Efficient Cooling System for Lithium-Ion Battery Cells by Using Different Concentrations of Nanoparticles of SiO₂-Water: A Numerical Investigation

Abstract

The performance, safety, and cycle life of lithium-ion batteries (LiBs) are all known to be greatly influenced by temperature. In this work, an innovative cooling system is employed with a Reynolds number range of 15,000 to 30,000 to minimize the temperature of LiB cells. The continuity, momentum, and energy equations are solved using the Finite Volume Method (FVM). The computational fluid dynamics software ANSYS Fluent is applied to calculate the flow and temperature fields and to analyze the thermal management system for 52 LiB cells. The arrangement of batteries leads to symmetrical flow and temperature distribution occurring in the upper and lower halves of the battery pack. The impacts of SiO₂ distributed in a base fluid (water) are investigated. The results show that SiO₂ nanofluid with the highest volume fractions of 5% has the lowest average temperature values at all investigated Reynolds numbers. The innovative cooling system highlights the enhancement of the cooling process by increasing the SiO₂ concentrations, leading to the recommendation of the concentration of 5 vol% due to better thermal diffusion resulting from the enhanced effective thermal conductivity. The flow turbulence is increased by increasing the Reynolds number, which significantly enhances the heat transfer process. It is shown that increasing the Re from 15,000 to 22,500 and 30,000 causes increases in the Nu value of roughly 32% and 65%, respectively.

1. Introduction

Global transportation is a substantial polluter, emanating roughly 7.3 Bn metric tons of CO₂ in 2020. In that year, passenger vehicles were the primary offenders, representing 41% of global transportation pollutants [1]. Switching to an electric vehicle may help reduce air pollution and stimulate green job creation (but only if the electricity is generated using renewable energy). Between now and 2050, more than 60 Bn tons of CO₂ might be avoided by raising the portion of electric vehicles (EV) and plug-in hybrid cars on the road to 60%. However, the broad acceptance and commercialization of EVs continue to be constrained by technological bottlenecks [2,3,4,5,6]. Ref. [7] inspected the effects of electric vehicle charging on the power grid. They also studied the effects of EV charging stations on the energy consumption of building sites. Ref. [8] employed a real-world driving cycle method to analyze the energy consumption of EVs in a metropolitan area. To design more practical batteries, ref. [9] studied a variety of battery technologies at the material, pack, module, cell, and electrode levels to demonstrate their contributions to the overall performance of the battery module. Ref. [10] examined the effect of subsidy strategies on the local adjustment and environmental benefits associated with the spread of EVs in Korea, taking into account the change in the country’s power mix. Numerous researchers have determined that the performance of any electric car is highly dependent on the vehicle’s battery pack and its Thermal Management Systems (TMS) [11,12]. Both extremely high and extremely low temperatures can have an unfavorable effect on the battery’s efficiency. Operating a battery at a high temperature might result in overheating or even an explosion. If a battery works at a low temperature, it will not perform efficiently [13,14]. Thus, the batteries in EVs have a dedicated TMS that is constantly being studied and improved to enhance their performance and, in turn, the battery’s performance [15,16,17] presented a new polycarbonate matrix (PCM) composed of paraffin (PA), styrene butadiene styrene (SBS), and aluminum nitride (AlN). The results indicate that the innovative PCM composite integrated in the battery module may significantly reduce the thermal contact resistance, consequently increasing thermal control performance. Then, they examined a flexible form-stable composite PCM using expanded graphite (EG) as a thermal conductivity booster [18,19] demonstrated a hybrid battery TMS using paraffin wax as a PCM connected cooling plate organized in a honeycomb pattern and cooled with glycol. Ref [20] employed an artificial neural network to estimate LiB temperature under a variety of operating situations when equipped with a passive battery TMS based on nano-enhanced PCM. Ref. [21] investigated the performance of the phase change cooling of a battery pack equipped with 25 parallel 18650 LiBs.

