This paper investigates the effect of vertical fins, as an enhancement technique, on the heat transfer rate and energy density of a latent heat thermal energy storage system. This contributes with knowledge on the interaction of heat transfer surface with the storage material for optimizing storage capacity (energy) and power (heat transfer rate). For the assessment, numerical modeling is employed to study the melting process in a two-dimensional rectangular cavity. The cavity is considered heated isothermally from the bottom with surface temperatures of 55 degrees C, 60 degrees C or 70 degrees C, while the other surfaces are insulated from the surrounding. Aluminum and lauric acid are considered as fin/enclosure material and phase change material, respectively. Vertical fins attached to the bottom surface are employed to enhance the charging rate, and a parametric study is carried out by varying the fin length and number of fins. Thus, a broad range of data is provided to analyze the influence of fin configurations on contributing natural convection patterns, as well as the effects on melting time, enhanced heat transfer rate and accumulated energy. The results show that in addition to increasing the heat transfer surface area, the installation of vertically oriented fins does not suppress the natural convection mechanism. This is as opposed to horizontal fins which in previous studies have shown tendencies to reduce the impact of natural convection. This paper also highlights how using longer fins offers a higher rate of heat transfer and a better overall heat transfer coefficient rather than increasing the number of fins. Also, fins do not only enhance the heat transfer performance in the corresponding melting time, but also maintain similar total amount of stored energy as compared to the no-fin case. This paper discusses how this is the result of the enhanced heat transfer allowing a larger portion of sensible heat to be recovered. For example, in the case with long fins, the relative mean power enhancement is about 200% with merely 6% capacity reduction, even though the amount of PCM in the cavity has been reduced by 12% as compared to the no-fin case. Although the basis for these results stems from the principles of thermodynamics, this paper is bringing it forward with design consideration. This is because despite its importance for making appropriate comparisons among heat transfer enhancement techniques in latent heat thermal energy storage, it has not been previously discussed in the literature. In the end, the aim is to accomplish robust storage systems in terms of power and energy density.