This study investigates numerically the convective heat transfer mechanisms in a nanofluid saturated porous medium inside a trapezoidal enclosure under the local thermal non-equilibrium condition. For mathematical formulation, the horizontal walls of the enclosure are well-thought-out to be adiabatic while having dissimilar temperatures for the inclined and vertical walls. The simulation is done using finite element method of Galerkin weighted residual type. The simulated data for Nusselt number are presented graphically for the key model parameters. The controlling parameters for the nanofluid and the solid matrix of the porous medium to be in thermal equilibrium are identified.