Enhancing heat transfer efficiency in li-ion battery packs for EV powertrain through nanofluid cooling

 Corresponding author: Olusegun Abiodun Balogun Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0. Enhancing heat transfer efficiency in li-ion battery packs for EV powertrain through nanofluid cooling Zolani Ndlovu 1, Peter Ohenhen 2, Olusegun Abiodun Balogun 3, *, Victoria Adebisi Alao 4, Akinwale Ishola 5, Raphael Itodo Ochigbo 6 and Nicholas Akhaze Musa 7 1 Department of Mechanical Engineering, Pan African University institute for basic Science, Technology and innovation, Nairobi Kenya. 2 Department of Mechanical Engineering, University of Nebraska-Lincoln, USA. 3 Department of Mechanical Engineering, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya. 4 Department of Mechanical Engineering, University of Ilorin, Kwara, Nigeria. 5 Department of Sustainability, Eastern Illinois University, USA. 6 Department of Chemical Engineering, Federal University of Technology Minna, Nigeria. 7 Department of Mechanical Engineering, Federal University of Technology, Minna, Niger State, Nigeria. Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 Publication history: Received on 04 January 2025; revised on 09 February 2025; accepted on 12 February 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.22.2.0031 Abstract LIB (Lithium-ion) batteries play a crucial role in electric vehicles and are considered the most sustainable energy storage solution for modern electric transportation. These batteries serve various purposes, including supplying power for electronic devices like laptops and cell phones. However, managing battery temperature poses a significant challenge in design, particularly due to excessive heat generation during charging and discharging processes. Insufficient heat transfer between closely packed cells can compromise Li-ion cell performance and even lead to safety hazards such as explosions. Hence, the aim of this study is to enhance heat transfer and cooling processes across the battery pack of electric vehicles. A comprehensive investigation was conducted on the impact of water-copper (II) oxide nanofluid flow at varying speeds on temperature distribution within the battery pack. The adoption of copper (II) oxide nanofluid as a coolant resulted in improved thermal efficiency. This research centres on designing a Li-ion battery pack utilizing water copper (II) oxide nanofluid to enhance heat transfer and cooling efficiency throughout the battery pack. Keywords: Battery Thermal Management System; Lithium-Ion Batteries; Copper (II)Oxide; Nanofluid; Air; Electric Vehicle; Internal Combustion Engine; Battery Pack 1. Introduction Currently, there's a global urgency to find sustainable alternatives to fossil fuels like oil and gas, with electric vehicles emerging as a key solution to reduce environmental harm caused by transportation. The recent conflict between Russia and Ukraine has disrupted global oil and gas supplies, intensifying the demand for electric vehicles. In response, the UK plans to phase out traditional gasoline and diesel vehicles by 2030 and promote electric vehicle adoption through regulations mandating the installation of charging points in new constructions. This move is expected to significantly boost the demand for electric vehicles, compelling car manufacturers of all sizes to transition towards electric vehicle production. In electric vehicle design, batteries serve as the primary energy storage system, with modern technology offering increased durability, particularly in cold climates. Lithium-ion batteries dominate the market due to their versatility Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 121 and widespread use in various electronic devices. The design and configuration of these batteries depend on the manufacturer's specifications, with considerations for power, torque, and pack arrangement. Batteries not only enable greener transportation but also contribute to combating climate change and reducing reliance on fossil fuels. However, temperature control is crucial for lithium-ion battery safety and performance, as inadequate heat dissipation can lead to overheating and potential damage. Therefore, ongoing research aims to improve heat transfer processes within battery packs to enhance safety and efficiency. 