the batteries is within the normal working range at a discharge rate of up to 4 C. Kong et al 33 designed a comprehensive BTMS based on PCM and liquid cooling and analyzed the effects of battery spacing, cooling pipe number and coolant flow rate on battery temperature under different ambient temperatures.The effectiveness of the model was verified experimentally and numerically.The results show that the battery module could maintain the maximum temperature and temperature difference within 50 C and 5 C, respectively, even under a discharge rate of 3C and an ambient temperature of 30 C. Zhang et al 34 studied a BTMS of 106 batteries that combined PCM with liquid cooling using experiment and simulation.Moreover, PCM, liquid and PCM/liquid cooling schemes are compared.The results indicate that the scheme of PCM combined with liquid cooling has the best performance of heat dissipation and temperature uniformization even at a 5C discharge rate and 25 C. Song et al 35 proposed a PCM-liquid cooling BTMS of 106 batteries to experiment with the cooling performance at a 6C discharge rate and 25 C.It can be seen that the BTMS combined with PCM and liquid cooling is an effective method to lower the temperature level and uniformize temperature distribution in the battery module.
In this paper, an active BTMS combined with PCM and liquid cooling is proposed to solve the above problems and enhance the cooling performance of the PCMbased BTMS at high ambient temperatures and under charge-discharge cycles.In addition, aluminum fins are embedded in PCM as a skeleton between three cooling plates, forming the battery module's structure.The innovative embedding of aluminum fins in the PCM can not only form a seal for the PCM but also improve the temperature uniformity of the battery pack.The batteries are arranged in a cross or staggered manner to improve the volume utilization rate of the system.The CPCM is wrapped around the battery to better absorb the heat released by the battery.Three cooling plates sandwiched in the CPCM can also increase the cooling area.
The accuracy of the numerical model is verified by the charge and discharge experiments of a single-cell battery.The heat transfer model of the battery module is implemented in COMSOL multiphysics and is used for simulation under ambient temperatures and different charge-discharge rates.This research may help improve the thermal performance of the battery pack and the optimal design of the BTMS.

| Geometric model and material properties of BTMS
The geometry of the BTMS model is shown in Figure 1.The BTMS consists of a battery module, PCM, fins and cooling plates, with a volume of 113 mm Â 93 mm Â 65 mm.The battery module contains 20 LIBs, and the specifications for commercial LIB are shown in Table 1.The PCM, fixed by three cooling plates, envelops all the batteries and fills the whole space of the battery module.The cooling plates and fins are made of aluminum and are of the size 113 mm Â 42 mm Â 65 mm.The length and width of the cross-section of the internal channel are 63 and 2 mm, respectively.Fins with a thickness of only 1 mm are embedded in the PCM.The PCM-fin structure and liquid cooling can effectively transfer heat throughout the thermal management system.Fins transfer the heat absorbed by the PCM from the battery module, and the coolant in the cooling plate removes heat from the entire system.Table 2 shows the thermophysical properties of the materials used in this study.More parameters of CPCMs will be given in Table 3 later.

| Heat generation model of lithiumion battery
Heat generation in lithium-ion batteries comes from two mechanisms.One is the heat generated by the electrochemical reaction in the battery, and another is resistance heat from the positive and negative electrode tabs.The heat generation rate of the single cell is affected by multiple factors, such as current density and state of charge (SOC).Its high degree of nonlinearity also makes it difficult to be expressed accurately.The heat generation model of LIB proposed by Bernardi et al has been widely used, 36 in which the volume heat generation rate is expressed as: where T is temperature, q is the volume heat generation rate, VOL is the volume of the cell, U ocv is open-circuit voltage (OCV), U is the terminal voltage, and dU ocv =dT is the temperature entropy coefficient and becomes constant when the charge and discharge rates are determined.Lu et al 37 studied the cyclic volt-ampere characteristics of the battery and found that the first two terms in Equation ( 1) are the main heat sources during the charge and discharge process of LIB.The last three terms q mixing , q phase and q capacity represent the enthalpy-ofmixing term, phase-change term and heat-capacity effect, respectively, and can be neglected.Therefore the heat sources mainly include the irreversible heat q ir and a reversible heat q re : In Equation ( 2), the irreversible heat (q ir ) is mainly caused by ohmic loss, and R is the internal resistance.The reversible heat shown in Equation ( 3) is related to the electrochemical reaction.Reversible heat (q re ) is dominant at low discharge rates, and q ir is dominant at high discharge rates. 38

