Analytical modeling of pcm-based cooling system for lithium-ion batteries

Proper thermal management of lithium-ion cells is vital for safety, longevity, and reliable performance, especially in high-power applications where heat generation is considerable. Among passive cooling strategies, phase change materials (PCMs) have shown great promise due to their ability to absorb large amounts of heat. However, while many studies have experimentally and numerically examined this topic, gaps still exist in the theoretical modeling of phase change-based cooling for cylindrical lithium-ion batteries. This study aims to enhance battery thermal management pack design by developing a comprehensive analytical solution for the coupled heat transfer in a cylindrical lithium-ion cell surrounded by PCM. The model incorporates realistic time-dependent boundary conditions, significantly improving its accuracy and applicability for battery pack design. By integrating the perturbation method for the PCM and the Green's function method for the cell, the model predicts time-dependent temperature profiles and the position of the moving phase change front. Unlike numerical methods, this analytical framework provides rapid yet accurate insights, validated against experimental and computational results with an error margin of less than 5%. The results confirm that while PCM cooling effectively regulates the surface temperature, the battery core remains relatively hotter. Therefore, improving the thermal conductivity of the battery itself is crucial for maximizing the effectiveness of PCM cooling and achieving a more uniform temperature distribution. Furthermore, increasing the thermal conductivity and latent heat of the PCM can also help control the core temperature up to an optimal threshold.