### Abstract

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

Original language | English |
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Pages (from-to) | 1029-1038 |

Journal | Applied mathematical modelling |

Volume | 26 |

DOIs | |

Publication status | Published - 2002 |

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## Cite this

Vriezinga, A., Pedreno, S., & Grasman, J. (2002). Thermal runaway in microwave heating : a mathematical analysis.

*Applied mathematical modelling*,*26*, 1029-1038. https://doi.org/10.1016/S0307-904X(02)00058-6