## 1 Introduction  
In the last years, open cell metal foams have been extensively investigated [1]. Metal foams are cellular structured materials consisting of stochastically oriented open cells. Their struts interconnect at nodes assuming the conventional shape of an open cell. Stochastic metal foams have specific features which make them suitable to be implemented and integrated in different applications related to heat transfer processes [2]. Open foams are characterized by high heat transfer area to volume ratio, attractive stiffness and strength, and they possess the ability to enhance the flow mixing. As an enhancement heat transfer technique, metal foams can be adopted in different fields, for instance: biomedical, geothermal operations, multifunctional heat exchangers, and cladding on buildings, as an air cooling means for condensers or for acting as compact heat sinks for power electronics. They have been proposed to be an interesting solution to solve the limited air cooling capacity in electronic equipment [3]. The thermal-hydraulic behavior of stochastic metal foams depends upon their geometrical characteristics such as the pore diameter, the pore density (number of pores per linear inch), struts diameter and length, the porosity, and the relative density as well as on the operating conditions. The porosity and the relative density are defined as the ratio between the volume of void and the total volume, and the ratio between density of the foam and of the metal one, respectively [2]. Extensive experimental studies involving open cell foams can be retrieved in the open literature. The influence of geometrical features on the pressure drop and heat transfer performance were investigated by [PERSON] et al. [4]. Adopting the Brinkman-extended Darcy momentum model and a heat transfer one developed for porous structures based on two equations, they obtained that, compared with the reference tubes, the metal foams performed up to 40 times better if considering the heat transfer. Aluminum metal foams with pore densities ranging from 10 to 45 PPI and porosities from 75% to 85% were used by [PERSON] et al. [5]. The authors aimed at analysing mass transfer and pressure drop properties. Results revealed that the higher the pore density, the higher the pressure drops. On the contrary, the lower the porosity, the higher the pressure drops. [PERSON] et al. [6] investigated the air forced convection using five graphite foams. By means of an electrical device, the samples were heated and thermal properties were analyzed. The authors stated that the pressure drop increases as the pore dimension decreases whilst the thermal performance improves as the inlet velocity increases. [PERSON] et al. [7] focused on forced convection across aluminum foams to study the effect of the porosity on the heat transfer performance. Three samples had constant porosity (0.92) and pore densities between 10 and 40 PPI, while the other three presented different porosities but constant pore density (20 PPI). [PERSON] et al. [8] experimentally evaluated the thermal-hydraulic behavior of six copper alloy foams. They measured heat transfer coefficient and pressure drops, finding that the overall heat transfer was affected by cell size more than by porosity. Aiming at obtaining a trade-off between pressure drops and heat transfer, [PERSON] et al. [8] proposed an optimal porosity which rose as Reynolds number reduced. [PERSON] et al. [9] experimentally investigated 20 to 60 PPI metal foams by measuring heat transfer coefficient and pressure drop. If compared to the compact-plate heat exchanger with empty channels, the foamed one presented heat transfer coefficients which increased from 3.5 to 5.1 times and pressure drops from 3.2 to 5.7 times. From this brief overview, stochastic open cell foams can potentially improve the thermal performance in air forced convection as compared to other extended surfaces. At the same time, it was demonstrated how their geometrical parameters highly influenced their performance.