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1 

 

 

 

Article 

Comparative analysis of electrochemical behaviors 

of lithium-ion batteries using the dual potential 

MSMD battery models: case studies on various 

thermal conditions 
Nirjhor Barua, Md. Arafat Rahman*, Md. Mamunur Roshid 

Department of Mechanical Engineering, Chittagong University of Engineering and Technology, Chittagong-4349,  
Bangladesh 

A R T I C L E   I N F O 
 

Article history: 
Received 12 May 2023  
Received in revised form 
25 June 2023 
Accepted 15 July 2023 
 
Keywords: 
Electrochemical, Simulation, Lithium-Ion Battery, 
Multi-Scale-Multi-Domain Model, Thermal 
Conditions 
 
*Corresponding author 
Email address:  
arafat@cuet.ac.bd 

 
DOI: 10.55670/fpll.fuen.3.2.1 

A B S T R A C T 
 

The high energy density and long cycle life of lithium-ion batteries make them 
a preferred option for electric vehicles. The efficiency and life span of lithium-
ion batteries are particularly sensitive to temperature; thus, it becomes 
essential to maintain an ideal temperature range. In this context, we 
concentrated on two widely used electro-chemistry (Equivalent Circuit Model 
and NTGK) models of a single cell of a dual potential MSMD Lithium-ion Battery 
while taking into account two significant methods of heat transfer under 
varying C-rates (0.25C, 1C, 2C, and 5C). We investigated the highest 
temperatures that two e-chemistry models could reach in varying ambient 
temperatures (typical summer, winter, and room temperature). The maximum 
temperature-raising tendency in the ECM due to natural convection is greater 
than the maximum temperature-raising tendency due to radiation regardless of 
the environmental temperatures and various C rates (0.25C, 1C, and 2C). 
However, the trend line of the maximum temperature rise is different in the 
NTGK model, where the maximum temperature rise due to radiation is greater 
than the maximum temperature rise due to convection for 0.25C, 1C, and 2C 
rates in -5°C and 40°C environmental temperatures. In the NTGK model, at 
0.25C, 1C, and 2C rates for winter and summer temperatures, the maximum 
temperature rise owing to radiation is larger than that due to convection. The 
NTGK model, however, produced somewhat superior findings for the radiation 
mode of heat transfer at ambient temperature. Therefore, it can be said that 
convection is a better thermal condition than natural convection in the NTGK 
model. 
 

 
1. Introduction  

Consumers are familiar with lithium-ion batteries after a 

great deal of research and use. It is commonly used in 

electrical items and electric cars. In recent years, a potential 

market for electric urban vehicles has formed, with 

competitive series among mobile device manufacturers. A 

special focus is being paid to developments in high-

performance lithium-ion batteries (such as a high level of 

energy density, high open circuit voltage, and minimal self-

discharge). Despite the widespread use of lithium-ion 

batteries in portable and small electronic devices, there are 

still some important issues that need to be resolved before 

practical applications of electrical vehicles (EVs), hybrid 

electrical vehicles (HEVs), and microgrids with significant 

energy storage capacity can be taken into account. Heat 

control and management are the most critical concerns in 

lithium-ion batteries, as excessive temperatures reduce 

charge/discharge efficiency and battery life and can 

potentially pose a safety risk. The significant temperature 

increase that occurs during the charging and discharging of 

HEVs and EVs is the main cause for worry in the heat 

regulation of lithium-ion batteries (LIBs) since it may result 

in thermal runaway. Understanding lithium-ion battery 

discharge behavior is crucial for the thermal management of 

LIBs in hybrid electric vehicles and electric vehicles [1]. 

Although a lot of research work has been conducted in recent 

years to enhance the thermal management of Li-ion batteries; 

however, relatively few have been devoted to the 

 

 

Future Energy 

Open Access Journal 

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May 2024| Volume 03 | Issue 02 | Pages 01-15 

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N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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investigation of the discharge behavior of lithium-ion 

batteries using ANSYS FLUENT. In common parlance, there is 

a relationship between battery temperature variation and 

electric efficiency. However, to make battery modeling 

simpler, it is frequently done by using a one-dimensional 

mass transfer model, which may work at least for cells with 

parallel plate electrodes. Chen and Evans suggested that due 

to the anisotropic thermal characteristics of a stack of many 

cells, a two -or three-dimensional model (of heat 

transmission) is required for battery thermal modeling and 

established a mathematical model to analyze the thermo-

physical properties of LIBs and LPBs (lithium polymer 

batteries) [2]. The purpose of thermal management was to 

analyze how factors in battery design and working conditions 

affect the temperature rise and profile and to assess the risk 

of thermal lag. The modeling results showed that under 

typical battery operation, battery temperatures were unlikely 

to reach the temperature that triggers thermal runaway, 

while during high-rate discharge (for example, during the 

relatively brief period of intense power extraction from a 

battery), heat may not be transferred out of a large cell stack. 

Localized heating may raise battery temperature to the 

thermal runaway onset temperature within one minute, 

according to research on heat transfer in the presence of 

extremely focused heat sources caused by battery abuse 

(such as short circuits). A Battery modeling at a constant 

environmental temperature of 25°C only, which was based on 

the localized heat production approach, considering a 

manganese oxide spinel/carbon cell using a 2D-coupled 

thermal-electrochemical technique, has been reported [3, 4]. 

The matrix and solution phases of the model include 

reversible, irreversible, and Ohmic heat. Most of the research 

works focused only on the convection mode of heat transfer 

for a better thermal management system of a Lithium-ion 

battery [5-7]. Van et al. [8] analyzed the effects of forced 

convection in the thermal management system. However, 

very few studies were carried out concerning radiation as the 

primary thermal condition. Hatchard et al. suggested that 

Radiation may be responsible for up to 50% of the heat that a 

Li-ion cell releases into the environment at oven exposure 

conditions. The label is usually the outermost surface of the 

cell, and its emissivity determines how well heat is 

transferred by radiation [9]. In this present study, we focused 

on two commonly used electro-chemistry (ECM and NTGK ) 

models of a single cell of a dual potential MSMD Lithium-ion 

Battery considering two dominant methods of heat transfer 

under various C-rates. We compared the maximum 

temperatures achieved by two e-chemistry models under 

different environmental temperatures (winter, room 

temperature, and summer). We compared the simulation 

results to explore which e-chemistry model performs better 

in thermal management systems under various 

environmental temperatures. 

