Thermal energy storage systems (TES) find their extensive application in industrial and solar-powered thermal systems due to their high energy storage density and ability to deliver heat at isothermal conditions. But, the lower thermal conductivity of phase change materials (PCM) reduces the overall rate of heat transfer. In the present work, solidification behavior in a medium temperature (160-200 degrees C) finned TES with varying proportion of Graphene nano plates (GNP) is presented. The effect of anisotropy, aspect ratio, concentration, interfacial thermal resistance and non-linearity has been included to evaluate the overall thermal conductivity of GNP-PCM composite. The objective of the present study is to enhance the solidification process of a binary eutectic salt LiNO3-KCl in an optimized finned TES dispersed with the different volume fraction of GNP. The detailed experimentation process starts with the preparation of binary eutectic mixture, followed by dynamic Differential scanning calorimetry analyses along with rheology testing. Empirical correlations have been developed using quadratic and cubic polynomials for viscosity and specific heat respectively. Several numerical models are analyzed to study the solidification enhancement of binary eutectic PCM using the real-time plant data of a high temperature solar absorption chiller. Effects of Stefan and Reynolds number on the thermal performance of storage system has also been studied. Reducing the Stefan number and increasing the Reynolds number of heat transfer fluid (HTF) results in enhancing the rate of solidification process. It has been observed that natural convection currents enhances the rate of solidification and causes faster solidification in the upper annulus of TES. A reduction of 49% in the solidification time has been observed with finned TES dispersed with 5% GNP as compared to pure binary eutectic PCM.