## 3 Results and Discussion
### All Cordierite versus All SiC
#### 3.1.2 Effect of the Inlet Gas Velocity  
Figure 5 shows the plots of maximum wall temperature, \(T_{\text{wall\_max}}\), (outlet) bulk gas temperature, \(T_{\text{bulk}}\), and (outlet) propane conversion versus \(V_{\text{in}}\).  
Figure 4: Axial profiles of (catalytic) reaction rate along the inner and outer walls of the inlet channel at \(V_{\text{in}}=0.5\) m/s. All Cordierite and All SiC.  
In the case of the low-conductive corderite, temperatures were higher and extinction, which is regulated by competition between the heat losses toward the external environment and the heat produced by combustion, occurred at a lower value of V\({}_{\text{in}}\) than with SiC (0.13 m/s versus 0.32 m/s). In contrast, in the case of SiC, blowout occurred at a higher value of V\({}_{\text{in}}\) than with corderite (19.75 m/s versus 8 m/s).  
From a practical point of view, the trend depicted in Figure 5, with better extinction stability at low thermal conductivity and better blowout stability at high thermal conductivity, implies that, for low-power systems, insulating materials are needed and, conversely, for high-power systems, conductive materials are needed.  
Figure 5: Maximum wall temperature, T\({}_{\text{wall\_max}}\), (outlet) bulk gas temperature, T\({}_{\text{bulk}}\), and (outlet) propane conversion versus V\({}_{\text{in}}\): All Corderite and All SiC. Arrows indicate extinction (at low values of V\({}_{\text{in}}\)) and blowout (at high values of V\({}_{\text{in}}\)).  
Figure 5 also shows some features that have already been found by [PERSON]'s group, although for a different configuration of catalytic heat-recirculating micro-combuster [29]: at extinction, both the maximum temperature and the fuel conversion are substantially independent of the thermal conductivity, whereas at blowout, the fuel conversion decreases with increasing thermal conductivity.  
In Figure 6, the maps of temperature and propane mole fraction are shown at different values of \(\mathrm{V_{in}}\).  
Figure 6: Maps of temperature, T, and propane mole fraction, \(\mathrm{X_{Propane}}\), at different values of \(\mathrm{V_{in}}\): All Cordierite; All SiC. A scaling factor equal to 2 was used to scale the computational domain along the transverse direction.  
As the inlet gas velocity was increased, the reaction front was progressively shifted downstream. However, this effect was particularly marked on the outer side of the inlet channel of the micro-combustor made of cordierite. In this case, the outer wall remained cold along much of its length, and unconverted propane left the inlet channel, turning around the inner wall, already at V\({}_{\text{in}}\) = 4 m/s. Conversely, in the case of SiC, temperature was sufficiently high also for the outer wall, and the inlet channel could be fully exploited as a reactor to obtain (almost) complete propane conversion up to V\({}_{\text{in}}\) = 7 m/s.  
The reason behind the fact that cordierite exhibited higher susceptibility to blowout than SiC is directly linked to its low thermal conductivity. The geometrical asymmetry of the U-bend configuration--with the inlet channel directly exposed to the heat losses toward the external environment on the one side and protected by the presence of the outlet channel on the other side--seems to have made the low thermal conductivity of the outer wall especially responsible for the poor resistance to blowout of the micro-reactor made of cordierite. In this case, if we consider the inlet channel, the outer wall remained cold due to insufficient pre-heating of the fresh incoming reactants, i.e., insufficient axial heat conduction in the upstream direction. Conversely, the inner wall attained high temperatures as heat recirculation (transversely across and axially along the solid wall) was effective in pre-heating the cold feed.  
On the basis of the above-presented results, differentiating the thermal conductivity between inner and outer walls can be expected to have an impact on the stability of the U-bend catalytic micro-combustor.