The present numerical studies analyzed three-dimensional natural convection heat transfer in an inclined parallelepiped box filled with fluid saturated porous medium and subjected to end-to-end temperature difference.The three-dimensional natural convection includes non-Darcy’s extensions,viz. Brinkman viscous terms and Forchheimer non-linear inertial terms characterized by Darcy number and Forchheimer number respectively. The governing equations have been obtained in terms of vector potential and vorticity-vector for Darcy-Brinkman-Forchheimer flow model. Numerical solutions to the governing equations have been obtained employing the Successive Accelerated Replacement (SAR) Scheme. The problem being computationally intensive, all the computations have been carried out on Super Computer Param 10000.