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Abstract

This work presents the design and optimization of a phase change material (PCM)-based hybrid battery thermal management system (HBTMS). In the first stage, experiments are performed to measure the battery cell temperatures under various charge rates with and without the usage of PCM. Thereafter, a numerical model is developed to conduct a parametric study on the effect of the thickness of PCM layer around the battery cell. The results show that with the PCM thicknesses of 6–12 mm, the maximum cell temperature (36.35 °C) and thermal nonuniformity are within the safe range. In the second stage, a parametric study is conducted in the 6S1P battery module to optimize the spacing between the cells at constant inlet velocity. The result shows that an increase in cell spacing decreases the maximum temperature within the cells. The maximum temperature is within the optimal range when the cell spacing is 10 mm. At the constant cell spacing of 10 mm, an increase in inlet velocities from 0.25 m/s to 2.5 m/s gradually improves the thermal uniformity. The maximum temperature and thermal nonuniformity for the 6S1P battery module are found to be 42.07 °C and 1.17 °C respectively. In the third stage, the 6S1P battery module is optimized for PCM thickness, cell spacing, and inlet air velocity. It is found that effective thermal management is possible with PCM-based HBTMS at a low airflow rate of up to 1.5 m/s. The optimized PCM-based HBTMS shows 53.95% and 40% reductions in PCM mass and air flowrate, respectively.

1 Introduction

The increasing concerns about environmental pollution and global warming have forced the world to reduce the use of conventional energy that mainly comes from fossil fuels. One of the major consumers of fossil fuels is the automotive sector, and hence it is also the prominent sector responsible for air pollution. Among the various alternatives for decarbonization of the automotive sector, electrification of the powertrains has become most attractive in the last few years. An electrical vehicle (EV) offers zero tail-pipe emissions, robust performance, low noise, and significantly less running cost compared to a conventional internal combustion engine (ICE) vehicle [1]. One of the major components in an EV is the battery that decides the overall performance of the EV.

Reversible electrochemical batteries having reasonable cyclic charging and discharging capabilities were introduced in portable applications during the 1970s. Later on, the technology kept on improving on various aspects such as high specific energy density, high nominal voltage (up to 3.7 V), long cycle life, and low self-discharge, and reached a level, where it can be incorporated in small- and large-scale applications, e.g., EVs [2]. Lithium-ion (Li-ion) batteries are widely used in light and heavy-duty vehicles nowadays. A Li-ion battery cell is comprised of anode, cathode, electrolyte, and a separator. Generally, anode consists of graphite and titanium-based materials. Cathode material depends on the requirement and application of the battery. The first commercially successful form of layered transition metal oxide cathode is lithium cobalt oxide (LiCoO2) having energy density of ∼199 mAh/g and ∼765 Wh/kg [3]. However, due to the drawback of low charge rates, its application is limited to small-scale devices such as mobile phones, laptops, etc. Currently, lithium iron phosphate (LiFePO4) batteries are most widely used in the EV industry due to their low cost, low toxicity, long-term stability, well-defined performance, and high energy density of 114–236.5 Wh/kg [4]. Lithium manganese nickel oxide/spinel (LiMn1.5Ni0.5O4) cathode material is coming into the spotlight as it can be charged at high voltages ∼5 V and has high energy density when compared with LiCoO2 and LiFePO4. Lithium manganese nickel oxide (LMNO)-based batteries can be used, where there is a requirement for high energy capacity; however, the high cost limits its application in EVs.

Li-ion batteries are well known for their heat generation characteristics and resulting rise in the battery temperature especially during high charge and high discharge rates [5]. The operational temperature of a Li-ion battery is the critical parameter that significantly affects the other parameters such as performance, capacity, energy ratio, efficiency, and life cycle. Various studies have been performed to check the performance and life cycle of Li-ion batteries at different operating temperatures. Different researchers have reported different optimal temperature ranges for Li-ion batteries—Renlang et al. [6] reported −10–50 °C, Bin et al. [7] reported 20–50 °C, Xin et al. [8] reported 20 to 55 °C, and Chenguang et al. [9] reported 25–40 °C in their studies. It has been found that when the battery is operated at a reasonably low temperature, its performance, and reversibility degrade resulting in decreased life. A study performed by Nagasubramanian [10] on an 18,650 Li-ion battery showed that the power and energy density of 800 W/L and 100 Wh/L at 25 °C reduced to less than 10 W/L and 5 Wh/L at −40 °C respectively. The State of Charge (SOC), which represents the ratio of present capacity to available capacity, was observed to be degraded to approximately 23% when the battery operational temperature was brought to 25 °C from −15 °C [11]. The main reason for the degradation of battery performance at low temperatures is the change in internal properties of the electrolyte. When the battery is operated at a considerably low temperature, the viscosity and internal resistance offered for Li-ion transport increases. The charge transfer resistance, which causes the performance degradation was found three times more when the LiFePO4-based battery was operated at −20 °C than at 25 °C [12]. Zhang et al. [13] reported that the charge resistance was higher during discharging than at charging of the battery, which makes discharging difficult compared to charging at low temperatures. Another major phenomenon that occurs at lower temperatures is plating. At low temperatures, the polarization of the anode leads to the formation of an ion layer at the electrode and electrolyte interface [14]. The continuous deposition of Li-ions on the electrode leads to the formation of dendrites, which penetrates through the separator and may lead to internal short circuit [15]. In the review conducted by Jaguemont et al. [16], the degradation of battery performance and increased aging effects were seen rapidly when the battery was operated below 25 °C.

Studying the high-temperature effects on a battery is more complicated compared low-temperature effects. The temperature of a battery is raised due to heat generation caused by the movement of ions (charge transfer) and chemical reactions [17]. These chemical reactions are both reversible and irreversible types [18]. The entropic heat generation, which is a reversible process of heat generation occurs due to the entropy change during the electrochemical reaction [19]. However, heat generation due to irreversible processes such as active polarization, Ohmic heating, internal mixing, and enthalpy changes dominate the thermal effects and hence contribute more to the temperature rise of the battery [2022]. The over-potential may occur; then, there is a sudden load drop, which leads to polarization at the electrodes. This results in high resistance for the movement of Li-ions at the electrode and electrolyte interface [23], leading to heat generation. The resistance offered by electrode and electrolyte in the moment of ions contributes to heat generation also known as Ohmic heating [17]. Heat generation also occurs due to the mixing of ions during charging and discharging as the distribution of ions is heterogeneous [18]. If the batteries are operated at high temperatures for a long duration, it may lead to thermal runaway. Thermal runaway is a condition in which a battery cell catches fire that translates into a chain reaction of fire within the full battery module [24]. In-operando high-speed synchrotron X-ray computed tomography and radiography technologies were introduced by Finegan et al. [24], which allowed studying the thermal runaway behavior. A diagnosis was conducted on an 18,650 Li-ion battery to study the thermal runaway characteristics of individual components. When the temperature was >6 °C, the electrode–electrolyte layer started decomposing, at temperature >110 °C, the separator started melting, at temperature >150 °C micro short circuit happened causing gas formation and change in physical structure, at temperature >230 °C, and a internal short circuit as separator ruptured completely. It was found that when the battery temperature was raised above 250 °C, all the components (anode, electrolyte, and binder) were decomposed and converted into gas. When these gases encountered oxygen in the atmosphere, they ignited, and a tremendous rise in temperature was noted. Consequently, thermal runaway is the most critical concern in the battery packs with high energy demand.

