The efficiency and effectiveness of a battery thermal management system (BTMS) primarily depend on the lesser heat capacity of the phase change material (PCM). To improve the performance of BTMS, the bare batteries with different extended surfaces (straight and arc) are considered to enhance the dissipation of heat, leading to significant enhancement of bare battery performance. In the present study, numerical simulations are carried out to study the impact of extended surfaces and the influence of CuO (10%) nano additive dispersion in PCM. Also, analyses are carried out by modifying the geometries of the arc fins to enhance the thermal performance of the battery. Results reported that the proposed extended surfaces improved the battery life by 61%-90% compared to conventional BTMS systems. Extended surfaces boost heat exchange surface area, improve battery-to-PCM/CuO heat dissipation, and form a novel method for heat conduction during liquid fraction melting. This network expands by increasing arc fin radial distance, enhancing thermal performance. At ambient temperature range of 15 degrees C-45 degrees C, the PCM/CuO/fin system substantially improved compared with the PCM-based system by 163%, 192%, and 212%, respectively. These findings demonstrate the possibility of straight and arc fin shapes to improve PCM battery thermal control. The experimental and numerical results show how these fin designs optimize heat transport, increasing battery life and improving thermal control under varied operating situations. This novel approach overcomes PCM-based system restrictions to improve battery performance and lifetime.