The effect of wall thermal conductivity on the flame location of the gas fired burner is illustrated in Figure 5 at different external heat-transfer coefficients. The location of the flame shifts as a function of operating parameters. The flame location as a convenient criterion for the stability or robustness of a burner is defined as the axial position with the highest reaction rate. As the wall thermal conductivity decreases to low values, the flame location shifts downstream for all external heat-transfer coefficients. For high wall thermal conductivity and low external-heat-loss coefficients, increasing wall thermal conductivity to high values has a minor effect on the flame location. On the other hand, for high external-heat-loss coefficients in systems, increasing wall thermal conductivity shifts the reaction downstream. This nonlinear behavior is caused by the interaction between two competing modes of heat transfer, namely upstream heat transfer through the walls to preheat the feed, and transverse heat transfer resulting in heat loss to the surroundings. The former is critical for ignition and flame stabilization in microchannels, as it allows preheating of the feed without the need for an external preheater. If the upstream heat transfer is insufficient to increase the fluid temperature to the ignition temperature, a flame is not stabilized within the burner. Since the conductivity of the walls is orders of magnitude higher than that of the fluid, heat conduction through the walls is the primary mechanism of upstream heat transfer. When this upstream heat transfer is limited by low wall thermal conductivity, it takes a greater distance to achieve the preheating, resulting in the reaction zone shifting downstream. This makes the flame less stable. For a given wall thermal conductivity, increasing the external heat loss coefficient shifts the reaction zone downstream as more of the heat generated is lost to the surroundings. Low wall thermal conductivities cause the flame to shift downstream. Increasing wall thermal conductivity has little effect on flame location unless there are significant external heat losses. The wall thermal conductivity alone does not determine the relative upstream heat transfer in the system. The wall thickness and the gap distance also play an important role. As the gap distance increases, the time scales for heat transfer from the reaction zone to the walls and from the hot walls to the inlet reactants increases because of the increased length scale. As a result of the latter, the flame location occurs further downstream and more conductive materials are needed for stable operation. As a result of the former, the system is more robust to exterior heat losses. In particular, for highly conductive materials and large external heat-transfer coefficients, the flame location does not shift downstream with increasing wall thermal conductivity. Consequently, the larger gap makes the burner very robust with respect to heat losses.