In addition to the maximum temperature within the cell or module, thermal uniformity is another factor that needs attention. Song et al. [25] numerically investigated the performance of a Li-ion battery under the effect of non-uniform thermal behavior and concluded that the battery capacity decreased at high thermal nonuniformity within the cell. Similarly, Cavalheiro et al. [26] investigated the degradation of batteries in a stack and found that the battery at a high temperature within the stack degraded faster compared to the battery at a low temperature. Furthermore, voltage imbalance occurs in a battery pack due to the thermal nonuniformity resulting in varying aging effects. The difference in Ohmic resistance within the battery module leads to current unevenness and energy degradation [27]. It has been reported in various studies that the maximum temperature difference within a battery should be below 5 °C [69]. Therefore, a properly designed Battery Thermal Management System (BTMS) considering these thermal factors is essential for the performance, safety, and aging (life cycles) of the battery pack.

Numerous works have been conducted by researchers on BTMS incorporating different types of heat transfer modes and combinations among them. Both passive and active methods have been studied in the literature for cooling and heating of Li-ion batteries. However, major active techniques are cold plates [28], bionic cooling plates [29], serpentine tubes around the battery, and mini channels [30], wherein different heat transfer mediums are studied such as liquids [28,30,31], nanofluids [32], air [27,33], and thermally enhanced fluids with additives like nanoparticles [34], ethanol glycol [35], liquid metals (like gallium and its alloys) [36] and their combinations. It has been shown that due to the lower specific heat capacity of air, a much higher volumetric flowrate is required to cater to the cooling demand [37]. On the other hand, most of the passive techniques used are heat pipe (HP) [38], loop heat pipe [39], Phase Change Material (PCM) [40], nano-enhanced PCM [41], and hybrid techniques like heat pipe combined with air cooling [42]. Al-Hallaj and Selman [43] developed a PCM-based BTMS, where they applied paraffin wax on eight 18,650-type battery cells in the 2P4S (two parallel and four series) arrangement. They found that PCM-based BTMS maintained both the thermal factors within the specified range and was more efficient in maintaining thermal uniformity when compared with air-based BTMS. In a similar study, Sabbah et al. [44] found that PCM-based BTMS was able to maintain the battery temperature within the range even at an ambient temperature of 52 °C under high discharge rates. In another study, PCM has been found to delay the decline of battery temperature under low-temperature operating conditions [45]. Rao et al. [46] found slow aging behavior in Li-ion batteries with PCM-based BTMS due to its capability of maintaining high thermal uniformity with the cell. Parsons and Mackin [47] were able to bring the battery pack temperature from 65.6 °C to 50.3 °C using PCM. However, PCM-based BTMS also has some disadvantages such as limited heat capacity (the amount of heat energy that can be absorbed and stored) and low thermal conductivity [48], which may result in rapid temperature rise and heat accumulation respectively after the completion of the phase change process. PCM could also slow down the battery warming rate in cold climates, affecting the battery performance during the initial driving conditions. Many techniques have been studied to improve the thermal conductivity of PCM such as introducing microencapsulated [45], fins [48], extended graphite [49], carbon fibers [50], nanoparticles, and metal foam [51]. On the other hand, the disadvantage of PCM due to limited heat capacity can be overcome by providing an excess amount of PCM. However, this approach could be counter-productive in weight-sensitive applications such as EVs. The alternative approach is to provide an effective means of external heat transfer to PCM to alter the time required for phase change and hence avoid sensible heating/cooling. Therefore, combined active and passive techniques based on BTMS, also known as Hybrid Battery Thermal Management (HBTMS), have been studied in the literature. The advantage of hybrid BTMS using PCM is that it can delay the temperature rise and hence offers more time for cooling action. The ramp-up rate of battery temperature is reduced when compared with only PCM-based and air-based BTMS [52]. Ling et al. [53] studied air and PCM-based techniques on 20 battery cells in a 4P5S arrangement and recommended HBTMS due to the limited thermal capacity of PCM. Zhao et al. [54] studied a hybrid technique, where PCM and liquid cooling were employed. It was found that heat accumulation occurred at the walls of the battery, and conjugate heat transfer helped in the reduction of heat accumulation. Furthermore, excess imposition of PCM around the battery cells results in heat accumulation, which could be counter-productive [55]. Few studies have been conducted in the literature on the effect of thicknesses of PCM around cylindrical battery cells. Javani et al. [56] found that 3-mm PCM thickness provided 10% more thermal uniformity as compared to that with 6 mm, 9 mm, and 12 mm thicknesses. Verma et al. [57] stated that 3 mm thickness is optimal when conducting an experiment on prismatic-type batteries, where the maximum temperature is maintained at 32 °C. Li et al. [58] carried out studies to minimize PCM in cylindrical batteries. It was found that PCM thickness of 48 mm and spacing of 55 mm are optimal conditions, where thermal nonuniformity was in the range of 2.9–3.5 °C. Another major issue associated with PCM-based BTMS in EVs is weight addition, which affects the range and performance of the vehicle.

Based on the review of the literature, some research gaps have been identified and efforts have been made to bridge them as follows: it has been found that most of the previous works have neglected the mass of PCM, which has a direct impact on the space occupied and weight of the battery module. In the present work, a methodology is presented for the optimization of both PCM mass and cell space. The previous numerical works have neglected the PCM container, which holds the liquid PCM. A leak-proof cylindrical copper capsule is considered to accommodate both battery and PCM in the present work. Furthermore, most of the previous works lack adequate experimental validations. In the present work, all the numerical models are experimentally validated under the reference operating conditions. The performance of a PCM-based BTMS is affected not only by the design but also by the operating parameters. Therefore, in the present work, optimization of the energy requirement for active cooling has also been considered, and its effect on the system performance has been highlighted.

