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Full-Text Articles in Physics
The Occurrence Of Limit-Cycles During Feedback Control Of Microwave Heating, Prof. Tim Marchant
The Occurrence Of Limit-Cycles During Feedback Control Of Microwave Heating, Prof. Tim Marchant
Tim Marchant
The microwave heating of one- and two-dimensional slabs, subject to linear feedback control, is examined. A semianalytical model of the microwave heating is developed using the Galerkin method. A local stability analysis of the model indicates that Hopf bifurcations occur; the regions of parameter space in which limit-cycles exist are identified. An efficient numerical scheme for the solution of the governing equations, which consist of the forced heat equation and a Helmholtz equation describing the electric-field amplitude, is also developed. An excellent comparison between numerical solutions of the semianalytical model and the governing equations is obtained for the temporal evolution …
The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant
The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant
Tim Marchant
The microwave heating of three-dimensional blocks, by the transverse magnetic waveguide mode TM11, is considered in a long rectangular waveguide. The governing equations are the forced heat equation and a steady-state version of Maxwell's equations, while the boundary conditions take into account both convective and radiative heat loss. Semi-analytical solutions, valid for small thermal absorptivity, are found using the Galerkin method. The electrical conductivity and the thermal absorptivity are assumed to be temperature dependent, while both the electrical permittivity and magnetic permeability are taken to be constant. Both a quadratic relation and an Arrhenius-type law are used for the temperature …