Analysis of Geometrical Arrangement and Packing Material on Heat Generation in Lithium-Ion Battery Banks

Nomenclature

1  Introduction

The lithium-ion battery (LIB) is difficult to utilize in numerous applications due to the limited range of working conditions and discharge temperature. The thermal variations induce substantial changes in both the material’s structural form and intrinsic characteristics [1,2]. This makes the design of batteries forms a real challenge against safety problems such as the explosions. A MIL-STD-810 (G) is a military standard that tests the durability of smartphones in extreme atmospheric conditions. This type is tested using two methods, 501.5 and 502.5, to determine the suitable working temperature range, with tailoring to geographical conditions considered in the product life cycle [3,4]. In some types, the temperature was selected to be −20°C to 40°C as shown in Fig. 1, while the discharge operating temperature ranged from −20°C to 60°C as illustrated in Fig. 2 [5]. Satisfying the heat generation ranges of the LIB can be achieved by using it in cold conditions. In contrast, it is unsuitable in hot conditions due to poor insulation. Fig. 1 illustrates a clear positive correlation between ambient temperature and total energy outcome, with energy growing steadily from about 2550 mWh at 0°C to a peak of around 3350 mWh at 55°C. The polynomial fitting equation (with R2 = 1) confirms the strong dependency of energy output on temperature.

Figure 1: Energy rate vs. ambient temperature [3]

Figure 2: Discharge temperature characteristics for a typical high-power NCR18650B battery [3]

Fig. 2 shows the discharge voltage profiles at various ambient temperatures as observed. Higher temperatures (25°C and 40°C) resulted in higher discharge voltages and longer durations before voltage droped significantly, indicating enhanced electrochemical performance. In contrast, at sub-zero temperatures (e.g., −20 and −10°C), the battery displayed lower voltage levels and reduced discharge capacity, reflecting limitations in ion mobility and internal resistance under cold conditions.

The depletion of global oil resources, coupled with efforts to reduce carbon dioxide emissions, has made the development of sustainable energy storage systems such in EVs/HEVs and solar power techniques a priority [2,6], which will be considered a major issue for the future. Therefore, the battery has been used to provide optimal performance by supplying power to the EV/HEV during the driving operation. Consequently, the LIB technology globally used in electronic applications was designated as the best candidate due to its higher energy density and lower self-discharge [7]. Hence, the thermal management of lithium-ion batteries plays a crucial role in determining battery life and safety. Additionally, accurate heat generation calculation and low battery heat generation can alleviate the complexity of battery thermal management [8].

Lithium-ion batteries, one of the most widely used energy storage units, are now found everywhere due to their high energy density, high power output, low self-discharge rate, and minimal memory effect. Nevertheless, these advancements also have some counterparts, potentially causing a thermal runaway (TR) phenomenon due to their lower thermal stability [9,10]. Due to varying energy demands, battery cells are typically arranged in series or in parallel to function as a battery pack or a battery system. Angelo [7] adopted a theoretical and numerical approach to consider the battery thermal management systems (BTMS). A one-dimensional computational model was developed by combining the thermal circuit with the thermal model of the heat pipe. This model was validated by comparing its results with those obtained analytically, based on variable separation and numerical results from a three-dimensional CFD simulation. As a result, the one-dimensional computational model was considered sufficient to represent the temperature distribution in BTMS using heat pipes at 27.6°C.

