# Melting of Paraffin Waves Embedded in a Porous Matrix Made by Additive Manufacturing
## 2 Porous Matrix  
The porous matrix, inside which paraffins were embedded, was printed at LAMA FVG Lab. The technique Selective Laser Melting (SLM) was implemented for additive manufacturing. The matrix is made of AlSi\({}_{10}\)Mg, which is an aluminum alloy.  
The porous matrix is made of the repetition of base cells defined as body-centered cubic (BCC). The BCC structure derives from chemistry: the BCC crystal structure is a way for atoms to arrange themselves in metals. In this structure, eight atoms are located at the vertices of a cube, and one atom is in the middle of the cube. This idea can be taken to create cells that can form periodic cellular structures. In this concept, a cube with eight spheres located at the vertices and one sphere in the middle of the cube is considered. If the spheres have a radius that is greater than half of the edge of the cube, the subtraction between the volume occupied by the cube and the volume occupied by the nine spheres gives, as a result, a structure such as that reported in Figure 1a. In the proposed structure, the base cube has an edge of 5 mm. Since, as can be seen in the figure, the BCC structure presents very thin edges, which cannot be printed with AM technology, these thin edges were thickened in such a way that the thinest edge was 0.4 mm, which is a value compatible with the SLM printer. The so-created modified BCC structure is reported in Figure 1b, and it represents the base element the entire structure is made of. This structure has a porosity, intended as the ratio between the volume occupied by the empty spaces and the total volume (solid matrix and empty spaces), of 0.87. A lateral view of the modified BCC structure is reported in Figure 1c, along with the dimensions.  
This modified BCC structure tends to overcome the limits regarding porosity exploited by metal foams. As stated by [PERSON] [23], open-celled metal foams are considered as one of the most promising classes of materials to be used to enhance the transfer with phase change materials due to their high thermal conductivities and high heat transfer areas per unit of volume. Taking, for instance, Duocel(r) foams, due to the physics of small-scale structures, the majority of Duocel(r) foams are manufactured in the 90-97% porosity range. The proposed modified BCC structure overcomes this limit about porosity: AM technology permits the creation of periodic cells with porosities lower than those of metal foams guaranteeing open cells, which are needed to be filled with the PCM, avoiding any close cells that would be detrimental for the heat transfer mechanisms.  
The entire structure is made by the repetition of the modified BCC structure, and it has a volume of 100 \(\times\) 100 \(\times\) 20 mm\({}^{3}\), i.e., the base cell is replicated 20 times along two coordinates and four times along the third coordinate. Furthermore, the final structure was printed between two 10 mm thick plates made of the same material. Since the structure was printed all together, there are no thermal resistances between the porous matrix and the two plates. Figure 2 shows a schematic of the entire structure. Six holes were drilled in each of the plates to host as many T-type thermocouples to monitor the wall temperature during the heating process. The location of these thermocouples is similar to that reported in [PERSON] and [PERSON] [24], to which reference should be made for further details.  
Figure 1: (**a**) BCC structure; (**b**) modified BCC structure; (**c**) lateral view of the modified BCC structure with dimensions.