2. Literature Review The lithium-ion battery pack consists of rechargeable cells, with graphite commonly used at the negative terminal consists of an electrode, while the positive terminal contains a tightly compressed lithium compound. In contrast to batteries such as lithium-iron phosphate cells (LFP cells), lithium-ion batteries offer superior energy storage, absence of memory effect, and minimal self-discharge (Wu et al. 2019). Their popularity in electric vehicles stems from their capacity to consistently generate energy and power density. However, due to the flammable electrolytes they contain, improper charging or damage could lead to explosions and flames, posing a safety risk to life and property. Therefore, enhancing the design of lithium-ion battery packs and improving heat transfer to dissipate heat generated during operation is crucial. Design considerations such as the computational fluid dynamics model, battery pack configuration, and thermal performance were taken into account by Widyantara et al. (2021). Stiffeners and Plexiglas were added to withstand static and dynamic loads from the electric structure. Energy from the battery was transferred to other electronic components via the conductor plate. The Battery Management System (BMS) was housed in an enclosure, which may include an active or inactive cushion (Wahid et al. 2021). Figure 1 Configuration of Lithium-ion battery pack (Widyantara et al. 2021) The airflow inlet and outlet were positioned on opposite sides of the battery housing to optimize temperature distribution within the pack through forced convection facilitated by a cooling fan. The details regarding the 240-cell cylindrical battery pack made of lithium nickel manganese cobalt oxide (NMC) are detailed in Table 1, with the choice of 240 cylindrical cells being influenced by their common usage in electric vehicle batteries. The battery pack was simplified for modelling purposes, retaining components susceptible to heat sources to ensure an accurate result. The initial design completely made it challenging to adjust airflow within the battery housing with the aid of Ansys Discovery Live program, potentially leading to errors and prolonged simulation times. Lithium-ion Battery consist of separator, anode, cathode, and current collector layers. The cylindrical cell structure shown in Figure 2 did not significantly affect the thermal performance of the battery (Wu et al. 2019). Therefore, the parameters listed in Table 1 were utilized to represent the entire battery. Figure 1 depicted a detailed view of the battery housing, comprising 240 cells enclosed in a rectangular housing. Each cell was depicted as a cylindrical shape with a diameter of 18.3 mm and a height of 64.5 mm. There existed a 1 mm deviation between the 240 cylinders and the box on every surface. Proximity and cell mass play a crucial role in enhancing energy density in electric vehicles, and this close arrangement was implemented to ensure a high-density and compact form of the planned battery pack (Wahid et al. 2021). The space between adjacent cells was 1.7 mm, with a centre-to-centre distance Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 122 of 20 mm. The pack was designed to function as a fluid, with an inlet on one side and an outlet on the other. Some hybrid electric vehicles utilize anywhere from 120 Li-ion cells to over 240 cells, depending on the manufacturer's decision to boost energy storage capacity. Tesla employs 2170 cells with an energy capacity of 5000mAH in the Tesla Model 3/Y Long-Range battery packs (Evannex, 2022). Xiongbin et al. (2020) conducted a thermal analysis and optimization of a 20-cell, air-cooled lithium-ion battery pack. In their study, 20 cells with each voltage of 3.6 volts were chosen for simulation in COMSOL software due to computational efficiency. Each cell had a height of 65.15 mm and a radius of 