Presently, liquid cooling will remain the primary method of BTMS. Upgrading the typical cooling medium to one with higher thermal conductivity is an important research path to enhance the effectiveness of LiB cells’ cooling systems. On the other hand, several researchers demonstrated the benefits of using nanofluids in different applications [22,23,24,25]. After 1995, Choi and his scientific team [26] synthesized a new fluid with excellent thermal properties that they dubbed a nanofluid. Recently, researchers started to used nanofluid in thermal management applications; among these are BTMs. Mokashi et al. [27] examined the Nusselt number for the thermal management of batteries using five types of cooling mediums such as hot oils, ordinary oils, gases, liquid metals, and nanofluids. It was found that the increase in and the fluctuation of the temperature are greatly controlled by the Reynolds (Re) number and the thermal conductivity (k) up to certain limits. Chen et al. [28] studied experimentally the thermal management of LiBs in EVs under various ambient temperatures and operating conditions. The system was based on a pulsating heat pipe (PHP), including a nanofluid. Their results reveal that a PHP with nanofluid limited the maximum temperature of the LiB to 42.22 °C and achieved a more uniform distribution of temperature across the surface of the battery, and the maximum temperature gradient across the LiB was less than 2 °C. Tousi et al. [29] employed an AgO nanofluid in a liquid-cooling battery TMS designed for 18650/21700- types LiBs. The result showed that when the input velocity and nanofluid volume percentage increased, the maximum temperature and temperature differential dramatically reduced. An experimental setup and a numerical tool were used by El-Khouly et al. [30] to examine the effects of employing nanofluids for cooling electronic chips. The findings demonstrated that using nanofluids increased the thermal conductance by 8.1% for the tested electronic chip, which had a surface area of 5 cm by 5 cm and a dissipated power of 130 W, over the analyzed working range. In order to quantify the temperature profile and pressure loss utilizing nanofluids flowing in the corrugated mini-channel of the EV battery cooling unit, Wiriyasart et al. [31] provided a computational analytical technique. It was discovered that coolant kind, mass flow rate, and coolant flow direction have a significant impact on temperature distributions. To remove the heat produced by an EV battery, Zhou et al. [32] designed a hybrid oscillating heat pipe (OHP) using ethanol aqueous solutions of CNTs. According to experimental findings, the vertical OHP charged with CNT nanofluids performed better in terms of heat transmission and start-up than the ethanol–water combination. The cooling capabilities of one-battery and five-battery systems were examined by Yutao Huo et al. [33]. The simulation findings demonstrate that the temperature can be maintained using a nanofluid-based BTM. Additionally, introducing nanoparticles may improve cooling performance in a system with five batteries, and significantly lower the average battery temperature. For their nanofluid-based BTM, Fanchen Wu et al. [34] used the lattice Boltzmann method to mimic free convection. The outcomes demonstrate that incorporating Cu nanoparticles could improve cooling and reduce the BTM’s temperature difference. Additionally, when the Rayleigh number varies from 10⁴ to 10⁶, the enhanced natural convection significantly increases the intensity of heat transfer. Using a 3-D CFD model, Liu et al. [35] investigated the effectiveness of nanofluids in improving the thermal performance of mini-channel TMS for a high-power LiB. The results showed that the inclusion of nanoparticles has a minimal impact on temperature homogeneity but may significantly lower the maximum temperature of the cell. A unique battery TMS with an HS, nanofluid cooling and metal foam–paraffin PCM composite was designed and examined by Kiani et al. [36]. The studies were done with three different kinds of nanofluids (Al₂O₃/AgO/CuO) and pure water. The results of the experimental tests show that AgO was the best choice, and that the cooling efficiency of the system based on nanofluids increased dramatically. In another study [37], they examined the impact of adding an alternating magnetic field. Mashayekhi et al. [38] developed a hybrid TMS for LiBs with high discharge rates. The hybrid TMS consisted of two parts, a passive part where refined paraffin in block form was joined with porous copper, and an active part where an Al₂O₃–water nanofluid flowed through an aluminum mini-channel. The results prove that at high discharge rates, applying passive and active cooling separately was inefficient in keeping the battery temperature below the safety limit of 60 °C. However, the hybrid TMS displayed a suitable thermal performance under the same circumstances. Alqaed et al. [39] explored the flow of non-Newtonian nanofluids (NNFs) inside an LiB connected to a solar cooling system. They observed that the coefficient of heat transmission is enhanced when the volume fraction of nanoparticles is raised and the mean battery temperature is lowered. Srinivaas et al. [40] investigated the function of flow directions, channels and nanofluids using a analytical approach. The research found that utilizing a converging channel would aid in regulating the temperature increase, whilst divergent channels benefit in lowering the variance in temperature. References [41,42,43,44,45,46,47] contain other developments concerning lithium-ion batteries.

