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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

Microwave Heating
Steady-state Solution
Penetration
Multiplicity
Microwave
Phase Plane
Term
Absorption
Industry
Decay

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

The multiplicity of steady-state solutions arising from microwave heating. I. Infinite biot number and small penetration depth. / Nelson, M. I.; Wake, G. C.; Chen, X. D.; Balakrishnan, E.

In: ANZIAM Journal, Vol. 43, No. 1, 2001, p. 87-103.

Research output: Contribution to journalArticle

@article{1848495faa794fa9959a7f570b5616b0,
title = "The multiplicity of steady-state solutions arising from microwave heating. I. Infinite biot number and small penetration depth",
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.",
author = "Nelson, {M. I.} and Wake, {G. C.} and Chen, {X. D.} and E. Balakrishnan",
year = "2001",
language = "English",
volume = "43",
pages = "87--103",
journal = "ANZIAM Journal",
issn = "1446-1811",
publisher = "Cambridge University Press",
number = "1",

}

TY - JOUR

T1 - The multiplicity of steady-state solutions arising from microwave heating. I. Infinite biot number and small penetration depth

AU - Nelson, M. I.

AU - Wake, G. C.

AU - Chen, X. D.

AU - Balakrishnan, E.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33747216805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747216805&partnerID=8YFLogxK

M3 - Article

VL - 43

SP - 87

EP - 103

JO - ANZIAM Journal

JF - ANZIAM Journal

SN - 1446-1811

IS - 1

ER -