Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions
Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions
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DOI：
10.1137/0143090
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发表时间：
1983-12
影响因子：
1.9
通讯作者：
A. Lacey
中科院分区：
文献类型：
--
作者：
A. Lacey
研究了一类高活化能放热化学反应的抛物初值问题，包括Frank-Kamenetskii近似。据发现，对于许多这样的系统有有限的时间爆破的解决方案时，弗兰克-Kamenetskii参数$\delta $，或等效的，是大于上限$\delta ^ * $的频谱相应的稳定状态。当上界位于谱中时，当$\delta $从上界接近$\delta ^ * $时，爆破时间增加为O（{\delta - \delta ^ * }）^{-1/2} $。对于$\delta < \delta ^ * $，确定初始数据的下限，在该下限以上也必须发生热失控。
Parabolic initial value problems, including the Frank–Kamenetskii approximation for a high-activation energy exothermic chemical reaction, are studied. It is found that for many such systems there is finite time blow-up of the solution whenever the Frank–Kamenetskii parameter $\delta $, or equivalent, is greater than the upper bound $\delta ^ * $ to the spectrum of the corresponding steady state. When the upper bound lies in the spectrum the blow-up time is found to increase as $O( {\delta - \delta ^ * } )^{ - 1 /2} $ as $\delta $ approaches $\delta ^ * $ from above. For $\delta < \delta ^ * $ lower bounds on the initial data are determined above which thermal runaway must also occur.