Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


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.