Hot spot formation in microwave heated ceramic fibres

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-Blot-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.