A combination of phase change materials (PCMs) with highly conductive substances could be a promising technique to deal effectively with the relatively low thermal conductivity of PCMs. It can promote the development and commercialization of PCMs in the field of thermal management and energy storage. In this numerical study, firstly, the characterization of the PCM solidification process incorporating different metal oxide nanoparticles, namely Al2O3, ZnO, CuO, and SiO2, with volume fractions of 0–4% along with their thermophysical properties inside a triplex-tube are examined. Moreover, a comparative study at different heat transfer fluid temperatures and tubes diameters between three common thermal energy storage units, including triplex-tube, shell-and-tube with inner and outer cooling, are carried out for an identical volume of the storage unit to identify, which type of the units provides higher performance. The results show that among the considered nanoparticle-PCMs, the Al2O3-PCM reflects a higher solidification rate at a volume fraction of 2%, while at a volume fraction of 4%, the CuO-PCM possesses a lower solidification time. Moreover, the triplex-tube reflects better solidification time at any heat transfer fluid temperature and tubes diameter compared to other considered units. Finally, the Taguchi method is employed to determine the optimum solidification time. According to the Taguchi analysis, dispersing nanoparticles in PCM is the less effective parameter, and the minimum solidification time can be achieved by employing CuO-PCM 4% in a triplex-tube with the low temperature of heat transfer fluid and larger tubes diameter.