Abstract
The microwave heating of a thinly carbon-coated ceramic fibre is modelled and analysed in the small Biot number regime. The electric field is assumed known and uniform throughout the cross-section, and constant along the axis of the cylinder. The mathematical model consists of a nonlinear heat equation with an idealized source term that models the thin carbon coating and simplified reaction kinetics. The analysis yields an asymptotic approximation of the heating process on two time scales. The first captures the initial heating of the carbon coating and the ceramic, and the carbon reaction, while the second determines the long time behaviour of the sample. The results show a qualitative relationship between the coating thickness and the final temperature of the fibre. If the coating thickness is not uniform along the fibre axis, then the model explains the mechanism for the formation and propagation of hot-spots.
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