The article has been organized as follows: Sec. 2 explains the materials and methods used in the study, Sec. 3 discusses the results, and Sec. 4 highlights the conclusions of the work.

2 Materials and Methods

2.1 Selection of the Battery Module Configuration.

Multiple battery cells are connected in series and parallel arrangements to make a battery module. A group of battery modules are put together according to the required capacity to form a battery pack. The battery cells are commercially available in three different shapes—cylindrical, prismatic, and pouch. However, they are available in many different sizes such as 18,650 (18 mm diameter and 65 mm height), 32,700, etc., for cylindrical cells, and 173 × 115 × 32 mm (height × length × width) (100 Ah) [5], 250 × 65 × 50 mm (50 Ah), etc., for prismatic cells to form battery modules for medium and heavy-duty EVs. Nevertheless, it is a common practice to accommodate battery modules in a rectangular shape container to form the battery pack. Cylindrical battery cells are most commonly used in EVs, where they are arranged in different manners and spacing between the cells. In the literature, studies are available on various patterns such as 6S2P (Total 12 cells, where 2 cells arranged in parllel and 6 such pairs are arranged in series) [2], 6S3P [6], 5S1P [7], 5S3P [8], 8S4P [31,59], and 10S6P [60] arrangements packed in a rectangular enclosure. It should be noted that thermal management can be studied on a single battery module because the same strategy can be applied to the whole battery pack. Therefore, in the present work, a 6S1P-type battery module comprised of six cylindrical cells (type—LiFePO4, 32,700) having a capacity of 6 Ah is considered for the study. Initially, the study is performed on a single battery cell, and later, the 6S1P battery module is studied both numerically and experimentally in a rectangular duct. The electrical and thermophysical properties of the battery cell are given in Table 1. Also, the thermophysical properties of PCM material used in the work are given in Table 2.

Table 1

Electrical and thermophysical properties of the battery cell

ParametersDetails
Cell diameter, mm32 ± 0.3
Cell length, mm70 ± 0.2
Capacity, Ah6
Nominal voltage, V3.6
Cell mass, g145
Mass density, kg/m32879
Thermal conductivity, W/m-K [61]0.743
Specific heat, J/kg-K880
ParametersDetails
Cell diameter, mm32 ± 0.3
Cell length, mm70 ± 0.2
Capacity, Ah6
Nominal voltage, V3.6
Cell mass, g145
Mass density, kg/m32879
Thermal conductivity, W/m-K [61]0.743
Specific heat, J/kg-K880
Table 2

Thermophysical and electrical properties of PCM material

PCM (OM35)
ParametersDetails
Solid density, kg/m3900
Liquid density, kg/m3870
Specific heat, J/kg-K2570
Solid thermal conductivity, W/m-K0.2
Liquid thermal conductivity, W/m-K0.16
Viscosity, kg/m-s0.001372
Pure solvent melting heat, J/kg171,000
Solidus temperature, °C33
Liquid temperature, °C34
Basic materialOrganic
Thermal stability, cycle∼2000
Maximum operating temperature, °C120
PCM (OM35)
ParametersDetails
Solid density, kg/m3900
Liquid density, kg/m3870
Specific heat, J/kg-K2570
Solid thermal conductivity, W/m-K0.2
Liquid thermal conductivity, W/m-K0.16
Viscosity, kg/m-s0.001372
Pure solvent melting heat, J/kg171,000
Solidus temperature, °C33
Liquid temperature, °C34
Basic materialOrganic
Thermal stability, cycle∼2000
Maximum operating temperature, °C120

2.2 Numerical Methodology.

A 3D numerical model of the battery module has been developed in this work using commercially available computational software ANSYS FLUENT v18.1 to study the multiphysics phenomenon. The following are the main assumptions considered in the study:

  1. The top and bottom surfaces of the battery, and the duct walls are considered adiabatic.

  2. The heat generation within the cell at different charge rates is constant.

  3. The motion of liquid PCM is considered incompressible and its expansion is ignored.

  4. All the thermophysical properties of the PCM are taken constant except density.

In the numerical model, PCM acts as a Newtonian fluid and the natural convection dominates during the melting process. The following continuity and momentum equations are used in the numerical solution:
(1)
(2)
(3)
where S is the momentum source term; it depends on the porosity in the mushy zone and is expressed as follows:
(4)
where ɛ is a very small value to avoid the division with zero, which is taken as 0.001, and β is the liquid volume fraction.
The enthalpy porosity method is used for modeling of melting and solidification of PCM. In this method, each cell is associated with an enthalpy balance, calculated at every iteration. The solid–liquid interface is mentioned as a mushy zone, where the porosity is rated between 0 and 1. When the cell is in the solid state, its porosity is 0 and when it is in the liquid state, its porosity is 1. The liquid fraction is represented with respect to the porosity of the element.
(5)
where H is the specific enthalpy and can be expressed in terms of sensible enthalpy (h) and latent heat content (ΔH):
(6)
The sensible enthalpy (h) is expressed as
(7)
The latent heat content (ΔH) of the PCM changes between the solid (0) and liquid state (L), which is related to liquid fraction (∅) as:
(8)

2.3 Modeling Parameters and Mesh Description.

The numerical models of the 32700-type battery cell and 6S1P battery module with thermophysical properties of the materials mentioned in Tables 1 and 2 are prepared using ANSYS v18.1 design modular. The meshing is performed using the ICEM CFD meshing tool, and quadrilateral dominant mesh is generated in all the domains. The grid independence test is carried out for all the models to check and finalize the mesh quality. The details of various domains in the model and the number of elements considered after the grid independency test are shown in Table 3. The validated model with the experimental results is selected for further study.

