Physical modeling of systems involving electromagnetic heating of materials

The technique of physical scale modeling of electromagnetic problems that include heat generation is described. The scaling groups required for modeling, which depend on the ratio of conduction to displacement currents, are derived from simple physical arguments which are suitable for presentation to undergraduates in a first course on Mawell's equations. The modeling of some practical problems is considered, and the approximations that must be made to the scaling groups to solve these problems are discussed. Three special cases are considered in some depth. In the first case conduction current greatly dominates the current flow in the full-scale system (such heating can be referred to as resistive heating). In the second case both conduction and displacement currents are significant. In the third case conduction current is much greater than displacement current and the system dimensions are comparable to or greater than the wavelength and depth of penetration.<
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