Equivalence of the criticality condition for both the semenov and the frank-kamentskii problems: Comments on jean-claude Lermant and Sidney Yip, a generalized Semenov model for thermal ignition in nonuniform temperature systems, combust. flame 57:41–54 (1984)

✍ Scribed by Ahmad R. Shouman; Walter Gill

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 208 KB
• Volume: 58
• Category: Article
• ISSN: 0010-2180
• DOI: 10.1016/0010-2180(84)90082-8

✦ Synopsis

Criticality in the thermal explosion problem was defined as the attainment of an inflection in the temperature-time trajectories before the maximum temperature was reached by Rice et al. in 1935. The location of such a point was determined through numerical integration of the governing differential equations. The same procedure was followed by Todes and Malent'ev [2 3] in 1939 and 1940 as well as Tyler and Wesley [41 in 1967. Recently, Lermant and Yip [5] applied an analytic approach to the Semenov problem which helps greatly in handling the mathematics of the problem. They examined the variation of a modified Semenov number with temperature for a constant ambient temperature. They demonstrated the existance of a jump phenomenon in the steady-state solution indicating ignition. They also analytically determined the location