Table 3

The details of the various domains and number of elements selected after grid independency test in the model

ModelMaterialsNumber of domainsMaximum model sizeDimension (mm)Number of elements
1Battery1Battery diameter, mm32 ± 0.311,256
Battery length, mm70 ± 0.2
2Battery, PCM, and copper enclosure3Enclosure diameter, mm32 + PCM thickness (2 mm) + copper shell thickness (1 mm)15,654
Enclosure Length, mm70
3Battery and fluid2Fluid domain in duct222 × 52 × 70 (L × W × H)1,225,972
4Battery, PCM, copper enclosure, and fluid4Fluid domain in duct298 × 52 × 70 (L × W × H)1,721,865
ModelMaterialsNumber of domainsMaximum model sizeDimension (mm)Number of elements
1Battery1Battery diameter, mm32 ± 0.311,256
Battery length, mm70 ± 0.2
2Battery, PCM, and copper enclosure3Enclosure diameter, mm32 + PCM thickness (2 mm) + copper shell thickness (1 mm)15,654
Enclosure Length, mm70
3Battery and fluid2Fluid domain in duct222 × 52 × 70 (L × W × H)1,225,972
4Battery, PCM, copper enclosure, and fluid4Fluid domain in duct298 × 52 × 70 (L × W × H)1,721,865

The transient analysis with a time-step of 0.1 s, and a maximum of 20 iterations per time-step is conducted for 900 s (4C Rate). The effect of gravity, 9.81 m/s2, is considered to study the convection-driven forces within the PCM and fluid domains. The ambient and initial temperatures of PCM and copper are taken at 27 °C. The walls of the duct are assumed to be adiabatic. A constant heat generation condition of 95,000 W/m3 is considered for each battery cell, and the surface of the battery provides a natural heat transfer coefficient of 2.5 W/m2K [62]. kε turbulent model is chosen to study the heat transfer characteristics of the system.

2.4 Numerical Solution.

Second-order upwind interpolation scheme is used to discretize convective terms in the momentum equations. First-order upwind interpolation scheme is used to discretize the convective terms in the energy equation. The SIMPLE algorithm is used for pressure–velocity coupling and PRESTO is used for pressure correction. The residual value of 10−9 is set for energy, continuity, and momentum equations in convergence criteria. Maximum temperature (Tmax) and maximum temperature difference (ΔT) within a battery cell and module are studied with different system variables.

3 Experimental Methodology

The experiments are conducted to record the temperature profile with respect to time at different charging rates (C-rate). IT6500 series wide-range high-power supply and IT8918A series wide-range high-power DC electric load from ITECH are used for charging and discharging, respectively. K-type thermocouples and FluxTeq COMPAQ four-channel data acquisition system are used to record temperature profiles. The details of the equipment used in the experiment are provided in Table 4. The data point interval is set to 1 s, and temperature is recorded at both center and top of the battery cell. The detail of the experimental setup is shown in Fig. 1.

Fig. 1
Experimental setup showing all the modules and equipment: (a) Single battery used for measuring surface temperature at different charge rate, (b) single battery placed in copper enclosure containing PCM, (c) BTMS 6S1P module, and (d) HBTMS 6S1P module
Fig. 1
Experimental setup showing all the modules and equipment: (a) Single battery used for measuring surface temperature at different charge rate, (b) single battery placed in copper enclosure containing PCM, (c) BTMS 6S1P module, and (d) HBTMS 6S1P module
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Table 4

Specifications of the equipment used in the experiment

MeasurementInstrumentDescriptionRangeResolution
Charging machineIT6500 series wide-range high-power supply (ITECH)Charge battery at different charge rates0–650 V±5 mV
0–204 Amp±10 mA
Discharging machineIT8918A series wide-range high-power DC electric load (ITECH)Discharge battery0–800 V±5 mV
0–600 Amp±10 mA
TemperatureK-Type thermocouplesTemperature of battery0–900 °C±0.1 °C
Data acquisition systemFluxTeq COMPAQ four-channelRecord the temperature of the batteryNANA
DC-regulated power supplyIT6932A
ITECH DC-regulated power supply
For regulating blower speed0–60 V±5 mV
0–10 Amp±10 mA
Air velocityTesto 405i-Hot wire anemometerInlet velocity of air0–30 m/s±0.01 m/s
MeasurementInstrumentDescriptionRangeResolution
Charging machineIT6500 series wide-range high-power supply (ITECH)Charge battery at different charge rates0–650 V±5 mV
0–204 Amp±10 mA
Discharging machineIT8918A series wide-range high-power DC electric load (ITECH)Discharge battery0–800 V±5 mV
0–600 Amp±10 mA
TemperatureK-Type thermocouplesTemperature of battery0–900 °C±0.1 °C
Data acquisition systemFluxTeq COMPAQ four-channelRecord the temperature of the batteryNANA
DC-regulated power supplyIT6932A
ITECH DC-regulated power supply
For regulating blower speed0–60 V±5 mV
0–10 Amp±10 mA
Air velocityTesto 405i-Hot wire anemometerInlet velocity of air0–30 m/s±0.01 m/s

Furthermore, the experimental works are carried out to study the temperature profile of battery cells with PCM in a copper enclosure as shown in Fig. 1(b). The battery cell is placed at the center of the cylindrical enclosure having an inner diameter of 38 mm and a thickness of 2 mm. The PCM (OM35) is filled in the gaps in the liquid state to avoid non-uniform distribution and air gaps.

Finally, the experimental work is carried out on the 6S1P battery module with and without HBTMS as shown in Figs. 1(c) and 1(d). Four thermocouples are placed to measure the 1st, 2nd, 5th, and 6th battery cell surface temperatures at the center position. A DC power supply is used to regulate the speed of the blower to vary the inlet air velocity. As the blower takes air from the ambient, the inlet temperature of the duct will be the same as the ambient temperature. Specific details of the experiments are discussed in the subsequent sections.

3.1 Workflow in the Development of Hybrid Battery Thermal Management (HBTMS).

The present work is a comprehensive study starting from cell-level investigation to battery module-level optimization. Therefore, the study is presented in three stages for ease of understanding.

  1. Stage I: Optimization of the PCM thickness for a single battery cell.

  2. Stage II: Optimization of the cell spacing and inlet air velocity for 6S1P battery module.

  3. Stage III: Optimization of the PCM thickness, cell spacing, and inlet air velocity for HBTMS.

However, different parameters are used, and a generalized optimization methodology is employed that remains the same for all three stages. The methodology adopted in the present study and workflow for optimization of HBTMS are represented in a flowchart as given in Fig. 2. It is divided into three steps—validation, parametric analysis, and optimization. In the validation step, the numerical model is validated with the experimental work. It is followed by a parametric analysis step, where the validated model is studied with different system parameters, such as PCM thickness, cell spacing, and/or inlet air velocity. Finally, in the optimization step, the obtained results are analyzed, and the output parameters are filtered based on the set selection criterion. The two important selection criteria considered in this work are maximum temperature (Tmax = 45 °C) and maximum temperature difference (ΔT < 5 °C) within a cell or module.

