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Semi-analytical solutions describing microwave heating and thawing

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posted on 2024-11-11, 15:43 authored by Matthew Lee
Semi-analytical solutions for one-dimensional models of microwave thawing and one and two-dimensional models of microwave reactors are presented. Each of the models includes, as part of the governing equations, a forced heat equation and a steady-state version of Maxwell's equations. The temperature dependent properties of a material, the electrical conductivity and the thermal absorptivity, result in the coupling of these equations. Numerical models presented validate the semi-analytical results for the heating and thawing scenarios considered in this thesis. The microwave thawing of a one-dimensional slab and cylinder are both considered, where power-law temperature dependencies are assumed. The speed of the moving phase boundary is governed by the Stefan condition. A feedback control process is used to examine and minimise slab melting times. This allows a thawing strategy to be developed which greatly shortens the thawing time whilst avoiding thermal runaway, hence improving the efficiency of the thawing process. One and two-dimensional continuous-flow microwave reactors are also examined, which are unstirred so the effects of diffusion are important. A reaction-diffusion equation describes the reactant concentration with the reaction rate described by the Arrhenius law. A stability analysis is performed on the semi-analytical reactor model. This analysis allows the prediction of Hopf bifurcations, and hence periodic solutions called limit-cycles.

History

Year

2002

Thesis type

  • Doctoral thesis

Faculty/School

School of Mathematics and Applied Statistics

Language

English

Disclaimer

Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.

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