The effect of changing the State of Charge (SOC) parameter of electrodes on the reversal heat and ohmic heat was investigated numerically and analytically by Chen et al. [8]. A numerical study was conducted using a thermo-electrochemical model to determine which components have the greatest impact on the three components of heat generation. Additionally, the effects of the highest active material concentration and the solid radius on the polarisation heat in lithium-ion batteries were discussed. It was demonstrated that reducing heat generation during the charging process increases the reversal endothermic time. Then, Li et al. [9] investigated the internal heat of the battery experimentally and numerically by using a three-dimensional CFD model of a house. The results revealed that an increase in battery current causes rising heat dissipation to the environment, leading to a 2.93% temperature increase. Additionally, combining BTMS with a composite phase change material (CPCM), a flat heat pipe (FHP), and a cooling liquid was considered analytically by Xin et al. [11]. Three BTMS configurations were evaluated: CPCM alone, CPCM with aluminium thermal sheets, and CPCM combined with flat heat pipes (FHP) and cooling liquid. Using the orthogonal method, the study found that the CPCM–FHP–liquid combination most effectively reduced maximum battery temperature by lowering liquid temperature and increasing cooling tube count. This setup enabled the battery to achieve a 2°C charge rate at an ambient temperature of 37°C. Hence, Chen et al. [12] utilised the Bernardi model alongside a cooling system to analyse the effect of reversible heat on EV battery pack performance, with results validated experimentally and numerically under real-world conditions. Similarly, Xun et al. [13] examined the thermal behaviour of cylindrical and flat plate LIB models during discharge using both analytical and numerical methods. Changing the size and number of cooling channels-while maintaining a constant volume ratio-had no impact on the battery’s average temperature; however, larger channels improved cooling efficiency, albeit with uneven temperature distribution. To enhance thermal management, Son and Du [14] introduced a fault detection and diagnosis (FDD) algorithm that effectively identified defects in LIBs through a two-step approach, outperforming Monte Carlo simulations. Yang and Cao [15] examined the role of interfacial thermal resistance in heat generation and dissipation using steady-state and transient methods. Their findings indicated that the flash diffusivity method in the transient case provided the highest thermal conductivity accuracy in both cross-plane and in-plane directions.

Additionally, the thermal behaviour of lithium iron phosphate (LiFePO4) batteries contributes to an improved understanding of their temperature response under various conditions. Ismail et al. [16] developed a MATLAB model to predict battery temperature under constant ambient conditions, showing good agreement with manufacturer data. The increasing demand for portable electronics has led to the development of various LIB types with differing thermal behaviours. Budget batteries typically produce more heat and operate less efficiently due to higher internal impedance [17]. Thermal abuse conditions further impact performance depending on the state of charge (SoC), with deep discharge posing the highest risk of failure [18]. Despite broad applications, efficient Battery Thermal Management Systems (BTMS) remain essential to maintain performance and safety. Enhancing cycle life-a key performance metric-can be achieved using thermoelectric coolers (TECs), which significantly improve thermal regulation [19–21]. Optimal BTMS design requires careful consideration of thermochemical properties and operational temperature ranges. Villano et al. [22] addressed this by analysing the specific heat capacities of lithium polymer batteries.

The preceding analysis of literatures emhasise the importance of temperature regulation, where maintaining optimal thermal conditions can significantly enhance battery efficiency, energy output, and discharge behaviour. Therefore, good thermal management is crucial in battery applications that operate across a wide range of temperatures. However, limited researches were focused on the integrated optimisation of battery pack design. Accordingly, the main contributions of this study are:

•   adopted a combined analytical and numerical approach to optimise the NCR18650B battery pack, considering cell count, material parameters, and geometric configuration across a wide temperature range.

•   This study combined one-dimensional analytical thermal resistance models with three-dimensional numerical simulations to achieve both computational efficiency and detailed thermal analysis. The one-dimensional model offers fast initial evaluation, while the three-dimensional simulations capture complex heat transfer and spatial temperature distribution. This hybrid approach ensures accurate and efficient thermal optimisation of the battery pack.

•   The analysis was considered two conditions (hot and cold) boundary conditions that leads to a decision of the safer design; which suits those conditions.

2  Battery Model

In this work, a battery pack is presented with different models aimed at determining the best design based on material parameters, the number of batteries, and geometrical arrangement. The parameters associated with the material include using the battery pack’s cover materials, using filler material to increase conduction among batteries, using an aluminium base, and using a fire-proof insulator. Table 1 presents the type, location, and thickness of material parameters under study. The physical models of the battery pack structure and the number of batteries considered are illustrated in Fig. 3a–c for nine batteries, 10 batteries, and a single battery, respectively.

Figure 3: Physical model of NCR18650B battery pack with (a) 9 batteries and (b) 10 batteries, and (c) a single battery

Inside the pack, the batteries are surrounded by filler material, which is covered by a pack cover of a specific thickness and then by an external layer of insulator. The pack arrangement models of rectangular and hexagonal shapes for 9 and 10 batteries studied in the work are shown in Fig. 4. Four different configurations have been simulated and analysed, namely, Pack-A, Pack-B, Pack-C, and Pack-D.