| Governing equations for domains of battery, PCM and coolant
During the charging-discharging process, due to the poor fluidity of the electrolyte, the convective and radiant heat transfer in the internal materials of the LIBs can be ignored.Therefore, heat conduction is the primary heat transfer method of LIBs.The energy conservation equation of the battery in Cartesian coordinates can be written as: where ρ b , c p,b and λ b represent density, specific heat capacity and thermal conductivity coefficient of the battery, respectively.The physical properties of PCM are listed in Table 3.For the PCM, the apparent heat capacity method 39 applied can be written as: where L, ρ PCM , c p,eff and λ PCM are the latent heat, density, effective specific heat and thermal conductivity of PCM, c p,s and c p,l , are the specific heat capacities of the solid and liquid states of PCM, respectively.The values of c p,s and c p,l are equal according to Ref. [40], γ is the liquid fraction of PCM, and T l À T s ¼ ΔT PCM is the temperature range of phase transition, which is the difference of temperature at beginning and at ending of phase change.
The energy equation for fins and cooling plates is expressed as follows: where ρ Al ,C p,Al and λ Al are the density, specific heat capacity and thermal conductivity of aluminum, T Al is the temperature of the fins and the cooling plates.The mass, momentum and energy equations of coolant are as follows: where ρ c , C p,c and λ c are density, specific heat capacity and thermal conductivity of coolant, u !, P and μ denote the coolant velocity vector, static pressure and dynamic viscosity, respectively.The coolant is assumed as an incompressible fluid.
T A B L E 3 Thermophysical and crystallization parameters of CPCMs. 25

| Interface and boundary conditions
The conditions at the interface between batteries and PCMs are expressed as follows: where n is the normal direction outward to the object surface, T PCM is the temperature of PCM, and ∂T=∂n is the temperature gradient along the normal direction.
The interface condition between PCM and fins is expressed as: The interface condition between PCM and cooling plates is: where T pl is the temperature of the cooling plates.The boundary condition between cooling plates and the coolant: where h c and T c are heat transfer coefficient and coolant temperature, respectively.The heat transfer between the cooling plate and the ambient can be expressed as: where h is the coefficient of natural convection, T a is the ambient temperature.The Reynolds number of fluid flow is defined as follows: where u, D, μ, A and P sec are fluid velocity, characteristic length, dynamic viscosity, cross-section area and the perimeter of the flow-through section, respectively.The characteristic length is the hydraulic diameter for noncircular pipes, which refers to the ratio of the flow crosssectional area to the perimeter, and D is 0.00388 m.

| Single-cell experiment and verification
The INR18650-25R cell produced by Samsung is considered to analyze the temperature changes under different discharge rates in this work, and the basic parameters are shown in Table 1.The volumetric heat generation rate of different discharge rates is obtained under the natural convection condition.The single cell is placed in a constant-temperature incubator at a room temperature of 26 C. The battery voltage, current and temperature are measured in the cell cycle test under discharge rates of 1, 2 and 3 C, the charge rate of 1.6 C and a resting period of 217 seconds, and then the volumetric heat generation rate is calculated by Equation ( 1).The temperature rises during the cycle test are simulated by COMSOL software and compared with the experimental data, as shown in Figure 2.
The results demonstrate that the maximum deviation between the simulated and experimental results is less than 2%.The simulation results agree with the experimental results under one cycle test of various discharge rates in Figure 3. Therefore, the heat generation model used in this paper is feasible.

