A scope of enhancing heat transfer during thermal convection in enclosure is explored in this work considering the free aspiration of surrounding fluid. The illustration is made using a two-sided lid-driven porous cavity under differential heating, which is expanded into possible four (assisting, opposing, upward and downward) flow-configurations. The aspiration ports are provided diagonally opposite corners for partial inflow of cold surrounding fluid and partial venting of hot cavity fluid. It leads to primary (or bottom) aspiration and depending upon the direction of sidewall motion, secondary (or top) aspiration. The resulting complex mixed-flow (shear flow, buoyant flow and aspirated flow) through porous medium is modeled by applying Brinkman-Forchheimer-Darcy model (BFDM) and Boussinesq approximation. The evolved nonlinear-coupled equations are solved by an in-house code for the wide ranges of parameters (Reynolds number Re = 10-500, Richardson number Ri = 0.1-100), Darcy number Da =10(-3)-10(-7) and porosity epsilon = 0.1-1) rigorously. The results reveal heightened heat transfer from the aspirated cavity compared to the identical non-aspirated cavity. Depending upon the combination of the parameters, the enhancement could be as high as similar to 180%. The upward-flow configuration yields the maximum heat transfer when no external baffle is used for flow partitioning during the case of top aspiration. With the baffle, the opposing flow shows the maximum heat transfer of similar to 339%. The study reveals that the aspiration can magnificently enhance heat transfer without any additional expenses for pumping power of it. (C) 2017 Elsevier Ltd. All rights reserved.