In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy-Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 106, Darcy number Da, 10-5 ≤ Da ≤ 10-3, and Prandtl number Pr, 0.2 ≤ Pr ≤ 100) in terms of stream functions and isotherm contours, and local and average Nusselt numbers. © 2006 Elsevier Ltd. All rights reserved.