Experimental and Theoretical Analysis of Immersion Cooling of a Li-Ion Battery Module

Li-ion cells play a key role in energy storage and conversion in electric vehicles (EVs) and several other engineering systems. Improving the energy density and discharge rates in battery packs is of critical importance for maximizing the performance and driving range of EVs. A key technical challenge here is the strong temperature sensitivity of Li-ion cells, including rapid performance degradation at both low and high temperatures [1,2]. Moreover, serious safety concerns related to thermal runaway and fire occur when the battery temperature exceeds a certain threshold [3]. Therefore, a well-designed thermal management system for the automotive battery pack is critical [4]. Since experimental measurements may often be time-consuming and expensive, the development of robust theoretical models and numerical simulations is essential for scientific understanding and engineering optimization [3].

A vast amount of past work on modeling and simulations for battery thermal management is already available, for both steady-state [5] and transient [6] conditions. A conjugate analytical model for flow cooling of a battery pack has been proposed [7]. Thermal resistance network-based modeling has been carried out to predict the performance of an air-cooling system coupled with a micro heat pipe array for cooling a prismatic battery pack [8]. Multiscale multidomain modeling has been carried out for a liquid-cooled Li-ion battery pack of 24 prismatic cells, which claims to maintain the peak temperature in the battery pack under 40 ℃ and maximum temperature difference across the whole battery pack around 5 ℃ even at a discharge rate of 5 C [9]. Another study using COMSOL Multiphysics has been carried out to compare forced air convection, heat pipe, and heat pipe with copper sheets, for which, an improvement in temperature uniformity of 39%, 67%, and 73%, respectively, has been reported [10]. Analytical models have also been used to predict the internal temperature of a Li-ion cell, which is an important parameter that is difficult to measure directly [11–14]. Thermal simulation models that account for the dynamics of electrochemical heat generation have also been reported [15,16]. Several studies have modeled thermal effects using resistance network techniques [15–21]. The sub-modeling technique has been used for resolving the large variation in length scales in thermal simulation of a large battery pack comprising thousands of cells [22].

Key battery thermal management techniques include cooling based on air [23,24], liquid [25,26], heat pipe [12,27], thermoelectric [28,29], and phase change materials [30,31]. Hybrid approaches that combine multiple techniques have also been reported [32–34]. Among these techniques, immersed liquid cooling offers very high efficiency due to high heat capacity and heat transfer coefficient, reduced equipment cost, and lower thermal expansion compared to phase change materials (PCMs) [30]. Unlike cooling by liquid flow in serpentine tubes between cells, immersion cooling enables direct cell-coolant contact, leading to greater heat dissipation, and thus reduced thermal runaway propagation [35,36]. Experimental investigation of immersion liquid cooling for a battery pack and comparison with a thermal management system based on serpentine tubes between rows of cells has been presented previously [35]. In another work, a 47% reduction in battery pack peak temperature at 3 C discharge rate was reported for immersion cooling with a dielectric fluid compared to natural convective cooling [36]. A study of preheating the battery pack in a cold ambient using a hot fluid flowing around the battery in an immersed arrangement has been reported. It was found that preheating resulted in very good temperature uniformity, within 4 ℃ throughout the battery pack [37]. A numerical study of fast-charging of a Li-ion battery pack based on direct immersion cooling using hydrofluoroether showed improved energy density and lower coolant pump power consumption [38]. Despite the clear benefits of immersion cooling, however, there remains a lack of work that investigates the impact of immersion cooling on the electrochemical performance of the battery pack. Such concerns may arise, for example, due to prolonged exposure to the dielectric fluid and the possibility of non-uniform cooling of cells during immersion cooling.

This paper presents an experimental and simulations-based investigation of the thermal and electrochemical impact of immersion cooling during fast charging of a Li-ion cell module. The module is subjected to a fast charge duty cycle comprising fast charge profiles interspersed with rest periods and nominal discharge for up to five weeks. A Reference performance test (RPT) is carried out each week to characterize aging effects by measuring discharge capacity fade, power fade, and resistance growth. Electrochemical impedance spectroscopy (EIS) measurements are carried out to identify possible degradation mechanisms in Li-ion batteries such as lithium plating and their effects. Analytical and numerical simulation models are developed to identify the dominant thermal and electrochemical effects of immersion cooling. A comparison between measurements and models is carried out in order to help understand the impact of immersion cooling on cell aging, and possible underlying mechanisms.

