Suspensions containing the Nano-encapsulated Phase Change Material (NEPCM) are an innovative type of fluid that combines the advantages of nanofluids with the heat storage capabilities of phase change materials. The focus of this study is to analyze how external vibrations influence the natural convection of an NEPCM suspension inside an enclosure saturated with a porous medium. The enclosure is subjected to periodic vibrations in the vertical direction, and the energy equations of the porous medium are subjected to the application of the local thermal non-equilibrium condition. It is found that among the studied parameters, the Rayleigh number, the interfacial coefficient, and the porosity have the highest impact. Increasing the vibration Rayleigh from 1e6 to 1e7 increases by >3.5 times the Nusselt number in the fluid. Reducing the interfacial heat transfer coefficient from 5000 to 100 decreases the Nusselt amplitude in the solid by 4 times and raises the Nusselt amplitude in the fluid by 7 times. Augmenting the porosity from 0.6 to 0.95 decreases the Nusselt number by 15% in the solid. Altering the properties of the nanoparticles, i.e., their fraction and fusion temperature, also affects heat transfer but to a lesser extent.
