**2. Problem Description**

The single 18650 LIB used in this paper has a voltage of 3.6–4.2 V and a capacity of 2600 mAh. The main aim of this study is to reduce the MaxT and temperature standard deviation (TSD) of the battery during operation by optimizing the configuration of the BTMS for the battery module, which is composed of 20 cells. For a multi-cell module, the design of the BTMS must cover many aspects. The layout of the battery, the positioning scheme of the inlets and outlets, the number of inlet and outlet as well as the structural size of the battery module all a ffect the final cooling e ffect of a BTMS. First, the layout plan of the battery pack was analyzed and designed, then the optimal inlet and outlet position was designed based on the optimized layout plan. Then the influence of the number of inlet and outlet on the thermal performance of the battery was explored by increasing the number of inlets and outlets. Finally, the optimized configuration was determined. Details of the research method and technical route are shown in Figure 2. The specific steps to solve this multi-objective coupling problem are as follows:


**Figure 2.** Research methods and the technical route.

### **3. Heat Dissipation Model of Computational Fluid Dynamics**

There are four main sources of heat production in working batteries, namely, reaction heat (RH), side reaction heat (SRH), joule heat (JH) and polarization heat (PH). The total calculation of the heat generation is shown in Equation (1).

$$P\_{\text{total}} = P\_{\text{re}} + P\_{\text{sr}} + P\_{\text{jo}} + P\_{\text{po}} \tag{1}$$

where *P*total represents the power of the total heat, *P*re represents the power of RH, *P*se represents the power of SRH, *<sup>P</sup>*jo represents the power of JH, and *<sup>P</sup>*po represents the power of PH.

RH refers to the heat generated by the chemical reaction in the electrodes in charging and discharging. Generally, the charging process of LIB absorbs energy to reduce ambient temperature and in reverse, its discharging process releases heat [22]. This results in a side reaction, that is, heat is generated by a series of chemical reactions other than the main chemical reaction, such as the partial decomposition of electrolyte at high temperature and self-discharge caused by the change in electrode material structure. These side reactions are intensified in the period before the battery fails. However, during the life of the battery, the side reactions are so weak that the heat of the side reaction is usually ignored. JH is the work done by the current on the internal resistance (IR). This part of the heat can be calculated by Joule's law as shown in Equation (2):

$$P\_{\text{jo}} = I^2 R\_{\Omega} \tag{2}$$

where *R* Ω is IR, and *I* refers to the current on *R* Ω.

PH refers to the heat generated when the positive and negative electrode potential deviates from the equilibrium potential. When polarization occurs, the voltage di fference between the battery's open circuit voltage and the terminal voltage generate PH. Generally, it is assumed that there is a polarization IR *Rp*, and the heating power is calculated by Joule's law, as shown in Equation (3),

$$P\_{\rm PO} = I^2 R\_p \tag{3}$$

### *3.1. Acquisition of Battery's Thermodynamic Parameters*

Before the heat dissipation model is built, the battery parameters need to be determined. These parameters include the IR, SHC, heat yield and thermal conductivity (TC) of the single battery. In order to obtain these parameters, it is necessary to conduct charge and discharge experiments on a single battery. The equipment generates cycles of charge and discharge, and the measurement of the parameters of current, voltage and temperature. The Arbin machine battery testing system was adopted, which can charge/discharge batteries at a set constant current or voltage value and record the respective current, voltage, capacity, and impedance per minute simultaneously. Besides the Arbin machine, several temperature sensors and a miniature blower were needed. The equipment is shown in Figure 3a and each battery is equipped with three temperature sensors, as shown in Figure 3b. For determining the measurement error, every single cell is installed with three temperature sensors that are attached at the cathode, middle and anode of the cell. The temperature utilized in this study is the average value.

**Figure 3.** (**a**) Experimental equipment. (**b**) The battery with temperature sensors.
