Phase change materials (PCMs) may be employed in thermal energy storage to bridge the gap between supply and demand for energy. The main obstacle to PCMs' broad adoption is their limited heat conductivity, leading to their rates of energy recovery and storage being sluggish. This work focuses on tackling this difficulty by adopting a honeycomb structure to improve the performance of a phase-change material using a two-dimensional numerical simulation of melting time. The thermal behavior of a two-dimensional rectangular thermal storage container with phase change material and a honeycomb structure HCS partly filled in the enclosure was the focus of the studies. The current work compares the thermal behavior during melting in a rectangular cavity filled with (Pure PCM alone, Bottom, and Top HCS configurations) that are exposed to a continuous heat source, both with and without natural convection. The solidification/melting module of the commercial CFD software ‘ANSYS Fluent’, which is based on the enthalpy-porosity model, permits modeling based on a transient calculation, making it feasible to examine the charging process of eicosane. For all three configurations, the evolution of the liquid fraction is represented. The storage unit's thermal performance is improved by the use of partially filled honeycomb structures (HCS), according to numerical findings. The optimal reduction in total melting time is attained through the implementation of a top-HCS arrangement, yielding a significant 11% enhancement when natural convection is neglected, while the inclusion of a honeycomb matrix enables only a 3% improvement for the bottom-HCS configuration. Moreover, outcomes reveal that natural convection minimizes melting time differences between the three studied configurations and expedites the process, notably benefiting the reference configuration compared to the two other scenarios. Furthermore, the outcomes demonstrate that natural convection reduces discrepancies in melting times among the three studied configurations and accelerates the charging process. The influence of natural convection is notably more significant for the reference case.