Influence of convective heat transfer coefficients on thermal behaviour of a lithium-ion cell: a numerical study

In the current study, the impact of C-ratio, convective heat transfer coefficient, and free stream temperature on the maximal cell temperature and temperature uniformity was computationally and statistically examined. Results revealed that the free stream temperature was the main influential factor for the maximal cell temperature for both natural and forced convection conditions while the C-ratio was the most effective parameter for the temperature uniformity for both natural and forced convections. On the other hand, the contribution of the free stream temperature to the maximum battery temperature increased from 63% to 94% when the conditions were changed from natural convection to forced convection. Moreover, the contribution of the C-rate to the temperature uniformity decreased from 89% to 79% when the conditions were changed from natural convection to forced convection. The results obtained from this study are significant in terms of determining which factor should be given more importance under natural and forced convection conditions.


Introduction
In recent years, the focus on environmentally friendly vehicles has increased, particularly hybrid electric vehicles and electric vehicles [1].This feature of electric vehicles will play an important role in eliminating many problems, especially global warming [2].In electric vehicles, technologically advanced energy storage devices are used instead of traditional fossil fuels [3].In recent years, lithium-ion batteries (LIBs) have come to the fore among energy storage devices [4].It should be noted that lithium-ion batteries have the potential to generate heat while in use [5].In excessive operating conditions such as high discharge rates, the amount of heat released increases significantly [6].It can be stated that high temperatures may have a negative impact on the performance of LIB cells.Therefore, the heat released during the discharge of LIB cells should be removed [7].
There are many articles in the literature examining the thermal behaviour of LIBs.Cooling systems such as air cooling [8,9], liquid cooling [10,11], and phase change material cooling [12,13] have been studied to improve the thermal performance of LIB cells.Hai et al. analysed the impact of air inlet velocity on the thermal behavior of the LIB cell pack [14].The temperature of the batteries with aligned and nonaligned arrangements was obtained by simulations.It was found that the cell package temperature and outlet air temperature decreased with the increment in the air flow rate.Moreover, the results revealed that the aligned battery pack exhibits better thermal behavior.Hasan et al. designed a system based on air cooling for enhancing the thermal behaviour of LIBs [15].The result indicated that the average air temperature decreased and the temperature distribution improved with the increase in Reynolds number.In addition, the results displayed that the average heat transfer rate (Nusselt number) of the cell pack increased with the increment L/h.Similarly, for a discharge rate of 2C, the flow rate should be greater than 12 L/h.Li et al. developed a composite phase change material by incorporating an electrically insulating material [18].The result revealed that the composite phase change material exhibited better thermal properties than other structures.The result also indicated that the composite phase change material enhanced the cooling capacity of the cell module compared to natural cooling.Zhou et al. examined the influence of various phase change material parameters such as phase change temperature, structure, and thickness on the cooling capacity of prismatic lithium-ion cells [19].The result demonstrated that decreasing the phase change temperature and increasing thickness enhanced the cooling capacity of the battery system.Moreover, it was determined that the phase change thickness of 25 mm was optimal thickness considering the temperature uniformity.
There are three multiscale multidimensional (MSMD) models namely Newman, Tiedemann, Gu, and Kim (NTGK), pseudo 2 dimensional (P2D), and equivalent circuit model (ECM) in ANSYS Fluent.In addition to the studies summarized above, there are many studies in the literature in which the thermal behavior of LIB cells is studied numerically.According to Zhang et al., the NTGK model can be utilized to analyse the thermal performance of lithium-ion battery packs [20].The designed cooling system based on water cooling indicated that the cell temperature and temperature uniformity can be ensured at a tolerable level by adjusting the temperature and inlet velocity at a 5C discharge rate.Kök and Alkaya analyzed the discharge operation of the LIBs by using the NTGK model to investigate the thermal performance [21].It was determined that the cell temperature increased by increasing the discharge rate from 0.5C to 3C.Moreover, heterogeneous temperature distribution was observed under high discharge rates.Celik et al. examined the thermal behavior of cylindrical LIB cells under distinct discharge conditions by the NTGK model [22].The effects of free stream temperature, C-ratio, and convective heat transfer coefficient (HTC) on the cell temperature were obtained.As the discharge rate increased, the study found that the convective HTC had a greater impact.Furthermore, it has been found that increasing the convective HTC is necessary to avoid battery overheating during high discharge rates.Paccha-Herrera et al. conducted a comparison of thermal models for a 26650 lithium-ion battery composed of LiCoO 2 [23].The results revealed that the NTGK model has a low error rate at low discharge rates and a higher error rate at high discharge rates.All models exhibited the same amount of error for the driving cycle, and the lumped model was found to be more suitable for implementation under wide operating conditions.In a recent study, Kumar et al. used a single particle model to obtain the charge-discharge behavior of a prismatic LIB under distinct C-rates [24].The discharge profiles obtained with the single particle model were used to obtain the thermal behaviors with the NTGK model at 0.5, 1, and 2 C rates.The results showed that the errors between the experimental studies and the simulation results were less than 1%.
Although there have been a number of studies in the literature, there is nonetheless room for the prediction of the thermal behavior of lithium-ion cells by the NTGK method.In this study, the NTGK model was applied to evaluate the thermal behaviour of LIB cells under distinct convection conditions.Furthermore, the impacts of free stream temperature, C-ratio, and convective HTC on maximal cell temperature and temperature uniformity were determined quantitatively.

