Influence of upstream versus downstream heat loss on the structure and stability of planar premixed burner-stabilized flames

The asymptotic structure and diffusional-thermal instability of a planar premixed burner-stabilized flame suffering either upstream or downstream volumetric heat loss with a rate described by a linear dependence on temperature is studied using activation-energy asymptotics. A brief review of the results for a flame without volumetric heat loss is presented. The results are compared to those obtained recently for a flame suffering combined upstream/ downstream volumetric heat loss. For the structure, the analysis predicts that the expressions for the burning rate and the specific heat loss rate to the burner are not identical, unlike that shown for the freely propagating flame with volumetric heat loss. This is in agreement with earlier investigations of a flame suffering the three separate heat loss modes studied using thin-flame theory. Also in agreement with these earlier studies, the analysis predicts that the downstream heat loss mode is larger in magnitude than the upstream heat loss mode. For the diffusional-thermal instability, the analysis demonstrates that for the linear stability model considered, the effects of upstream and downstream heat loss appear in additive form. For fixed mass flux and volumetric heat loss intensity, it is found that the downstream heat loss mode is more effective than the upstream heat loss mode in promoting flame instability. These results are similar to those of the freely propagating flame with volumetric heat loss. A flame diagram dependent on the thermochemical data and volumetric heat loss mode is produced, which illustrates the stable flame region and the predicted extinction limits for low to medium values of the mass flux. It is found that at high mass flux no extinguishment point may be identified