On the heating of a two-dimensional slab in a microwave cavity: Aperture effects

The steady-state heating of a two-dimensional slab by the TE10 mode in a mi crowave cavity is considered. The cavity contains an iris with a variable a perture and is closed by a short. Resonance can occur in the cavity, which is dependent on the short position, the aperture width and the temperature of the heated slab. The governing equations for the slab are steady-state versions of the force d heat equation and Maxwell's equations while fixed-temperature boundary co nditions are used. An Arrhenius temperature dependency is assumed for both the electrical conductivity and the thermal absorptivity. Semi -analytical solutions, valid for small thermal absorptivity, are found for the steady-s tate temperature and the electric-field amplitude in the slab using the Gal erkin method. With no-iris (a semi-infinite waveguide) the usual S-shaped power versus te mperature curve occurs. As the aperture width is varied however, the critic al power level at which thermal runaway occurs and the temperature response on the upper branch of the S-shaped curve are both changed. This is due to the interaction between the radiation, the cavity and the heated slab. An example is presented to illustrate these aperture effects. Also, it is show n that an optimal aperture setting and short position exists which minimise s the input power needed to obtain a given temperature.