The effect of wall thermal conductivity on the wall outer edge temperature of the gas fired burner is illustrated in Figure 4 along the length of the burner. The material thermal conductivity affects the temperature profile within the wall and the possibility of hot spots. For low-wall-thermal-conductivity materials, significant axial temperature gradients are observed. Hotspot temperatures in excess of 2000 K can occur, an undesirable situation, as it exceeds the maximum operating temperatures of most materials of construction [55, 56]. Exceedingly high wall temperatures are characteristic of thermally stabilized burners [57, 58]. As the wall thermal conductivity increases, the wall temperature profiles become more uniform and the wall hot spot is eliminated. Despite the apparent advantages of a higher wall thermal conductivity for material stability, most materials that offer high conductance are metals, and therefore would not be inert to radical quenching. A more reasonable solution would be thicker walls of a more inert material that may have a lower thermal conductivity. Low wall thermal conductivities result in large axial wall-temperature gradients and high maximum temperatures. High wall thermal conductivity leads to uniform temperature profiles without hotspots. Flame surface area density is defined as the flame surface per unit volume and serves as a method of modeling the flame propagation based on the fact that the flame progression transports, generates, and diffuses the flame surface area density. The flame propagation is estimated by modeling the flame generation in such a manner that the flame generation resulting from laminar flow is inversely proportional to the chemical reaction characteristic time and proportional to the flame stretch rate. After combustion begins, the combustion first starts as a laminar flame. The growth of the flame is expressed by expressing the generation of the flame surface area density in terms of the growth of the laminar flame. The generation of the flame surface area density is expressed by combining the growth resulting from the mode of combustion, namely the laminar combustion flame growth. The laminar combustion flame growth is inversely proportional to the chemical reaction characteristic time and a function of the Reynolds number. The laminar combustion flame growth is proportional to both the laminar flame speed and to the ratio of the temperature of a burned portion to the temperature of an unburned portion. The generation of laminar combustion and the resistance imposed on the flame by air can be expressed and the flame propagation can be predicted with good accuracy with respect to combustion modes that are dominated by laminar combustion. It is possible to predict the flame propagation at fields where at the beginning of combustion the turbulence is very weak and laminar combustion dominates due to a very small Reynolds number. Consequently, it is possible to reproduce a situation in which the flame speed increases as the turbulence of the field strengthens and the flame propagation in various fields of weak turbulence can be predicted.