| Initial conditions and mesh independence verification
In this study, the initial ambient temperature is 26 C, the inlet boundary condition is the flow velocity of the coolant, and the outlet boundary condition is the pressure.When the coolant velocity is 0.3 m s À1 (liquid flow is 3.78 EÀ5 m 3 s À1 ), Re is 1051 from Equation (17), so the coolant flow is considered laminar.The heat transfer coefficient is 5 W m À2 K À1 , according to An. 41 The contact thermal resistance between materials is ignored.Considering the liquid leakage problem of PCM, the outermost part of the battery pack is usually fixed with an acrylic sheet 42 or PET box 43 in the experiment to play a supporting role and to ensure that the PCM will not leak when it melts.However, in this paper, the simulation method is mainly used to study the thermal performance of the BTMS.Therefore, the model is simplified during the simulation, assuming no PCM leakage during the battery discharge process.
The COMSOL generates the mesh of geometric configuration with the option user-controlled to ensure the efficiency of computational fluid dynamics (CFD).The 20 cells are swept and meshed through the triangular prism to reduce the computational complexity, in which the maximum and minimum element sizes are 2.26 and 0.0226 mm, respectively, the maximum element growth rate is 1.3, and the curvature factor is 0.2.The rest geometry is discretized by choosing the "Free tetrahedral grid" option, where the maximum and minimum element sizes are set as 9.27 and 1.44 mm, respectively.The maximum unit in the channel in the cold plate is 1.7 mm, the minimum unit is 0.111 mm, and the curvature factor is 0.3.The outer walls of the cold plates are set as the boundary layers, and the number of the boundary layers is 2. The boundary layer stretching factor is 1.2, and the minimum and maximum angles for trimming are 240 and 50 , respectively.Good quality grid is obtained through the above mesh generation method, as shown in Figure 4.
Meanwhile, grid independence is performed to confirm the right choice of grid density with enough accuracy and reasonable computing time.Figure 5 presents the curve of volume mesh number vs the maximum temperature of LIBs under the conditions of a discharge rate of 3C, a coolant flow velocity of 0.01 m s À1 and an ambient temperature of 26 C. When the difference of T max between the simulation results of different grid numbers is only 0.1 C, the three-dimensional geometric model meets the requirements in this paper.When the number of grids increases from 690 006 to 875 116, the T max changes from 39.1 C to 37.8 C. While the number of grids continues to increase, the T max remains basically unchanged.Therefore, the geometric model with 875 116 grids is selected to improve the calculation efficiency and satisfy the accuracy.

| RESULTS AND DISCUSSION
The BTMS should meet two basic requirements: the T max and ΔT max should be within the limit of 60 C and 5 C, respectively.According to these two indicators, the factors affecting the thermal performance of BTMS from different perspectives are studied.According to the previous study, 30 the maximum temperature of the battery pack decreases, and the maximum temperature difference of the battery pack increases with the decrease in coolant temperature.At the same time, excessively low coolant temperatures consume much additional power.Therefore, this paper assumes that the coolant is not precooled or the coolant temperature is the same as the ambient temperature for simplifying the study on the effects of flow direction and velocity of the coolant on the thermal performance of BTMS.

