The Interaction between Upstream and Downstream Heat Transfers on the Burning and Extinction of Dilute Spray Flames

The extinction of dilute spray flames under the influence of the external heat transfer existing in both upstream and downstream regions is studied using activation energy asymptotics. A completely prevaporized burning model and a partially prevaporized burning model are identified. The internal heat transfer embedded in the rich and lean spray respectively provides heat loss and heat gain for the system. However, the external heat transfer results in globally external heat loss and external heat gain, respectively, to the spray system with increasing wall temperature. The C-shaped and S-shaped extinction curves are clearly classified and mapped with parameters of the wall temperature, the initial droplet size and the external heat transfer coefficient. Characteristics differing from previous findings regarding upstream heat transfer are discussed. Furthermore, the phenomenon of reproducing an S-shaped extinction curve from the original C-shaped extinction curve is also presented and discussed.