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Temperature modulations in a circuit model of microwave heating

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Abstract

The problem of temperature-induced modulations on the electric field during microwave heating can be modelled as the problem of a voltage response to a periodically excited resonant circuit with a thermistor. However, even this simplified model is formulated in terms of partial differential equations. Asymptotic methods are used to reduce the problem to a phase-plane problem for the temperature profile coupled to the envelope equation for the voltage. It is shown how relaxation oscillations arise where the temperature modulates the voltage response. This strongly suggests the possibility of wave modulation in the problem of microwave heating.

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References

  1. C. García Reimbert, A. A. Minzoni and N. F. Smyth, Effect of radiation losses onhotspot formation and proplagation in microwave heating. IMA J. Appl. Math. 57 (1996) 165–179.

    Google Scholar 

  2. C. A. Vargas and G. Kriegsmann, Thermistor effects on tuned circuit. A Model of Microwave CavityDeturning. (In preparation).

  3. G. Kriegsmann and S. I. Varatarajah, Formation of hot spots in microwaveheated ceramic rods. Ceramic Trans. 36 (1993) 221–228.

    Google Scholar 

  4. G. Kriegsmann, Patternformation in microwave heated ceramics, cylinder and slabs. IMA J. Appl. Math. 66 (2001) 1–32.

    Google Scholar 

  5. E. Coddington and N. Levinson, Theory of Ordinary Differential Equations. New York: McGraw-Hill(1955) 429 pp.

    Google Scholar 

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Authors and Affiliations

  1. FENOMEC, IIMAS, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20–726, Delegación Alvaro Obregón, 01000, México, D.F

    C. García Reimbert, M.C. Jorge, A.A. Minzoni & C.A. Vargas

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  1. C. García Reimbert
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  2. M.C. Jorge
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  3. A.A. Minzoni
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  4. C.A. Vargas
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Reimbert, C.G., Jorge, M., Minzoni, A. et al. Temperature modulations in a circuit model of microwave heating. Journal of Engineering Mathematics 44, 199–206 (2002). https://doi.org/10.1023/A:1020824314529

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  • DOI: https://doi.org/10.1023/A:1020824314529

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