On the microwave heating of materials with temperature dependent properties

The time dependent microwave heating of a one-dimensional, semi-infinite body 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 square of the amplitude of the electric field. The dependence of the values of the electromagnetic properties on the temperature is represented by two different power laws and solutions are obtainedin each case. Approximate analytical solutions are obtained for the coupled equations, using perturbation analysis, when the thermal diffusivity is constant and is smaller than the heating rate. The effect of a finite, and possibly nonlinear thermal diffusivity is also considered.