2. Model development  

 In this study, ANSYS FLUENT (Version 2023 Ansys-R1) 

software was used to perform the computational fluid 

dynamic (CFD) analysis, which makes use of the finite-volume 

approach to separate the physics equations by figuring out 

the mathematical equations of the fluids. The combined heat 

transmission nodal points, which include two dominant heat 

transfer methods, including convection and radiation, are 

modeled using mathematical formulas. ANSYS commonly 

uses the following models to predict the behavior of chemical, 

thermal, and electrical processes in a battery: 

• Empirical Battery Model with Single Potential 

• Multi-Scale Multi-Domain Dual-Potential Battery Model 

(MSMD) 

2.1 Single-potential empirical battery model  

This model is based on investigations that have been 

performed by [10] and [11]. The integral form of the electric 

potential equation is as follows: 

∫ ∇. (σ∇ϕ)
v

dV = ∫ jdA
A

                                                 (1) 

The term "A" stands for apparent current density, "j" for local 

interface area, and "ϭ" for electrical conductivity. For the 

Single Potential Empirical Battery Model (SPEBM) The 

mathematical equations are used  according to [10] and [11]: 

j = Y(ϕc - ϕα - U)                                                                       (2) 

Here, (ϕc − ϕα) is the Difference between the cathode and 

anode side electric potentials at the separator interface, and 

Y and U are GU’s parameters. The single-potential empirical 

battery model (SPEBM) is limited in its capacity to study a 

wide range of electrochemical events in battery systems, 

especially those with complex geometries. 

2.2 Multi-scale multi-domain (MSMD) dual-potential 

battery model  

 By effectively linking the physics of batteries, battery 

discharge, safety, and thermal management, the multi-scale 

multi-domain (MSMD) battery model, sometimes referred to 

as the "multi-scale multi-domain" battery model, is used to 

study the discharge of lithium-ion batteries. The ANSYS 

FLUENT Dual Potential Multiscale Multi-Dimensional Battery 

Model (MSMD) addresses various physics in many solution 

domains by using a homogenous model related to a multiscale 

multidimensional method to resolve these constraints. It is 

important to note that the MSMD method uses three different 

electrochemical submodels, which are as follows: 

• The Newman, Tiedemann, Gu, and Kim (NTGK) model. 

•  Equivalent Circuit Model (ECM). 

•  Newman's Pseudo-2D (Newman's P2D) model. 

In this study, Equivalent Circuit Model (ECM) and The 
Newman, Tiedemann, Gu, and Kim (NTGK) models are 
discussed considering various C-rates, States of Charge, and 
Depth Of Charge. The ECM model, which works with batteries 
of all types, not only Li-ion batteries, is both affordable and 
highly adaptable. Using a 2D table that plots each parameter 
against the temperature and SOC. Notably, this is the only 
form where the impact of temperature is taken into account 
explicitly. In charge/discharge cycles when the electric load 
doesn't exhibit any sudden fluctuations, the NTGK model is 
satisfactory. Additionally, some models, such as the ECM, will 
be more accurate if the electric load changes quickly since 
they neglect the inertial variations. However, the pseudo-2D 
model, created by Newman's team utilizing a porous 
electrode and concentrated solution theory, is a physics-
based model that accurately simulates the transit of lithium 
ions in a battery [12]. Although Newman's pseudo-2D model 
is the most popular electrochemistry model, it is 
computationally more expensive than the other two e-



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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chemistry models [12]. So, for computational simplicity, only 
ECM and NTGK models are discussed in this study. 
The multiscale multidomain (MSMD)  technique is useful for 
assessing various physical parameters in several solution 
domains. Based on the conservation of charge during 
discharge, the Poisson equations are as follows: 

∇.(σ+∇ϕ+)ǀ Ω+ = -j                                                        (3) 

∇.(σ-∇ϕ-)ǀΩ- = +j                                                         (4) 

Here, the effective electrical conductivities of the positive and 
negative electrodes are σ+ and σ–, the phase potentials of the 
positive and negative electrodes are ϕ+ and ϕ –, the transfer 
rate of the volumetric current, calculated using an 
electrochemical submodel, is j (A/m3), and the domains of the 
positive and negative electrodes are Ω+ and Ω–, respectively. 
The functional form is determined by the electrode 
polarisation curve. H. Gu and Huo et al. found that j varies 
linearly with cell voltage [11]  and [13]. The NTGK model was 
suggested by Kwon et al. [14]: 

j = αY[U - (ϕ+ - ϕ-)]                                                                          (5) 

where, α is the specific area m2 /m3 of the electrode sandwich 
sheet in the battery cell, while U and Y are the empirical fitting 
parameters. The following U and Y functions were proposed 
by Huo et al. [13]. 

𝑈 = ao + a1(DOD) + a2(DOD)2 + a3(DOD)3 + a4(DOD)4 +
a5(DOD)5                           (6) 

𝑌 = bo + b1(DOD) + b2(DOD)2 + b3(DOD)3 + b4(DOD)4 +
b5(DOD)5                              (7) 

Where, the coefficients ai and bi (i = 0, . . . 5) are constants to 
be calculated experimentally. The fitting parameters used to 
determine the potential and current density distributions on 
the electrodes during discharge are shown in Table 1. 

Table 1. The fitting parameters were used in the NTGK model 

Parameter Constant Value 

 
a0 4.3104 

 a1 -1.9184 

U 
a2 2.8835 

a3 -6.8305 
 a4 -9.7601 
 a5 -4.8786 

 
b0 879.2 

 b1 -4606.2 

Y b2 -23,007.5 

b3 -86,540.6 
 b4 101,993.2 
 b5 -44,914.4 

 
According to Van-Thanh et al. [8], the nominal capacity 

multiplied by the C rate equaled the discharging current, and 

the discharge rate dictated how long a battery could operate. 

The lower the discharge rate, the longer the battery could 

operate. The maximum temperature was outside the 

manufacturer's working range at discharge conditions 

greater than 3C. Yi et al. [15] discovered that the ambient 

temperature is extremely sensitive during this sort of 

experiment. Because of the electron transfer during 

electrochemical processes, a substantial amount of heat is 

created in the Li-ion battery at a high discharge rate. The Li-

ion battery's heat generation q (W) is separated into three 

parts: reaction heat qr (W) polarisation heat qp (W), and Joule 

heat qj (W) [13]. The volumetric heat source in the battery cell 

can be expressed as irreversible heat from the internal 

resistance of the cell j[Voc - (ϕ+ - ϕ-)] and reversible heat 

from the electrochemical reaction inside the cell –jT
𝑑𝑉oc

𝑑𝑇
. 

