Abstract
The microwave heating of a one-dimensional, semi-infinite material with low conductivity is considered. Starting from Maxwell’s equations, it is shown that this heating is governed by a coupled system consisting of the damped wave equation and a forced heat equation with forcing depending on the amplitude squared of the electric field. For simplicity, the conductivity of the material and the speed of microwave radiation in the material are assumed to have power law dependencies on temperature. Approximate analytical solutions of the governing equations are found as a slowly varying wave. These solutions and the slow equations from which they are derived are found to give criteria for when ‘hotspots' (regions of very high temperature relative to their surroundings) can form. The approximate analytical solutions are compared with numerical solutions of the governing equations.
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