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

Published online by Cambridge University Press:  17 February 2009

M. I. Nelson ,
G. C. Wake ,
X. D. Chen  and
E. Balakrishnan
M. I. Nelson
Affiliation:
Department of Fuel and Energy, The University of Leeds, Leeds LS2 9JT, England.
G. C. Wake
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand.
X. D. Chen
Affiliation:
Department of Chemical and Materials Engineering, The University of Auckland, New Zealand.
E. Balakrishnan
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, Sultanate of Oman.
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Abstract

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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 function that decays exponentially with distance. The latter describes the penetration of 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 1 , July 2001 , pp. 87 - 103
Copyright
Copyright © Australian Mathematical Society 2001

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