Fig. 2
Workflow of the optimization process carried out for HBTMS in the present work
Fig. 2
Workflow of the optimization process carried out for HBTMS in the present work
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4 Results and Discussions

4.1 Stage I: Optimization of Phase Change Material Thickness for a Single Battery Cell

4.1.1 Temperature Profile of a Battery Cell at Different Charge Rates.

The experiments were conducted to record the temperature profile with respect to time for a battery cell (type 32700) at different charge rates. The Charge rates define the amount of charge added to the battery per unit of time. For example, a battery charging at 2C, 1C, and 0.5C charge rates will get fully charged in half an hour, one hour, and two hours, respectively. Temperature is recorded at both center and top of the battery cell; please refer to the experimental setup shown in Fig. 1(a). The battery is maintained at a controlled ambient temperature of 27 °C. The charging voltage and current are controlled with the help of automatic test software provided by ITECH. Battery cell surface temperatures recorded for different charge rates at 0.5C, 1C, 2C, and 4C are shown in Fig. 3.

Fig. 3
The surface temperature of the battery at different discharge rates
Fig. 3
The surface temperature of the battery at different discharge rates
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It can be observed that the cell surface temperature at the 4C charge rate reached the maximum value of 58.1 °C, which is beyond the acceptable temperature range. Furthermore, the thermal nonuniformity of 4.1 °C was observed at 4C rate. With an increase in C-rate, the number of ions traveling between charge collectors and their velocity is increased. It eventually results in a higher joule's heating effect, and hence, higher temperatures are noted at high C-rates. A thermal management system is highly recommended at a high C-rate as battery cell temperature crosses the permissible maximum temperature. As maximum heat generation occurs at a high C-rate, the thermal management system is designed for these conditions. Therefore, further studies are carried out for 4C charge rate, and duration of 900 s (15 min).

4.1.2 Analysis of the 3D Numerical Model of a Battery Cell With Different Heat Generation Rates.

A 3D numerical cell (32700 cylindrical types) with thermophysical properties mentioned in Table 1 is developed using the methodology explained in Sec. 2.2. The developed numerical model is studied with varying heat generation rates within the cell and tuned with the experimentally obtained temperature profiles shown in Fig. 3. The transient analysis is performed at different heat generation rates to validate with experimentally obtained Tmax and tduration (time taken to reach maximum temperature). At 95,000 W/m3, which is 5.4 W emitted by the battery cell at a 4C charge rate, the cell temperature reached 59.05 °C in 816 s. It shows a 1.63% deviation which is 0.95 °C from the experimental results, which is acceptable for the present investigation. The temperature variation in the radial direction can be observed from the temperature contour shown in Fig. 4(a).

Fig. 4
Experimental module, 3D geometry model, mesh, and contours in case 1
Fig. 4
Experimental module, 3D geometry model, mesh, and contours in case 1
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As the Tmax for the battery cell reached 59.05 °C, which is beyond the optimal temperature range, it suggests the requirement for a thermal management system. Therefore, a passive thermal management technique using a layer of PCM around the cell in a copper enclosure as shown in Fig. 4(b) is proposed.

4.1.3 Optimizing the Thickness of Phase Change Material for a Single Battery Cell.

To start with, the temperature profile of the battery cell with the PCM model was validated with the experimental base case. The battery cell was placed at the center of the cylindrical enclosure having an inner diameter of 36 mm and thickness of 1 mm. The PCM (OM35) having the transition temperature of 35–36 °C was filled in the gap. The temperature profiles obtained from both the experimental and numerical works with battery cells placed in PCM of thickness of 2 mm and enclosed in a copper cylinder are compared in Fig. 5. It is observed that the results obtained from the numerical model are close to the experimental results with a maximum deviation of 2.2 °C. It is also noticed that with the introduction of passive cooling i.e., PCM of thickness 2 mm, the Tmax is decreased by 5.2 °C; however, it is still not within the optimal temperature range. Therefore, further efforts were made to reduce the cell temperature by varying the PCM thickness around the battery cell. One of the restrictive qualities of PCM is its low thermal conductivity, which is approximately 0.2 W/m-K in the present case. It acts as insulation between the cell and the heat transfer medium. Therefore, the optimal value of PCM thickness needs to be determined, which mainly depends on its thermal energy capacity and thermal conductivity. The numerical study was conducted to optimize the thickness of the PCM layer around the battery cell keeping all the other parameters constant.

Fig. 5
Battery cell temperature profile with and without PCM-based passive cooling: (a) experimentally obtained temperature profile for bare cell, and numerically obtained temperature profile of the cell with PCM thickness of 10 mm when operated at 4C charge rate. (b) Experimental results of the temperature profile for 2 mm PCM thickness, and numerical results for 2 mm and 10 mm PCM thicknesses.
Fig. 5
Battery cell temperature profile with and without PCM-based passive cooling: (a) experimentally obtained temperature profile for bare cell, and numerically obtained temperature profile of the cell with PCM thickness of 10 mm when operated at 4C charge rate. (b) Experimental results of the temperature profile for 2 mm PCM thickness, and numerical results for 2 mm and 10 mm PCM thicknesses.
Close modal

The results of Tmax values for all the thicknesses of the PCM layer are shown in Table 5. It is observed that at low thickness values (below 6 mm), the battery temperature is beyond the optimal temperature range due to the insufficient heat storage capacity for the given time period. There is a decrease in Tmax with an increase in the thickness of PCM to 12 mm. However, a further increase in the thickness from 12 to 13 mm results in a decrease of temperature difference (Tmax − (Tmax)PCM) and hence degradation in heat transfer rate as seen in Fig. 6. Therefore, it can be considered that the optimal thickness of PCM beyond cell temperature is negatively affected. Nevertheless, complete melting of PCM is not observed in the cases with 10 mm and 11 mm thicknesses. Hence, a PCM thickness range from 5 mm to 9 mm is recommended to avoid excess utilization of PCM. The maximum temperature attained when the thickness of PCM is maintained at 10 mm is 36.5 °C as shown in Fig. 6. The Tmax is decreased by 21.5 °C, which brings the system within the optimal temperature range. The thermal nonuniformity of 1.8 °C is noted within the cell for the mentioned conditions.

