Pattern formation in microwave heated ceramics: cylinders and slabs

Analyses of microwave heating of a thin ceramic cylinder and a thin ceramic slab in a single mode, highly resonant cavityare presented. Realistic assumptions regarding the effectiveelectrical conductivity, thermal parameters, and physical dimensionsare adhered to throughout. Consequently, the models developedherein incorporate most of the features of actual experiments.They incorporate both the effects of cavity detuning and alocal electric field perturbation on the heating process. The models presented take the form of one- and two-dimensionalreaction–diffusion equations which contain a functionaland 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 boththe mathematical structure and physical mechanism for the formationof hot-spots. The two-dimensional equation supports a hot stripe pattern, due to preferential electromagnetic heating, whichbecomes unstable and evolves into an oval-like spot. Accuratenumerical methods which approximate the solutions of theseequations and their stability are presented and these agreequalitatively with experiments and predict observed trends. Received 1 June, 1999. ⁺ antoine@mip.ups-tlse.fr