The current work focusses on fluid transport, heat transport and temperature distribution of nine containers involving porous medium on the basis of unit cross sectional area (1 sq. unit) and identical heating at the bottom wall. The nine porous containers have been categorized into three classes based on their geometric configuration [class 1 porous containers: square, tilted square and parallelogram, class 2 porous containers: trapezoidal type 1, type 2 and triangle and class 3 porous containers: convex, concave and curved triangular]. The role of heatlines on thermal management for the porous containers is depicted by tuning the dimensionless parameter, Darcy number (10−5≤Dam≤10−2) at Prandtl number, Prm=155 (engine oil) and Rayleigh number, Ram=106. Heat transfer is evaluated in terms of average Nusselt number (Nub¯) along with spatial average temperature (θ^) for the nine porous containers. On the basis of enhanced heating criteria (higher Nub¯ and θ^), porous container for each class is preferred as follows, class 1 porous container: square and parallelogram, class 2 porous container: trapezoidal type 2 and triangle (higher Nub¯), trapezoidal type 1 (higher θ^) and class 3: concave (higher Nub¯), convex (higher θ^). Porous containers with curved walls [convex (higher θ^) and concave (higher Nub¯)] depict the enhanced thermal processing rate of engine oil compared to other classes of porous containers involving equal heat input and area. © 2020