## 4 Conclusions  
In this study, a battery thermal management system (BTMS) for a battery pack housing a battery module consisting of a hundred NCR18650 lithium ion cells was designed and tested in relatively cold ambient conditions. The BTMS performance was tested for two major objective function criteria which are:  
* maximum temperature recorded by a cell in the battery pack which at any instant should be kept below 40 \({}^{\circ}\)C and
* maximum temperature difference between any cells in the battery pack during testing which should not exceed a threshold of 5 \({}^{\circ}\)C.  
The temperature limit threshold for operating LiBs was optimally obtained from various literature and battery data specification documents. Design variables--three levels of cooling-air flow rate and two levels of current rate were combined using a full factorial experiment design method to develop a full array of experiments performed on the BTMS for the battery pack after experimentation. General BTMS performance trends were observed in the obtained results such as higher current rate experiments produced relatively higher  
Figure 26: Regression model predicted output vs. actual output for a sample input. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Charge at 0.5 C**} & \multicolumn{3}{c}{**Discharge at 0.5 C**} \\ \hline  & 1.4 (m/s) & 2.4 (m/s) & 3.4 (m/s) & 1.4 (m/s) & 2.4 (m/s) & 3.4 (m/s) \\ \hline Actual (\({}^{\circ}\)C) & 30.70 & 26.30 & 26.70 & 29.40 & 26.90 & 25.80 \\ \hline Predicted (\({}^{\circ}\)C) & 30.42 & 26.85 & 26.42 & 29.77 & 26.17 & 26.17 \\ \hline \% Error & 0.91\% & 2.08\% & 1.04\% & 1.25\% & 2.72\% & 1.42\% \\ \hline  & \multicolumn{3}{c}{**Charge at 0.75 C**} & \multicolumn{3}{c}{**Discharge at 0.75 C**} \\ \hline  & 1.4 (m/s) & 2.4 (m/s) & 3.4 (m/s) & 1.4 (m/s) & 2.4 (m/s) & 3.4 (m/s) \\ \hline Actual (\({}^{\circ}\)C) & 36.40 & 31.40 & 27.90 & 37.70 & 29.70 & 27.50 \\ \hline Predicted (\({}^{\circ}\)C) & 36.67 & 30.85 & 28.17 & 37.33 & 30.43 & 27.13 \\ \hline \% Error & 0.75\% & 1.76\% & 0.98\% & 0.97\% & 2.47\% & 1.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Absolute Relative Error between Regression Model and Actual Experiment. maximum temperature amongst the cells and significant changes in maximum cell temperature and temperature difference are observed as air flow rate is increased. Upon investigating the effects of increasing air flow rate on maximum cell temperature, a 15.09% reduction in maximum temperature recorded by a cell was achieved during a charging experiment with a 0.5 C current rate by increasing the air flow rate from 1.4 m/s to 2.4 m/s. For the same charge experiment, there was no significant improvement in the maximum temperature recorded at a higher air flow rate of 3.4 m/s. On the contrary, at a higher current rate of 0.75 C charging, a 13.20% reduction in the maximum temperature of a cell was achieved by increasing the air flow rate from 1.4 m/s to 2.4 m/s. Further increment of the air flow rate to 3.4 m/s produced a 22.81% reduction in the maximum cell temperature. The results summarized above aids in drawing a hypothesis that for the investigated battery pack design, for each current rate, there exists an optimal cooling-air flow rate that if exceeded, will yield little or no improvement in an operating BTMS performance at a specific range of ambient conditions. This hypothesis will prove vital in scenarios where power consumption of an operating BTMS is a critical objective function to be minimized. This will be applicable and vital to the development of an intelligent/dynamic BTMS where cooling operation of a BTMS will operate in a dynamic mode depending on the current profile the battery module. When assessing the BTMS performance based on temperature difference between cells, for a cooling-air flow rate of 1.4 m/s for every cycle experiment, there was always an instant where the maximum temperature difference between monitored cells exceeded 5 \({}^{\circ}\)C, reducing the performance of the BTMS.