Finite element simulation of the mixed convection within porous square cavities for Darcy-BrinkmanForchheimer model has been carried out in the present work. The penalty optimization based Galerkin finite element method is used to solve the partial differential equations of heat and fluid flow. Bejan's heatline concept has been employed to visualize the heat flow within the closed cavities based on the motion of the horizontal wall(s) (cases la-id) or vertical wall(s) (cases 2a-2c) involving isothermally hot bottom wall, cold side walls and insulated top wall for various fluids with Prandtl number, Pr-m = 0.026, 0.7 and 7.2, Reynolds number, Re = 10-100 and Grashof number, Gr = 10(3)-10(5). The higher permeability at Da(m) >= 10(-3) leads to the enhanced buoyancy convection for all the cases. Although the direction of the motion of wall(s) significantly influences the fluid flow field within the enclosure, due to the decoupling between the fluid and thermal fields at the low Pe(m) (Pe(m) = 0.26 and 2.6), conductive heat transfer occurs as seen from the end-to-end heatlines. It is also found that the overall heat transfer rates at the bottom wall (Nu(b)) are identical for the cases 1a-id and cases 2a-2c at Pr-m = 0.026, irrespective of Gr and Re at Da(m) = 10(-2). At Pr-m = 0.7 and 7.2, the convection dominant heat transfer occurs for all the cases for Gr = 10(5), Re = 10 and 100 and Da(m) = 10(-2). The strong convective circulation cells are observed at Pr-m = 0.7 and 7.2 for all the cases. The plume shaped isotherms are also observed along the centerline at Pr-m = 7.2, Re = 10, Gr = 10(5) and Da(m) = 10(-2) for all the cases. At Pr-m = 7.2, Gr = 10(5), Da(m) = 10(-2) and. Re = 100, the multiple convective heatline cells are observed for the cases la-id. It is observed that, the strengths of fluid and heat circulation cells are less at Re = 100 compared to Re = 10 for all the cases due to weak buoyancy force at the high Re. In order to achieve the high heat transfer rate at the bottom wall (Nu(b)) for the mixed convection involving various moving walls, case 2b (a case of the vertically moving wall) is preferred at Pr-m = 0.7, Re = 100, Gr = 10(5) and Da(m) = 10(-2). At the high Pr-m (Pr-m = 7.2, Re = 100, Gr = 105 and Da(m) = 10(-2)), case 2a (a case of the vertically moving wall) is preferred based on the maximum heat transfer rate at the bottom wall (Nu(b)). (C) 2016 Published by Elsevier Masson SAS.