| Thermal performance under different cooling strategies
The layout designs of four various cooling strategies are shown in Figure 6.Design I and II are passive BTMSs only using PCM, while Design III and IV are hybrid active BTMSs combining PCM and liquid cooling.In Design II and IV, the cooling fins are embedded in PCM.The initial flow velocity of liquid in the active BTMS is 0.01 m s À1 , and the ambient temperature is consistent with the liquid temperature.
Four designs are simulated at the 3C discharge rate under the ambient temperature of 26 C, 35 C and 40 C, respectively.The curves of T max and ΔT max are presented in Figure 7. From Figure 7, we can conclude that the cooling effect of Design IV is the optimal solution for all three ambient temperatures, 26 C, 35 C and 40 C.Under these ambient temperatures, the T max of Design IV are 34.98C, 42.71 C and 45.14 C, respectively, and the temperature differences of batteries are all kept within 5 C throughout the whole discharge process.
Figure 7A shows that under the 26 C ambient temperature, the curves of T max in Design I and Design II have inflection points due to the latent heat effects of PCM in the early 600 seconds.The temperature rise rate of the batteries decreases, and the maximum temperatures (T max ) of two designs at the end of discharge are 44.6 C and 44.4 C, respectively.While the existence of liquid cooling in Design III and Design IV reduces the heat accumulation problem of the battery module, thus significantly extending the time for the PCM to start phase change.The temperature difference between Design I and Design IV reaches 9.6 C during the discharge process.
Especially in Design IV, the PCM-fin structure can substantially increase the temperature uniformity of the battery module, as shown in Figure 7D.
Expanded graphite (EG) helps increase the thermal conductivity of CPCM and reduce the maximum temperature difference in the battery pack.Adding fins further reduces the maximum temperature difference in a battery pack.Although adding fins does not significantly control the temperature uniformity of the battery pack, the supplement advantage of fins is to form an efficient path of heat conduction.
Under the 35 C ambient temperature, according to the maximum temperature curves illustrated in Figure 7B, the latent heat of passive BTMS in Design I and Design II is completely exhausted within 900 seconds, and the heat generated by LIBs cannot be dissipated, resulting in a sharp temperature rise.It should be noted that there is no second inflection point in the maximum temperature curves of Design III and Design IV, indicating that the latent heat of PCM in BTMS still plays a role in heat absorption.
Under the ambient temperature of 40 C, the maximum temperature curves of the four designs from Figure 7C keep the same trend within 800 seconds because the ambient temperature is close to the melting temperature range of pure paraffin as the PCM.Due to the depletion of latent heat of PCM, the advantage of the cooling effect of the active BTMS gradually appears in the last 400 seconds, and the temperature difference between Design I and Design IV reaches up to 3 C.
As mentioned above, the BTMS with PCM cooling as the only passive heat dissipation method loses its cooling function due to the premature depletion of latent heat of PCM, which cannot be recovered until the temperature of PCM decreases to a certain range below the melting temperature.The introduction of liquid cooling can significantly improve the cooling performance of BTMS with PCM cooling.Hence, active BTMS coupling with PCM and liquid cooling is undoubtedly needed.

| Effect of coolant flow direction
In this section, the effects of two different flow directions on the thermal performance of the battery module for Design IV are compared by simulation under the 3 C As shown in Figure 9A, the T max in the parallel flow scheme is significantly lower than that with the alternative flow scheme under the 26 C ambient temperature.When the ambient temperature increases to 35 C, the T max of the two schemes is basically the same.When it increases to 40 C, the curve of T max shows that the cooling effect of the alternate flow scheme is better than that of the parallel flow scheme.
The simulation results from Figure 9B show that the alternate flow can significantly improve the temperature uniformity of the battery module.The temperature difference decreases by 13%, 8% and 18% under environmental temperatures of 26 C, 35 C and 40 C, respectively.In particular, the temperature difference of the battery module will decrease with the ambient temperature increase.The reason is that the phase change can occur earlier and uniform the temperature distribution in the battery module when the ambient temperature is closer to the melting temperature of the PCM.
Figure 10 shows the surface temperature distribution at the end of LIBs discharge at 26 C, 35 C and 40 C, respectively.Alternate flow can improve the temperature uniformity of the battery module, and parallel flow can lower its temperature level.The T max of BTMS with the two schemes does not exceed the normal working temperature range of the battery pack.Although both parallel and alternate flow schemes meet the requirement that ΔT max in the battery module should be kept below 5 C, but it is clear that the alternate flow scheme has better temperature uniformity.Hence, the following research of this paper uses the alternate flow scheme for liquid cooling in the BTMS.

