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This study investigates utilizing phase change materials (PCMs) along with metallic fins for passive cooling of lithium-ion batteries. PCMs have low thermal conductivity, which is enhanced by incorporating copper or aluminum fins. Numerical simulations using ANSYS FLUENT's Solidification & Melting solver in an axisymmetric configuration are performed. PCM cooling outperforms air cooling, providing up to 15 °C lower maximum battery temperatures as long as PCM remains solid. The findings from the analysis of air cooling versus cooling with PCM demonstrate that the use of phase-change materials enhances battery cooling performance for a specific duration, provided that these materials do not fully liquefy. Adding fins further improves cooling for 0.2 mm thickness, 6 copper fins of 11.67 mm height give optimal performance with 8 °C lower peak temperatures than without fins. Copper fins outperform aluminum due to 60 % higher thermal conductivity but have 3X higher density. For longitudinal fins, 4 fins of 10 mm height perform better than 10 fins of 3 mm height. With high conductivity PCMs like paraffin wax (0.242 W/m.K), varying fin count has minimal impact as heat distributes rapidly. This study establishes guidelines for optimizing PCM-fin geometries and materials to maximize passive lithium-ion battery cooling performance.