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Thermal runaway in microwave heating: a mathematical analysis

机译：微波加热中的热失控：数学分析

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摘要

A study is made of the solution of a differential equation modelling the heating of a layer of material specimen by microwave radiation. Depending on the microwave power bistable steady-state temperatures may be expected. When changing the power, a switch from one stable branch to another one may arise. The sudden increase of temperature, known as thermal runaway, is studied from the differential equation using asymptotic methods. Such analysis reveals distinct stages in the process of thermal runaway. At the moment the solution leaves a branch, and becomes unstable a particular type of behaviour is observed (onset of runaway). The most specific element at this stage is a time shift delaying the rapid change in temperature. For this shift a simple expression in terms of the parameters of the system is given. Next it is shown that the rapid transition from one branch to the other can be put in a mathematical formula that smoothly matches the two steady state solutions.
机译：对微分方程的求解进行了研究，该微分方程对微波辐射材料样本层的加热进行了建模。取决于微波功率，可以预期双稳态稳态温度。更改电源时，可能会发生从一个稳定分支到另一分支的切换。使用渐近方法，根据微分方程研究了温度的突然升高（称为热失控）。这种分析揭示了热失控过程中的不同阶段。此刻，解决方案离开一个分支，变得不稳定，观察到特定类型的行为（开始失控）。在此阶段，最具体的元素是时移，延迟了温度的快速变化。对于这种移位，给出了关于系统参数的简单表达式。接下来，表明可以将一个分支快速过渡到另一个分支的数学公式平稳地匹配两个稳态解。

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