In this research, the impact of employing varied nanoparticle concentrations of a (SiO₂–water) nanofluid for cooling 52 cylindrical LiB cells using an innovative cooling system is explored by a computational fluid dynamics (CFD) model. The batteries are arranged in a way that the symmetrical flow and heat transfer occur in the upper and lower halves of the battery pack. The different nanoparticle concentrations of SiO₂ (1–5%) with a fixed nanoparticles diameter of dp = 20 nm are utilized to increase the heat transfer and reject the heat from LiB cells. The innovative cooling system is developed to minimize the operating temperatures of devices and remove the heat from cylindrical battery cells, and thus reducing the temperature of LiBs. The computational fluid dynamics software Ansys Fluent is utilized to compute the flow and temperature fields and to analyze the TMS of 52 LiB cells. LiB cells are sensitive to temperature fluctuations. Extreme environmental conditions impair their cycle life and function. Therefore, proper cell temperature regulation is necessary for safe and reliable battery operation. Additionally, the high manufacturing costs of electric automobiles must be mitigated by the versatility of the battery pack design (EVs). The ideas underpinning CFD modeling rely on the finite volume approach. Basically, CFD is usually utilized as a design tool, notably for the objectives of design optimization, process optimization, and parametric analysis.

2. Physical Model

Figure 1 displays the novel design of the innovative cooling system for 52 LiB cells, where the spacing distance between the battery cells is S = 6 mm. A 2D view of the battery pack system domain of the battery cells, along with the coordinate system, is presented. Symmetrical flow and heat transfer could be obtained for the entire domain by considering only the upper or the lower half of the battery pack. Depending on the battery pack, the thermal properties of the battery cell are different, as in tabs zones. The total length of the battery (L) is 65 mm, and the width W is 18 mm, with 2 mm being the thickness of the battery cell. The TMS designed in this work consists of an efficient, innovative cooling system for cooling the battery surface, rejecting the heat, and improving the performance at different Reynolds numbers (Re = 15,000, 17,500, 20,000, 22,500, 25,000, 27,500 and 30,000). To investigate the influence of heat transfer enhancement on the cooling performance, different nanoparticle concentrations of SiO₂ (1–5%) with nanoparticle diameters of dp = 20 nm and different flow rates of the cooling fluid are considered. The temperature of T = 360 K is applied to the wall of the battery cells.

3. Numerical Technique and Boundary Conditions

3.1. System Description

Figure 1 shows the schematic of the innovative cooling system for cooling 52 cylindrical LiB cells using a SiO₂–water nanofluid as a coolant fluid in order to reduce the temperature of the LiB. As described above, different nanoparticle concentrations of SiO₂ for the SiO₂–water nanofluid are used to enhance the heat transfer and reject the heat from LiB cells. In total, 52 LiB cells are placed in the cooling pack, and the distance between each cell is S = 6 mm. In this study, the diameter of the inlet and outlet, the diameter of the cylindrical battery, and the spacing between the LiB cells are maintained at 10 mm, 8 mm, and S = 6 mm, respectively.

The boundary conditions of the computational domain are supplied for the specified issue, as shown in Figure 1. The physical model depicts an effective cooling method for LiB modules that applies a constant temperature directly to the LiB’s surface. The k-epsilon ($k-\epsilon$) turbulence model and the RNG technique are taken into consideration in the present simulation in order to achieve accurate prediction in the circular tube. The Navier–Stokes equations, which are used to quantitatively characterize momentum and mass transport, are solved for Newtonian fluids using the Finite Volume Method (FVM). This method is used to solve the time-independent incompressible Navier–Stokes equations and the turbulence model. The pressure field is assessed using the Semi Implicit Method for Pressure-Linked Equations (SIMPLE) pressure–velocity coupling technique. The turbulence intensity at the intake is kept at 1%. To solve equations and produce geometry and grids, Ansys Fluent is employed as the fluid simulation software. Air enters the tube at a constant temperature and velocity of 300 K throughout the fully grown stage. The channel walls are insulated, and the no-slip boundary condition is imposed on them. At the end of the tunnel, the air has an absolute pressure of 101,325 Pa. According to Figure 1, the boundary conditions are given for the computational domain of the current issue. This figure shows the innovative cooling system applied to 52 cylindrical LiB cells. The cylindrical walls are exposed to a constant temperature, with velocity taken in on the left and pressure exiting on the right. The uniform temperature T = 360 K is applied to the wall of the cylindrical LiB. In order to adapt the flow behavior of any application, the turbulence model is crucial. The finite volume approach is used to solve the time-independent incompressible Navier–Stokes equations and study the turbulence model. The pressure–velocity coupling method SIMPLE (Semi Implicit Method for Pressure-Linked Equations) is used to assess the pressure field. It is also noted that when the normalized residual values for all variables approach 10⁻⁵, the solutions converge.

