Microwave heating of carbon-coated ceramic fibres: A mathematical model

The microwave heating of a thinly carbon-coated ceramic fibreis modelled and analysed in the small Biot number regime. Theelectric field is assumed known and uniform throughout the cross-section,and constant along the axis of the cylinder. The mathematicalmodel consists of a nonlinear heat equation with an idealizedsource term that models the thin carbon coating and simplifiedreaction kinetics. The analysis yields an asymptotic approximationof the heating process on two time scales. The first capturesthe initial heating of the carbon coating and the ceramic, andthe carbon reaction, while the second determines the long timebehaviour of the sample. The results show a qualitative relationshipbetween the coating thickness and the final temperature of thefibre. If the coating thickness is not uniform along the fibreaxis, then the model explains the mechanism for the formationand propagation of hot-spots.