In the experimental study presented here, the effectiveness of using hybrid nanoparticles of Graphene nanoplatelet (GNP) aggregates and Silver (Ag) nanoparticles as a thermal conductivity enhancer (TCE) in an organic solid-liquid phase change material (PCM) is examined. An in-situ reduction method was used to synthesize the GNP-Ag hybrid nanoparticles, and these were characterized by SEM, TEM, EDS, and XRD. PCM composites were prepared by embedding different concentrations of GNP and GNP-Ag hybrid nanoparticles into a paraffin-based PCM. The effective thermophysical properties of the composite PCMs, such as specific heats, latent heats of solidification, and thermal conductivities, were determined using a T-History analysis from the Time-Temperature and Temperature-Enthalpy curves. The study finds that the Base PCM's effective thermal conductivity was augmented by 52% with 1 wt.% of GNP-Ag hybrid nanoparticles. In comparison, the increase was only 27% when dispersed with the same amount of GNP alone. A heat transfer analysis was also conducted in a cylindrical PCM enclosure to investigate the effect of these nano-additives in the natural convection-dominated melting process of the PCM. An investigation on the dynamic viscosity of NEPCMs and quantitative analysis of Grashof number confirmed that GNP-Ag nanoparticles outperform GNP in the melting heat transfer of the PCMs.