3.2. Governing Equations

To finish the CFD analysis of the twin-pipe heat exchanger with louvered strip inserts, the governing equations (continuity, momentum, and energy) must be established. The two-dimensional form of the continuity, the time-averaged incompressible Navier–Stokes equations, and the energy equation regulate the phenomena under investigation. These equations take the following form in the Cartesian tensor system [42]:

• Continuity equation:

$$\frac{\partial }{\partial x_i}\left(\rho u_i\right)=0$$

(1)

• Momentum equation:

$$\frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\left[\mu \left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)\right]-\frac{2}{3}\mu \frac{\partial u_k}{\partial x_k}{\delta }_{ij}$$

(2)

• Energy equation:

$$\frac{\partial }{\partial x_j}\left(\rho u_j{C}_{p}T-k\frac{\partial T}{\partial x_j}\right)=u_j\frac{\partial p}{\partial x_j}+\left[\mu \left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)-\frac{2}{3}\mu \frac{\partial u_k}{\partial x_k}{\delta }_{ij}\right]$$

(3)

where $C_P$ is the specific heat at constant pressure, (kJ/kg·K).

The Reynolds-averaged approach to turbulence modeling requires that the Reynolds stresses $\left(-\overline{\rho \acute{u_i}\acute{u_j}}\right)$ in Equation (2) are modeled.

For the closure of the equations, the $k-\epsilon$ turbulence model is chosen. A common method employs the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients:

$$\left(-\overline{\rho \acute{u_i}\acute{u_j}}\right)=\mu \left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)$$

(4)

The turbulent viscosity term ${\mu }_t$ is to be computed from an appropriate turbulence model. The expression of the turbulent viscosity is:

$${\mu }_t=\rho C_{\mu }\frac{K^2}{\epsilon }$$

(5)

where $k$ is the turbulent kinetic energy, (${\mathrm{m}}^2/{\mathrm{s}}^2)$, and ε is the turbulent dissipation rate, $({\mathrm{m}}^2/{\mathrm{s}}^3$).

In the present study, the $k$ − ε turbulence model with RNG technique is used, as follows:

$$\frac{\partial }{\partial x_i}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{u_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]+G_k-\rho \epsilon$$

(6)

Similarly, the dissipation rate of the turbulence kinetic energy (TKE) $\epsilon$ is given by the following equation:

$$\frac{\partial }{\partial x_i}\left(\rho \epsilon u_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{u_t}{{\sigma }_k}\right)\frac{\partial \epsilon }{\partial x_j}\right]+C_{1\epsilon }\frac{\epsilon }{k}{G}_k-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}$$

(7)

where $G_k$ is the rate of generation of the TkE, while $\rho \epsilon$ is the destruction rate.

$G_k$ is written as:

$$G_k=\left(-\overline{\rho \acute{u_i}\acute{u_j}}\right)\frac{\partial u_j}{\partial x_i}$$

(8)

3.3. Mesh Independence Test

A mesh-independent test is performed on the physical model to obtain the most suitable mesh face sizes. In this study, eight mesh faces are considered, which are 916, 21,416, 41,416, 52,516, 63,616, 74,716, 85,816, and 96,916 at Re = 30,000, with a spacing distance of (S = 6 mm). All eight mesh faces are used to plot the average Nusselt number $N{u}_{av}$ at the wall of the cylindrical LiB in the same XY plot. The discretization grid is unstructured and non-uniform, as shown in Figure 2. All four-mesh faces give similar results for the average Nusselt number (Figure 2). However, any number of mesh faces in these four cases can be used. In this case, the mesh faces with 85816 are used because they are the best in terms of both accuracy and computational time. In fact, better accuracy can be obtained by grid sizes with more nodes, but increasing the density of the cells would make the computational time longer.

