The swift advancement of electronics, along with the demand for compact design and production, creates a significant challenge when it comes to managing heat, which is crucial for ensuring the performance, durability, and dependability of electronic components. To enhance heat dissipation rates, a unique fin structure with varying cross-sections, taking into account the melting characteristics within the medium, is introduced for a heat sink that relies on phase change materials (PCM). Phase change materials’ (PCMs’) comparatively poor thermal conductivity coefficient is the main barrier to their utilisation in thermal energy storage systems. To enhance heat transfer, researchers have looked into a variety of tactics, such as using expanded surface techniques like fins with varied structures. This study examines the melting of a PCM in a new multi-square box with bottom and vertical heating. Lauric acid serves as the PCM in the square box. While aluminium fins are used to improve the thermal conductivity of the whole system, a two-dimensional finite difference method based on the specific heat capacity technique has been developed using COMSOL software. The addition of fins increases the rate of heat transmission when comparing bottom heating to vertical heating. To enhance heat transport during the melting process, we investigate numerically how variations in fin length, indicated by varying numbers of fins, affect the quantity of energy storage in PCM. In numerous instances, altering the fin’s length has been taken into consideration.