The melting of nano-enhanced phase change material (NEPCM) in a latent heat thermal storage system is investigated for PCM loaded within an annulus between an outer wavy cylinder and an inner Koch snowflake cylinder. The inner Koch snowflake cylinder is used in this study to increase the heating surface area and enhance the NEPCM melting process. The inner cylinder is hot, while the outer one is insulated. The system governing equations and the associated boundary conditions were numerically solved by employing the Galerkin weighted residual finite element method. The impacts of nanoparticle concentration, undulation number of the outer cylinder, annulus eccentricity, and inner cylinder geometry on the melting performance of the storage unit were examined and represented by the liquid fraction, isotherms, Bejan number, velocity, and Nusselt number. The usage of more blades and snowflake surfaces near the hot source's periphery portions disrupts the PCM surface's cohesiveness and increases heat penetration between the PCM layers. The nanoparticle concentration of 6 vol% enhances the melting time by about 32 %, and the undulation number of 8 participates in 25 % of performance enhancement. Putting the hot cylinder closer to the bottom of the storage unit expands the buoyancy effect and enhances the melting process by >3.2 times. The utilization of a Koch snowflake cylinder instead of a triangular one also shows an enhancement of >30 %.