Figure 4: Considered cases of battery arrangement in the pack with (a) Pack-A: 9 batteries, rectangular shape, (b) Pack-B: 9 batteries, optimized shape, (c) Pack-C: 10 batteries, rectangular shape, and (d) Pack-D: 10 batteries, hexagonal shape

To obtain the relationship between the temperature and battery power, the datasheet of the NCR18650B battery was used to find the exact relation [23]. In other words, the power-temperature curve fitting was determined (refer to Fig. 1). There are certain assumptions necessary to model the battery that are necessary to achieve meaningful results. Firstly, the 18650 battery, as given in its name, is 18 mm in diameter and 65 mm long, while the zero indicates its cylindrical shape, as depicted in Fig. 5 [5]. Secondly, the axial conductivity of the battery is 30 W/m·K, and the heat capacity is 1700 J/kg·K (Jiang et al., 2023). Thirdly, assume the battery’s power supply is constant, which is sufficient for the system and the heat generated by the battery. Finally, assume an identical charge level for each battery in all models. Table 2 [5] lists the specifications of typical NCR18650B battery while Table 3 shows its material properties which are the density, specific heat capacity and thermal conductivity of Filler material, silicon rubber [24,25], fire-proof insulator [26], aluminium [27], copper [28], Delrin [29], 18650 cell material [30], the axial and radial properties of 18650 battery [31,32].

Figure 5: Battery NCR18650B dimensions

3  Thermal Resistance Network Analysis

As referred to in the introduction part, the working temperature range of the battery is −20°C to 60°C. However, the operational conditions were chosen as −30°C to 45°C, in the worst-case scenario, to select the optimum battery pack design for cold weather conditions. The case study of the battery was divided into two parts. Firstly, studying the effect of the cold side (negative pole) temperature that ranged between −20°C and −30°C as a boundary condition. Secondly, considering the impact of the hot side (positive pole), the temperature ranged from 45°C to 60°C as a boundary condition. A one-dimensional (1D) analytical approach to thermal resistance in the battery was adopted for both cold and hot cases. However, the system was assumed to be a single combined battery with a constant total output power of 1.5 W. Then, the thermal resistance analysis was used to determine the boundary conditions of the numerical model for the combined single battery (see Fig. 3c) for both cold and hot cases. Next, the output heat can be determined by using Fourier’s law as a function of thermal resistance and temperature difference [33] as given by the following equation;

Q˙=ΔTRequiv(1)

The temperature operating range of the battery is crucial for saving the battery life cycle. In intense conditions such as excessive heat in summer or cold in winter, the possibility of battery damage during the operation is very likely. In other words, rising temperature leads to battery life reduction while diminishing the temperature out of the operating range leads to the battery forfeiting the working capacity. In a cold case at −20°C battery temperature and −30°C ambient condition, it is expected that the coldest point of the battery occurs on the surface due to internal heat generation. Therefore, the thermal resistance calculation is analyzed from the surface to the ambient. The thermal resistance network of cold case is demonstrated in Fig. 6a. The total thermal resistance (Rtot) can be determined by the sum of contact thermal resistance (Rcont), conduction thermal resistance (Rcond), and convection thermal resistance (Rconv) [34]. The total resistance in the cold case, which was about 6.67°C/W can be calculated by using Eqs. (2)–(5) [9,34]. Next, the hot case is operated between 45°C to 60°C due to heat generation since the hottest point occurs in the axis of the battery. Accordingly, the 1-D analytical approach adopted to calculate the thermal resistance of the battery in hot case can be started from the battery middle to the ambient as shown in Fig. 6b. However, in the hot case, there is one more resistance which is battery resistance (RB), which can be computed by Ohm’s Law as given by Eq. (6). Subsequently, the resistance analogy was applied for the hot case to calculate the equivalent thermal resistance (Requiv) that has been computed by Eq. (7) approximately 10°C/W [12]. The conduction thermal resistance is given by;

Rcond=tkA(2)

where t = 64 mm and k = 30 W/m·K. The contact thermal resistance is defined as;

Rcont=1hcontA(3)

where hcont = 1000 W/m2·K. The convection thermal resistance is computed by;

Rconv=1hconvA(4)

where hconv = 25 W/m2·K. The total thermal resistance can be computed by;

Rtot=Rcond+Rcont+Rconv(5)

Figure 6: One-dimensional resistance network of (a) cold side (Negative pole) and (b) hot side (Positive pole)

The internal resistance of the battery is calculated by Ohm’s law as follows;

RB=VI(6)

The equivalent resistance then can be determined as;

Requiv=RB+Rtot(7)

As a result of these thermal resistance calculations, the relation between total resistance and battery resistance has been deduced. According to this relation, the following conditions have been achieved [7,13];

Rtot≤6.67∘C/W and 0≤RB≤3.33∘C/W

Accordingly, the worst case of the battery will be determined between hot and cold conditions, depending on the battery’s thermal resistance. When the battery resistance is lower than 3.33°C/W, batteries will be protected from overheating. However, the cold side will be more severe. On the other hand, if the battery thermal resistance is higher than the limit, the hot side will be more dangerous, and it may experience an overheating risk.