Moreover, the heat produced by the resistance of the current 

collecting tab and the electrical contact between it and the 

lead wire is included, however, the heat produced by the 

resistance of the electrical contact between it and the lead 

wire is excluded. The entire amount of heat generated can be 

expressed as the equation given by Van-Thanh et al. [8]: 

q = j[ Voc- (ϕ+ - ϕ-) -T
dVoc

dT
  ]  + σ + V2 ϕ + σ -V2 ϕ –                        (8) 

where, Voc is the open-circuit potential of the cell (V), and T is 
the working temperature of the battery. 
We have considered two different dominant thermal 
conditions (convection and radiation) to study the cases of 
different discharge rates. According to Newton's law of 
cooling, the quantity of heat dissipated owing to the 
movement of a fluid (air) can be calculated using the following 
equation. 

qa= ha(Tb-Ta)                                                                (9) 

where Tb is the battery temperature, Ta is the ambient 
temperature and ha is the coefficient of air convective heat 
transfer coefficient of air, which is 5 W/𝑚2𝑘 in this present 
study. 
In this study, we illustrated the effect of radiation heat 
transfer in the thermal management system for both 
electrochemistry models (NTGK and ECM). Hence, we have 
considered the radiation emissivity of the battery cell to the 
maximum possible (ε = 1). The heat dissipation of a single cell 
of a Lithium-Ion Battery can be calculated by the equations 
used by Hatchard et al. [9]. 

Pr(T) = Aσε(T4-Tw 4)                                                        (10) 

where Pr(T) is radiation power in J/s as a function of 
temperature, A is the surface area, Tw is the temperature of 
the surrounding (assumed to be a black body), and ε is the 
emissivity of the surface. Emissivity (ε) is a dimensionless 
quantity between 0 and 1. It represents the fraction of 
blackbody radiation that the surface in question emits (a 
black body by definition has ε = 1), σ is the Stefan-Boltzmann 
constant (5.669 x 10-12 W/(cm2 K)). For values of T near Tw, 
Eq (10) can be expanded in a Taylor series:   

𝑃(𝑇) = 4𝐴𝜎𝜀𝑇𝑊
3 ∆𝑇 + 6𝐴𝜎𝜀𝑇𝑊

2 ∆𝑇2 + 4𝐴𝜎𝜀𝑇𝑊∆𝑇3 + 𝐴𝜎𝜀∆  

(11) 

Here, ∆T is the temperature difference between the surface 
and the surroundings and if ∆T= Tw-T, rearranging Eq (11) 
gives 

 
𝑃(𝑇)

𝐴∆𝑇
= 4𝜎𝜀𝑇𝑤

3 + 6𝜎𝜀𝑇𝑤
2∆𝑇 + 4𝜎𝜀𝑇𝑤∆𝑇2 + 𝜎𝜀∆𝑇3                      (12) 

Eliakim and Karmeli put out an accurate, acceptable, and 
comprehensive electrical battery model [16]. Figure 1 shows 
the electrical battery model that was used in the equivalent 



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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circuit model. The six-parameter ECM model has been 
adopted by ANSYS [1]. 

 
Figure 1. The electrical battery model is used in the ECM 
model [1] 
 
Where, Rseries=Rs, Rtransient_ S=RI, Rtransient_ L=R2. The 
voltage-current relationship can be obtained by solving the 
following mathematical formulas of electrical circuits used by 
Madani et al.  [1] and M. Chen et al. [16]: 

𝑉(𝑡) = VOCV(SOC) + V1 + V2 + R2(SOC)I(t)                                  (13) 

dV1

dt
= −

1

R1(soc)C1(soc)
V1 −

1

C1(soc)
I(t)                                                 (14) 

dV2

dt
= −

1

R2(soc)C2(soc)
V2 −

1

C2(soc)
I(t)                                             (15) 

d(soc)

dt
= −

I(t)

3600QAh
                                                                             (16) 

The open-circuit voltage, resistor resistances, and capacitor 
capacitances are dependent on the state of charge of the 
battery for a specific battery (SOC). These two dependents 
can be illustrated in various procedures in ANSYS as the 
following set of equations used by  [1] and [16]: 

Rs = ao + a1(SOC) + a2(SOC)2 + a3(SOC)3 + a4(SOC)4 +

a5(SOC)5                      (17) 

R1 = bo + b1(SOC) + b2(SOC)2 + b3(SOC)3 + b4(SOC)4 +

b5(SOC)5                    (18) 

C1 = co + c1(SOC) + c2(SOC)2 + c3(SOC)3 + c4(SOC)4 +

c5(SOC)5                  (19) 

R2 = do + d1(SOC) + d2(SOC)2 + d3(SOC)3 + d4(SOC)4 +

d5(SOC)5                 (20) 

C2 = eo + e1(SOC) + e2(SOC)2 + e3(SOC)3 + e4(SOC)4 +

e5(SOC)5                     (21) 

VOCs = fo + f1(SOC) + f2(SOC)2 + f3(SOC)3 + f4(SOC)4 +

f5(SOC)5                 (22) 

Chen's function is represented by the following set of 
equations [16] :  

Rs = a0exp[a1(soc)] + a2                                           (23) 

R1 = b0exp[b1(soc)] + b2                                            (24) 

C1 = c0exp[c1(soc)] + c2                                              (25) 

R2 = d0exp[d1(soc)] + d2                                           (26) 

C2 = e0exp[e1(soc)] + e2                                             (27) 

Vocv = f0exp[f1(soc)] + f2                                            (28)                                       

The source terms for the aforementioned equations are 

calculated as the following [1] : 

jECh = I/Vol                                                          (29) 

𝑞𝐸𝐶ℎ̇ =
I

Vol
[Vocv − (ϕ+ − ϕ−) − T 

dU

dT
]                                        (30) 

Where, Vol=The battery volume, I= Current, Vocv= The open 

circuit voltage, and  ϕ+& ϕ−are phase potentials. 

2.2.1 Physical modeling 

A single Lithium-Ion Battery cell has been modeled 

using ANSYS DESIGN MODULER. A three-dimensional 

rectangular-shaped battery cell is designed.  

 
Figure 2. Dimensions of a single-cell Li-ion battery 

In Figure 2, the geometry and dimensions of the single cell of 
the MSMD dual potential Lithium-Ion battery are illustrated. 
All the units are taken as millimeters. The thickness of the cell 
is taken as 2mm. The Geometry properties of the simulation 
are given in Table 2. 

Table 2. Geometrical properties of the experiment 

 

2.2.2 Mesh generation  

To assure the accuracy of transient simulations, grid 
number is crucial. Mesh details of the experiment are given in 
Table 3. 

