## 2 Materials and Methods
### Methodology
#### 2.2.3 Experimental Testing  
Convection Coefficient Determination  
The lattice geometry is introduced in a Bentrup TC 504 oven (Rohde, Prutting, Germany) and heated until 250 \({}^{\circ}\)C at a 10 \({}^{\circ}\)C-min\({}^{-1}\) rate. This temperature is held for 5 min to ensure the homogeneous heating of the sample. Afterwards, the component is extracted and positioned on a refractory surface that ensures that no heat is lost toward the contact surface. Hence, the only heat loss mechanism for the lattice structure is convection. Note that the radiation losses are not considered due to the relatively low temperatures of the samples studied; hence, their influence is included within the convection coefficient.  
The cooling stage takes 300 s, which ensures that the sample is cooled down to room temperature, 22 \({}^{\circ}\)C, and, during this process, the temperature of the sample is continuously monitored. In this condition, the cooling process is controlled by Equation (2), where \(m_{lattice}\) is the mass of the lattice [kg], \(c_{p}\) is the specific heat [J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)], \(T\) is the temperature of the lattice measured by the thermocouple [\({}^{\circ}\)C], \(h\) is the convection coefficient [W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\)], \(A_{lattice}\) is the area of the lattice in contact with the air [m\({}^{2}\)], and \(T_{room}\) is the room temperature [\({}^{\circ}\)C], which is monitored by a thermocouple positioned close to the lattice structure. This equation allows us to obtain a temperature-dependent convection coefficient as a function of the lattice temperature; see Equation (3). The lattice mass and area values are provided in Table 4.  
\[m_{lattice}\cdot c_{p}(T).\frac{dT}{dt}+h\cdot A_{lattice}\cdot(T-T_{room})=0 \tag{2}\]  
\[h(T)=\frac{m_{lattice}\cdot c_{p}(T).\frac{dT}{dt}}{A_{lattice}\cdot(T-T_{ room})} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & \(m_{lattice}\) **(kg)** & \(A_{lattice}\) **(m\({}^{2}\))** \\ \hline
1 & 0.0125 & 0.0049 \\
2 & 0.0161 & 0.0059 \\
3 & 0.0195 & 0.0084 \\
4 & 0.0306 & 0.0174 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Physical properties of the lattices required to obtain the convection coefficient.  
Figure 2: Mesh comparison for (**a**) lattice 1 and (**b**) the equivalent solid block 1.  
Heat Transfer Capability of the Lattice Structure  
The lattice structures are manufactured with a solid plate attached to the base, which ensures that the lattice can be properly heated by means of an induction hob. The lattice is heated for 200 s at 2000 W power. Due to the non-magnetic nature of Inconel 718, a steel plate is mounted between both to ensure the heating of the Inconel 718 structure; see Figure 3a.  
During the tests, four thermocouples are employed, with two positioned on the baseplate of the lattice structure and two on its top, as shown in Figure 3b. In this way, the average temperatures are extracted in order to compare them with the simulation values.  
During the tests, a 22 \({}^{\circ}\)C constant room temperature is measured, which is also the initial temperature for the heating tests. In the air surrounding the lattice structure, there is no external ventilation or airflow, which ensures that the only heat dissipation mechanism of the lattice is natural convection. Moreover, the heating tests are monitored through an Optris PI thermal camera (_Optris_ GmbH, Berlin, Germany), whose emissivity is adjusted with discrete thermocouple measurements; see Figure 4. In this way, the full thermal field of the lattice is defined.  
Figure 4: Temperature measurements in the lattice heating tests: (**a**) discrete temperatures using thermocouples and (**b**) temperature field obtained by means of a thermal camera.  
Figure 3: (**a**) Experimental setup for the lattice heating and (**b**) positioning of the four thermocouples employed to monitor the heating cycle: two on the base (T1 and T2) and two on the upper face (T3 and T4).