*4.1. Validation*

The *Y* and *U* functions were developed as a function of depth of discharge and these functions were curve fitted using the experimental study. The experimental study was conducted at a 1C discharge rate, with a fully-charged coin cell at 4.2 V, with a discharge cut-off voltage of 2.75 V. The results of voltage and temperature from the developed numerical model were compared with the experimental study, as shown in Figure 3. Similar trends were observed for the experimental and numerical studies for voltage and temperature profiles. The maximum deviation for the voltage and temperature results of numerical models, as compared to the experimental study, were within ±5%, as shown in the Figure 3. Thus, the developed numerical model is considered valid for conducting numerical simulations.

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**Figure 3.** Voltage and temperature results comparison for the experimental study and the developed numerical model. **Figure 3.** Voltage and temperature results comparison for the experimental study and the developed numerical model.

#### *4.2. Effect of Discharge Rate 4.2. E*ff*ect of Discharge Rate*

The discharge rate of 1C discharges a fully-charged 100% SOC LIB in approximately 1 h. For the safety and longevity of the battery life, the LIBs are advised to charge less than 100% and not to discharge fully to 0% SOC. In simple terms, the continuous discharge rate indicates rate of energy extraction from battery, whereby the higher the discharge rate, the higher the energy extraction rate will be. However, during high-discharge output, LIBs suffer enhanced heat generation, which must be dissipated to safely operate LIBs. Moreover, the batteries suffer performance degradation at extreme temperatures, resulting in lower performance or sometimes malfunctioning. In this section, the effect of different discharge rates during normal operation is compared to coin cell behavior with penetrating element. Figure 4a shows the temperature profiles for different discharge rates and with penetrating element. The trend is similar to the one observed by Vyroubal et al. [19]. As expected for normal discharge tests, the temperature increases as the discharge rate of the coin cell is increased. For safety reasons, the LIR2450 coin cell temperature must not exceed 60 °C during normal operation. Therefore, either the discharge rate should be maintained low, or a high heat transfer co-efficient cooling system needs to be provided. As the discharge rate increases from 1C to 4C, the maximum coin cell temperature increases by 26.2 °C, and with the penetrating element the temperature increases by 84.0 °C. The temperature of the coin cell with penetrating element increases sharply due to development of a secondary current at the short-circuit site. Interestingly, the maximum temperature is observed at the center of the coin cell in both cases—without penetrating element and The discharge rate of 1C discharges a fully-charged 100% SOC LIB in approximately 1 h. For the safety and longevity of the battery life, the LIBs are advised to charge less than 100% and not to discharge fully to 0% SOC. In simple terms, the continuous discharge rate indicates rate of energy extraction from battery, whereby the higher the discharge rate, the higher the energy extraction rate will be. However, during high-discharge output, LIBs suffer enhanced heat generation, which must be dissipated to safely operate LIBs. Moreover, the batteries suffer performance degradation at extreme temperatures, resulting in lower performance or sometimes malfunctioning. In this section, the effect of different discharge rates during normal operation is compared to coin cell behavior with penetrating element. Figure 4a shows the temperature profiles for different discharge rates and with penetrating element. The trend is similar to the one observed by Vyroubal et al. [19]. As expected for normal discharge tests, the temperature increases as the discharge rate of the coin cell is increased. For safety reasons, the LIR2450 coin cell temperature must not exceed 60 ◦C during normal operation. Therefore, either the discharge rate should be maintained low, or a high heat transfer co-efficient cooling system needs to be provided. As the discharge rate increases from 1C to 4C, the maximum coin cell temperature increases by 26.2 ◦C, and with the penetrating element the temperature increases by 84.0 ◦C. The temperature of the coin cell with penetrating element increases sharply due to development of a secondary current at the short-circuit site. Interestingly, the maximum temperature is observed at the center of the coin cell in both cases—without penetrating element and with penetrating element at center.

