## 2 Experimental Setup and Procedure  
An experimental setup was established in order to investigate the temperature distribution of Li-ion batteries discharging in air and distilled water for both 50% and 100% immersion ratios. It should be noted that heat transfer between fluids and battery can be considered natural convection since neither a circulation fan nor pump was used in the test box. In the experiments, a LiFePO4 battery with a nominal capacity of 20 Ah was used, and its parameters are given in Table 1.  
Firstly, ten T-type thermocouples are attached to one side of the battery (T\({}_{1}\), T\({}_{2}\), T\({}_{3}\), T\({}_{4}\) and T\({}_{5}\)) and the other side of the battery (T\({}_{6}\), T\({}_{7}\), T\({}_{8}\), T\({}_{9}\) and T\({}_{10}\)) for temperature measurements, and they are attached to the battery tabs. Besides thermocouples and charge/discharge cables, serpentine copper tubes, water inlet and outlet pipes are mounted to cover the test section. Then, charge/discharge cables are attached to battery tabs, as shown in Figure 1a. After connecting them, the battery is mounted to a test box with a plexiglass case supported by thick sheet metal, and it is insulated with EPS foam to avoid heat transfer between the test box and the environment. It should be noted that plexiglass material is used to determine the level of immersion. The photo of the test box during insulation can be seen in Figure 1b. The schematic representation and photo of the established experimental setup can be seen in Figure 2a,b, respectively. The red/blue, black and brown lines in Figure 2a show water coolant circuit, connection cables and thermocouple wires, respectively. It should be noted that the inside temperature of the test section is also measured by means of T-type thermocouples, and inlet and outlet temperatures of water are measured by using Pt100 sensors. All thermocouples and Pt100 sensors are connected to the data acquisition system. The temperature measurement devices were calibrated in a water bath using a reference temperature sensor. In addition, a serpentine copper tube is added to the test section to condition it. Moreover, the test section is insulated with insulation material in order to avoid heat transfer between the test section and the ambient. The water coolant circuit is established by using a water bath (chiller), turbine-type flow meter, pump and Pt100 sensors to obtain constant coolant water inlet temperature. It is a closed loop, and the desired inlet temperature of cooling water is adjusted by means of a water bath. Uncertainties for \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Nominal capacity & 20 Ah \\ \hline Nominal voltage & 3.3 V \\ \hline Charge cut-off voltage & 3.65 V \\ \hline Discharge cut-off voltage & 2 V \\ \hline Cathode material & LiFePO4 \\ \hline Anode material & Graphite \\ \hline Weight & 496 g \\ \hline Dimensions & 7.25 \(\times\) 160 \(\times\) 227 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of the battery. The working principle of the experimental setup is summarized as follows:  
* Before each experiment, the battery is charged using an electronic power supply at 3.65 V under constant current and constant voltage (CC/CV) mode. * The experiments are started by discharging the battery at a desired charge (1C, 2C, 3C and 4C) rate by using an electronic load; the voltage and current values of the battery are recorded during the experiment. * Then, the cooling water is circulated by means of a frequency-controlled water circulation pump, and its temperature is measured with a data acquisition system at the inlet of the test section. * After the test section, its temperature is measured again with the data acquisition system, and it is directed to the water bath. The cooling water, which is conditioned by using a water bath, is directed to a flowmeter for flow rate measurement.