## 3 Results
### Approximation of the Lattice Structures Through Solid Bodies  
Finally, the thermal behavior of the lattice structures is approximated by solid bodies. Following the same procedure as in the lattice structure simulation, in the solid bodies, the heat introduced by the induction hub is modeled by imposing the experimentally measured temperatures in the lower face of the geometry. In addition, the convection effect is included. However, as the convection indicates the heat dissipation per surface area, the lower area of the solid is compensated for by escalating the convection coefficient by an area ratio, \(R\), defined according to Equation (4), where \(A_{lattice}\) and \(A_{solid}\) are the external areas of the lattice and solid body, respectively.  
\[R=\frac{A_{lattice}}{A_{solid}} \tag{4}\]  
The approach of a lattice structure through a solid body implies that the density of the solid body needs to be reduced proportionally to the fill percentage of the lattice, which, in the present study, is 5.16% in all cases. Moreover, reducing the amount of material implies lowering the heat conduction capabilities of the body. Initially, the conduction coefficient was reduced in the same proportion as the fill percentage, i.e., 5.16%. However, the temperatures in the upper face were far too high--see the last column of Table 6--and this implied that the conduction coefficient needed to be further reduced.  
The reduction in the conductivity coefficient of the solid block is iteratively calculated until an error below 2% regarding the lattice simulation is obtained. The conductivity reduction is named \(k\)% in Table 6, and, as can be seen, the more stretched the lattice  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**R**} & **Lattice** & **Lattice** & **Solid Block** & **Solid Block** & \multirow{2}{*}{**\%**} & **Solid Block** \\  & & **Experimental** & **Simulation** & **Simulation** & **Error** & \(k\)**\%** & **Simulation T [\({}^{\circ}\)C]** \\  & & T [\({}^{\circ}\)C] & T [\({}^{\circ}\)C] & T [\({}^{\circ}\)C] & **[\%]** & & **If k = Fill \%** \\ \hline
1 & 2.27 & 80.79 & 77.0  
structure is in the direction in which the heat is being transferred, the higher the effective conductivity of the equivalent solid block.  
Based on the obtained low error rate between the simulated lattice and solid blocks, which is below 2% at the end of the 200 s simulation, it can be stated that the approach consisting of solid blocks with fictitious properties can be employed successfully to analyze the thermal behavior of complex lattice structures. In Figure 11, a comparison between the thermal fields for cases 3 and 4 is provided. As can be seen, strong resemblance is obtained in the thermal fields, not only in the temperatures of the upper and lower faces but also in its variation between them.  
Consequently, the proposed geometrical simplification implies a minimum error but entails considerable savings in terms of the computational cost. As an example, in Table 7, the numbers of the performed simulations are detailed. In case 1, the resulting file size is reduced by 95% and the computational time by around 88%. Note that the execution time varies depending on the computer used, which, in the present case, was a DELL OPTI 7010 TOWER with a 13 th Gen Intel(r) Core(tm) i7-13700 and 32 Gb RAM.  
Figure 11: Comparison between the thermal results in case 3 at t = 200 s time step ((**a**) solid block and (**b**) lattice structure) and case 4 at t = 200 s time step ((**c**) solid block and (**d**) lattice structure).  
Moreover, it is concluded that, with lattice structures, it is possible to adjust the effective conductivity of the geometry, even if the same fill percentage factor is employed. This is especially interesting if variable conductivity regions are to be defined or anisotropic thermal behavior is desired, because it allows one to control the conductivity of the component without varying its weight.