4  Numerical and Analytical Modelling

A three-dimensional (3D) numerical approach was employed to investigate the thermal performance of the NCR18650B battery pack by varying material parameters, the number of batteries, and the geometrical arrangement. This analysis aims to determine the optimal model that yields the best temperature range for enhancing the battery life cycle. Boundary conditions are defined as a 3-D model that includes ambient temperatures of −30°C for the cold case and 45°C for the hot case, respectively. Steady-state thermal analysis was performed to determine the cold and hot battery regions. Temperature contours on the battery surface were analysed to determine the lowest temperature in the battery pack under cold ambient conditions.

On the other hand, the maximum temperature is also analysed numerically at the central axis of the battery, where heat is generated for hot ambient conditions. Next, a numerical and analytical solution approach, along with the key design, can be achieved in this study by following specific procedures. The procedure steps are investigated by developing a resistance network and obtaining an analytical solution. At room temperature, the required number of batteries to provide 60 Wh of energy is eight. However, due to low-temperature degradation, the design options are simulated with 9 and 10 batteries rather than 8. Then, determine the number of batteries required for 40-h operational conditions under the worst-case temperature scenario.

Additionally, design the insulator to allow for the discharge of the battery within a specified temperature range, thereby preventing overheating of the battery. The battery life under normal conditions can be known. Thus, the one-dimensional analysis constraint is not working due to the internal heat generation in the battery. However, the one-dimensional analysis can be used to solve the constraints analysis of the battery. The limitation of the temperature difference between hot and cold conditions is approximately 5°C, calculated between the surface and axis battery positions for cold and hot conditions, respectively. If the temperature difference in the battery is less than 5°C, the hot conditions are less severe on the battery working than the cold conditions in all design options. Therefore, the 1-D battery model was solved analytically by studying the 1-D heat generation model of the infinite cylinder with finite length. Hence, the basic heat conduction law can be written by following the equations [35];

1rddr(rdTdr)+E˙genk=0(8)

where E˙gen=Q˙πrw2h.

By performing the derivative in the first term of Eq. (8), the temperature behaviour through the battery is given as;

d2Tdr2+1rdTdr+e˙genk=0(9)

Defining the temperature difference (θ) between any point in the cylinder and its wall as;

θ(r)=T(r)−Tw(10)

The boundary conditions using the temperature difference become;

dθ(0)dr=0and(rw)=0

By using the temperature difference, Eq. (9) can be written as;

d2θdr2+1rdθdr+e˙genk=0(11)

The solution of this equation gives the following parabola equation;

θ(r)=ar2+br+c

Applying boundary conditions given by;

dθ(0)dr=0→b=0andθ(rw)=0→θ(rw)=arw2+c=0→c=−arw2

The solution obtained is given as;

θ(r)=ar2−arw2(12)

By deriving Eq. (12) twice, the following equation is obtained. To solve the non-homogeneous part (in this case, “a” remaining a constant) by solving the differential Eqs. (13) and (14) to get;

d2θdr2+1rdθdr+e˙genk=0→2a+2a+e˙genk=0→a=−e˙gen4k andc=e˙genrw24k(13)

So, the solution is given as;

θ(r)=−e˙gen4k(r2−rw2)(14)

Then, at r = 0, the temperature difference between the battery center and its wall is determined by;

θ(0)=e˙genrw24k=Q˙πrw2hk=0.01∘C

As a result of θ < 5°C, the cold case was selected as the worst case for testing the optimum design.

5  Results and Discussion

5.1 Analytical Approach Results

The analytical results of battery temperature at different cover thicknesses for the cold case are illustrated in Fig. 7. The results are obtained for 9 and 10 batteries with different materials, aluminium and Delrin. Since this analysis is for a cold case, the higher the temperature, the more optimal the conditions (material, battery number, and thickness) are.