The rest of this paper is organized as follows: Sec. 2 describes the experimental setup and measurements carried out in this work. Section 3 presents a theoretical heat transfer model and simulations carried out to model the system-level thermal dynamics during immersion cooling and to estimate cell internal temperature. Key results are discussed in Sec. 4, followed by conclusions in Sec. 5.

Despite the significant potential for effective thermal management of Li-ion cells using immersion coolants, there are no standards available for evaluating the performance of immersion coolants. This section describes an experimental test bed for investigating the immersion cooling of a battery pack. Key experimental details, including cells, coolants, measurement setup, and process, are described as follows.

A seven-cell module shown in Fig. 1(a) is constructed using LG Chem (Seoul, South Korea) M50T 21700 cylindrical cells with lithium nickel manganese cobalt oxide (NMC) cathode and graphitic anode. This is a commonly used Li-ion cell chemistry. The nominal cell capacity is 18.2 Wh. The manufacturer-specified cell impedance of 30 mΩ [39] is assumed to remain constant. As shown in Fig. 1(a), the cells are interconnected in a 7PS1 configuration using spot welding on Nickel metal bus bars to form a flower-shaped cross section. The cell-to-cell gap is approximately 0.5 mm and remains fixed. Omega K-type thermocouples are glued using thermal paste and taped on the cylindrical surface of each cell. The SBT-2050 Power Cycler from PEC Corp., Boca Raton, FL, is used for implementing a fast charge current profile. Data acquisition from all thermocouples is carried out using an National Instruments (Austin, TX) Compact-RIO-based data acquisition system.

In addition, for experiments involving internal temperature measurements, the central cell in the flower configuration of the 7PS1 module is drilled axially from the negative tap side (Fig. 1(b)). The drill bit is handled carefully to avoid damage to the jelly roll inside the cell. Once the thermocouples are inserted inside the cell, the opening is quickly sealed with marine epoxy [11,40]. The locations of thermocouples for testing during baseline and immersion cooling cases are shown in Fig. 2(a). For the experiment with internal temperature monitoring, thermocouples are also placed in the core cavity of the jelly roll of the cell, as indicated by locations 1, 2, and 3 in Figs. 1(b) and 2(b).

Figure 3 presents pictures of the overall experimental setup and the specific test rig that houses the battery pack. Figure 4 shows a schematic of the fluid flow circuit and related instrumentation. The module is positioned centrally in the test rig, which is customized to allow coolant flow around the cells. The test rig is large enough to accommodate the module with a clearance of around 5 mm between the outer cells and walls of the test rig. This avoids direct electrical contact and offers sufficient space for thermocouples and other essential wirings from the module to the cell cycler. At a flowrate of 1.5 liters per minute (LPM), the liquid sweeps out the entire coolant volume in the test rig every 10–20 s. The test rig is designed with only 38% excess fluid volume compared to the volume of seven cells, resulting in a compact configuration with minimum add-on weight to remain conducive for practical applications. Coolant flowrate and temperature are controlled using a flow control valve and a three-way mixer valve, respectively, as shown in Fig. 4. The mixer valve mixes cold fluid from a heat exchanger leg and hot fluid from the heater leg to produce the target temperature. As shown in Fig. 5, the fluid inlet and outlet are on one of the side faces and the top face, respectively. Both are instrumented with thermocouples to measure inlet and outlet coolant temperatures. In addition to baseline measurements without any immersion cooling, fast charge aging tests are also conducted for a single-phase immersion coolant liquid, referred to as “Fluid X.” Thermal conductivity, heat capacity, and mass density of the liquid are 0.143 Wm⁻¹ K⁻¹, 2.1 kJkg⁻¹ K⁻¹, and 806 kgm⁻³, respectively.

Experiments are conducted using K-type thermocouples to measure the surface temperatures of the battery cells. It is important to note that K-type thermocouples have associated uncertainties in temperature measurements, around ±1–2 °C. To minimize measurement errors, the placement of thermocouples is carried out carefully. Measurements are repeated multiple times to ensure consistency and repeatability.

Measurements are carried out with two key goals—to evaluate cell performance and capacity fade due to multi-week cycle aging, and to monitor the internal temperature of the cell for a few cycles carried out in a 24-hour period. Performance with immersion cooling at 1.5 LPM flowrate and 25 °C inlet temperature is compared with the baseline case with no immersion cooling.

