The work is adopting the high order Galerkin finite element method (GFEM) for handling the natural convection of nano-encapsulated phase change material (NEPCM) within a grooved cavity saturated by a porous medium. The grooved cavity is containing an oval shape with zero velocities and an adiabatic condition. The impacts of the pertinent parameters Darcy parameter, a radius of an inner oval shape, Rayleigh number, porosity, fusion temperature, and Stefan number are investigated. The major findings are concluded that an increment of a fusion temperature shrinks the intensity of the streamlines and shifts the heat capacity position toward the hot wall. Increasing the Darcy parameter lows the porous resistance of the nanofluid flow and accordingly, the nanofluid movements and intensity of the streamlines are enhanced. A lower Darcy parameter enhances the isotherms and changes the heat capacity patterns inside a grooved cavity. The inner oval shape represents blockage in a grooved cavity and therefore the nanofluid movements are slowing in a cavity during an expanded radius of an inner oval shape. An extra Rayleigh number improves the intensity of the fluid flow and convective heat transfer in a grooved cavity.