Analytical solution, optimization and design of a phase change cooling pack for cylindrical lithium-ion batteries

Due to the world's transition to clean energy, the utilization of energy and power storage systems such as lithium-ion batteries has been widely welcomed. The most crucial problem of using these batteries is the large amount of heat production during their operation, which can affect their correct function. Many methods have been investigated to manage and control the temperature of these batteries. One of these methods is to employ phase change materials (PCMs). Despite numerous experimental and numerical studies about cylindrical lithium-ion batteries, there is still a gap in an analytical solution for PCM-based thermal management of them. In the present study, the cooling process of 18650 cylindrical lithium-ion batteries through PCM has been analytically investigated in cylindrical coordinates. For this purpose, the exact solution of the phase transition in cylindrical coordinates is generalized and coupled with the thermal resistance method for the cooling process of this type of battery. In this solution, the temperature distribution in both solid and liquid phases has been considered. Also, the effect of two different types of PCM, namely calcium chloride hexahydrate (PCM1) and paraffin wax (PCM2), and parameters such as ambient temperature, rate of charge/discharge, and thermophysical properties of the PCM on the battery cooling process have been investigated. Moreover, the effect of considering cell internal temperature field and natural convection of the liquid PCM has been evaluated. The results show that for PCM1 in discharge rates of 2C, 4C, and 6C the corresponding required PCM thicknesses are 1.5, 3.1, and 3.8 mm, respectively. In addition, their temperature rises are 2.4, 3.7, and 4.6 degrees C, in their maximum operation times, respectively. Also, since the thermal conductivity of PCM1 (������������ = 1.008, ������������ = 0.561 W/(m.K)) is higher than that of the PCM2 (������������ = 0.21, ������������ = 0.18 W/(m.K)), the temperature rise in the cell is about 6 degrees C lower when the former is applied for a single cell. Eventually, the obtained results are generalized for the design of the optimal battery pack which contains 18650 cells surrounded with PCM.