The module undergoes charge–discharge cycling for 5 days, as shown in Fig. 6(a), followed by RPT on the sixth and seventh days, as shown in Fig. 6(b). Charge–discharge cycling comprises 1 hour of rest period, followed by constant current constant voltage (CCCV) charging at a C-rate of 0.7 C, which is the maximum continuous current specification, then 1 hour rest, and finally constant current (CC) discharge at 0.2 C, corresponding to the nominal current. The module is cycled between 4.2 V and 2.5 V. Cell capacity at the end of each charge–discharge cycle is determined by charging the module at 0.3 C rate under CCCV conditions to 100% SOC and then discharging at 0.2 C rate under CC conditions to measure the static capacity in Amp-hours. Note that per battery nomenclature, the C-rate of a charge/discharge process refers to the reciprocal of the number of hours taken to complete the process. The larger the C-rate, the more aggressive is the process.

There are three components to the RPT, as shown in Fig. 6(b). Static capacity measurement assesses the energy storage capability of a cell by measuring its capacity to deliver a constant current over a specified time, typically at a slow discharge rate. In contrast, power capacity measurement evaluates the ability to deliver high currents for brief durations, often in seconds or less, representing its power output potential under load. Finally, pulse power fade measurement focuses on the ability to sustain repeated high-current pulses, simulating real-world, high-demand scenarios. These three measurements are interconnected—static capacity provides insights into total energy storage, power capacity quantifies the ability to meet sudden power demands, and pulse power fade testing reveals how these characteristics evolve under stress or repeated use, which is essential for optimizing battery performance and lifespan in applications like electric vehicles and portable electronics. The RPT shown schematically in Fig. 6(b) combines each of these measurements to obtain a comprehensive picture of the health of the module at any given time. RPT similar to the present work has been used in past work to understand how cell characteristics change during cyclic aging [41].

EIS is a non-invasive frequency response technique to highlight electrochemical phenomena within a cell, including patterns of lithium plating. Each EIS measurement is carried out while the pack is in ambient air at 25 °C. A Gamry 1010 EIS analyzer (Warminster, PA) is used to stimulate the cell with sinusoidal currents of amplitude 20 mA with frequencies from 0.1 Hz to 5 kHz. The resulting frequency response Nyquist plot in the complex domain helps understand the lithium plating process and other internal electrochemical processes [42]. For example, Fig. 7 shows a typical Nyquist plot showing different frequency regimes that may be used to understand different transport processes that occur within the cell. Specifically, the minima shown in Fig. 7 provide information about the nature of lithium plating in the cell. Since this method is ex-situ, an impulse response-based pseudo-EIS procedure [43] is also carried out. This procedure can be carried out real time or in situ during life testing or in an actual battery management system (BMS) in a vehicle or grid storage. The real impedance value is extracted from both types of EIS tests and may be plotted as a function of the State of Charge (SOC) of the cell. These electrochemical measurements help understand the dynamics of lithium plating that may occur in the cell, especially at large C-rate.

Theoretical and simulations-based analysis is carried out for an improved understanding and interpretation of experimental data, particularly towards understanding the impact of immersion cooling on cell aging. For the immersion cooling method, radiative heat dissipation is likely to be negligible due to the continuous flow of a dense liquid, such as the one used here, around the cells. This analysis first focuses on showing that radiation effects are negligible and investigating the likelihood of large temperature differentials between the core and surface of the cell. For the baseline case, the module is assumed to be surrounded by stagnant air at room temperature, with heat transfer occurring due to natural convection alone. In contrast, in cases where immersion coolant due to liquid flow around the module occurs, the dominant heat transfer is assumed to be forced convection. The central cell of the module experiences the most severe thermal conditions compared to other cells on the periphery of the module. Measured surface temperatures of all seven cells indicate that the temperature difference between cells in the module is within 1 ℃ for the immersed cooling case, and within 3 ℃ for the baseline case, with the highest temperature rise in the center cell in both cases. Therefore, all the analysis carried out in this section is based on measurements of the center cell.

Finally, the analysis carried out in this paper focuses only on the charging process, due to much higher temperatures observed during relatively faster charging than during discharge.

In this sub-section, analytical modeling for the baseline case as well as the immersion cooling case is described.

Equations (3)–(5) are numerically solved using Simulink software in order to determine T_Cell, T_Surf, and T_Core as functions of time.

Equations (3)–(5) are ordinary differential equations (ODEs) that govern the cell temperature distribution as a function of time. These equations are converted to a block diagram in the Simulink workspace using integrator, algebraic, and functional blocks from various libraries. ODE45 solver is used for numerical integration of the ODEs. Temperature, heat estimates, and other state data are collected into the workspace for post-processing.

