## 3 Results and Discussion
Figure 5: Simulation of temperature distributions near defects with the following sizes determined for different compaction forces: (**a**) 100 MPa and 420 \(\upmu\)m, (**b**) 200 MPa and 488 \(\upmu\)m, (**c**) 300 MPa and 170 \(\upmu\)m, (**d**) 100 MPa and 489 \(\upmu\)m, (**e**) 200 MPa and 137 \(\upmu\)m, (**f**) 300 MPa and 188 \(\upmu\)m, (**g**) 100 MPa and 515 \(\upmu\)m, (**h**) 200 MPa and 376 \(\upmu\)m, (**i**) 300 MPa and 194 \(\upmu\)m, (**j**) 100 MPa and 503 \(\upmu\)m, (**k**) 200 MPa and 197 \(\upmu\)m, (**l**) 300 MPa and 110 \(\upmu\)m, (**m**) 100 MPa and 443 \(\upmu\)m, (**n**) 200 MPa and 198 \(\upmu\)m, (**o**) 300 MPa and 154 \(\upmu\)m.  
According to Table 3, the temperature evolution in the sample \(P_{1}\) presented the highest value of 1210 \({}^{\circ}\)C for the highest diameters of the holes (defects approximated as spheres with diameters of 489 and 515 \(\upmu\)m). Similarly, the samples \(P_{2}\) and \(P_{3}\) presented the same behaviors, reaching 1212 \({}^{\circ}\)C for the sphere with a diameter of 488 \(\upmu\)m and 1196 \({}^{\circ}\)C for a diameter equal to 194 \(\upmu\)m. This behavior led to the conclusion that, during the MHH process, the risk of occurrence of the thermal runaway phenomenon is higher near to defects in the materials. The 3D thermal maps of temperatures near the defects are presented in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{\(P_{1}\) **(100 MPa)**} & \multicolumn{2}{c}{\(P_{2}\) **(200 MPa)**} & \multicolumn{2}{c}{\(P_{3}\) **(300 MPa)**} \\ \hline \(d_{max,H}\) & \(k_{NUI}\) & \(d_{max,H}\) & \(k_{NUI}\) & \(d_{max,H}\) & \(k_{NUI}\) \\ (\(\upmu\)m) & \(k_{NUI}\) & (\(\upmu\)m) & (mm) & (\(\upmu\)m) & (mm) \\ \hline
420 & 8.55 & 488 & 9.94 & 170 & 3.46 \\
489 & 9.96 & 137 & 2.79 & 188 & 3.83 \\
515 & 10.49 & 376 & 7.66 & 194 & 3.95 \\
503 & 10.24 & 197 & 4.01 & 110 & 2.24 \\
443 & 9.02 & 198 & 4.03 & 154 & 3.14 \\ \hline \end{tabular}
\end{table} 
Table 2: Dimensions of defects detected for different compaction procedures. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{\(P_{1}\) **(100 MPa)**} & \multicolumn{2}{c}{\(P_{2}\) **(200 MPa)**} & \multicolumn{2}{c}{\(P_{3}\) **(300 MPa)**} \\ \hline \(d_{max,H}\) & \(T_{max}\) & \(d_{max,H}\) & \(T_{max}\) & \(d_{max,H}\) & \(T_{max}\) \\ (\(\upmu\)m) & (\({}^{\circ}\)C) & (\(\upmu\)m) & (\({}^{\circ}\)C) & (\(\upmu\)m) & (\({}^{\circ}\)C) \\ \hline
4 According to Figure 6, the local overheating around the defects depends on the spheres' diameters. The sample compacted at 100 MPa with a defect assimilated to a sphere having 515 \(\upmu\)m diameter tended to suffer local overheating up to 1512 \({}^{\circ}\)C. The lowest temperature was 1377 \({}^{\circ}\)C in the case of the sample compacted at 300 MPa. For both cases, \(T_{ss}\) > \(T_{cat}\), indicating that the thermal runaway of the Barium Ferrite W-type material will occur. The  
Figure 6: Three-dimensional thermal maps for thermal runaway occurrence during the MHH process: (**a**) samples compacted using 100 MPa, (**b**) samples compacted using 200 MPa, (**c**) samples compacted using 300 MPa. results of the thermal runaway simulation for the most relevant five temperatures higher than 1200 \({}^{\circ}\)C are presented in Figure 7.  
According to Figure 4, the hottest spot, around 2000 \({}^{\circ}\)C, could be found in samples compacted at 100 MPa. However, at least one defect in the samples compacted at 200 MPa presented a peak temperature of 1985 \({}^{\circ}\)C. The rest of the defects for the samples compacted at 200 MPa and 300 MPa presented a similar behavior in terms of thermal runaway. The highest level of risk for thermal runaway was for the defects with temperatures higher than 1400 \({}^{\circ}\)C. Figure 8 shows the microwave powers absorbed by the Barium Ferrite W-type samples compacted at 100 MPa, 200 MPa and 300 MPa.