On the velocity, size, and temperature of gaseous dendritic flames

Abstract

Dendritic combustion in Hele-Shaw cells is investigated qualitatively using a simplified one-dimensional thermo-diffusive model. Formulas for the velocity, size, and temperature of the flamelets are derived. The temperature and velocity of the flames increase for small radii to allow for their survival regardless of the activation energy. In addition, the results obtained with very large activation energy were compared with experimental results, finding that additional tests are required due to the strong influence of gravity on the velocity and size estimations. Conditions for the existence of this anomalous propagation are investigated, confirming analytically that it can only happen for low Lewis numbers.