## 3 Results and Discussion
### Differentiating the Thermal Conductivity between Inner and Outer Walls
#### 3.2.1 Roles of the Inner and Outer Walls  
Figure 7 shows the plots of T\({}_{\text{wall\_max}}\), T\({}_{\text{bulk}}\), and propane conversion versus V\({}_{\text{in}}\) for the cases of Table 3 Cordierite + SiC (outer wall made of cordierite and inner wall made of SiC) and SiC + Cordierite (outer wall made of SiC and inner wall made of cordierite). For the sake of comparison, the plots obtained in the cases All Cordierite and All SiC are also shown. Let us focus on extinction. The outer wall surely plays a role in determining extinction, given that the case All Cordierite resulted in the best extinction resistance. However, in spite of its higher volume-averaged solid thermal conductivity (23.3 W/m K versus 11.5 W/m K), the case SiC + Cordierite exhibited a better extinction stability (V\({}_{\text{in}}\) @ extinction = 0.23 m/s) than the case Cordierite + SiC (V\({}_{\text{in}}\) @ extinction = 0.25 m/s). This means that extinction was mainly ruled by the inner wall. On the other hand, [PERSON] et al. [32] have highlighted the key role of the inner walls in determining stability on the basis of CFD simulations of a catalytic heat-recirculating micro-combustor with symmetric configuration performed by varying the external heat transfer coefficient. Figure 8 shows the temperature maps at extinction for the three cases All Cordierite, Cordierite + SiC, and SiC + Cordierite. In all cases, the hottest zone was located downstream. However, the thermal pattern established in the case SiC + Cordierite was rather similar to that predicted in the case All Cordierite, with the inner wall attaining the maximum temperature. In the case Cordierite + SiC, the thermal pattern was completely different: the wall that attained the maximum temperature was the outer one and, thus, the stabilizing action of the inner wall was lost. As far as blowout is concerned, Figure 7 shows that the cases Cordierite + SiC and SiC + Cordierite exhibited the same behavior as the cases All Cordierite and All SiC, respectively. This confirms what conjectured in the previous sub-section: the outer wall controls blowout. In Figure 9, the maps of temperature and propane mole fraction are shown as computed at \(\rm V_{in}\) = 7.5 m/s for All Cordierite and Cordierite + SiC, and at \(\rm V_{in}\) = 13 m/s for All SiC and SiC + Cordierite. According to Figure 7, these were the highest values of \(\rm V_{in}\) that still allowed for 100% propane conversion. Figure 7: Maximum wall temperature, \(\rm T_{wall\_max}\), (outlet) bulk gas temperature, \(\rm T_{bulk}\), and (outlet) propane conversion versus \(\rm V_{in}\): Cordierite + SiC and SiC + Cordierite. For the sake of comparison, the plots obtained in the cases All Cordierite and All SiC are also shown. Arrows indicate extinction (at low values of \(\rm V_{in}\)) and blowout (at high values of \(\rm V_{in}\)). Figure 8: Maps of temperature at extinction: All Cordierite; Cordierite + SiC; SiC + Cordierite. A scaling factor equal to 2 was used to scale the computational domain along the transverse direction. Figure 9: Maps of temperature, T, and propane mole fraction, \(\mathrm{X_{Propane}}\), at the highest values of \(\mathrm{V_{in}}\) that still allowed for complete fuel conversion: All Cordierite; Cordierite + SiC; SiC + Cordierite; All SiC. A scaling factor equal to 2 was used to scale the computational domain along the transverse direction. Let us look at the inlet channel. Thanks to heat recirculation, the inner wall attains high temperatures regardless of the material it is made of and, therefore, does not play a substantial role in determining blowout. The differences in the high-velocity behavior are in fact to be attributed to the outer wall. As in the case All Cordierite, even in the case Cordierite + SiC, due to its low thermal conductivity, the outer wall remained cold along much of its length and, thus, the inlet channel could be only partially exploited as a reactor.