Thermal energy storage systems based on Phase change materials (PCM) are an attractive option to bridge the temporal and spatial gap between the energy demand and supply. But, these systems possess poor thermal conductivity causing reduced rate of heat transfer. The objective of the present study is to numerically analyze the melting process in an optimized finned latent heat storage system dispersed with varying volume fraction of Graphene nano plates (GNP). The individual effect of incorporating fins, GNP and a combination of both at different volume fraction has been studied. Effective thermal conductivity of nano-composite PCM has been theoretically evaluated including the effect of aspect ratio, interfacial thermal resistance, anisotropy, non-linear effects as well as concentration for the dispersed GNP. In this work, Dynamic differential scanning calorimetry tests are performed to evaluate the phase change temperature, latent heat and specific heat of the sugar alcohol (d- mannitol). Transient variation of liquid fraction, average temperature and radial/longitudinal temperature differentials are presented which would be useful for designing medium temperature (160-200 degrees C) storage systems for various applications. Fin height is varied to obtain an optimum fin size such that natural convection currents are not impeded. Various heat transfer models (including natural convection) are analysed using the actual plant data of a double effect solar absorption system at different arrangements of fins and GNP. Effect of Reynolds number and inlet temperature of HTF on the system performance have also been studied. A reduction of 68% in total melting time is observed in finned LHSS with 5% GNP as compared to a conventional system.