*3.1. Air-Cooling*

In the first case the cooling fluid is air. The inlet velocities considered in this case are *v* = 13.9 m/s, *v* = 27.8 m/s, and *v* = 38.9 m/s, which correspond to the Reynolds number is in the range (900–13,000). The characteristic length for the Reynolds number is the channel width *c*. The maximum temperature of the cells obtained for the case of plastic 1 with air-cooling are summarized in Figure 6.

**Figure 6.** Maximum temperature of the cells obtained for the case of plastic 1 and air as a cooling fluid. Inlet velocities are *v* = 13.9 m/s (grey), *v* = 27.8 m/s (orange), and *v* = 38.9 m/s (blue).

The figure shows that the maximum temperature of the cells decreases as the air velocity increases. Moreover, the maximum temperature of the cells decreases as the channel width *c* increases, while its dependence on the axial distance between the cells is weak. The best geometry is n. 12, with *c* = 5 mm and *p* = 3 mm. These results can be compared with the maximum temperatures on the cells obtained for the case with plastic 2, as shown in Figure 7.

Figures 6 and 7 show similar trends, but the values of the maximum temperatures obtained with plastic 2 are about 10 ◦C lower than those obtained with plastic 1. The best geometry with air-cooling is again the n. 12 for low velocities (*v* = 13.9 m/s or *v* = 27.8 m/s), while for high velocities (*v* = 38.9 m/s) the geometry with *c* = 3 mm and *p* = 2 mm is the one which gives the lowest maximum temperature of the cells. The temperature distribution on the cells and in the channel, obtained for the geometry n. 12, is shown by Figure 8 for the case of plastic 1.

**Figure 7.** Maximum temperature of the cells obtained for the case of plastic 2 and air as a cooling fluid. Inlet velocities are *v* = 13.9 m/s (grey), *v* = 27.8 m/s (orange), and *v* = 38.9 m/s (blue).

**Figure 8.** Temperature of the cells obtained for the case of geometry n. 12 and air as cooling fluid. Inlet velocities are *v* = 13.9 m/s (**top**), *v* = 27.8 m/s (**middle**), and *v* = 38.9 m/s (**bottom**).

The figure shows that the maximum temperature difference between the first and the last cell is 9 ◦C for the case with *v* = 13.9 m/s, while it is 6 ◦C for the case with *v* = 27.8 m/s and 5 ◦C for the case with *v* = 38.9 m/s. The number of cells along the direction of the flow has been varied from 8 to 16 to show that the cell temperature is a linear function of the cell number. Figure 9 shows the cell temperature as a function of the cell number obtained for geometry n. 12.

**Figure 9.** Temperature of the cells as a function of the cell number, obtained for the case of geometry n. 12, and air as cooling fluid. Inlet velocities are *v* = 13.9 m/s (blue line), *v* = 27.8 m/s (red line), and *v* = 38.9 m/s (grey line).

The slope of the central part of the curves shown in Figure 9 is a crucial parameter for the battery design, which has to be minimized to find the optimal parameters. For the case of air-cooling, the results of the simulations can be summarized as follows:


## *3.2. Water-Cooling*

In the second case the cooling fluid is water. The inlet velocities considered in this case are *v* = 0.1 m/s and *v* = 1 m/s; i.e., the Reynolds number is in the range (100 ÷ 6000). The characteristic length in the Reynolds number is the channel width *c*. The results for the case of plastic 1 with water cooling are summarized in Figure 10.

The figure shows that the maximum temperature of the cells increases as the channel width *c* increases and decreases as the axial distance *p* between the cells increases. The best geometry is n. 7, with *p* = 3 mm and *c* = 1 mm. These results can be compared with the results obtained with plastic 2 with the same geometry, as summarized in Figure 11.

The Figures 10 and 11 show similar trends but the values of the maximum temperature are about 6–7 ◦C lower with the plastic 2. The best geometry with water cooling is the n. 7, i.e., the one with the smallest channel. The temperature difference on the cells for the geometry n. 7 is shown by Figure 12 for the case of plastic 1.

**Figure 10.** Maximum temperature of the cells obtained for the case of plastic 1 and water as a cooling fluid. Inlet velocities are *v* = 0.1 m/s (blue) and *v* = 1 m/s (orange).

**Figure 11.** Maximum temperature of the cells obtained for the case of plastic 2 and water as a cooling fluid. Inlet velocities are *v* = 0.1 m/s (blue) and *v* = 1 m/s (orange).

The figure shows that the maximum temperature difference between the first and the last cell is 4 ◦C for the case with *v* = 0.1 m/s, and it is 2 ◦C for the case with *v* = 1 m/s. The number of cells along the direction of the flow has been varied from 8 to 16 to show that the cell temperature is a linear function of the cell number. Figure 13 shows the cell temperature as a function of the cell number obtained for a channel width *c* = 1 mm. The inlet velocity is *v* = 0.1 m/s.

The slope of the central part of the curves shown in Figure 13 is a crucial parameter for the battery design, which has to be minimized to find the optimal parameters. For the case of water-cooling, the results of the simulations can be summarized as follows:


**Figure 12.** Temperature of the cells obtained for the case of geometry n. 7 and water as cooling fluid. Inlet velocities are *v* = 0.1 m/s (**top**) and *v* = 1 m/s (**bottom**).

**Figure 13.** Temperature of the cells as a function of the cell number, obtained for the case of channel width *c* = 1 mm and water as cooling fluid. The distances between the cells are *p* = 1 mm (blue line), *p* = 2 mm (red line) and *p* = 3 mm (grey line).

## **4. Conclusions**

A survey of the existent thermal management systems for lithium batteries has been presented, showing, in particular, some air-cooling and liquid-cooling approaches. The benefits resulting with the installation of a baffle plate and the importance of the design of the cell arrangements' structures have been shown. In this context, a hybrid system that combines heat conduction between cells in the longitudinal direction and forced convection in channels between the cells lines is presented. This approach is studied numerically using a CFD approach. It is shown that a combination between cooling fluid, solid material that connects the cells, and distances between the cells leads to the determination of the optimal thermal management arrangement. This means that the lowest temperature of the cells and the lowest temperature differences within the battery are obtained by this methodology. The best dimensions of the channels with air-cooling and water-cooling are discussed, showing that with air-cooling the best choice is to increase the width of the channel, while with water-cooling, the best choice is to reduce it. A linear temperature increase in the cells along the direction of the flow is found, and the dependence on the solid matrix thermal conductivity is found. These results show that a multi-parameter optimization approach gives the best arrangement in terms of number of cells and their packing density, as a function of the thermal characteristics of the solid matrix where the cells are embedded.

**Author Contributions:** Data curation, M.F., E.P.B.D.V., A.H. and B.P.; methodology, A.H. and B.P.; investigation, M.F., E.P.B.D.V.; validation, E.P.B.D.V.; formal analysis, A.H., C.R. and B.P.; writing original draft, M.F. and B.P.; supervision, B.P.; funding acquisition, B.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was fund by Emilia-Romagna Region, under the PORFESR program, years 2018–2019, thanks to the LiBER project.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would also like to thank Tommaso Brugo, Luca Frigerio and Andrea Bitto from the Department of Industrial Engineering, University of Bologna, for their support in the CAD design of the brick geometries analyzed.

**Conflicts of Interest:** The authors declare no conflict of interest.