2.2.3 Material selection 

There are mainly two types of material defined in the 

MSMD battery model. They are fluid and solid materials. The 

Fluid material is defined as ‘AIR’ and The solid material is 

defined with three different materials. The active cell zone is 

Details of Body  

Body FFF/Solid 

Volume  5.568e-05 m3 

Surface Area 0.057028 m2 

Faces 6 

Edges  12 

Verticles 8 

Fluid/Solid Solid  

Shared Topology Method Automatic  

Geometry Type Workbench 



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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defined as lithium hexafluorophosphate. The positive 

electrode is defined as aluminum and the negative electrode 

is defined as copper. The Material properties are provided in 

Tables 4-7. 

Table 3. Details of the mesh of the experiment 

Element order  Linear 

Element size 1.e-003m 

Growth rate  default by ANSYS (1.2) 

Average surface area  3.6582e-003 m3 

Maximum Layers 5 

Inflation Algorithm Pre-Executive 

Mesh metric  Skewness 

Nodes 97230 

Elements 63780 

 

Table 4. Active cell zone material properties (lithium 
hexafluorophosphate) 

Material name Lithium hexafluorophosphate 

Density 1500 kg/m3 

Specific Heat Coefficient 871 j/(kg K) 

Electrical conductivity  1e+07 S/m 

 
Table 5. Positive electrode material properties (Aluminium) 

Material name Aluminium 

Density 2092 kg/m3 

Specific Heat Coefficient 871 j/(kg k) 

Electrical conductivity 3.541e+07 S/m 

 

Table 6. Negative electrode material properties (Copper) 

Material name Copper 

Density 8978 kg/m3 

Specific Heat Coefficient 381 j/(kg k) 

Electrical conductivity 1e+07 S/m 

 
Table 7. Surrounding fluid properties (Air) 

Material name Air 

Density 1.225 kg/m3 

Specific Heat Coefficient 1006.43 j/(kg k) 

Electrical conductivity defined per UDS S/m 

Viscosity 1.7894e-05 

 

3. Results and discussion  

To analyze the results two dominant thermal conditions 

(Convection, and radiation) have been considered, and the 

two most common electrochemical models ( ECM and NTGK) 

are used. We have varied the C rates(0.25C, 1C, 2C, and 5C ) to 

analyze the thermal conditions of a single cell of the MSMD 

dual potential Lithium-ion battery. In the case of convection, 

certain boundary conditions are also taken into account. The 

temperature of the free stream temperature (-5°C,  27°C, and 

40°C) is varied considering different temperature conditions 

according to the average temperature of the winter and 

summer seasons of Bangladesh. The heat transfer coefficient 

is taken as  5 W/𝑚2𝑘 for each case of the free stream 

temperature. The initial heat generation rate is considered to 

be 0 W/m3. For radiation, we have considered the same 

temperatures for external radiation (-5°C,  27°C, and 40°C). 

We have considered the entire outer surface of the single cell 

of the Lithium-ion battery as a black body and therefore took 

the maximum emissivity of the surface (ε=1). The same 

thermal conditions are implemented in both ECM and NTGK 

models, and then we carried out our simulations for 1000 

iterations and 1500 seconds flow time. The lowest stop 

voltage and the highest stop voltage are considered as 3v and 

4.3v respectively, and the nominal capacity of the battery cell 

is considered as 14.6 Ah. 

3.1 Equivalent circuit model 
3.1.1 Thermal condition: convection 

Typically, heat generation within the LIBs occurs at 

normal temperatures as a result of charge transfer and 

chemical processes during charging and discharging [17, 18]. 

The total heat generation of battery discharge consists mainly 

of electrochemical reaction heat, ohmic heat, and active 

polarization heat. During the battery's discharge, these 

temperatures are generated in the positive electrode, 

electrolyte, and negative electrode. The three types of heat-

generating sources mentioned above vary in cell space. 

Lithium extraction and intercalation occur during the 

discharge electrochemical process at the anode/electrolyte 

and cathode/electrolyte interfaces, respectively. Lithium 

extraction heat and lithium intercalation heat are two 

different components of the electrochemical process heat. 

Similarly to this, the terms for lithium extraction and 

intercalation make up the active polarization heat. The anode 

and cathode electron-conduction resistance as well as the ion-

conduction resistance contribute to the ohmic heat [17]. To 

understand the thermal behavior and overall heat generation 

resulting from the aforementioned sources, we explored the 

ECM e-chemistry model based on different boundary 

conditions (Convection and Radiation) considering different 

environmental temperatures. Contours of total static 

temperatures in the whole cell of the dual potential MSMD Li-

Ion Battery are shown in Figure 3, Figure 4, and Figure 5 

considering the boundary conditions as convection for 

various environmental temperatures of 268K, 300K, and 

313K respectively. The nominal capacity multiplied by the C 

rate gave the discharging current its value. The discharge rate 

of a battery determines its working time, so the greater the 

discharge rate, the longer the battery's operating period will 

be. 

 



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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In Figure 3, temperature variations are shown in a single 
cell of dual potential MSMD Li-Ion Battery with various C-
rates (0.25C, 1C, 2C, and 5C ) with  Equivalent Circuit Model. 
Natural convection is considered in the boundary condition. 
The free stream temperature is taken as 268K (typical winter 
temperature in Asia). In Figure 3(a), for the 0.25 C rate, the 
minimum temperature is 268.6371 K, and the maximum 
temperature is 268.6637 K, which shows a very slight  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
increase from the environmental temperature (268K). In 
Figures 3(b), 3(c), and 3(d), the C-rate was varied from  1 C, 2 
C, and 5 C, and the maximum temperature was obtained 
275.0931 K, 295.6211 K, and 402.9109 K respectively. As we 
can see for increased C-rates, the maximum temperatures are 
increased rapidly. For 1 C, the maximum temperature 
increased by only 2.64%, while for the 2 C rate the battery cell 
showed a significant temperature rise of 10.30% from the 

Figure 3. Temperature variation in a single cell of dual potential MSMD Li-Ion Battery with various C-rates with  Equivalent 
Circuit Model considering free stream temperature of 268k: a) for 0.25C-rate, b) for 1C-rate, c) for 2C-rate, and d) for 5- rate 

 

Figure 4. Temperature variation in a single cell of a dual-potential MSMD Li-Ion battery with various C rates with an 
equivalent circuit model considering free stream temperature of 300k: a) for 0.25C-rate, b) for the 1C rate, c) for the 2C rate 
and d) for the 5- rate 

 



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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ambient temperature, and for the 5 C rate, the temperature 
rose drastically by 50.339% from the ambient temperature. 
The simulation ended after 570s for 5 C-rate because the 
maximum temperature at the 5 C rate was above the 
designated operating range. 