Materials
A publicly available LiMn 2 O 4 /graphite prismatic battery was utilized for the simulations.The available potential interval of the Li-ion batteries is between 3.00 V (0% SOC) and 4.20 V (100% SOC).The nominal capacity was 14.6 Ah.Table 1 presents LiMn 2 O 4 -14.6 Ah lithium-ion prismatic cell specifications.Figure 1 shows the general geometry of LIB cell.Thermophysical features of LIB cells and tab materials are presented in Table 2.

Methods 2.2.1. Governing equations and NTGK modeling
Valuable information in analyzing battery thermal behavior can be obtained by battery thermal simulations.Concerning the NTGK model, input factors and coefficients can be obtained by discharge data.The NTGK model parameters obtained in [25] were implemented in the current work.The heat generated by a LIB cell during operation is represented in Equation 1 [26,27].6) 3  (5) where C p and ρ present specific heat and density of the battery.σ + and σ − represent the effectual conductivity.φ + and φ − represent the phase potentials.Q g is the heat generated by the battery.j ECh and j short are the volumetrical current transference rate and the current transference rate, respectively.There is a functional relationship between the U and Y coefficients and the depth of discharge (DoD) [14,15] ∇(σ+∇ (7) where x 0 -x 6 are the fitting parameters.Y and U coefficients implemented in our work were received from the work of [15].The depth of discharge (DoD) is described as: where J is the current intensity dispersion, t shows the time elapsed during the charge/discharge process, and Q T is the electrode capacity (Ah/m 2 ).

Mesh independence
The results obtained with the simulation are highly dependent on the mesh structure.Therefore, a mesh independence test should be applied before the simulations are run.Therefore, the relationship between different mesh numbers and the maximal battery temperature was determined at a 4C discharge ratio.The convective heat transfer coefficient and free stream temperature were 5 W/mK and 300 K, respectively.The mesh structure of the LIB cell is depicted in Figure 2. The results of mesh independence are presented in Figure 3. Figure 3 revealed that the maximum cell temperature first decreased and then nearly remained constant as the number of meshes increased.The maximal battery temperature changed from 313.9549 K to 313.9556 K as the mesh count rose from 51,744 to 69,064.The amount of change was less than 0.1%.For this reason, the mesh number 51,744 was chosen for further studies in order to ensure that the result is independent of the mesh number and to get faster results.

Experimental validation
It is expected that the results obtained with the simulation will be in agreement with the experimental result.Therefore, a confirmation test was performed at different discharge rates, including 1C, 3C, and 5C.Free stream temperature and HTC were 300 K and 5 W/mK, respectively.Results shown in Figure 4 revealed that the simulation outcomes matched well with the experiential findings.

Statistical analysis
In this study, the effects of free stream temperature (FST), convective heat transfer coefficient (HTC), and C-ratio on maximal cell temperature and temperature uniformity were investigated by the Taguchi experiment design method.Experimental design not only allows simulations to be performed with a small number of performances but also allows statistical evaluation of the results.In other words, the results that could not be obtained as a result of the examinations made with the traditional methods were obtained by using the Taguchi experimental design method.Determining the objective function is the 1st step of the Taguchi method.The objective functions in the current work are maximal battery temperature and temperature uniformity.In this work, while it was desired to minimize the maximum cell temperature by controlling various factors, a homogeneous temperature distribution was also expected.The 2nd stage of the Taguchi design is to determine the determinants that can influence the objective function.Controllable factors in this study were selected as FST, C-rate, and HTC.Controllable factors and their levels are shown for natural convection and forced convection in Table 3.The third step in Taguchi's experimental design is the determination of the orthogonal array.The L9(3 3 ) orthogonal arrangement is shown in Tables 4 and Table 5 for natural and forced convection, respectively.The fourth step of the Taguchi design is to run simulations and collect data.In this step, simulations were performed according to the conditions given by the orthogonal array.Minimal cell temperature and maximal cell temperature values were obtained with simulations.Temperature uniformity was determined by calculating the difference between the maximal cell temperature and the minimum cell temperature.The final step of the Taguchi design is the analysis of the collected data.The analysis process was carried out using the smaller-is-better characteristic since it was desired that the maximal cell temperature and temperature uniformity functions be minimal.

