The effect of wall thermal conductivity on the critical external heat loss coefficient of the gas fired burner is illustrated in Figure 6 for the butane fuel. These bell-shaped envelopes separate the region of self-sustained combustion below the curve from the region above the curve where combustion cannot be self-sustained. The conductivity of several materials is also indicated by arrows. There exists a critical wall thermal conductivity for butane-air mixtures below which combustion cannot be self-sustained, even with insulating walls. When the wall thermal conductivity increases from low values, the allowable-heat-loss coefficient first increases quickly, and then decreases and levels off in the range of metals or high-thermal-conductivity ceramics, for example, silicon carbide. The allowable-heat-loss coefficient reaches a maximum for insulating ceramics such as alumina and silica. The behavior observed for low-conductivity materials is at first counterintuitive. Highly insulating materials are poor for flame stability due to the lack of a continuous ignition source, needed to preheat the cold incoming gases. Typical ceramics allow maximum external heat loss coefficients. Materials with lower wall thermal conductivities limit the upstream heat transfer. Materials with higher wall thermal conductivities result in enhanced heat transfer to the surroundings. Flames are quenched in these small dimensions because of two primary mechanisms, namely thermal and radical quenching. Thermal quenching occurs when sufficient heat is removed through the walls, that combustion cannot be self-sustained. Radical quenching occurs via adsorption of radicals on the system walls and subsequent recombination, which results in lack of homogeneous chemistry. The small scales of these systems make them significantly more prone to both quenching mechanisms because of the high surface area to volume ratios, namely enhanced heat transfer from the flame to the walls and increased radical mass transfer. In addition to flame quenching, blowout can occur when the burner exit velocity exceeds the flame burning velocity. In this mechanism, the reaction shifts downstream until it exits the burner. While flame propagation at the microscale is feasible, the interplay of kinetics and transport in flame stability and combustion characteristics of these systems is poorly understood. The inability of conducting spatially resolved measurements, inherent to the microscale, underscores the need for detailed mathematical modeling.