3.4. Validation of the Code

In order to ensure that the numerical code has been checked against other prior efforts and is prepared for further runs, code validation is crucial for any numerical task. The outcomes should be identical to or extremely similar to those of earlier studies that have been looked at. Additionally, it is critical to grasp the capabilities and constraints of any numerical code, in addition to ensuring the high accuracy of such a code. The experimental investigation of [41] is used to verify the numerical model. They carried out an experimental investigation of the thermal and flow properties of a channel made of a bank of aligned round tubes. Using air as a test fluid, the effects of the geometrical parameters on heat transfer and fluid flow were also investigated. Figure 3 compares the experimental findings from Lin et al. [41] with the numerical results of the Nusselt number and Reynolds number. The numerical findings and the outcomes of the experimental investigation are in reasonable agreement, as shown in Figure 3.

3.5. Thermophysical Properties of Nanofluids

The effective thermophysical characteristics of nanofluids must first be computed in order to perform the simulations for nanofluids. SiO₂ are the nanoparticles in use in this instance. The effective thermal conductivity ($k_{eff}$), the effective dynamic viscosity (${\mu }_{eff}$), the effective mass density (${\rho }_{eff}$), and the effective specific heat ($c{p}_{eff}$) are the main characteristics needed for simulations. In relation to these, the mixing theory is used to compute the effective qualities of mass density, specific heat, thermal conductivity, and viscosity.

For the density:

The density of the nanofluid, ${\rho }_{nf}$, can be obtained from the following equation [42]:

$${\rho }_{nf}=\left(1-\varphi \right){\rho }_f+\varphi {\rho }_{nf}$$

(9)

where ${\rho }_f$ and ${\rho }_{nf}$ are the mass densities of the based fluid and the solid nanoparticles, respectively.

For the heat capacity:

The effective heat capacity at a constant pressure of the nanofluid can be calculated from the following equation [42]:

$${\left(\rho c_p\right)}_{nf}=\left(1-\varphi \right){\left(\rho c_p\right)}_f+\varphi {\left(\rho c_p\right)}_{np}$$

(10)

where ${\left(\rho c_p\right)}_f$ and ${\left(\rho c_p\right)}_{np}$ are the heat capacities of the base fluid and the solid nanoparticles, respectively.

For the effective thermal conductivity:

Using the Brownian motion of nanoparticles in a circular tube, the effective thermal conductivity can be obtained by using the following mean empirical correlation [42]:

$$k_{eff}=k_{static}+k_{Brwnian}$$

(11)

$$k_{static}=k_f\left[\frac{\left(k_{np}+2k_f\right)-2\mathsf{\Phi }\left(k_f-k_{np}\right)}{\left(k_{np}+2k_f\right)+\Phi \left(k_f+k_{np}\right)}\right]$$

(12)

$$k_{Brwnian}=5\ast {10}^4\beta \varphi {\rho }_f{C}_p{}_f\sqrt{\frac{KT}{2}}f\left(T,\varphi \right)$$

(13)

where the Boltzmann constant is $k=1.3807\ast {10}^{-23}\mathrm{J}/\mathrm{K}.$ The values of β for different particles are listed in

Table 1. Values of β for SiO₂ nanoparticles.

Type of Particals	β	Concentration (%)	Temperature (K)
SiO2	$1.9526 {\left(100\varphi \right)}^{-1.4594}$	1% ≤ φ ≤ 10%	298 K ≤ T ≤ 363 K

.

Modeling,$f\left(T,\varphi \right)$

$$\begin{gathered} f\left(T,\varphi \right)=\left(2.8217\ast {10}^{-2}\varphi +3.917\ast {10}^{-3}\right)\left(\frac{T}{T_0}\right)+\left(-3.0669\ast {10}^{-2}\varphi -3.3991123\ast {10}^{-3}\right); \\ For 1\%\le \varphi \le 4\% and 300 \mathrm{K}\le T\le 325 \mathrm{K} \end{gathered}$$

For the effective viscosity:

The effective viscosity can be obtained by using the following mean empirical correlation [42]:

$${\mu }_{eff}={\mu }_f\ast \left(\frac{1}{1-34.87{\left(\frac{d_p}{d_f}\right)}^{-0.3}\ast {\varphi }^{1.03}}\right)$$

(14)

$$d_f={\left[\frac{6M}{N\pi {\rho }_{f_0}}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$

(15)

where M is the molecular weight of the base fluid, N is the Avogadro number = 6.022 × 10²³ mol⁻¹, and ${\rho }_{f_0}$ is the mass density of the base fluid calculated at temperature T₀ = 293 K.