with penetrating element at center. The discharge of LIBs at different C-rates is associated with exothermic reactions. Moreover, the heat generation rate is also dependent on the material of construction of electrodes and electrolyte. In the present study, the LiCoO<sup>2</sup> chemistry-based LIR2450 coin cell is considered. The in-depth heat generation rate during normal charging–discharging has been previously studied [28]. Figure 4b The discharge of LIBs at different C-rates is associated with exothermic reactions. Moreover, the heat generation rate is also dependent on the material of construction of electrodes and electrolyte. In the present study, the LiCoO<sup>2</sup> chemistry-based LIR2450 coin cell is considered. The in-depth heat generation rate during normal charging–discharging has been previously studied [28]. Figure 4b shows the heat generation rate variation with various discharge rates and penetrating element. For discharge

shows the heat generation rate variation with various discharge rates and penetrating element. For

rates of 1C and 2C, the total heat generation rate increases steadily, whereas for higher discharge rates the heat generation rate spikes slightly. During the normal operation of LIBs, the major part of heat is generated due to electrochemical reaction. Moreover, this heat generation is dependent on operating temperature, as electrochemical reactions are very sensitive to temperature. The complexity of electrochemical modeling arises as the continuous increase in temperature of the cell affects the electrochemical reaction. In addition, for the cases involving thermal abuse caused by nail penetration or crash, more complexity is added as LIB may behave abruptly, leading to fire or explosion, if thermal runaway temperature is reached. As shown in Figure 4b, in the case of penetrating element, the heat generation rate increases abruptly initially and then increases steadily. The abrupt increase in the heat generation rate is attributed to the formation of a high-current density area at the site of penetrating element, with very low resistance compared to battery internal resistance. In addition, the small sub-peaks for heat generation observed during the discharge process are related to the phase change influence of electrodes [28]. discharge rates the heat generation rate spikes slightly. During the normal operation of LIBs, the major part of heat is generated due to electrochemical reaction. Moreover, this heat generation is dependent on operating temperature, as electrochemical reactions are very sensitive to temperature. The complexity of electrochemical modeling arises as the continuous increase in temperature of the cell affects the electrochemical reaction. In addition, for the cases involving thermal abuse caused by nail penetration or crash, more complexity is added as LIB may behave abruptly, leading to fire or explosion, if thermal runaway temperature is reached. As shown in Figure 4b, in the case of penetrating element, the heat generation rate increases abruptly initially and then increases steadily. The abrupt increase in the heat generation rate is attributed to the formation of a high-current density area at the site of penetrating element, with very low resistance compared to battery internal resistance. In addition, the small sub-peaks for heat generation observed during the discharge process are related to the phase change influence of electrodes [28].

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Figure 4c shows the voltage response of a coin cell when different discharge rates are employed and compared with voltage response, with penetrating element of diameter 3 mm at 1C discharge rate. For the normal operation of the coin cell, the voltage response shows a general trend. With penetrating element, a discharge cut-off voltage of 2.75 V is reached at around 1200 s with 1C discharge. The rapid attainment of a discharge cut-off voltage attributes to the flow of a secondary high-density current due to an internal short circuit at the site of penetrating element. The results of maximum temperature, heat generation rate, and voltage profiles of the coin cell at different discharge rates and with penetrating element show that the discharge rate as well as penetration have a substantial effect on the thermal behavior of the coin cell. Figure 4c shows the voltage response of a coin cell when different discharge rates are employed and compared with voltage response, with penetrating element of diameter 3 mm at 1C discharge rate. For the normal operation of the coin cell, the voltage response shows a general trend. With penetrating element, a discharge cut-off voltage of 2.75 V is reached at around 1200 s with 1C discharge. The rapid attainment of a discharge cut-off voltage attributes to the flow of a secondary high-density current due to an internal short circuit at the site of penetrating element. The results of maximum temperature, heat generation rate, and voltage profiles of the coin cell at different discharge rates and with penetrating element show that the discharge rate as well as penetration have a substantial effect on the thermal behavior of the coin cell.

**Figure 4.** *Cont.*

**Figure 4.** (**a**) Temperature profiles for different discharge rates and with penetrating element. (**b**) Heat generation rate profiles for different discharge rates and with penetrating element. (**c**) Voltage profiles for different discharge rates and with penetrating element. **Figure 4.** (**a**) Temperature profiles for different discharge rates and with penetrating element. (**b**) Heat generation rate profiles for different discharge rates and with penetrating element. (**c**) Voltage profiles for different discharge rates and with penetrating element.

*4.3. Effect of Penetarting Element Size*
