TY - JOUR

T1 - Thermal runaway in microwave heating : a mathematical analysis

AU - Vriezinga, A.

AU - Pedreno, S.

AU - Grasman, J.

PY - 2002

Y1 - 2002

N2 - 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

AB - 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

U2 - 10.1016/S0307-904X(02)00058-6

DO - 10.1016/S0307-904X(02)00058-6

M3 - Article

VL - 26

SP - 1029

EP - 1038

JO - Applied mathematical modelling

JF - Applied mathematical modelling

SN - 0307-904X

ER -