12.925 mm. The spacing between cells was set at 2.55 mm, as increasing the distance between heat-generating cells enhances the flow of cooling fluid, thereby significantly impacting exchange of heat within the Li-ion battery housing (Julia et al. 2022). Table 1 The lithium-ion cell properties (Rao et al. 2017 & Jiaqiang et al. 2018). Properties Spec Capacity 2.6 Ah Voltage 3.6 V Cell unit mass 0.0475 kg thermal conductivity (axial direction) 37.6 W/mK thermal conductivity (radial direction) 0.2 W/Mk Specific capacity 1200 J/kgK Diameter of cell 18.3 mm length of cell 64.5 mm 2.1. Lithium-Ion BTMS (Battery Thermal Management System) Temperature plays a crucial role in battery performance, as highlighted by Xu et al. (2019). Effectively controlling battery heating, as emphasized by Wang et al. (2015), presents a notable challenge. Thus, the adoption of an efficient battery thermal management system (BTMS), as advocated by Jilte et al. (2019), is vital for maintaining optimal temperature levels during operation. Top of Form Excessive heat production or inadequate dissipation can cause the battery to overheat, potentially leading to the detachment of active materials on the electrodes and accelerating the degradation of the electrolyte, ultimately causing harm to the battery pack (Weng et al. 2019). These irreversible changes can result in permanent damage to the batteries. Excessive heat presents safety concerns, including the risk of battery short circuits that may harm internal parts and potentially initiate a fire or explosion (Wang et al., 2020). If not managed properly, the issues with one battery can impact the entire battery pack, worsening thermal runaway and making the pack difficult to control. Thus, the development of a reliable Battery Thermal Management System (BTMS) for electric vehicles is essential (Liu et al., 2014). Effective thermal management improves battery pack performance (Gachot et al. 2012). (a)Prismatic shape (b) pouch shape (c) cylindrical shape Figure 2 Lithium-Ion battery geometry form (Xiongbin, et al. 2020) Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 123 The three Lithium-Ion battery geometric configurations are illustrated in Figure 2. Customizing the prismatic battery allows meeting customers' requests, making it suitable for nearly all electric vehicles. Establishing a universal standard for prismatic batteries is challenging due to their adaptability, resulting in variations in size, nominal voltage, and other characteristics. Pouch batteries are produced and packed using superposition. Soft-pack batteries, however, lack consistency and require more advanced control and monitoring systems. The cylindrical battery has undergone extensive research, leading to a high level of standardization and ease of producing a uniform industry standard. The cylindrical battery offers inherent advantages in heat dissipation, creating a good heat dissipation space when packed together. 2.2. Design, simulation, and testing of EV battery pack A crucial component in Electric Vehicle is the propulsion battery, which converts excess mechanical energy into electrical energy. However, continuous recharging and discharging of the battery cause its temperature to rise, potentially beyond its optimal operating range if not adequately cooled. This overheating diminishes the battery's energy storage and transmission capabilities, shortening its lifespan. To ensure the battery functions properly throughout its intended lifespan, maintaining a consistent and suitable temperature is essential. In vehicles like the Tesla, Renault etc, their battery housing is typically located in the rear compartment. Johnson Electric tackled cooling challenges by introducing a secondary blower system that channels air-conditioned cabin into the trunk. However, achieving adequate air return from the rear to the front HVAC module poses difficulties due to the dual heat load system. Consequently, the vehicle operates with two opposing airflow circuits dictated by pressure differentials. Designing an efficient HVAC system becomes crucial to minimize airflow demands for the battery pack and optimize air return to the front AC system, particularly in recirculation mode. This strategy reduces negative pressure from battery fan operation and lowers noise levels by operating the fans at reduced speeds. Considering the numerous direct sound transmission paths for rear passengers, noise reduction becomes pivotal for overall comfort. Pesaran (2001) highlighted the importance of addressing challenges related to hybrid electric vehicle battery thermal cooling early in the design process. 