Results and discussions
The temperature results for both natural convection and forced convection were presented as functions of the FST, the C-ratio, and the HTC.Then the results were discussed considering the Taguchi design.Results of battery temperatures (maximal cell temperature and minimal cell temperature) for natural convection and forced convection are tabulated in Table 6 and Table 7, respectively.Temperature uniformity (dT) was reflected by the distinction between the maximal battery temperature and the minimal battery temperature.Concerning the natural convection conditions, the biggest maximal cell temperature of 317.7783K was estimated for n9 while the biggest minimum cell temperature of 316.7337K was also estimated for n9.On the other hand, for the natural convection conditions, the largest temperature uniformity value (1.1203) was calculated for n8.Concerning the forced convection conditions, the highest maximal battery temperature of 313.5813K was obtained for f9 while the highest minimum cell temperature of 313.3024K was also estimated for f9.Similarly, for the forced convection conditions, the largest temperature uniformity value (0.3317) was calculated for f8.The S/N ratios for the maximal cell temperature and dT are also shown in Table 6 and Table 7 for the natural and forced convection conditions, respectively.
Table 8 shows the response Table for the maximal cell temperature for natural convection.As can be seen from Table 8, the FST factor had the highest delta value with a value of 0.1368, indicating the highest impact of the FST on the maximal cell temperature.The delta (Δ) value of the C-ratio was 0.0604 which was lower than the HTC.The HTC exhibited the lowest delta value of 0.02.Additionally, Table 8 showed that the FST's contribution to the maximal cell temperature was 63%.For natural convection, the contribution of C-rate and HTC to the maximum battery temperature was 28% and 9%, respectively.Table 9 shows the response Table for the maximal cell temperature for forced convection.The highest delta value for the forced convection conditions was obtained for the FST factor with a value of 0.1408 for the maximal cell temperature.The highest Δ value of the FST demonstrated that concerning the forced convection conditions the impact of the FTS on the maximal cell temperature was the highest.The Δ value of the C ratio and the HTC factors was 0.0070 and 0.0018, respectively.This indicated that the impact of the C-ratio on the maximal cell temperature was larger than that of the HTC for forced convection conditions.Additionally, Table 9 showed that the FST's contribution to the maximal cell temperature was 94%.For forced convection, the contribution of C-rate and HTC to the maximum battery temperature was 5% and 1%, respectively.Table 10 shows the response Table for the temperature uniformity for natural convection.The largest Δ value of 8.5512 was obtained for the C-ratio.The Δ value of the HTC (0.9083) was lower than that of the FST (0.1976).These results revealed that the C-ratio was the most powerful factor in the temperature uniformity for natural convection conditions.Moreover, concerning the natural convection conditions the influence of the HTC on the temperature uniformity was higher than that of the FST.Additionally, Table 10 presented that the contribution of the C-ratio to the temperature uniformity was 89% for the natural convection conditions.Furthermore, the contribution of the HTC and FST to the temperature uniformity was 9% and 2%, respectively.Table 11 shows the response Table for the temperature uniformity for forced convection.According to Table 11, the delta values of the factors were 6.4167, 0.9875, and 0.6878 for the C-rate, HTC, and FST, respectively.The largest Δ value calculated for the C-ratio revealed the biggest impact of the C-ratio on the temperature uniformity for forced convection conditions.Moreover, the impact of the HTC on the temperature uniformity was higher than that of the FST for forced convection conditions.Furthermore, Table 11 indicated that the contribution of the C-ratio to the temperature uniformity was 79% for the forced convection conditions.Additionally, the contribution of the HTC and FST to the temperature uniformity was 12% and 9% for the forced convection conditions, respectively.

Conclusion
An L9 (33) orthogonal array was employed to assess the impacts of the C-ratio, heat transfer coefficient, and free stream temperature on maximal cell temperature and temperature uniformity.The primary results that can be drawn from the current study are listed below: • The control factor with the most important impact on the maximal cell temperature was free stream temperature with a contribution of 63% and 94% for natural and forced convections, respectively.
• The control factor with the most significant influence on the temperature uniformity was C-rate with a contribution of 89% and 79% for natural and forced convection conditions, respectively.
• The heat transfer coefficient has the least notable influence on the maximum cell temperature.Moreover, less attention can be paid due to the limited contribution to the free stream temperature for temperature uniformity.
• The results obtained can offer quantitative information to assist in the creation of thermal management systems for LIB cells.

Figure 4 .
Figure 4. Relationship between the simulations and experimental result.

Table 1 .
Physical parameters of lithium-ion cell.

Table 2 .
Thermal and physical properties of lithium-ion cell.

Table 3 .
Levels of factors for natural convection and forced convection.

Table 4 .
Orthogonal matrix for natural convection.

Table 5 .
Orthogonal matrix for forced convection.

Table 6 .
Results of battery temperatures for natural convection.

Table 7 .
Results of battery temperatures for forced convection.

Table 8 .
Response Table for maximal battery temperature for natural convection.

Table 9 .
Response Table for maximal battery temperature for forced convection.

Table 10 .
Response Table for temperature uniformity for natural convection.

Table 11 .
Response Table for temperature uniformity for forced convection.