The development of positive-energy buildings is nowadays an important societal challenge and the research objective of many laboratories. Working towards this direction, we describe in the present report the development of active and reactive walls, by employing a multi-fiber, volumetrically structured porous medium. Flow and transfer characterization in such a foam structure is not fully understood due to the strong nonlinearities included. These are amplified by heterogeneities and porosity changes, where the local and global flow affect the thermal field and the resulting heat transfer. Thus, a finite volume method with immersed structure interfaces was implemented to study heat transfer through these media, with the aim of obtaining their ratio equivalent to fluid thermal conductivity (i.e. Nusselt number). Furthermore, our analysis shows that in such active wall constituted by two solid phases, under fixed weight constraints, the optimal value is difficult to predict a priori. Thus, different evolution laws of thermal gradient were studied, resulting in the change of the pore size distribution along some new anisotropic structures, in order to achieve the most one predictive.