Hot spot formation in microwave heated ceramic fibres

Document Type

Article

Publication Date

1-1-1997

Abstract

An analysis of microwave heating of a thin ceramic cylinder in a single mode, highly resonant cavity is presented. Realistic assumptions regarding the effective electrical conductivity, thermal parameters, and physical dimensions are adhered to throughout. Consequently, the model developed herein incorporates most of the features of an actual experiment. It contains the effects of both cavity detuning and a local electric field perturbation on the heating process. The model presented takes the form of a one-dimensional reaction-diffusion equation which contains a functional. The development of this equation is the product of a systematic modelling process that involves S-matrix theory, a small-Biot-number asymptotic analysis, and a matched asymptotic analysis of a non-standard electromagnetic scattering problem. This equation reveals both the mathematical structure and physical mechanism for the formation of hot spots. An accurate numerical method which approximates the solution of this equation is presented. The results agree qualitatively with experiments and predict observed trends.

Identifier

0031251423 (Scopus)

Publication Title

IMA Journal of Applied Mathematics Institute of Mathematics and Its Applications

External Full Text Location

https://doi.org/10.1093/imamat/59.2.123

ISSN

02724960

First Page

123

Last Page

148

Issue

2

Volume

59

Grant

DMS 9305828

Fund Ref

National Science Foundation

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