| Effect of coolant flow velocities
This paper proposes the active BTMS composed of PCM cooling and liquid cooling.The role of liquid cooling is to transfer the heat of the PCM and fins to the environment.This section mainly analyzes the influence of different flow velocities of coolant on the BTMS for Design IV.The T max and ΔT max during discharge can be obtained from  In summary, the T max and ΔT max are significantly reduced when the coolant in the hybrid BTMS maintains a certain flow velocity.The coolant flow can effectively absorb the heat and prevent the latent heat of the PCM from being exhausted quickly.The coolant flow velocity of about 0.04 to 0.06 m s À1 is suitable for the thermal management of the addressed battery system in daily operating conditions.When the flow velocity continues to increase, the improvement in heat dissipation of the entire thermal management system is negligible.In actual vehicle operation, further increasing the coolant velocity will increase the power consumption of the whole system and reduce the endurance mileage.

| Effect of CPCMs
The thermal conductivity and latent heat of CPCMs vary with the mass fraction of expanded graphite (EG).The cooling strategy proposed in this study needs to meet the cooling requirement at high ambient temperature.Therefore, the CPCMs with the various mass fractions of EG are selected to study the effect of CPCMs with different thermal conductivity on the battery module.In the current case, the densities of CPCMs range from 710 to 950 kg m À3 .The EG percentage should not be larger than 40 wt% to ensure sufficient latent heat of composite materials. 44s listed in Table 3, the crystallization properties of CPCM, such as melting point and latent heat, are adopted from the reference [25].RT44HC is an HC serial PCM of Rubitherm Technologies (RT) with a phase change temperature of 44 C. The thermal conductivity of CPCM will increase when the mass fraction of EG increases.At the same time, the latent heat and specific heat will decrease.Under the flow velocity of 0.01 m s À1 , Figure 12 presents the thermal performance of BTMS for Design IV under the ambient temperature of 26 C, 35 C and 40 C, respectively.The thermophysical parameters of CPCMs can be obtained by measurement or estimated by modeling.A simple model is the rule of mixture, which can estimate the properties of the mixture, composite PCM, from the properties of its components, PCM and EG, under the different percentages of EG.
Figure 12 shows that a certain amount of EG is added to the pure paraffin, the T max can be effectively reduced, but the change of ΔT max is not obvious.The T max appears in the BTMS with paraffin, and the T max are 34.8C, 42.8 C and 44.8 C, under the 26 C, 35 C and 40 C ambient temperatures, respectively.The simulation results present the best cooling effect of the BTMS using PCM composed with EG of 30 wt%.
When the BTMS used CPCM with 3 wt% EG, the T max is reduced by 2.3 C, 1.31 C and 1.17  was increased to 12 wt%, and the T max decreased by 4.5 C, 3.53 C and 1.75 C under the three ambient temperatures, respectively.After that, further increasing the mass fraction of EG has a less cooling effect on the battery module.By comparing the maximum temperature curves of three different ambient temperatures, shown in Figure 12A,C,E, it is found that the onset times of phase transition of the BTMS using CPCMs with 0 wt% EG and 3 wt% are 650 to 1150 seconds respectively when the ambient temperature increased to 35 C. In contrast, the CPCM with other different mass fractions of EG did not reach its phase transition point in the whole discharge process.Under the 40 C ambient temperature, phase transition occurred in the BTMS with different EG mass fractions from Figure 12E.The BTMS with pure paraffin led sharp temperature rise to a higher level due to the depletion of latent heat under worse heat conduction.
The thermal conductivity of CPCM increases and its latent heat decreases with the increase of the mass fraction of EG.The improvement of heat conduction allows the BTMS to make up for the deficiency of the cooling effect caused by the reduction of latent heat because of the existence of liquid cooling.Figure 12B,D,F shows that the ΔT max always kept within 5 C under the three ambient temperatures, which meets the requirements of BTMS.
For the coolant velocity range from 0 to 0.3 m s À1 , the curves of T max in Design IV for the CPCMs with different EG ratios are illustrated in Figure 13.The CPCMs with different EG ratios give the same trend of maximum temperature curves.The simulation results from Figure 13 show that the ambient temperature significantly affects the heat dissipation of the BTMS with CPCM.The optimum mass fraction of expanded graphite depends on the ambient temperature.The zero velocity means that liquid cooling is not involved in the process.There is no significant difference in the T max when the mass fractions of EG change from 3 to 30 wt% under the ambient temperature of 26 C. When the ambient temperature continues to rise to 35 C, the BTMS with 6 wt% EG has the best cooling effect at a flow velocity of 0 m s À1 .The T max decreases with the increase of the mass fraction of EG in the range of 0 to 12 wt% under the ambient temperature of 40 C. When the mass fraction of EG continues to increase to 30 wt%, the cooling performance of the BTMS will slightly reduce because of the increase in thermal conductivity and decrease of the talent heat of CPCM.
At the same time, we can see from Figure 13 that when the flow velocity exceeds 0.1 m s À1 and the mass fractions of EG exceeds 12 wt%, the heat dissipation capacity of the BTMS shows little change.Thus, the composed PCM (CPCM) has better cooling performance than pure PCM.The CPCM with 12 wt% EG combined with liquid cooling is the optimal scheme for meeting the cooling requirements.