Fig. 6
Maximum temperature difference with varying thicknesses
Fig. 6
Maximum temperature difference with varying thicknesses
Close modal
Table 5

Effect of PCM thickness on maximum cell temperature and temperature difference

t (mm)(Tmax)PCM (°C)Tmax (°C)–(Tmax)PCMs
0.556.62.4
154.05.0
252.96.1
349.19.9
445.312.8
544.814.5
643.115.9
739.819.2
837.121.9
936.522.5
1033.325.8
1132.226.9
1234.324.8
t (mm)(Tmax)PCM (°C)Tmax (°C)–(Tmax)PCMs
0.556.62.4
154.05.0
252.96.1
349.19.9
445.312.8
544.814.5
643.115.9
739.819.2
837.121.9
936.522.5
1033.325.8
1132.226.9
1234.324.8

4.2 Stage II: Optimization of the Cell Spacing and Inlet Air Velocity for 6S1P Battery Module.

In this stage, the study has been carried out for the 6S1P battery module to optimize the spacing between the cells. Furthermore, the numerical work has been carried out on the 6S1P battery module with different air velocities considering all the parameters obtained in stage I.

4.2.1 Validation of the Numerical Model With the Experimental Results.

A 3D transient numerical model is developed for the 6S1P battery module as illustrated in Fig. 7. Six battery cells represented in different colors are arranged in series with a spacing of 2 mm between each battery cell and 10 mm from the walls of the duct. The battery Tmax and ΔT are studied with an inlet air velocity of 2.5 m/s. The numerical model is validated with the experimental results carried out on a 6S1P battery module as explained in Sec. 2.2. A comparison of temperature profiles for individual cells (1, 2, 5, and 6) obtained with numerical and experimental works is shown in Fig. 8. It can be seen from Fig. 8 that the numerical model can predict maximum temperature and thermal uniformity closely to that of the experimental results with a deviation of 2.85% which is 1.6 °C. It is also observed that the average battery cell temperature increases in the direction of fluid flow, and the maximum temperature is noted at the last cell in the series. As the fluid gains thermal energy in the direction of flow, the fluid temperature keeps on increasing. Therefore, the temperature difference between the fluid and battery cell keeps on decreasing in the direction of the flow and results in a lower heat transfer rate. The maximum temperature of 55.8 °C and minimum temperature of 54.4 °C are noted experimentally, whereas the thermal nonuniformity (ΔT) is 1.4 °C. The numerically obtained results for the maximum and minimum cell temperatures are 54.3 °C and 53.3 °C, respectively, with the ΔT of 1 °C.

Fig. 7
Isometric view of 6S1P battery module considered for numerical and experimental work
Fig. 7
Isometric view of 6S1P battery module considered for numerical and experimental work
Close modal
Fig. 8
Comparison of numerical study with experimental results of Tmax for each cell in the 6S1P battery module
Fig. 8
Comparison of numerical study with experimental results of Tmax for each cell in the 6S1P battery module
Close modal

4.2.2 Parametric Investigation of Battery Cell Spacing and Inlet Air Velocity.

A parametric study using the developed numerical model was performed by varying the cell spacing from 2 mm to 10 mm with an increment of 2 mm keeping all the other parameters the same with a constant inlet air velocity of 2.5 m/s. The maximum temperatures of each battery cell after 900 s are shown in Fig. 9. It is observed that between the cell spacings of 8–10 mm, all the battery cells are within the optimal temperature range. It is because, with an increase in cell spacing, the area available for fluid movement increases, which increases the effective area of heat dissipation. It leads to higher effective air velocities around the cells and increases the local heat transfer coefficient. The effects of cell spacing on the temperature and velocity contours of the 6S1P battery module are shown in Fig. 10. It can be seen that as the cell spacing is increased from 2 mm to 10 mm, the air velocities get stronger around the cells. Also, the thermal nonuniformity within the cell and battery module increases with decreasing the cell spacing, which can be seen by comparing Figs. 10(a) and 10(b). Considering some factors of safety, 10-mm cell spacing is considered for further work.

Fig. 9
Effect of cell spacing on the temperature of 6S1P battery module at the air flowrate of 2.5 m/s
Fig. 9
Effect of cell spacing on the temperature of 6S1P battery module at the air flowrate of 2.5 m/s
Close modal
Fig. 10
Temperature and velocity contour at different battery cell spacing: (a) 2 mm and (b) 10 mm
Fig. 10
Temperature and velocity contour at different battery cell spacing: (a) 2 mm and (b) 10 mm
Close modal

The parametric study was extended to include the effect of low inlet air velocities in order to understand the thermal behavior of the system in more detail. The inlet air velocities between 2.5 m/s and 0.5 m/s with an interval of 0.5 m/s were studied on the setup with a cell spacing of 10 mm. The effect of inlet air velocity on the temperature of the 6S1P battery module at 10-mm cell spacing is shown in Fig. 11. It can be seen that the cell temperatures exceed the optimal temperature range when the air velocity is less than 2.5 m/s. Furthermore, this effect is dominant till air velocity falls below 2 m/s after which the cell temperature becomes less sensitive to the air velocities. It can also be seen that the thermal nonuniformity increases gradually as the air inlet velocity decreases. The thermohydraulic performance in the direction of the flow decreases when the velocity of the fluid decreases over a heating element in series [63]. As shown and discussed in the previous sections, PCM can provide high thermal uniformity, and the use of PCM in the present system may overcome these thermal issues. Therefore, in Sec. 4.3, both PCM and air convectional cooling-based HBTMS are explored.

Fig. 11
Effect of inlet air velocity on the temperature of 6S1P battery module at 10-mm cell spacing
Fig. 11
Effect of inlet air velocity on the temperature of 6S1P battery module at 10-mm cell spacing
Close modal

4.3 Stage III: Optimization of the Phase Change Material Thickness, Battery Cell Spacing, and Inlet Air Velocity for HBMTS.

In this stage, a battery module of six cells arranged in a 6S1P configuration is considered where each cell is placed in a cylindrical copper enclosure containing PCM. The system has provision for an inlet to supply air as the cooling medium as shown in Fig. 12. A numerical model is developed to study the proposed HBTMS. This numerical model is first validated with the experimental base case followed by parametric investigation to optimize the PCM thickness, cell spacing, and inlet air velocity.

