The latent heat of phase change materials (PCM) during the transition from solid to liquid has made them the subject of interest in many renewable energy applications such as thermal energy storage systems. Although, their low thermal conductivity is their main limitation. This paper extensively presents the melting behavior of phase change material inside the 3D cylindrical enclosure and proposes discrete and continuous novel fins shapes like annular, rectangular, and spiral for enhancing melting rate. The lauric acid with ferric oxide nanoparticles (0.03 %wt) is considered as PCM and the enthalpy-porosity method has been employed for simulating the melting process. Melting behavior and dominated heat transfer mechanism during the melting process have been analyzed. The results were compared with the cylindrical case without fins. Employing fins improved the melting rate because of increasing heat transfer area to 37.87 % and 31.8 % for continuous rectangular and spiral fins, respectively. The effect of applying a non-uniform magnetic field to the outer walls of the enclosure has been investigated and accelerated the melting rate of spiral fins up to 78 %. Furthermore, the effect of fins material on melting rate was examined and concluded that by employing copper fins, melting rate enhanced up to 3 % in comparison with aluminum fin.