Figure 7: The effect of casing thickness on battery temperature

The maximum limit of cold-case battery temperature was achieved for a 9-battery pack covered with Delrin, and it was approximately −15.7°C. On the other hand, the 10-battery pack has achieved the minimum battery temperature limit of approximately −20°C when using Delrin. It can be deduced that the best model is obtained using a hexagonal-shaped battery pack covered with Delrin of 1.8 mm in thickness. Although the 1-D analytical method is insufficient for estimating the accurate battery temperature, it helps to understand the worst-case condition, which is crucial for determining the main design features of the battery pack. Since the 1-D solutions for different design models are the same, it is not possible to compare different design options in 1D. Therefore, numerical analysis has been adopted to obtain more detailed information about the optimum configuration of the battery pack.

5.2 Numerical Analysis Results of a 9-Battery Pack

For a 9-battery pack, Fig. 8a–d shows the numerical results of different models: base case, base case with filler material, base case with 2.5 mm rubber, and base case with shape optimisation for cold and hot cases. The results of the maximum temperature achieved for both hot and cold cases were 53.7°C and −21.34°C, respectively, for the base case compared to the other cases. This is because the reference model (base case) did not contain any improvement by adding other materials such as amorphous carbon filler, Silicon rubber, Fire-proof insulator, aluminium base, and Delrin. In conclusion, the thermal performance of the 9-battery pack has not exceeded the allowable maximum limit of 54°C. However, the results obtained for cold conditions show a deficiency in the operation temperature, which has fallen below the minimum accepted limit of −15.7°C.

Figure 8: Temperature distribution of the 9-battery pack for (a) the base case model, (b) the base case model with filler material, (c) the base case model with a 2.5 mm rubber cover, and (d) the base case model with shape optimization

5.3 Numerical Analysis Results of a 10-Battery Pack Conventional Arrangement

For 10-batteries pack, Fig. 9a–f depicts the numerical results at cold and hot conditions of the base case with 1.2 mm Al base thickness, 1.4 mm Al base thickness, 1.5 mm Al base thickness with fire-proof insulator Al, 2.5 mm rubber and 1.5 mm Al base, 5 mm rubber with 1.5 mm Al base, and filler material with 1.4 mm Al base, respectively. The results showed that using an aluminium base with a thickness of 1.5 mm, along with top and bottom insulators (Fig. 9c), produces the highest temperatures of 52.81°C and −22.2°C in hot and cold conditions, respectively, compared to other models. This is attributed to the aluminium material having the largest specific heat and thermal conductivity (see Table 3). The insulator reduces heat dissipation from the battery to the environment, leading to increased battery temperature in both cold and hot cases. In the context of the operation temperature range, the same scenario with a 9-battery pack has been repeated with a 10-battery pack. The hot solutions were below 53°C, which meets the requirements, while this was not the case with cold cases, which have exceeded the temperature limit of −15.7°C. In the base case with filler material, the temperature comparison between the 9 and 10 batteries, shown in Figs. 8b and 9f show a hot and cold trend for each case. The results illustrated that the lowest temperature achieved for 10 batteries was −22.45°C, compared to −52.55°C for the nine batteries. This is because the cold case temperature for the 10 batteries was very close to the battery temperature range of the 9-battery model.

Figure 9: Temperature distribution of the 10-battery pack for (a) the base case model with 1.2 mm Al base thickness, (b) the base case model with 1.4 mm Al base thickness, (c) the base case model with 1.5 mm Al base thickness and fire-proof insulator, (d) the base case model with 1.5 mm Al base thickness and 2.5 mm rubber, (e) the base case model with 1.5 mm Al base thickness and 5 mm rubber, and (f) the base case model with filler material with 1.4 mm Al base

5.4 Numerical Analysis Results of a 10-Battery Pack in a Hexagonal Arrangement

The new model is designed in a hexagonal shape to enhance battery modelling, thereby improving the temperature range in both hot and cold conditions. Fig. 10a–g illustrates the numerical simulation results of 10 batteries for cold and hot cases of base case, base case model with insulator at top and bottom, base case model with Delrin thickness 2, 2.5, 3, 10 mm, and base case with shape optimisation model, respectively. The results revealed that the maximum battery temperatures of −20.6°C and 56.17°C have been generated in the base case hexagonal shape model with 2.5 mm Delrin for cold and hot cases, respectively. The reasons are that increasing the Delrin thickness reduces the heat conduction from the battery to the ambient, which is evident at a Delrin thickness of 10 mm (see Fig. 10e).