In Figure 4, temperature variations are shown in a single 
cell of dual potential MSMD Li-Ion Battery with various C-
rates(0.25C, 1C, 2C, and 5C ) with  Equivalent Circuit Model 
considering natural convection as the boundary condition, 
and the free stream temperature is taken as 300K (room 
temperature in Asia). Just like in Figure 3, the temperature 
variations show a similar pattern in Figure 4. In Figures 4(a), 
4(b), 4(c), and 4(d), the maximum temperatures for 0.25C, 1C, 
2C, and 5C rates are 300.4373 K, 306.8669 K, 327.3949 K, and 
430.1342 K respectively. For 0.25 C, the maximum 
temperature is slightly increased, while for 1C, 2C, and 5C 
rates the maximum temperature rose to 2.28%, 9.13%, and 
43.37% from the ambient temperature. 

In Figure 5, temperature variations are shown in a 

single cell of dual potential MSMD Li-Ion Battery with various 

C-rates(0.25C, 1C, 2C, and 5C ) with  Equivalent Circuit Model 

considering natural convection as the boundary condition, 

and the free stream temperature is taken as 313K (typical 

summer temperature in Asia). Just like in Figure 3 and Figure 

4, the temperature variations show a similar pattern in Figure 

5. In Figures 5(a), 5(b), 5(c), and 5(d), the maximum 

temperatures for the 0.25C, 1C, 2C, and 5C rates are 

313.3455K, 319.775K, 340.303K, 441.1937 K, respectively. 

For 0.25 C, the maximum temperature is just slightly 

increased from the environmental temperature, while for 1C, 

2C, and 5C rates the maximum temperature rose 2.258%, 

8.723%, and 40.96% respectively from the ambient 

temperature.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In Figures (3-5), it is seen that for higher 

environmental temperatures the maximum temperature 

increase rate is lowered in each C-rates for convective 

boundary conditions. This is because the ambient 

temperature has significant effects on the electrolyte 

property in the Li-ion battery [19]. However, the maximum 

temperatures for each C rate tend to rise higher with an 

increase in environmental temperatures. In each case, the 

maximum temperature is obtained in the active cell zone 

regardless of the C-rates and environmental temperature.  

3.1.2 Thermal condition: radiation 
The configuration of the cell's surface has a significant 

impact on how much heat is released by radiation. The label 

is usually the cell's exterior surface, and its emissivity 

determines how well heat is transferred via radiation. Li-Ion 

Battery Cells with the largest thermal endurance will result 

from choosing labels with the highest possible emissivity (ε = 

1) [9]. Therefore, in this study, we have considered the 

maximum possible external thermal emissivity (ε = 1) for 

each case. We have considered the initial heat generation rate 

to be 0 W/m3. Contours of total static temperatures in the 

whole cell of the dual potential MSMD Li-Ion battery are 

shown in Figure 3, Figure 4, and Figure 5 considering the 

boundary conditions as radiation for various external 

radiation temperatures of 268K, 300K, and 313K, 

respectively. 

In Figure 6, temperature variations are shown in a single cell 

of dual potential MSMD Li-Ion Battery with various C-rates 

(0.25C, 1C, 2C, and 5C ) with  Equivalent Circuit Model. 

Radiation is considered in the boundary condition.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5. Temperature variation in a single cell of dual potential MSMD Li-Ion Battery with various C-rates with  Equivalent 
Circuit Model considering free stream temperature of 313k: a) for 0.25C-rate, b) for 1C-rate, c) for 2C-rate and d) for 5- rate 

 



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The external radiation temperature is taken as 268 K (typical 

winter temperature in Asia). In Figure 6(a), for 0.25 C rate and 

maximum temperature is 268.8422K. which shows a very 

slight increase from the environmental temperature(268K). 

In Figures 6(b), 6(c), and 6(d), the C-rate was varied from 1 C, 

2 C, and 5 C, and the maximum temperature was obtained 

275.7793K, 295.33K, and 371.8228K respectively. For the 1C 

rate, then the maximum temperature of the single Li-Ion 

battery cell increased up to 2.90% from the environmental 

temperature. The maximum temperature considerably rose 

with greater C rates. For the 2 C rate, the maximum 

temperature rose by 10.19% and for the 5C rate, the 

maximum temperature increased rapidly to 38.73% from the 

ambient temperature. While taking the heat transfer mode as 

radiation, the maximum temperature exceeded the 

designated working range for 5 C, and the simulation stop 

conditions arrived after 570s just like the previously 

discussed convective boundary conditions. 

In Figure 7, temperature variations are shown in a single cell 

of a dual potential MSMD Li-Ion battery with various C rates 

(0.25C, 1C, 2C, and 5C ) with the Equivalent Circuit Model 

considering radiation as the heat transfer mode. The external 

radiation temperature is taken as 300 K (room temperature 

in typical Asia). Figure 7(a) shows that the maximum 

temperature obtained for the 0.25 C rate is 300.3606 K, which 

is almost the same as the environmental temperature. From 

Figures 7(b), 7(c), and 7(d) we can see that for higher C-rates 

higher temperatures are obtained. For 1C, 2C, and 5C the 

maximum temperatures are found as 305.5259K, 320.6266K, 

and 386.0818K respectively. At 1C rate, the maximum 

temperature increased by only 1.84%. For higher C rates, the 

maximum temperature rose rapidly. For 2C and 5C rates, the 

maximum temperature increased up to 6.87% and 28.69% 

from the ambient temperature, respectively. 

In Figure 8, temperature variations are shown in a single cell 

of a dual-potential MSMD Li-Ion battery with various C-rates 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.25C, 1C, 2C, and 5C) with an Equivalent Circuit Model 

considering Radiation as heat transfer mode. The external 

radiation temperature is taken as 313 K (typical summer 

temperature in Asia). Figure 8(a) shows that the maximum 

temperature obtained for the 0.25 C rate is 313.0591K, which 

is almost the same as the environmental temperature. From 

Figures 8(b), 8(c), and 8(d) we can see that, for 1C, 2C, and 3C 

the maximum temperature is 314.2582K, 317.8055K, and 

419.8545K. It indicates that for 1C, 2C, and 5C the maximum 

temperature increased by up to 0.40%, 1.535%, and 34.13% 

from the ambient temperature, respectively.  

In the aforementioned Figures 6-8, increasing the 

environmental temperatures, the maximum temperature 

increase rate is decreased in each C-rates for radiative 

boundary conditions, which shows a similar trend discussed 

in Figures 3-5. However, the maximum temperatures for each 

C rate tend to rise higher with an increase in environmental 

temperatures. In each case, the maximum temperature is 

obtained in the active cell zone regardless of the C-rates and 

environmental temperatures. 