Table 2. The thermo-physical properties of water and different nanoparticles at T = 300 K.

Thermo-Physical Properties	Water	SiO2
Density $\rho$ $\left(\mathrm{kg}/{\mathrm{m}}^3\right)$	998.2	2200
Dynamic viscosity, $\mu$ $\left(\mathrm{Ns}/{\mathrm{m}}^2\right)$	1.00 × 10−3	0
Thermal conductivity,$k \left(\mathrm{W}/\mathrm{m}·\mathrm{K}\right)$	0.6	1.2
Specific heat, $C_P \left(\mathrm{J}/\mathrm{kg}·\mathrm{K}\right)$	4182	703

shows the thermo-physical properties of water and the nanoparticles.

4. Results and Discussion

For the battery pack shown in Figure 1, fifty-two cylindrical LiBs are cooled with SiO₂ nanofluid to keep the operating temperature within the recommended range (288–338 K). The effects of different concentrations of SiO₂ on battery temperature and Nusselt number are discussed in this section.

4.1. Effect of Nanoparticles Concentration and Reynolds Number on the Battery Pack Temperature

Five SiO₂ concentrations (1, 2, 3, 4, and 5 vol%) are considered to investigate the best cooling process for the battery pack at different flow velocities (the Reynolds number varies from 15,000 to 30,000). Figure 4 shows that the SiO₂ nanofluid with the highest volume fraction of 5% has the lowest average temperature values at all investigated Reynolds numbers. In fact, increasing the volume fractions of nanofluid leads to an increase in the effective thermal conductivity of the fluid, which is favorable for heat transfer enhancement. As the coolant nanofluid cools battery cells consecutively from cell 4 to cell 49, the temperature increases. This is because the temperature difference between a battery and the fluid gets smaller and smaller as it progresses downstream, owing to the absorption of heat from earlier batteries, and the maximum temperature is reached at the last cells, the battery cell 49. To show the improvement in temperature reduction yielded by increasing the nanoparticle concentration, let us take Re = 15,000 and the battery cell 24 as an example. At these conditions, the battery temperature is 311, 310, 309, 308, and 307 K at the investigated concentrations of 1, 2, 3, 4, and 5 vol%, respectively, demonstrating the minimization of the temperature by more than 4 K by incorporating nanoparticles with pure water.

While a higher concentration leads to better thermal performance, Figure 4a–c also shows that the increase in the Re number decreases the temperature significantly. It can be seen that the temperature difference between cell 4 and cell 49 becomes very small for higher Re due to the elevation of the turbulent flow and the enhancement of the convection heat transfer coefficient. The temperature difference between cell 4 and cell 49 is about 11.6, 10.1, and 9.1 K for Re = 15,000, 22,500, and 30,000, respectively, at a SiO₂ concentration of 1%. The temperature difference values are 10.1, 10.0, and 7.0 K for Re = 15,000, 22,500, and 30,000, respectively, at a SiO₂ concentration of 5%. This shows how a higher Re enhances thermal performance and heat transfer. However, reasonable Re values should be used to avoid larger pressure drops, thus necessitating greater pumping power.

The temperature profiles of five SiO₂ concentrations are presented in detail for three battery cells (4, 29, and 49) at different Reynolds (Re) numbers in Figure 5. This figure provides evidence of the decrease in temperature that occurs with an increase in Re. The temperature profiles shown in Figure 5b,c exhibit a linear and uniform decrease in temperature with respect to Re. This suggests that the cooling process is consistent across the cells, and the increase in Re results in a decrease in temperature.

However, Figure 5a shows for cell 4 a deviation from the uniform behavior due to the effect of the entrance region. Cell 4 is located at the beginning of the battery pack, and this region is known to have a non-uniform temperature distribution, which affects the overall temperature profile of the cell. This highlights the importance of considering the location of the cells in the battery pack and the impact of the entrance region on the temperature profiles.

