Energy storage is critically important for intermittent renewable sources such as solar or wind. This paper presents a numerical study on a shell and tube thermal energy storage unit using a common organic phase change material (PCM) - paraffin wax. To overcome the problem of slow charging due to low thermal conductivity of paraffin wax, this research applies a multiscale heat transfer enhancement technique, with circular plate fins on outer surface of the heat transfer fluid (HTF) tube and highly conductive nanoparticles (Al2O3) dispersed in the PCM on the shell side. The novelty of this research is that by simultaneous application of two enhancement methods, we are able to analyze the interactions between the two, which was not possible in previous studies on separate technique. A computational fluid dynamics (CFD) model is developed to simulate melting of the PCM with the following parameters: nanoparticle concentration phi from 0 to 4 vol%; fin angle alpha from -45 degrees to 45 degrees, and pitch p from 45 to 65 mm. The obtained numerical data was analyzed with a traditional method and a statistical response surface method (RSM). The latter represents another novelty of this research. The RSM analysis shows that fin angle and nanoparticle concentration are two significant parameters in affecting the PCM melting, but pitch of the fins does not show noticeable effect. Numerical results demonstrate that adding nanoparticles in the PCM does not accelerate the charging process; on the contrary it leads to longer charging time and lower overall heat transfer rate due to reduction of natural convection in the melted PCM. A strong interaction is also found between these two significant parameters, for example the charging time considerably increases when nanoparticles are added at alpha = -45 degrees, but this effect is less pronounced when alpha = 45 degrees. Positive fin angles are found to be favorable for PCM melting due to enhanced natural convection with strong local vorticities formed below the fins. A moderate fin angle of 35 degrees leads to the shortest charging time among all studied cases. These new findings can be valuable in design of PCM units for renewable energy storage, waste heat recovery, or thermal management in engineering systems.