A finite volume model is developed in ANSYS Fluent in order to visualize the nature of fluid flow in the experimental setup. The geometry of the experimental setup is created in ANSYS SpaceClaim. Enclosure and battery module are modeled according to the description in Sec. 2.1. Suitable fluid domains are created to simulate fluid flow around the cells inside the enclosure. Grid independence is verified, resulting in a mesh comprising around 1.5 million nodes and 9 million elements. Only the momentum equations are solved in these simulations, since the focus is to visualize the flow field to verify and support the assumptions used in analytical modeling. Values of convective heat transfer coefficients are obtained from these simulations, for use in Simulink models described in Sec. 3.2.

Figure 9 plots the measured percentage discharge capacity fade as a function of the number of RPTs, where an RPT is carried out at the end of every week of cycling. Each RPT in Fig. 9 represents roughly one week of calendar time and 20 fast charge cycles. It can be observed that after four RPTs, the total capacity fade in the presence of immersion cooling is around 5%, compared to 4.2% for the baseline case. The more rapid deterioration of battery capacity in the case of immersion cooling may be somewhat counter-intuitive. Based on aging data on these cells at various temperatures measured in the past, Fig. 10 shows that an average rise of temperature of around 2 °C for the immersion-cooled cells is needed to explain the increased capacity fade. The model which calculates the capacity fade for LG M50T 21700 cell cycling is deduced from an experimental data set acquired from the cell characterization testing at beginning-of-life.

The following hypotheses are tested as possible explanations for this phenomenon:

1. (Hypothesis A) Reduced radiation heat transfer due to lower emissivity caused by fluid occlusion: It has been reported [47] that certain coatings on cylindrical cells may result in high surface emissivity and thus enhanced radiation heat transfer. This may result in faster heat dissipation in the baseline case compared to the immersion cooling case.

2. (Hypothesis B) Greater non-linear thermal gradient inside the jelly roll due to aggressive surface cooling: It has been shown [48,49] that a non-uniform thermal gradient developed inside the cell directly affects the performance and eventually deteriorates the life of the cell. The temperature gradient may result in simply a higher core temperature or an intermediate maximum inside the jelly roll if the core temperature is not significantly high. Using estimates of convective heat transfer coefficient for the baseline and immersion cooling cases in the present work, the value of the Biot number for these cases is estimated to be around 0.02 and 0.57, respectively. This indicates that there may be a temperature maxima inside the jelly roll in the immersion cooling case. Further, analytical modeling of surface-cooled and tab-cooled Li-ion battery arrangement [48,49] has shown that the tab-cooled cell has better performance despite greater operational temperature, compared to a surface-cooled cell, which has a much more non-homogeneous temperature distribution. This finding provides justification to consider this hypothesis.

3. (Hypothesis C) It is well-known that Li-ion cells exhibit lithium plating at low temperatures [2]. The aggressive cooling in the immersion cooling case may result in the surface temperature being close to ambient even while the battery is being fast charged. This may result in increased lithium plating and higher capacity fade. EIS measurements are carried out to explore this hypothesis further.

For baseline case experiments, the surrounding medium is stagnant air and, thus, the dominant heat transfer mechanism is natural convection around the cells, with convective heat transfer coefficient h varying as a function of air temperature [50,51]. To explore Hypothesis A discussed in Sec. 4.1, a radiative heat transfer term is considered. A suitable value for the emissivity of the outer cell surface, ɛ = 0.7 [47] is used. Surface temperature of the cell can be calculated by solving Eq. (3) in Simulink, initially considering the effect of radiative heat transfer. Referring to Fig. 11(a), a transient thermal distribution for the surface temperature of the cell over multiple charge–discharge cycles shows that the theoretical model that includes radiation does not match well with the experimental results. The consideration of radiative heat dissipation along with convective heat dissipation results in under-estimation of the surface temperature. On the other hand, referring to Fig. 11(b), without consideration of radiative heat dissipation, i.e., ɛ = 0, there is much better agreement, with a surface temperature rise of approximately 30 ℃. This shows that radiation is not likely to be a dominant heat transfer mechanism in the immersion cooling conditions considered here. Based on this analysis, Hypothesis A is ruled out.

