## 2 Materials and Methods  
### Numerical Model--Geometry and Boundary Conditions  
The geometrical model was developed based on the work of [PERSON] et al. [27]. Kelvin cell-based metal foams were obtained, arranging in series four single units (Figure 10(i)), as shown in Figure 10(iii). Firstly, as reported in Figure 10(i), the elementary unit was generated and then replicated by symmetry along its faces resulting in a single Kelvin cell unit (Figure 10(ii)). As done by [PERSON] et al. [27], five different fiber structures were modeled: one cylindrical (C\({}_{0}\)) and four elliptical (E1-1, E1-2, E2-1, E2-2). The configurations denoted as \"E1-X\" consist of elliptical struts whose section presents the same perimeter with respect to the circular one of the cylindrical fibers. Differently, the \"E2-X\" were obtained, imposing that the circle and ellipse had equivalent areas. X could assume values of 1 or 2: 1 if the ratio \(\beta\) between the minor strut diameter and the cylindrical strut diameter was 0.815; 2 if the ratio was 0.556. If calculating the ratio \(\alpha\) between the major strut diameter and the cylindrical strut diameter, different values for \"E1-X\" and \"E2-X\" were obtained, as shown in Table 1.  
It is clear from Table 1 that the \"E2-X\" foams presented an \(\alpha\) parameter always greater than \"E1-X\" assuming equal the ratio \(\beta\). For the sake of brevity, the other geometrical features were not reported here since they can be retrieved in [27]. Focusing on Figure 1 ii, it can be noticed that the bounding cube has a side of 2 mm, corresponding to the diameter of the single cell unit. This implies that the periodical foams have a pore density of 40 PPI, with an almost constant porosity of 0.9 (ranging from 0.88 and 0.9). The present work also investigated the effects of fiber inclinations (15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\)) (Figure 2) for the four elliptical fiber structures. The configurations with 0\({}^{\circ}\) fiber inclination had already been simulated by [PERSON] et al. [27] for all the five fiber structures. The fiber inclination was defined as the angle (also called \"angle of attack\", here) between the ellipse's major axis and the main flow direction. \begin{table}
\begin{tabular}{c c c} \hline  & \(\alpha\) & \(\beta\) \\ \hline E1-1 & 1.169 & 0.815 \\ E1-2 & 1.359 & 0.556 \\ E2-1 & 1.227 & 0.815 \\ E2-2 & 1.800 & 0.556 \\ \hline \end{tabular}
\end{table} 
Table 1: Kelvin cell elliptical struct foams’ design features. Figure 1: Kelvin cell generation and arrangement process. To ensure the fully-developed flow before the air entrance into the foams, an upstream duct of 40 mm was modeled (not at scale in Figure 3, for the sake of visualization). Similarly, a downstream duct with the same length was also added, as shown in Figure 3. Velocities ranging from 0.5 to 4 m s\({}^{-1}\) and temperature of 298 K were set to the inlet face, resulting in a laminar airflow with Reynolds number based on the strut diameter lower than 300 [27]. The pressure-outlet condition was applied at the exit, setting it at the ambient pressure (gauge pressure of 0 Pa). The up- and downstream ducts were considered adiabatic, therefore no heat or mass exchanges were possible. To heat the system, an aluminum heater of 2 \(\times\) 8 mm\({}^{2}\) and thickness of 0.1 mm was modeled; its face was defined as a wall at a constant temperature of 373 K. At both sides of the system, a periodical condition was set. Differently from [27], the present authors modeled half of the entire system. However, since the aim was to replicate the geometry and the operating conditions from [27], the uppermost face was considered as a symmetry plane, and a symmetry boundary condition was adopted consequently. The two systems are perfectly comparable. In Table 2, the material properties as taken from Ansys Fluent 18.2 database are reported.