2.3. Water-Al2O3 nanofluids cooled battery thermal management system Using air for BTMS (battery thermal management systems), especially during high discharge rates, may not be the optimal choice (Rao and Wang, 2011). While forced convection air conditioning can mitigate temperature rises in the cell, cooling becomes challenging when temperatures exceed 66 degrees Celsius, preventing the cell from reaching temperatures below 52 degrees (Nelson et al., 2002). Air cooling proves inadequate under severe battery operating conditions, such as higher ambient temperatures (>40°C) or increased discharge rates (Sabbah et al., 2008). In contrast, alternative cooling mediums like mineral oil, water, dielectric fluid, and ethylene glycol offer more efficient heat dissipation than air cooling (Nelson et al., 2002). Unlike air-based systems, which are unaffected by their location within the vehicle, liquid cooling systems typically add weight and cost (Pendergast et al., 2011). Studies comparing liquid cooling mediums like silicone transformer fluid to air cooling reveal the former's superior heat dispersal capabilities (Nelson et al., 2002). Researchers suggest increasing channel width in liquid-cooled systems to reduce average channel temperature and employing oblique mini-channels for higher heat transfer coefficients (Giuliano et al., 2012; Jarrett and Kim, 2011; Jin et al., 2014). Investigation into prismatic batteries suggests adjusting cooling measures based on ambient temperature, with liquid cooling proving most effective under normal conditions (Huo et al., 2015; Zhao et al., 2015). Efforts to enhance heat transfer in liquid-cooled systems include utilizing nanofluids, suspensions of nanoparticles in base fluids. Early studies by Choi et al. (2001) demonstrated the potential for nanofluids to enhance thermal conductivity, with subsequent research confirming their efficacy (Duangthongsuk and Wongwises, 2010; Mondal et al., 2017; Sefidan et al., 2017; Tran et al., 2017; Rani et al., 2017; Li et al., 2015; Hung et al., 2013). These studies explore various nanoparticle types and their effectiveness in improving battery cooling performance. 3. Methodology The 3D model design, depicted in figures 3, illustrates the battery pack configuration. It comprises 20 lithium-ion batteries arranged in a five-row, four-column layout. The battery pack holders, totalling 40, are divided with 20 positioned at the bottom and 20 at the top. Additionally, there are 36 Nickel strips, with 18 connected at the top and 18 at the bottom. The battery pack case, rectangular in shape, was uniquely designed and assembled using inventor assembly features like mating. Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 124 (a) Isometric view of battery pack (b) Top view of Lithium-Ion battery pack Side view of Lithium-Ion battery pack Figure 3 Battery pack assembly 3.1. Boundary Conditions Figure 4 boundary condition of battery pack The battery pack comprises four S5P Lithium-Ion cells connected by nickel strips. To analyse its behaviour, a 2D model was created, illustrating boundary layers and computational areas. These boundaries were selected to meet mathematical requirements, with labels corresponding to those in Figure 4. The pack's sidewalls, also known as x-axis no-slip boundaries, were depicted. The outlet boundary defines the pressure outlet, while the inlet boundary sets the Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 125 temperature and velocity of incoming flow. Within the computational simulation, the physical structure includes the Lithium-Ion battery domain (B1-B20), serving as the heat source. For the flow simulation in COMSOL Multiphysics, the following assumptions are made: • All flow for air and nanofluid is assumed to be laminar. • The computational domain's geometry is restricted to two dimensions (2D). • Heat loss to the surroundings from the battery pack enclosure is neglected due to insulation. • The nanofluid flow within the battery pack enclosure is treated as incompressible. • Heat transfer within the Lithium battery material is not accounted for. • The nanofluid is assumed to be homogeneous and possess constant properties throughout. 