A comparison of experimental measurements of immersion cooling case and the analytical model based on Eq. (3) presented in Fig. 12 shows a very good agreement between the two. Due to aggressive forced convective cooling, the surface temperature of the cell rises only by 1–2 ℃, compared to a 30 °C rise for the baseline case. Only convective heat transfer terms are considered in the model. From the numerical simulation model, which considered the mixed (annular and peripheral) flow effects and previous literature [50,52], a value of h = 90 Wm⁻² K⁻¹ is extracted for the lumped convective heat transfer coefficient for use in the Simulink model above.

For a set of parameter values consistent with experimental conditions, visualization of the flow field from the Fluent model is shown in Fig. 13. The flow field is as anticipated, and low flow resistance regions are clearly delineated. There is no significant flow between the cells, indicating that the center cell has the least direct exposure to fluid. This also shows that the location of the ports can cause significant stagnant regions, leading to asymmetric cell cooling in larger battery packs. It can be observed that the flow field is a combination of annular as well as circumferential flow, i.e., an axial flow along the cell length and a radial flow around the cell radius, respectively. The 0.5 mm gap between cells offers a much greater flow resistance compared to the 5-mm gap between cells and enclosure walls, which, in turn, promotes annular flow even if the inlet and outlet are designed to achieve circumferential flow. These results support the assumption related to the convective heat transfer coefficient to be around 90 W/m² K.

Internal temperature measurements are carried out in one of the cells in the immersed module to understand whether the core temperatures become too high during aggressive surface cooling. The goal of this experiment and analysis is mainly to explore Hypothesis B presented in the previous section. Equations (4) and (5) are solved simultaneously using Simulink to calculate the surface and core temperature of the cell, respectively. A comparison of measured and theoretically predicted internal and surface temperature is shown in Figs. 14 and 15 for baseline and immersion coolant cases, respectively. In both cases, there is good agreement for surface and core temperatures in the fast-charging region. The value of thermal conductive resistance—R_Cond—is based on previously reported experimental studies [46], which matched core temperature measurements with an analytical model to extract this parameter. The temperature difference between the core and surface temperatures of the cell in both cases is found to be around 1 ℃, which eliminates the possibility of a higher temperature difference from the core to the surface in case of immersion cooling. As a direct result of this observation, Hypothesis B may be ruled out. It is important to note, however, that this does not fully preclude the possibility of higher temperatures in the middle of the jelly roll with low temperatures at the core and surface.

To further understand other possible unobservable internal states, a sensitivity analysis is carried out to understand the sensitivity of the temperature gradient to varying properties such as thermal conductivity, convection heat transfer coefficient, and charge current. Results are presented in Fig. 16. It can be observed that while the core-surface temperature difference is influenced by the conduction resistance, it is largely insensitive to the value of the convective heat transfer coefficient. However, smaller values of convective heat transfer slow down the rate of temperature change, thus increasing the average temperature of the jelly roll. Charging current also has a prominent effect on the core-surface temperature difference, since heat generation in the cell directly depends on current. When interpreted in the context of fast charge rates for immersed battery packs, this result indicates that without proper thermal management, increasing charge current is detrimental to battery life due to higher internal temperatures. A key takeaway from the sensitivity analysis is related to the distribution of internal thermal conductivity of the jelly roll. The jelly roll can be considered as layers of cells in series and, as such, the thermal conductivity of each layer can change with internal temperature distribution and resistance inhomogeneity. If the thermal conductivity is thus lower in the middle of the jelly roll compared to the outer layers, this may lead to an excessive internal temperature peak. In this context, the Tesla-Panasonic 4680 cell design with dedicated tabs for inner layers may address the need to dissipate this inner heat more effectively. Unfortunately, a direct measurement is difficult since sensors are not usually embedded inside the jelly roll during manufacturing.

EIS results and analysis of beginning-of-life and aged baseline/immersion-cooled modules are shown in Fig. 17. These plots clearly show a shift in a mean resistance level, indicating aging and growth of Solid Electrolyte Interphase (SEI), which is a thin passivation layer formed due to electrolytic reduction on the anode. These observations, along with the expected increase in temperature gradient within the cell due to immersion cooling, support Hypothesis C as the explanation behind the increased capacity fade in immersion-cooled cells. Such an influence of temperature gradient within the cell on capacity fade has been observed in past papers as well, including one that directly investigated immersion cooling [41], and another, in which an inter-electrode temperature gradient is applied through other means [53].