3.2 NTGK model 
3.2.1 Thermal condition: convection 

To comprehend the physics underlying the 

complicated nature of lithium-ion batteries, electrothermal 

models are crucial. In this study, we focus on two commonly 

used electronic chemistry models to analyze the results 

comparatively. In Figures 9, 10, and  11, we discussed the 

maximum temperatures obtained by the single cell of an 

MSMD dual potential Li-Ion Battery considering the boundary 

conditions as natural convection. We varied the 

environmental temperature (free stream temperature) to 

explore the thermal behavior of Li-ion batteries in different 

situations.  

 

 

Figure 6. Temperature variation in a single cell of dual potential MSMD Li-Ion Battery with various C-rates with  Equivalent 
Circuit Model considering external radiation temperature of temperature of 268K: a) for 0.25C-rate, b) for 1C-rate, c) for 
2C-rate and d) for 5- rate 

 



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Contours of total static temperatures in the whole cell 

of the dual potential MSMD Li-Ion Battery are shown in Figure 

9, Figure 10, and Figure 11 considering the boundary 

conditions as Convection for various environmental 

temperatures of 268K, 300K, and 313K, respectively. The 

nominal capacity multiplied by the C rate gave the discharging 

current its value, just as same as in the previously discussed 

ECM e-chemistry model. The discharge rate of a battery 

determines its working time, so the greater the discharge rate, 

the longer the battery's operating period will be [6]. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In Figure 9, temperature variation in a single cell of a dual 

potential MSMD Li-Ion battery is shown with the NTGK 

electrochemistry model for various C rates while the 

boundary conditions are taken as natural convection. The 

environmental temperature is considered 268 K (typical 

winter temperature in Asia). Figures 9(a), 9(b), 9(c) and 9(d) 

represent the temperature variations in the battery cell for 

0.25C, 1C, 2C, and 5C rates, respectively. It is seen that for the 

0.25C rate, the maximum temperature increased to 

268.4804K, which is slightly higher than the ambient 

Figure 7. Variation of temperature in a single cell of a dual-potential MSMD Li-Ion battery with various C rates with an 
equivalent circuit model considering an external radiation temperature of 300 K: a) for 0.25C-rate, b) for the 1C rate, c) for 
the 2C rate and d) for the 5- rate 

 

Figure 8. Variation in temperature in a single cell of dual potential MSMD Li-Ion battery with various C-rates with 
Equivalent Circuit Model considering the external radiation temperature of 313 K: a) for 0.25C-rate, b) for the 1C rate, c) for 
the 2C rate and d) for the 5- rate 

 



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temperature. For 1C, 2C, and 5C rates, the maximum 

temperatures were 272.3053 K, 281.8218 K, and 439.7356 K, 

respectively. For 1C, the maximum temperature increased 

only 1.60% from the environmental temperature, while for 

higher C rates, it increased rapidly.  For 2C and 5C rates, the 

maximum temperatures increased up to 5.15% and 64.08% 

respectively. It shows that, in the NTGK model, the maximum 

temperature increase rate rapidly increases with higher C 

rates. For the 5 C rate, the battery simulation stop condition 

arrived after 570 s. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In Figure 10, temperature variations are shown in a single cell 

of the dual-potential MSMD Li-Ion battery with various C-

rates(0.25C, 1C, 2C, and 5C ) with the NTGK model 

considering natural convection as the boundary condition 

and the temperature of the free stream is taken as 300K 

(room temperature in Asia). In Figure 10(a), it is shown that 

the maximum temperature increased by 300.1283K, which is 

almost the same as the environmental temperature.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 9. Variation in temperature in a single cell of a dual potential MSMD Li-Ion battery with various C rates with the 
NTGK model considering the free flow temperature of 268 K: a) for 0.25C-rate, b) for the 1C rate, c) for the 2C rate, and d) 
for the 5- rate 

 

Figure 10. Variation of temperature in a single cell of a dual-potential MSMD Li-Ion battery with various C rates with the 
NTGK model considering the free stream temperature of 300 K: a) for 0.25C-rate, b) for the 1C rate, c) for the 2C rate, and 
d) for the 5-rate 

 



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

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From Figures 10 (b), 10 (c), and 10(d) we see that the 

maximum temperatures obtained for 1C, 2C, and 5C were 

302.19K, 308.111K, and 431.601K respectively. For 1C, 2C, 

and 5C rates the maximum temperatures increased up to 

0.73%, 2.70%, and 43.86% respectively from the 

environmental temperatures. 

In Figure 11, temperature variations are shown in a single cell 

of dual potential MSMD Li-Ion Battery with various C-rates 

(0.25C, 1C, 2C, and 5C ) with  NTGK Model considering natural 

convection as the boundary condition, and the free stream 

temperature is taken as 313K (typical summer temperature 

in Asia). The temperature variations show a similar pattern in 

Figure 11 just like in Figures 9 and 10. In Figures 11(a), 11(b), 

11(c), and 11(d), the maximum temperatures for 0.25C, 1C, 

2C, and 5C rates are 313.0101 K, 314.6604 K, 319.5787 K, and 

429.6515 K respectively. For 0.25 C, the maximum 

temperature is just slightly increased from the environmental 

temperature, while for 1C, 2C, and 5C rates the maximum 

temperature rose 0.53%, 2.101%, and 37.26% respectively 

from the ambient temperature. Figure 11 also showed a 

similar trend to the previous analysis where the maximum 

temperature increase rate decreased with the increase of the 

environmental temperatures. However, the maximum 

temperature always increased with the increase of C rates. 

3.2.2 Thermal condition: radiation  
We considered the maximum possible external 

thermal emissivity (ε = 1) for each case in the NTGK model, 

just like the model of the equivalent circuit previously 

discussed. We considered the initial heat generation rate to be 

0 W/m3. Figures 12, 13, and 14 depict contours of total static 

temperatures across the dual potential MSMD Li-Ion Battery's 

whole cell where boundary conditions are regarded as 

radiation for varying external radiation temperatures of 

268K, 300K, and 313K, respectively. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In Figure 12, temperature variations are shown in a single cell 

of dual potential MSMD Li-Ion Battery with various C-rates 

(0.25C, 1C, 2C, and 5C ) with  NTGK Model. Radiation is 

considered in the boundary condition. The external radiation 

temperature is taken as 268 K (typical winter temperature in 

Asia). In Figure 12(a), the 0.25 C rate and the maximum 

temperature are 268.8422K which shows a very slight 

increase from the environmental temperature (268K). In 

Figures 12 (b), 12 (c), and 12(d), the C-rate was varied from 1 

C, 2 C, and 5 C, and the maximum temperature was obtained 

275.7793 K, 295.33 K, and 371.8228 K, respectively. For the 

1C rate, the maximum temperature of the single Li-Ion battery 

cell increased up to 2.90% from the environmental 

temperature. For higher C rates, the maximum temperature 

increased significantly. For the 2 C rate, the maximum 

temperature rose by 10.19% and for the 5C rate, the 

maximum temperature increased rapidly to 38.73% from the 

ambient temperature. While taking the heat transfer mode as 

radiation, at 5 C rate the maximum temperature was outside 

the specified operating range, and the simulation stop 

conditions arrived after 570s just like the previously 

discussed convective boundary conditions. In Figure 13, the 

external radiation temperature is taken as 300K (room 

temperature in typical Asia), and temperature variations in a 

single cell of MSMD dual potential Li-ion battery are shown. 

