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

Published online by Cambridge University Press:  17 February 2009

T. R. Marchant  and
B. Liu
T. R. Marchant
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia.
B. Liu
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia.
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Abstract

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The steady-state heating of a two-dimensional slab by the TE10 mode in a microwave cavity is considered. The cavity contains an iris with a variable aperture 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 forced heat equation and Maxwell's equations while fixed-temperature boundary conditions 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-state temperature and the electric-field amplitude in the slab using the Galerkin method.

With no-iris (a semi-infinite waveguide) the usual S-shaped power versus temperature curve occurs. As the aperture width is varied however, the critical 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 shown that an optimal aperture setting and short position exists which minimises the input power needed to obtain a given temperature.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 1 , July 2001 , pp. 137 - 148
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Hill, J. M. and Marchant, T. R., “Modelling microwave heating”, Appl. Math. Modelling 20 (1996) 3–15.CrossRefGoogle Scholar
[2]Kenkre, V. M., Skala, L., Weiser, M. W. and Katz, J. D. “Theory of microwave effects on atomic diffusion in sintering: basic considerations of the phenomenon of thermal runaway”, in Microwave processing of materials 11 (eds. Snyder, W. B., Sutton, W. H., Iskander, M. F. and Johnson, D. L.), (Mater. Res. Soc. Proc. 189, Pittsburgh, 1990) 179–183.Google Scholar
[3]Kriegsmann, G. A., “Cavity effects in microwave heating of ceramics”, SIAM J. Appl. Math. 57 (1997) 382–400.CrossRefGoogle Scholar
[4]Landau, L. D. and Lifshitz, E. M., Statistical physics (Pergamon Press, London, 1958).Google Scholar
[5]Lewin, L., Theory of waveguides (John Wiley, New York, 1975).Google Scholar
[6]Liu, B. and Marchant, T. R., “The microwave heating of two-dimensional slabs with small Arrhenius absorptivity”, IMA J. Appl. Math. 62 (1999) 137–166.CrossRefGoogle Scholar