Moreover, the valley and peak in the middle of the ZTR plots for the immersion cooling case are shifted slightly to the left compared to baseline and fresh cells. Such a shift suggests alterations in charge transfer kinetics and ion transport processes, which could be attributed to other phenomena, such as temperature-dependent changes in ion mobility and electrode kinetics under immersion cooling conditions. This subtle shift suggests that while lithium plating remains a primary contributor to the observed aging enhancement, other mechanisms might play a secondary role in the degradation process as well. Given the relatively minor nature of such a shift, it is likely that contributions from these factors toward capacity fade are minor compared to the contribution of Li plating.

EIS results and analysis of beginning-of-life and aged baseline/immersion-cooled modules presented in Fig. 17 shed light on the underlying mechanisms of battery degradation. These plots distinctly reveal a noticeable shift in the mean resistance level, which clearly indicates SEI growth and aging. In order to further investigate the fundamental reasons behind battery degradation under immersion cooling, it is essential to consider the unique thermal and electrochemical conditions of this environment. Immersion cooling exposes the cell to a consistently low operating temperature, which can promote lithium plating—a phenomenon where excess lithium ions plate onto the anode’s surface during charging. This plating, if not carefully managed, can lead to the formation of dendrites and SEI thickening, contributing to increased internal resistance and reduced capacity retention over time.

In summary, while lithium plating is expected to be the primary cause for increased aging under immersion cooling observed in this work, the additional subtle shifts in EIS data point towards the intricate interplay of various electrochemical and thermal factors that influence battery performance in this unique environment. Further investigations into these mechanisms are essential for optimizing battery design and prolonging operational lifetime in such cooling scenarios.

Note that all immersion cooling measurements in this work are carried out while the cell-to-cell gap is fixed at around 0.5 mm. This small gap is representative of the goal of maximizing energy storage density. While heat removal rate from the cell may potentially increase by increasing the cell-to-cell gap due to greater coolant flow in between, this must be weighed against the resulting reduction in energy storage density.

Despite the promising nature of immersion cooling for Li-ion battery packs, several open questions remain, especially about the impact of immersion cooling on the aging of cells. The present work contributes towards addressing one of these through experimental and theoretical investigation of capacity fade caused by immersion cooling. Through a hypothesis-driven comparison of experimental measurements and theoretical modeling, a comprehensive understanding of this interesting and important phenomenon is developed. All the expected hypotheses in this study, targeting accelerated aging of cells, are examined one by one. Experimental measurements for both surface and core temperatures agree well with the respective theoretical models, for both baseline and immersion cases. EIS results indicate that lithium plating is likely to be the root cause for the observed accelerated aging in the immersion-cooled case. It is expected that the analysis in this work may contribute towards further development and eventual implementation of immersion cooling for Li-ion battery packs in a manner that provides effective thermal management with minimal potential deterioration of electrochemical performance and lifetime.

This material is partly based upon work supported by CAREER Award No. CBET-1554183 from the National Science Foundation. The authors would like to acknowledge the efforts of Mickey Argo, Barrett Mangold, and Yanyu Wang toward various aspects of testing. The testing described in this work was funded by the SwRI EVESE consortium.

There are no conflicts of interest.

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

f =

frequency (Hz)

h =

convective heat transfer coefficient (Wm⁻² K⁻¹)

m =

mass of cell (kg)

t =

time (s)

A =

surface area (m²)

C =

specific heat (Jkg⁻¹ K⁻¹)

I =

current (A)

L =

length (m)

Q =

heat transfer (W)

R =

thermal resistance (KW⁻¹)

T =

temperature (K)

U =

open circuit voltage (V)

V =

voltage (V)

R_e =

electrical resistance (Ω)

ZTR =

impendence at transition frequency (Ω)

ɛ =

emissivity

σ =

Stefan–Boltzmann constant, (σ = 5.67 × 10⁻⁸ Wm⁻² K⁻⁴)

Cell =

cell

Cond =

conduction

Conv =

convection

Core =

core of the cell

f =

surrounding fluid

Gen =

generation

OC =

open circuit

P =

constant pressure

Rad =

radiation

Surf =

surface

tr =

transition

BMS =

battery management system

CC =

constant current

CCCV =

constant current constant voltage

EIS =

electrostatic impedance spectroscopy

EV =

electric vehicle

LPM =

liters per minute

NMC =

nickel manganese cobalt oxide

ODE =

ordinary differential equation

PCM =

phase change materials

RPT =

reference performance test

SEI =

solid electrolyte interface

SOC =

state of charge