In Figure 13(a), the maximum temperature for the 0.25C rate 

is 300.1069K, which is only slightly higher than the 

environmental temperature. The maximum temperature 

increased rapidly with higher C rates. In the aforementioned 

Figures 13(b), 13(c), and 13(d) for 1C, 2C, and 5C the 

maximum temperature obtained was 301.8011K, 306.5999K, 

and 421.5734 K, respectively. For 1C, 2C, and 5C the 

maximum temperature increased to 0.60%, 2.199%, and 

40.52% respectively.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Figure 11. Variation in temperature in a single cell of dual potential MSMD Li-Ion battery with various C-rates with the 
NTGK model considering the free-flow temperature of 313k: a) for 0.25C-rate, b) for 1C rate, c) for 2C rate and d) for 5- rate 

 



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For the 5C rate at room temperature, the temperature in the 

battery cell increased drastically which indicates the battery 

conditions were outside the specified operating range. As the 

battery geometry was quite low and comparatively a large 

amount of current discharging conditions was provided, the 

battery simulation stop condition arrived and indicated a 

thermal runaway. In Figure 14, the external radiation 

temperature is taken as 313K (typical summer temperature 

in Asia), and temperature variations in a single cell of MSMD 

dual potential Li-ion battery are shown.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In the aforementioned Figure 14 (a), the maximum 

temperature for the 0.25C rate is 313.3035K, which is only 

slightly higher than the environmental temperature. For 

higher C rates, the maximum temperature increased rapidly. 

In the aforementioned figures 14 (b), 14 (c), and 14(d) for 1C, 

2C, and 5C the maximum temperature obtained was 

317.8952K, 331.4985 K, and 392.7853K   respectively. For 1C, 

2C, and 5C the maximum temperature increased by up to 

1.56%, 5.9%, and 25.49% respectively. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 12. Variation in temperature in a single cell of dual potential MSMD Li-Ion battery with various C-rates with the 
NTGK model considering an external radiation temperature of 268 K: a) for 0.25C-rate, b) for 1C rate, c) for 2C rate and d) 
for 5- rate 

 

Figure 13. Variation of temperature in a single cell of a dual-potential MSMD Li-Ion battery with various C rates with the 
NTGK model considering an external radiation temperature of 300 K: a) for 0.25C-rate, b) for the 1C rate, c) for the 2C rate, 
and d) for the 5-rate 

 



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Figure 14. Variation of temperature in a single cell of a dual-potential MSMD Li-Ion battery with various C rates with the 
NTGK model considering an external radiation temperature of 313 K: a) for 0.25C-rate, b) for the 1C rate, c) for the 2C rate, 
and d) for the 5-rate 

 

Figure 15. Maximum temperature vs. discharge rate for the ECM and NTGK models with different thermal conditions 

 



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From Figures 12, 13, and 14, it is observed that, for higher 

environmental temperatures, the increase rate of the 

maximum temperature from the environmental temperature 

is comparatively lower in the NTGK model than in the ECM 

model, while the boundary conditions are considered as 

radiation. Just like the previously discussed convective 

boundary conditions for the NTGK e-chemistry model in 

Figures (6-8), Figure 12, Figure 13, and Figure 14 also showed 

a similar trend where the maximum temperature increased 

with increasing environmental temperature. The maximum 

temperature was always obtained in the Active Material 

(electrolyte ) zone. 

In Figure 15, the maximum temperature vs. discharge rate is 

shown for both ECM and NTGK e-chemistry models 

considering convective and radiative boundary conditions. In 

each case, it is observed that for higher Discharge rates the 

maximum temperatures increased rapidly. Up to 2 C rate, the 

battery was inside the specified operating conditions and the 

temperature increased stably. However, at a high C rate (5 C), 

in each case, the battery was beyond operational condition.  

Due to the specified maximum and minimum stop voltages of 

the battery, the materials property of the battery cell, and the 

geometry of the battery cell, a sharp increase was observed in 

each environmental condition at 5C, regardless of the 

boundary conditions. The environmental temperature had a 

significant effect on the increase rate of the maximum 

temperatures. It was because the environmental temperature 

played a crucial role in the activation energy inside the Li-ion 

battery cell. 

4. Conclusion 
We have seen for each of the electrochemical models, the 

temperature rises drastically after the 2C rate and the 
maximum stop condition of the simulation arrived just after 
570s.  For the ECM model while taking the thermal condition 
as natural convection and the free stream temperature as  
268K, 300K, and 313K respectively, the highest temperature 
of the MSMD dual potential Lithium-ion Battery the single cell 
raised to 402.9109K, 430.1342K, and 441.1937K  respectively 
for 5C discharge rate. For the ECM model, in the natural 
convection mode of heat transfer, the battery cell 
temperature increased by up to 9.48% while the 
environmental temperature changed from winter (-5°C) to 
summer (40°C) temperature. For radiation, The battery cell 
temperature is increased to 371.8288 K, 386.0818 K, and 
419.8545 K for 5C rate with the corresponding environmental 
radiation temperature 268 K, 300 k, 313 k, which means the 
temperature increase rate of the cell raised to 12.91% but the 
maximum temperatures are lower than the ECM model’s 
highest temperatures for convection in each case. From 
Figure 13 it is also clearly visible that for various discharge 
rates (0.25C, 1C, and 2C ), the maximum temperature-raising 
tendency in the ECM  due to natural convection is greater than 
the maximum temperature-raising tendency due to radiation 
regardless of the environmental temperature (-5°C, 27°C, and 
40°C). Therefore, radiation is found to be a better thermal 
condition than natural convection in the ECM model. 
However, the trend line of the maximum temperature rise is 
opposite in the NTGK model, where the maximum 
temperature rise due to radiation is greater than the 
maximum temperature rise due to convection for 0.25C, 1C, 
and 2C rates at -5°C and 40°C environmental temperatures. 
For 5C in the NTGK model, the magnitude of maximum 
temperatures showed a variation from the temperature-

