Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T10:07:48.503Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of conductivity on hotspots

Published online by Cambridge University Press:  17 February 2009

N. F. Smyth
N. F. Smyth
Affiliation:
Department of Mathematics, The King's Buildings, University of Edinburgh, Mayfield Road, Edinburgh, Scotland, EH9 3JZ.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In industrial applications of microwave heating, it has been observed that rather than the heating taking place uniformly, regions of high temperature, called hot-spots, tend to form. Depending on the industrial application, these can be either desirable or undesirable, and hence a theoretical understanding of the properties of the material that lead to hotspot formation is necessary. It has been shown in previous studies that hotspot formation is a product of the nonlinear dependence of microwave energy absorption by the material on temperature. It is shown in the present work that the conductivity of the material can have a significant effect on hotspot formation and can, if large enough, stop a hotspot from forming.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 4 , April 1992 , pp. 403 - 413
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Ames, W. F., Nonlinear partial differential equations in engineering, Vol.1, (Academic Press, New York, 1965).Google Scholar
[2] Araneta, J. C., Brodwin, M. E. and Kriegsmann, G. A., “High temperature microwave characterisation of dielectric rods”, IEEE MTT- 32 (1984) 1328–1336.CrossRefGoogle Scholar
[3] Aris, R., The mathematical theory of diffusion and reaction in permeable catalysts, Vol. 1, the theory of the steady state, (Oxford University Press, Oxford, 1975).Google Scholar
[4] Barker, A. S., Ditzenberg, J. A. and Remeika, J. P., “Lattice vibrations and its transport spectra in β-alumina II: microwave spectra”, Phys. Rev. B. 14 (1976) 4254–4265.CrossRefGoogle Scholar
[5] Brodwin, M. E., Kriegsmann, G. A. and Watters, D. G., “Temperature instability in the microwave heating of a uniformly illuminated planar slab”, IEEE to appear (1991).Google Scholar
[6] Coleman, C. J., “On the microwave hotspot problem”, J. Austral. Math. Soc. Ser. B 33 (1991).CrossRefGoogle Scholar
[7] Frank-Kamenetskii, D. A., Diffusion and heat exchange in chemical kinetics, (Princeton University Press, Princeton, New Jersey, 1955).CrossRefGoogle Scholar
[8] Hill, J. M. and Smyth, N. F., “On the mathematical analysis of hotspots arising from microwave heating”, Math Engng. in Industry 2 (4) (1990) 267–278.Google Scholar
[9] Kingery, W. D., Bowen, H. K. and Uhlman, D. R., Introduction to ceramics (John Wiley, New York, 1976).Google Scholar
[10] Metaxas, A. S. and Meredith, R. J., Industrial microwave heating (IEE Power Engineering Series, 4, P. Peregrinus on behalf of the Institution of Electrical Engineers, London, 1983).Google Scholar
[11] Pincombe, A. H. and Smyth, N. F., “Microwave heating of materials with low conductivity”, Proc. Roy. Soc. Lond. A, 433 (1991) 479–498.Google Scholar
[12] Roussy, G., Bennani, A. and Thiebaut, J., “Temperature runaway of microwave irradiated materials”,. Appl. Phys. 62 (1987) 1167–1170.CrossRefGoogle Scholar
[13] Hippel, A. R. von, Dielectric materials and applications (MIT Press, Cambridge, MA, 1954).Google Scholar
[14] Wo, W., “Millimeter wave dielectric property measurements of gyration window materials”, ORNL Sub-83–51926, Vols. 1–2, Final report 1985–1986.Google Scholar