3.2. Nano fluid Flow specification The flow region is defined by mass flow rate (𝑚󰇗) as: 𝜌𝑛𝑓𝑉𝐴𝐼= 𝜌𝑛𝑓𝑣(𝑁𝑇𝑆𝑇𝐿). ……….Equation 1 𝑚󰇗 = 𝜌𝑛𝑓𝑉𝑚𝑎𝑥(2𝐴𝐷). ……….. Equation 2 the Reynolds number can be analysed as: 𝑅𝑒 = 𝜌𝑛𝑓𝑉𝑚𝑎𝑥𝐷 𝜇𝑛𝑓 = 𝑉𝑚𝑎𝑥𝐷 𝑣𝑛𝑓 . ………… Equation 3 The mean Nusselt number on the walls of the batteries can be approximated using the provided formula (Ahmed et al., 2017). The Nusselt number (Nu) illustrates the relationship between heat transfer within the fluid by convection and heat transfer occurring at the boundary walls of both the battery housing by conduction whille the 20 cells are immersed in the fluid: 𝑁𝑢 =1 𝐿∫(−𝑘𝑛𝑓 𝑘𝑓𝜕𝑇 𝜕𝑦)𝑑𝑥. ………………. Equation 4 The nanofluid's effective density is defined as: 𝜌𝑛𝑓 =(1−∅)𝜌𝑓+∅𝜌𝑠𝑝. ……………….Equation 5 where ∅ is the volume fraction of nanoparticles. In this research a volume fraction of 2% was considered. The thermal diffusivity: ∝𝑛𝑓 = 𝑘𝑛𝑓 (𝜌𝑐𝑠𝑝)𝑛𝑓. ……………….Equation 6 where (𝜌𝑐𝑠𝑝)𝑛𝑓 is the heat capacitance. Equation 3.14 can be used to calculate the effective thermal capacitance. (𝜌𝑐𝑠𝑝)𝑛𝑓 =(1−∅)(𝜌𝑐𝑠𝑝) 𝑓+∅(𝜌𝑐𝑠𝑝) 𝑠𝑝 ……………….Equation 7 The thermal expansion coefficient of the nanofluid can also be calculated using (𝑝𝛽)𝑛𝑓 =(1−∅)(𝑝𝛽)𝑓 +∅(𝑝𝛽)𝑠𝑝 . ……………….Equation 8 where 𝜇𝑛𝑓 is the effective dynamic viscosity which can be calculated below: 𝜇𝑛𝑓 =𝜇𝑓 (1−∅)2.5. ……………….Equation 9 Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 126 Mahdy & ElShehabey (2021) and Olamide et al. (2022), the thermal conductivity of the nanofluid 𝑘𝑛𝑓 can be derieved as: 𝑘𝑛𝑓 =𝑘𝑓[(𝑘𝑠𝑝+2𝑘𝑓)+2∅(𝑘𝑓+2𝑘𝑠𝑝) (𝑘𝑠𝑝+2𝑘𝑓)−∅(𝑘𝑓+2𝑘𝑠𝑝)]. ……………….Equation 10 where 𝑘𝑠𝑝 and 𝑘𝑓 are the thermal conductivity of nanoparticles and base fluid respectively. Equations 11 to 14, along with the specified boundary conditions, will be influenced by the properties of the nanoparticle fluid outlined in Equations 6 to 16. Equation 11 to 14 constitutes the mathematical framework for the battery assembly model, encompassing continuity in both x & y direction, momentum, and energy equations to describe the system's physical behaviours (Olamide et al. 2022): continuity: 𝜕𝑢 𝜕𝑥 +𝜕𝑣 𝜕𝑦 =0. ……………….Equation 11 xmomentum: 𝜕𝑢 𝜕𝑡 +𝑢𝜕𝑢 𝜕𝑥 +𝑣𝜕𝑢 𝜕𝑦 =1 𝜌𝑛𝑓 (−𝜕𝑝 𝜕𝑥 +𝜇𝑛𝑓 [𝜕2𝑢 𝜕𝑥2+𝜕2𝑢 𝜕𝑦2]). ……………….Equation 12 ymomentum: 𝜕𝑣 𝜕𝑡 +𝑢𝜕𝑣 𝜕𝑥 +𝑣𝜕𝑣 𝜕𝑦 =1 𝜌𝑛𝑓 (−𝜕𝑝 𝜕𝑦 +𝜇𝑛𝑓 [𝜕2𝑣 𝜕𝑥2+𝜕2𝑣 𝜕𝑦2]). ……………….Equation 13 Energy: 𝑢𝜕(𝜌𝑛𝑓𝑇) 𝜕𝑥 = 𝜇𝑛𝑓 𝑝𝑟𝑛𝑓 𝜕 𝜕𝑥[𝜕𝑇 𝜕𝑥]. ……………….Equation 14 3.3. Heat Dissipation Model for Lithium batteries The Heat Dissipation Model for Lithium batteries considers four primary sources of heat production during operation: chemical reaction heat (RH), side reaction heat (SRH), joule heat (JH), and polarization heat (PH). Equation 15 outlines the calculation for total thermal generation. 𝑃𝑇𝐻 =𝑃𝐶𝑅 +𝑃𝑆𝑅𝐻 +𝑃𝐽𝐻 +𝑃𝑃𝐻 ……………….Equation 15 PTH represents the total heat power, with PCR representing the power related to chemical reaction (CR), PSRH representing side reaction heat (SRH), PJH representing joule heat (JH), and PPH representing polarization heat (PH). CR refers to the heat released by chemical reactions within the electrodes during both charge and discharge processes. During the charge process of a Li-Ion battery (LIB), energy is absorbed, contributing to a decrease in ambient temperature, while heat is produced during discharge (Ismial et al., 2013). JH accounts for the work of current on internal resistance (IR), which can be determined using Joule's law, as demonstrated in Equation 16: 𝑃𝐽𝐻 =𝐼2𝑅Ω ………………. Equation 16 where 𝑅Ω is 𝐼𝑅, and 𝐼 refers to the current on 𝑅Ω. Typically, polarization