raising trend line in Figure.13 which was due to the arrival of 
the maximum stop condition of the simulation, where the 
simulation stopped just after 570 s of flow time. In the NTGK 
model, the maximum temperature rise due to radiation is 
greater than that due to convection for 0.25C, 1C, and 2C rates 
for winter and summer temperatures. However, at room 
temperature, the radiation mode of heat transfer showed a bit 
better result in the NTGK model. So, it can be said that in the 
NTGK model, convection is a better thermal condition than 
natural convection. After analyzing the simulation results of 
the highest temperatures reached by implementing two 
different electrochemical models in a single cell of a dual 
potential MSMD Lithium-Ion battery, we can conclude that 
the radiative thermal condition of the e-chemistry of the 
equivalent circuit model is just a little better than the 
convective thermal condition of the NTGK model at elevated 
summer temperature (40°C). However, the convective 
thermal condition of the NTGK model shows a significantly 
better thermal management system and less heat generation 
in winter (-5°C) and at room temperature(27°C) compared to 
the radiative thermal condition of the ECM model.  

Acknowledgment 
This work is supported by the University Grants Commission 
of Bangladesh-grant no. 37.01. 0000.73.06.065.22.1607. The 
corresponding author is responsible for ensuring that the 
descriptions are accurate and agreed upon by all authors. 

Ethical issue 
The authors are aware of and comply with best practices in 
publication ethics, specifically concerning authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere in any language. 

Data availability statement 
Data sharing does not apply to this article as no datasets were 

generated or analyzed during the current study.  

Conflict of interest 

The authors declare no potential conflict of interest. 

References 

[1] S. S. Madani, M. J. Swierczynski, and S. K. Kaer, “The 

discharge behavior of lithium-ion batteries using the 

Dual-Potential Multi-Scale Multi-Dimensional (MSMD) 

Battery Model,” 2017 12th Int. Conf. Ecol. Veh. Renew. 

Energies, EVER 2017, 2017, doi: 

10.1109/EVER.2017.7935915. 

[2] Y. Chen and J. W. Evans, “Thermal Analysis of Lithium-

Ion Batteries,” vol. 143, no. 9, pp. 2708–2712, 1996. 

[3] V. Srinivasan and C. Y. Wang, “Analysis of 

Electrochemical and Thermal Behavior of Li-Ion Cells,” 

J. Electrochem. Soc., vol. 150, no. 1, pp. A98–A106, 

2003, doi: 10.1149/1.1526512. 

[4] W. B. Gu and C. Y. Wang, “Thermal-Electrochemical 

Modeling of Battery Systems,” J. Electrochem. Soc., vol. 

147, no. 8, p. 2910, 2000, doi: 10.1149/1.1393625. 

[5] K. Smith and C. Y. Wang, “Power and thermal 

characterization of a lithium-ion battery pack for 

hybrid-electric vehicles,” J. Power Sources, vol. 160, no. 

1, pp. 662–673, 2006, doi: 

10.1016/j.jpowsour.2006.01.038. 



N.Barua et al. /Future Energy                                                                                                            May 2024| Volume 03 | Issue 02| Pages 01-15 

15 

 

[6] C. At, “Transient Thermal Analysis of a Fin,” pp. 1–16, 

2020. 

[7] J. Duan et al., “Modeling and analysis of heat 

dissipation for liquid cooling lithium-ion batteries,” 

Energies, vol. 14, no. 14, 2021, doi: 

10.3390/en14144187. 

[8] K. Van-Thanh, Ho; Khoungsik, Chang; Sang Wook, Lee; 

Sung Han, “Transient Thermal Analysis of a Li-Ion 

Battery,” 2020. 

[9] T. D. Hatchard, D. D. MacNeil, D. A. Stevens, L. 

Christensen, and J. R. Dahn, “Importance of heat 

transfer by radiation in Li-ion batteries during thermal 

abuse,” Electrochem. Solid-State Lett., vol. 3, no. 7, pp. 

305–308, 2000, doi: 10.1149/1.1391131. 

[10] Haariet Martique, “This is a reproduction of a library 

book that was digitized by Google as part of an ongoing 

effort to preserve the information in books and make it 

universally accessible. https://books.google.com,” 

Oxford Univ., vol. XXX, p. 60, 1994. 

[11] H. Gu, “Mathematical Analysis of a Zn / NiOOH Cell,” J. 

Electrochem. Soc., vol. 130, no. 7, pp. 1459–1464, 

1983, doi: 10.1149/1.2120009. 

[12] C. Vanaclocha Hervas, “Comparative study of three 

electrochemical cell models for the CFD simulation of a 

battery module,” 2021. 

 [13] Y. Huo, Z. Rao, X. Liu, and J. Zhao, “Investigation of 

power battery thermal management by using mini-

channel cold plate,” Energy Convers. Manag., vol. 89, 

pp. 387–395, 2015, doi: 

10.1016/j.enconman.2014.10.015. 

[14] K. H. Kwon, C. B. Shin, T. H. Kang, and C. S. Kim, “A two-

dimensional modeling of a lithium-polymer battery,” J. 

Power Sources, vol. 163, no. 1 SPEC. ISS., pp. 151–157, 

2006, doi: 10.1016/j.jpowsour.2006.03.012. 

[15] J. Yi, U. S. Kim, C. B. Shin, T. Han, and S. Park, “Modeling 

the temperature dependence of the discharge behavior 

of a lithium-ion battery in low environmental 

temperature,” J. Power Sources, vol. 244, pp. 143–148, 

2013, doi: 10.1016/j.jpowsour.2013.02.085. 

[16] M. Chen and G. A. Rincon-Mora, "Accurate electrical 

battery model capable of predicting runtime and I-V 

performance," in IEEE Transactions on Energy 

Conversion, vol. 21, no. 2, pp. 504-511, June 2006, doi: 

10.1109/TEC.2006.874229. 

[17] X. Zhang, “Thermal analysis of a cylindrical lithium-ion 

battery,” Electrochim. Acta, vol. 56, no. 3, pp. 1246–

1255, 2011, doi: 10.1016/j.electacta.2010.10.054. 

[18] M. Xiao and S. Y. Choe, “Theoretical and experimental 

analysis of heat generations of a pouch type 

LiMn2O4/carbon high power Li-polymer battery,” J. 

Power Sources, vol. 241, pp. 46–55, 2013, doi: 

10.1016/j.jpowsour.2013.04.062. 

[19] S. Ma et al., “Temperature effect and thermal impact in 

lithium-ion batteries: A review,” Prog. Nat. Sci. Mater. 

Int., vol. 28, no. 6, pp. 653–666, 2018, doi: 

10.1016/j.pnsc.2018.11.002. 

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