Fig. 12
The geometrical details of the proposed HBTMS model considered for the numerical work
Fig. 12
The geometrical details of the proposed HBTMS model considered for the numerical work
Close modal

4.3.1 Development of Numerical Model and Its Validation With the Experimental Work.

A 3D transient numerical model is developed for the HBTMS 6S1P battery module as illustrated in Fig. 12. Six cells represented in different colors are arranged in series with 10-mm spacing, 4-mm distance between the copper shells, and 10-mm distance from the walls of the duct. Each cell is covered with a 2-mm-thick PCM layer and 1 mm thickness of copper shell. The whole arrangement and details of the different numerical domains are described in Table 3. The numerical model is validated with the experimental work carried out on the 6S1P HBTMS battery module, where cells are connected in series as shown in Fig. 2(d). Four thermocouples are attached to measure the 1st, 2nd, 5th, and 6th battery surface temperatures at the middle position as it is found from stage 1 that the temperature of the battery cell is slightly higher at the middle position. Then, the PCM in the liquid state is poured in the gap available between the battery cell and copper enclosure, and they are arranged by maintaining a 10 mm gap between them. The battery module is placed in a rectangular duct and added with a speed-controlled blower at the inlet. The setup is operated by maintaining an atmospheric temperature of 27 °C, and inlet air velocity of 2.5 m/s.

The maximum temperature of 38.2 °C and minimum temperature of 36.5 °C were noted experimentally in the 6S1P HBTMS battery module. The corresponding values with the numerical study were 39.4 °C and 38.3 °C respectively, which are reasonably accurate for the proposed investigation. A comparison of the temperature profiles of the individual cells obtained numerically and experimentally is shown in Fig. 13. It can be seen that the numerical model slightly overpredicts the cell temperatures, which could be due to unaccounted heat losses from the system. One of the main reasons for unaccounted losses could be the constant heat generate rate assumption in the numerical model. In a battery, the heat generation would increase slowly at the start and then become constant. Nevertheless, the prediction pattern of the numerical model is consistent, and therefore, it is used for further investigations. It can be observed from the temperature contour shown in Fig. 14 that the thermal nonuniformity is decreased (both radially and axially) in HBTMS. When compared with the 6S1P model, approximately 0.14 °C reduction in ΔT is achieved by the proposed HBTMS. Similarly, Tmax in the 6S1P module and the HBTMS 6S1P module are 44.2 °C and 42.1 °C, respectively, which shows a reduction in Tmax as well.

Fig. 13
Comparison between numerically and experimentally obtained temperature profiles of each cell in the 6S1P HBTMS battery module
Fig. 13
Comparison between numerically and experimentally obtained temperature profiles of each cell in the 6S1P HBTMS battery module
Close modal
Fig. 14
Contour of temperature and melt fraction in the proposed HBTMS 6S1P model
Fig. 14
Contour of temperature and melt fraction in the proposed HBTMS 6S1P model
Close modal

The parametric study was conducted to optimize the thickness of PCM in the HBTMS at an inlet air velocity of 2.5 m/s. The upper limit for PCM thickness was kept at 4 mm as a further decrease in the gap between copper shells was not recommended due to heat accumulation and hot spot formation between the copper enclosure. Therefore, the study was conducted by considering the PCM thicknesses from 4 mm to 1 mm in the interval of 1 mm. The effects of change in PCM thickness on the surface temperature of the battery cell and melt fraction of PCM for the 6S1P HBTMS battery module are shown in Table 6. It has been found that the system satisfies both the thermal criterion when the PCM thickness is more than 2 mm. For 1-mm PCM thickness, the thermal nonuniformity is slightly higher than the optimal limit, as well as the PCM shows complete melting. Therefore, another case with PCM thickness of 1.5 mm was studied keeping all the other conditions unchanged. It was found that the surface temperature of all the cells was within the optimal range except for the sixth cell which exceeded by 0.2 °C. Therefore, a PCM thickness of 2 mm is considered for the next study for the optimization of inlet air velocity.

Table 6

Surface temperature of battery cells and melt fraction of PCM for 6S1P HBTMS battery module with variable PCM thickness

PCM thickness (mm)Maximum surface temperature (°C)Thermal nonuniformity (ΔT)
Cell 1Cell 2Cell 3Cell 4Cell 5Cell 6
437.237.537.737.737.838.10.9
338.338.538.738.738.939.41.1
240.141.241.341.641.842.11.4
1.543.443.644.444.444.745.21.8
145.544.645.345.346.547.62.1
PCM thickness (mm)Melt fraction
PCM 1PCM 2PCM 3PCM 4PCM 5PCM 6
40.670.690.750.760.800.85
30.810.850.870.890.890.92
20.840.910.960.970.970.99
1.50.950.991111
1111111
PCM thickness (mm)Maximum surface temperature (°C)Thermal nonuniformity (ΔT)
Cell 1Cell 2Cell 3Cell 4Cell 5Cell 6
437.237.537.737.737.838.10.9
338.338.538.738.738.939.41.1
240.141.241.341.641.842.11.4
1.543.443.644.444.444.745.21.8
145.544.645.345.346.547.62.1
PCM thickness (mm)Melt fraction
PCM 1PCM 2PCM 3PCM 4PCM 5PCM 6
40.670.690.750.760.800.85
30.810.850.870.890.890.92
20.840.910.960.970.970.99
1.50.950.991111
1111111

4.3.2 Parametric Study for Optimization of Inlet Air Velocity.

The parametric study was conducted to optimize the inlet air velocity, which decides the size and capacity of the blower/fan. The effect of change in the inlet air velocity on the surface temperature of battery cells and melt fraction of PCMs for the 6S1P HBTMS battery module is given in Table 7. It can be seen that the Tmax and ΔT are within the optimal temperature range when the inlet air velocity is 2.5 m/s with the proposed HBTMS 6S1P module. Further increase in the inlet air velocity decreases both the thermal factors. Consequently, a parametric study was conducted to study the proposed HBTMS at lower inlet air velocities as shown in Table 7. The decrease in inlet air velocity leads to an increase in the cell surface temperature and thermal nonuniformity. Initially, the last cell temperature rises faster; however, at much lower air velocities, the first cell temperature is more affected. The effects on the melt fraction of PCM for the 6S1P HBTMS battery module with variable inlet air velocities are shown in Table 8. There is a proper utilization of PCM as complete melting is observed by the end of 900 s when the thickness is maintained at 2 mm.