takes place at I.R 𝑅𝑝, and the heating power is calculated by Joule’s law, as shown in Equation 17, 𝑃𝑝𝑜 = 𝐼2𝑅𝑝 ……………….Equation 17 𝑑∅ 𝑑𝑡 = 𝐶𝑚𝑀𝑑𝑇 𝑑𝑡 ……………….Equation 18 The battery's Specific Heat Capacity (SHC), which is its ability to absorb heat, is directly linked to the heat it generates, leading to a temperature increase. This SHC is determined using the principle of conservation of energy (COE), where Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 127 the heat generated by the battery corresponds to its stored heat in an environment insulated from external heat exchange (adiabatic). Consequently, an increase in heat storage within the battery will result in a rise in its temperature. The SHC of the battery can be evaluated by observing the temperature increase over a defined period, as described in equation 18. Chen et al. (2019) conducted the relevant experimental procedures. 𝑃𝑇𝐻 = −𝐼𝑇𝑑𝐸 𝑑𝑇 +𝐼(𝐸−𝑈) ……………….Equation 19 Here, P represents the power generating heat, I stand for the current within the circuit, T denotes the current temperature of the battery, E represents the battery's open circuit voltage, and U signifies the battery's average terminal voltage (Xiongbin et al. 2020). From equation 19, the first 𝐼𝑇𝑑𝐸 𝑑𝑇 on the right side of equation is the formula to calculate the power of RH, which equals the 𝑃𝑇𝐻 in equation 21. The second item refers to summary of 𝐽𝐻 and 𝑃𝐻 and it shows the voltage attribution. The voltage drops (𝐸 − 𝑈) in the open circuit voltage and terminal voltage are attributed to internal DC resistance and their relationship is denoted by equation 21 below. 𝐼(𝐸−𝑈)= 𝐼2(𝑅Ω+𝑅𝑝) ……………….Equation 20 (𝑅Ω+𝑅𝑝) make up the internal DC resistance, which was expressed by 𝑅. The heat production was expressed by equation 21: 𝑃𝑇𝐻 = −𝐼𝑇𝑑𝐸 𝑑𝑇 +𝐼2𝑅 ………………. Equation 21 3.4 Setting up a heat transfer simulation for a 2D battery pack using COMSOL Multiphysics The design pattern was extracted from Inventor design software and transferred to COMSOL in the Model Builder interface. Figure 5 displays the uniform geometry of the 20 batteries. The lithium-ion battery specifications sourced from the COMSOL library, utilized for simulation, are outlined in Table 2. Table 2 Positive, Li-ion Battery properties Properties Value Electrical conductivity 100[S/m] Electric conductivity symmetry 3 Density 4650[kg/m^3] Temperature difference max(393.15, min(T, 223.15)) Specific Heat capacity 922.4 Thermal conductivity 141.2 Dynamic viscosity 1 Reference concentration 23000[mol/m^3] Figure 5 Positive, Li-ion Battery Global Journal of Engineering and Technology Advances, 2025, 22(02), 120-135 128 Table 3 CuO nanofluid properties nanofluid properties Value Unit Density 1013.924 kg/m³ Heat capacity at constant pressure 4106.16 J/(kg·K) Dynamic viscosity 0.00100803 Pa·s Thermal conductivity 0.607212675 W/(m·K) Figure 6 CuO fluid domain The focus of this study is on designing, analysing, and simulating a lithium battery. The 3D model comprises twenty standard cylindrical lithium cells, along with additional components such as nickel strips, battery clips, and a battery case. These cells, known as 4S5P batteries, are arranged in four series circuits and five parallel circuits, totaling twenty cells, chosen for computational simplicity in Comsol Multiphysics. This configuration mirrors that used by Xiongbin et al. (2020) in their research on heat transfer agents in electric vehicle battery packs. The goal here is to prototype an electric vehicle battery pack, optimizing heat dissipation from the cells. Nickel strips connect the batteries in parallel, allowing for both parallel and series configurations due to their high conductivity and resistance to corrosion. Battery clips firmly secure individual cells within the battery enclosure, with oval shape opening at both ends, enabling the flow of air or fluids like air or nanofluid around the contained cells. 4. Methodology 4.1. Grid Test Sensitivity Figure 7 Fluid flow domain mesh The process of achieving accurate simulation results for lithium-ion battery packs. 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