The free convection phase change heat transfer of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous space is theoretically addressed. The core of the nanoparticles is made of a phase change material and encapsulated in a thin shell. Hence, the core of the nanoparticles of the suspension undergoes a phase change at its fusion temperature and release/store large amounts of latent heat. The phase change of nanoparticles is modeled using a sine shape temperature-dependent heat capacity function. Darcy-Brinkman model is used to model the flow in the porous medium. The governing equations including the conservation of mass, momentum, and heat are transformed into a non-dimensional form before being solved by the finite element method in a structured non-uniform mesh. The influence of the porosity, Darcy number, Rayleigh number, fusion temperature of nanoparticles, and the unsteady time-periodic boundary conditions on the thermal behavior of the porous medium in the presence of NEPCM particles is investigated. The results show that the presence of NEPCM particles improves the heat transfer. The increase of porosity improves the heat transfer when the volumetric concentrations of NEPCM particles are higher than 3%. There exists an optimal dimensionless fusion temperature of NEPCM nanoparticles for the interval [0.25; 0.75]. (C) 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.