| Effect of fins
The purpose of inserting fins into the PCM is to improve the heat dissipation performance of BTMS, which dramatically improves the problem of the low thermal conductivity of PCM.Fins can transfer heat to the cooling plate in time, and coolant can quickly take away the heat generated by batteries, which significantly reduces the temperature of LIBs.Therefore, pure paraffin and different CPCMs are combined with fins to verify the cooling effect of fins on BTMS.
Figure 14A shows the T max of BTMS with fins, the Design without fins is used as the control group.By comparing the CPCMs with different EG mass fractions, the T max and ΔT max are effectively reduced when the fins are embedded in the BTMS.It can be concluded that the BTMS with the PCM-fin structure has a great cooling effect.The T max with embedded fins drops by 16% compared with the T max of BTMS without fins, from 41.7 C to 35 C at the 26 C ambient temperature.
However, the effect of fins in the BTMS is less obvious with the increase of the EG mass fraction.The temperature difference between the maximum temperature curves of the BTMS with fins and without fins gradually decreases.The thermal conductivity of CPCM increases as the EG amount increases in the BTMS.Especially when the mass fraction of EG is 30 wt%, the increase in thermal conductivity caused by the effect of fins in the BTMS is negligible.A further effect of fins is a significant improvement in the temperature uniformity in the battery module.From Figure 14B, the lower ambient temperature will cause a more significant temperature difference ΔT max in a battery module.When fins are added to the CPCM, the ΔT max in the BTMS with

