Approximate critical conditions in thermal explosion theory for a two-step kinetic model

作者：Ajadi S O^*; Nave O

来源：Journal of Mathematical Chemistry, 2010, 47(2): 790-807.

DOI：10.1007/s10910-009-9600-y

• Thermal explosion
• Asymptotic procedure
• Two-step reaction
• Radical termination

Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (I (cr) ) and critical temperature (theta (cr) ) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (delta (cr) ) and the critical temperature (theta (cr) ) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.

• 出版日期2010-2