Pattern formation in microwave heated ceramics: Cylinders and slabs

Document Type

Article

Publication Date

2-1-2001

Abstract

Analyses of microwave heating of a thin ceramic cylinder and a thin ceramic slab in a single mode, highly resonant cavity are presented. Realistic assumptions regarding the effective electrical conductivity, thermal parameters, and physical dimensions are adhered to throughout. Consequently, the models developed herein incorporate most of the features of actual experiments. They incorporate both the effects of cavity detuning and a local electric field perturbation on the heating process. The models presented take the form of one- and two-dimensional reaction-diffusion equations which contain a functional and an inhomogeneous source term for the cylinder and slab, respectively. The development of these equations 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. The one-dimensional equation for the cylinder reveals both the mathematical structure and physical mechanism for the formation of hot-spots. The two-dimensional equation supports a hot stripe pattern, due to preferential electromagnetic heating, which becomes unstable and evolves into an oval-like spot. Accurate numerical methods which approximate the solutions of these equations and their stability are presented and these agree qualitatively with experiments and predict observed trends.

Identifier

0035252019 (Scopus)

Publication Title

IMA Journal of Applied Mathematics Institute of Mathematics and Its Applications

External Full Text Location

https://doi.org/10.1093/imamat/66.1.1

ISSN

02724960

First Page

1

Last Page

32

Issue

1

Volume

66

Grant

DMS 9305828

Fund Ref

National Science Foundation

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