The multiplicity of steady-state solutions arising from microwave heating. I. Infinite biot number and small penetration depth

M. I. Nelson, G. C. Wake, X. D. Chen, E. Balakrishnan

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Abstract

Microwave heating of porous solid materials has received considerable attention in recent years because of its widespread use in industry. In this study, the microwave power absorption term is modelled as the product of an exponential temperature function with a function that decays exponentially with distance. The latter describes the penetration of the material by the microwaves. We investigate the phenomena of multiplicity in class A geometries, paying particular attention to how the penetration function affects the behaviour of the system. We explain why the phase-plane techniques which have been used in the case when the penetration term is constant do not extend to non-constant penetration.

Original languageEnglish
Pages (from-to)87-103
Number of pages17
JournalANZIAM Journal
Volume43
Issue number1
Publication statusPublished - 2001

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ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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