Figure 10: Temperature distribution of 10 battery packs for a hexagonal shape model, (a) a hexagonal shape base case model, (b) a hexagonal shape base case model with fire-proof insulator, (c) a hexagonal shape base case model with model with 3 mm Delrin thickness, (d) a hexagonal shape base case model with model with 2.5 mm Delrin thickness, (e) hexagonal shape base case model with model with 2 mm Delrin thickness, (f) hexagonal shape base case model with model with 10 mm Delrin thickness (g) optimization base case model

The result of the developed hexagonal configuration indicates an enhancement in the thermal behaviour of the battery pack, especially when using 10 batteries. Nevertheless, the results illustrated that the lowest and largest battery temperatures were achieved for the base case of hexagonal shape, −21.1°C and 53.92°C, and the base case −22.45°C and 52.65°C in cold and hot cases, respectively, at 10 batteries (see Figs. 9a and 10a). This is because the hexagonal shape has a good thermal enhancement by increasing the heat transfer area of the battery.

The numerical results of all models, using 9 and 10 batteries for both cold and hot cases, are listed in Table 4. In 9 batteries with different models, it is observed that there is no appropriate solution that meets the design requirements. This is due to the maximum and minimum battery temperature values for all models being outside the operating temperature range. Additionally, in 10 batteries, there are modifications to the base case model, such as a hexagonal shape with Delrin material. The results showed the best case was the base case hexagonal shape model with 2 mm Delrin thickness, which provided the largest temperature of −20.6°C in the cold case compared to other models because the Delrin material has lower thermal conductivity (0.210 W/m·K) compared to the aluminium material (205 W/m·K).

In the same context, the percentage difference between the standard operation temperature range and the current results is considered to show how the geometrical arrangement and materials affect the thermal performance of the battery package. For the minimum battery temperature, a significant deviation in the percentage difference between the considered cases can be observed, as shown in Fig. 11. This behaviour indicates the existence of a nearest minimum temperature, with a 3% difference from the common operation minimum temperature (−20°C), when using the hexagonal shape model with a 2 mm Delrin thickness. In contrast, the percentage difference for maximum temperature exhibits a higher level of uniformity, at approximately 34%, as represented by the trend line in red, as illustrated in Fig. 12.

Figure 11: The deviation of the predicted minimum temperature from the common value

Figure 12: The deviation of the predicted maximum temperature from the common value

The total thermal resistance for all cases of lithium batteries is illustrated in Figs. 13 and 14 on the cold and hot sides. The total resistance was determined for each side by calculating the equivalent and internal resistances (see Eqs. (1), (6) and (7)). The results showed that the lowest and highest values of total resistance were 0.06 and 0.29°C/kW at temperature differences for the cold side were 0.6°C and 2.8°C, respectively. The maximum and minimum results of total resistance were 1.34 and 1.06°C/kW at hot side temperature differences of 12.4°C and 11.6°C, respectively.

Figure 13: The total thermal resistance for all battery cases of the cold side

Figure 14: The total thermal resistance for all battery packing cases of the hot side

6  Conclusion

In this work, the thermal performance of the NCR18650B battery pack was considered using an analytical and numerical approach. The following remarks can be concluded:

•   The 9-battery pack did not meet the required operation temperature, as all models were out of the temperature range.

•   Increasing Delrin thickness from 2 to 3 mm led to a decrease in the minimum temperature by 2%.

•   The battery in a hot case met the requirements, while in cold cases, it did not satisfy the requirements.

•   Each battery should be as close to the others as possible to reduce the heat losses by convection.

•   Delrin material should be preferred instead of Al due to its low thermal conductivity.

•   When the thickness of Delrin was increased, the results became worse because of the rising thermal conduction resistance.

•   The candidate solution was the model that had a hexagonal shape instead of a rectangular shape, a minimum cross-section area, and a minimum Delrin thickness to decrease the conduction thermal resistance.

Acknowledgement: This work was supported in part by Ozyegin University, Istanbul, Turkey.

Funding Statement: The authors received no specific funding for this study.

Author Contributions: The authors confirm contribution to the paper as follows: Conceptualization, Seenaa Khudhayer Salman and Shaymaa Husham Abdulmalek; literature review, Shaymaa Husham Abdulmalek, Raaid Rashad Jassem Al-Doury and Ali Ahmed Gitan; methodology, Ali Ahmed Gitan, Thamer Khalif Salem and Raaid Rashad Jassem Al-Doury; software and analysis, Thamer Khalif Salem; writing and editing, Ali Ahmed Gitan. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: All data generated or analyzed during this study are included in the published article.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.

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