The microwave heating of a three-dimensional block in an infinitely long rectangular waveguide propagating the TE_(10) mode is considered. The electrical conductivity (the dielectric loss) is assumed to be a function of temperature, and modelled by the Arrhenius law. A coupled set of equations is obtained that describes the electromagnetic fields and the temperature distribution in the block. The numerical solutions of this problem are obtained by two methods, the well known FD-TD scheme and a frequency domain method which makes the further assumption that a single TE_(10) mode exists in the waveguide and material. The results show that an S-shaped temperature versus power response curve is possible, with thermal runaway occurring when the solution jumps from the lower (cool) branch to the upper (hot) branch of this curve. The results confirm the validity of the single-mode assumption and show a good comparison between the numerical and semi-analytical solutions.
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