| Effect of charge-discharge cycle test
The simulation was conducted under continuous charge and discharge of batteries to further study whether the PCM and liquid cooling hybrid BTMS may cause secondary heat storage in PCMs.
The cycle test of LIBs includes discharge, standing, and charging periods.The discharge rate is 3 C, the resting time is 218 seconds, and the charging rate is 1.6 C. For the above-defined four structure designs, the BTMSs with CPCM of 12 wt% EG are simulated in 5 cycles under the 26 C, 35 C and 40 C ambient temperatures.
It is evident that the passive BTMS in Design I and II, which only use CPCM of 12 wt% EG as a passive cooling strategy, cannot achieve the normal working requirements of the LIBs in the five cycles from Figure 15.The T max of Design I in the third cycle exceeds 50 C at the ambient temperature of 26 C. In Design II, under the ambient temperature of 26 C, the secondary energy storage of the CPCM can be obviously improved by adding the fins.The temperature of Design II at the end of the second cycle is less than the melting temperature of 41 C, and the highest temperature of Design II is 46 C at the end of the discharge of the fifth cycle.In the higher temperature environment, such as 35 C and 40 C, the T max exceeds the battery safety limit of 60 C in the second cycle in Design I and Design II.
Although the BTMSs in Design I and II can keep the temperature of batteries within a safe range in a single cycle, neither of the two designs can meet the cooling requirements for continuous operation of the batteries for more than two cycles.The results indicate that the cooling performance of the BTMS in Design IV is optimal in an extremely high temperature environment.The fin structure and liquid cooling greatly enhance the heat transfer of the BTMS and significantly improve the secondary heat dissipation capacity of CPCM, which can get effective heat dissipation and play a role in heat adsorption at the beginning of the next cycle.
A balanced optimal BTMS is obtained by considering the various factors mentioned above.The system combines CPCM and liquid cooling, where the coolant flow velocity is 0.06 m s À1 , and aluminum fins are embedded in CPCM of 12 wt% EG.This study aimed to enhance the heat dissipation from the PCM used in BTMS for LIBs operating continuously under different ambient temperatures.The heat generation model of single-cell is verified experimentally.Four different BTMS designs, including passive and active cooling, are examined.The factors affecting BTMS cooling performance based on PCM are analyzed using CFD software.
Simulation results suggest that the passive BTMS with PCM and natural air cooling will eventually fail the heat dissipation in the battery module, although the temperature of batteries can be maintained within a safe range for 5 charge-discharge cycles under the 26 C ambient temperature.When the ambient temperature is above 35 C, the maximum temperature exceeds the safety limit of 60 C after the single cycle, with a charge rate of 1.6 C and discharge rate of 3 C.
The cooling performance is greatly improved by the active BTMS with the structure of Design IV.The hybrid BTMS combined CPCM/fin structure and liquid cooling can control the battery temperature below 50 C.Actually, the highest temperature of batteries is 45 C in the five cycles of 3C discharge rate under the 40 C ambient temperature.We found that the innovative embedding of aluminum fins in the PCM can optimize the cooling performance of the hybrid BTMS.None of the cooling strategies in the research could limit the maximum temperature difference of batteries to 5 C without cooling fins in the charge-discharge cycles.
The heat dissipation performance of CPCMs is better than that of pure paraffin.The BTMS with CPCM of 12 wt% EG has a good cooling performance and can effectively control the maximum battery temperatures in five cycles at 43

F
I G U R E 1 Structure diagram of battery thermal management system model.T A B L E 1 Specifications for INR18650-25R lithium-ion battery.

F I G U R E 2 F
Comparison of simulation and experiment of the single-cell under the ambient temperature of 26 C and three discharge rates (A) 1 C, (B) 2 C and (C) 3 C and (D) summary of temperature curves for three discharge rates.I G U R E 3 Voltages and currents of single battery under one cycle, experimental and simulated of maximum temperatures of single-cell at different discharge rates (A) 3 C, (B) 2 C, and (C) 1 C. F I G U R E 4 Geometric model of battery module generated by COMSOL with 875 116 elements.
the batteries F I G U R E 5 Grid independence analysis of COMSOL model, verified by the maximum temperature simulation results of the battery module at 26 C ambient temperature and 3C discharge rate.discharge rate and 0.01 m s À1 flow velocity.The schematic diagrams of the two flow directions are shown in Figure 8.The flow directions of the cooling channels are parallel and alternate.

F I G U R E 6
Structure models of BTMS under four different types of cooling strategies (Design I: air and PCM, Design II: air and PCMfin, Design III: liquid and PCM, Design IV: liquid and PCM-fin).