Table 7

Surface temperature of battery cell for 6S1P HBTMS battery module with variable inlet air velocities

Inlet velocity (m/s)Maximum surface temperature (°C)Thermal nonuniformity (ΔT)
Cell 1Cell 2Cell 3Cell 4Cell 5Cell 6
0.146.147.251.7252.1752.2952.686.58
0.1545.9347.3150.6751.851.7752.116.18
0.245.1247.349.8751.1751.6751.015.89
0.2544.3346.6346.7947.9548.7549.55.17
0.542.8146.8747.2947.3547.4147.624.81
142.5443.143.1743.9144.3646.063.52
1.541.7543.6843.4444.1644.3544.913.16
241.2842.2342.5443.143.0643.672.39
2.540.941.1841.341.6641.8342.071.17
340.5940.8240.8241.1741.0241.210.62
3.540.2840.4740.9140.8240.9241.020.74
Inlet velocity (m/s)Maximum surface temperature (°C)Thermal nonuniformity (ΔT)
Cell 1Cell 2Cell 3Cell 4Cell 5Cell 6
0.146.147.251.7252.1752.2952.686.58
0.1545.9347.3150.6751.851.7752.116.18
0.245.1247.349.8751.1751.6751.015.89
0.2544.3346.6346.7947.9548.7549.55.17
0.542.8146.8747.2947.3547.4147.624.81
142.5443.143.1743.9144.3646.063.52
1.541.7543.6843.4444.1644.3544.913.16
241.2842.2342.5443.143.0643.672.39
2.540.941.1841.341.6641.8342.071.17
340.5940.8240.8241.1741.0241.210.62
3.540.2840.4740.9140.8240.9241.020.74
Table 8

Melt fraction of PCM for 6S1P HBTMS battery module with variable inlet air velocities

Inlet velocity (m/s)Melt fraction
PCM 1PCM 2PCM 3PCM 4PCM 5PCM 6
0.1111111
0.15111111
0.2111111
0.250.9911111
0.50.9911111
10.9911111
1.50.950.980.99111
20.930.990.99111
2.50.840.910.960.970.970.99
30.760.790.860.860.880.91
3.50.620.690.710.770.770.80
Inlet velocity (m/s)Melt fraction
PCM 1PCM 2PCM 3PCM 4PCM 5PCM 6
0.1111111
0.15111111
0.2111111
0.250.9911111
0.50.9911111
10.9911111
1.50.950.980.99111
20.930.990.99111
2.50.840.910.960.970.970.99
30.760.790.860.860.880.91
3.50.620.690.710.770.770.80

Hence, it is important to optimize the design and operating parameters such as PCM thickness, cell spacing, and fluid velocity for the adequate performance of the HBTMS. In the present work, it is observed that both the thermal factors could be maintained within the optimal range at the low inlet air velocity of 1.5 m/s. Therefore, the proposed HBTMS can satisfactorily operate at the design and operating conditions of 2-mm PCM thickness, 10-mm battery cell spacing, and 1.5 m/s inlet air velocity. It should be noted that alternative optimal conditions could be achieved with such HBTMS, like lower cell spacing can be achieved at the expense of higher fluid velocity. It depends on the product requirements and use cases, which makes the HBTMS more flexible.

5 Conclusions

In the present study, a PCM-based HBTMS with air cooling is developed. Its transient thermal behavior is studied both experimentally and numerically. Based on the results of these analyses, a comprehensive optimization approach is suggested and the performance of the optimized HBTMS is demonstrated. The following conclusions are drawn from the present investigation:

  1. The use of a passive cooling approach with PCM in the BTMS requires optimization of PCM thickness to achieve the required performance. In the present work, PCM thicknesses of 5–12 mm around the battery cell showed satisfactory performance. The use of less and high PCM leads to poor heat dissipation and excess PCM utilization respectively.

  2. A BTMS can also be developed using the active cooling approach, e.g., with air as the cooling medium. In such a system, battery cell spacing can be optimized considering a constant inlet velocity condition. In the present work, it is found to be more than 8 mm in the 6S1P battery module when the inlet air velocity is maintained at 2.5 m/s.

  3. On the other hand, the inlet air velocity can be optimized for a given battery module. In the present work, the optimized inlet air velocity is found to be 2 m/s for a constant cell spacing of 10 mm in the 6S1P battery module.

  4. A combined PCM and air convectional cooling-based HBTMS is proposed to offer improved performance, design flexibility, and higher reliability. The studied HBTMS is optimized at 2-mm PCM thickness, 10-mm battery cell spacing, and 1.5 m/s inlet air velocity.

  5. The optimized HBTMS shows a 53.95% reduction in PCM mass utilization as compared to BTMS in stage I (considering a minimum thickness value of 6 mm). In addition to that HBTMS also offers up to 40% reduction in active cooling requirement as compared to BTMS in stage II.

Author Contribution Statement

Kundrapu Ayyappa Swamy: Methodology, numerical work, experimental work, validation, visualization, and writing—original draft. Saket Verma: conceptualization, resources, writing—review and editing, supervision, and Project administration.

Acknowledgment

We would like to acknowledge the support of the Birla Institute of Technology and Science, Pilani campus, Pilani (BITS Pilani) under the Research Initiation Grant (RIG). We sincerely thank Coulomb Li-Tech India for their support of experimental investigations.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The authors attest that all data for this study are included in the paper.

Nomenclature

h =

hour

s =

second

g =

gravity, m/s2

h =

specific enthalpy, kJ/kg

k =

thermal conductivity, W/m-K

m =

meter, m

u =

velocity in X-direction

v =

velocity in Y-direction, m/s

H =

height, m

W =

watt, W

C =

charge rate, C-rate

H =

enthalpy, kJ/kg

L =

length, m

S =

moment source term

T =

temperature, °C

V =

voltage, V

W =

width, m

Cmushy =

mushy zone constant

Cp =

specific heat, J/kg-K

Tliquidus =

temperature of liquid PCM

Tm =

melt temperature, °C

Tmax =

maximum temperature of the cell/module, °C

(Tmax)PCM =

maximum temperature of cell enclosed in PCM, °C

Tpcm =

temperature of PCM domain, °C

Tref =

reference temperature, °C

Tsolidus =

temperature of solid PCM, °C

x, y =

position along axis

Ah =

amp hour

ΔH =

enthalpy change, kJ/kg

Greek Symbols

β =

liquid volume fraction

ε =

energy dissipation rates, m2/s3

k =

turbulent kinetic energy, m2/s2

μ =

dynamic viscosity

ρ =

density

=

liquid fraction

Subscripts

liquid =

PCM liquid state

max =

maximum

pcm =

phase change material

solidus =

PCM solid state

Acronyms

BTMS =

battery thermal management system

EVs =

electrical vehicles

HBTMS =

hybrid battery thermal management system

HEVs =

hybrid electric vehicles

HP =

heat pipe

ICE =

internal combustion engine

Li ion =

lithium ion

OM =

organic material

PCM =

phase change material

SOC =

state of charge

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