Despite this deviation, Figure 5 highlights the effectiveness of increasing SiO₂ concentrations in enhancing the cooling process. The figure shows a clear improvement in thermal diffusion, as evidenced by the decrease in temperature with increasing SiO₂ concentrations. This improvement is due to the enhanced effective thermal conductivity resulting from the presence of the NPs in the nanofluid. Based on the results presented in Figure 5, a concentration of 5 vol% is recommended as the optimal concentration for improved cooling performance.

4.2. Effect of Nanoparticles Concentration on Nusselt Number

To evaluate the enhancement of heat transfer due to the increase in nanoparticle concentrations and Re values, Figure 6 shows the average Nusselt number values of the battery pack. It shows that the incorporation of SiO₂ with water raises the Nu values, which explains the enhanced heat transfer. The concentration of 5 vol% leads to a significant enhancement in heat transfer compared to pure water, and that is why nanofluids are recommended for use in cooling applications instead of water. The inclusion of 5 vol% of SiO₂ with water increases the Nu values by 21% compared to pure water. Moreover, Figure 6 emphasizes that higher Re values could substantially enhance the turbulence and Nu values. For example, the increase in the Re from 15,000 to 22,500 increases the Nu value by 32%, and going further to Re = 30,000 raises the Nu number by 65%. Thus, high nanoparticle concentrations and high flow speed could be recommended when cooling batteries.

4.3. Temperature Extracted from the Battery Pack

Figure 7 provides a comprehensive analysis of the cooling temperature values of the battery cells at the recommended conditions using a 5 vol% SiO₂ concentration. This figure demonstrates the significant improvement in cooling performance achieved when using nanofluids, especially SiO₂, in the cooling system.

For example, in the entrance region of the battery pack, where battery cell 4 is located, the results show a decrease in temperature of almost 60 K at different Reynolds (Re) numbers. This reduction in temperature is particularly noteworthy, given that the flow in this region is not heated by other batteries. The location of battery cell 4 at the entrance region highlights the importance of considering the position of the cells in the battery pack and the impact of the entrance region on the cooling performance.

In the middle region of the battery pack, the results show that the temperature of battery cell 29 decreases from 52 K to 58 K as the Re value increases from 15,000 to 30,000, respectively. This highlights the improvement in the cooling performance in the middle region and demonstrates the effectiveness of the nanofluid in reducing the temperature of the battery cells.

Similarly, in the hotter exit region, where battery cell 49 is located, the results show a significant decrease in temperature, ranging from 47 K to 53 K, as the Re value increases from 15,000 to 30,000. This result further emphasizes the effectiveness of the nanofluid in reducing the temperature of the battery cells and demonstrates the importance of using nanofluids, especially SiO₂, in the cooling system to operate the batteries at desired temperatures with longer operation lives and improved efficiency.

In general, the results presented in Figure 7 provide clear evidence of the benefits of using nanofluids, especially SiO₂, in the cooling system to reduce the temperature of the battery cells and enhance the overall performance of the batteries.

5. Conclusions

An innovative cooling system using SiO₂ nanofluid for a battery pack consisting of 52 LiBs is investigated in this paper. The batteries are allocated in a staggered arrangement of three rows. A numerical solution is achieved using Ansys Fluent, and the model is validated against reported experimental data. Five SiO₂ concentrations are investigated, i.e., 1, 2, 3, 4, and 5%, to enhance the battery pack cooling process. Additionally, the flow speed is set between Reynolds numbers of 15,000 and 30,000. The nanofluid cooling temperature is set at 300 K. Based on the geometry and applied conditions, the following conclusions are drawn:

• Increasing the SiO₂ enhances the cooling process and minimizes the battery’s temperature due to improving the effective thermal conductivity of the nanofluid. About a 21% enhancement is achieved by increasing the nanoparticle concentration from 1 to 5 vol%;
• The temperature difference between the inlet and outlet is positively reduced with higher concentrations of nanoparticles;
• Increasing the Reynolds number improves the heat transfer process substantially due to increased flow turbulence. The increase in the Re from 15,000 to 22500 increases the Nu value by 32%, and going further to Re = 30,000 raises the Nu number by 65%;
• The applied cooling process can extract the batteries’ heat and minimize their temperature by more than 47 K.