Figure 11 ,
Figure 11, which shows that the cooling performance of the BTMS improves with the increase of the coolant flow velocity.When the fluid is stationary (0 m s À1 ), the maximum temperatures T max are 44.1 C, 44.9 C and 47.5 C at the ambient temperatures of 26 C, 35 C and 40 C, respectively.Under the ambient temperature of 26 C, the T max at 0.01 m s À1 is significantly reduced by 9.3 C to 34.8 C than the T max at 0 m s À1 .When the flow velocity increases from 0 to 0.06 m s À1 , the T max decreases by 11.6 C, 3.4 C and 3.3 C, respectively, under the three ambient temperatures.When the flow velocity continues increasing from 0.06 to 0.3 m s À1 , the T max decreases slightly by 0.2 C, 0.4 C and 0.4 C, respectively.In summary, the T max and ΔT max are significantly reduced when the coolant in the hybrid BTMS maintains a certain flow velocity.The coolant flow can effectively absorb the heat and prevent the latent heat of the PCM from being exhausted quickly.The coolant flow velocity

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Maximum temperatures of 4 designs at a 3 C discharge rate and ambient temperatures of 26 C (A), 35 C (B) and 40 C (C) and the maximum temperature differences (D).
C lower than pure paraffin under the three ambient temperatures of 26 C, 35 C and 40 C, respectively.The EG mass fraction F I G U R E 8 Schemes of liquid cooling of BTMS with parallel flow and alternate flow.

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Maximum temperature and maximum temperature difference of LIBs under 3C discharge rate in the parallel flow and alternate flow at 26 C, 35 C and 40 C ambient temperatures.(A) Maximum temperature and (B) maximum temperature difference.

F I G U R E 1 0
Surface temperature distribution of LIBs at 26 C, 35 C and 40 C, respectively, at time = 1200 seconds.

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I G U R E 1 2 Thermal performance of BTMS under the condition of CPCMs with different mass fractions of EG at three different ambient temperatures.Maximum temperature of LIBs at the ambient temperatures of (A) 26 C, (C) 35 C and (E) 40 C. The maximum temperature difference of LIBs at the ambient temperatures of (B) 26 C, (D) 35 C and (F) 40 C. CPCMs of different EG mass fractions decreases to less than 5 C.

F I G U R E 1 3
Maximum temperatures vs coolant velocity in the BTMS using CPCMs with different mass fractions of EG under ambient temperatures of (A) 26 C, (B) 35 C and (C) 40 C. The maximum temperature curves of Design III and Design IV in the cycle test are illustrated in Figure 16.The BTMS of liquid cooling coupled with CPCM of 12 wt % EG can effectively control the temperature of the battery module.However, the T max of Design III has reached 58 C in the discharge of the second cycle at the ambient temperature of 40 C.After five cycles of Design IV, the T max and ΔT max remain basically unchanged, the T max are 34.7 C, 42.8 C and 45.0 C under the ambient temperature of 26 C, 35 C and 40 C, respectively.

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I G U R E 1 4 Effects of a combination of different CPCMs and cooling fins on the thermal performance of BTMS (A: upper) maximum temperature of batteries, (B: lower) maximum temperature difference of batteries.Maximum temperature of batteries of the BTMS in Design I (PCM only) and Design II (PCM-fin) during five cycles under different ambient temperatures of 26 C, 35 C and 40 C.

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Maximum temperature of batteries of the BTMS in Design III (liquid and PCM) and Design IV (liquid and PCM-fin) during five cycles under different ambient temperatures of 26 C, 35 C and 40 C.
6roperties of heat transfer materials.6 Maximum temperature and maximum temperature difference of LIBs under different flow velocities at ambient temperatures of 26 C, 35 C and 40 C. (A) Maximum temperature and (B) maximum temperature difference.
.0 C, 43.6 C and 44.1 C under the 26 C, 35 C and 40 C ambient temperature, respectively.ΔT max maximum value of temperature differences of battery module ( C) ΔT PCM temperature range of phase transition ( C) u