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Quasi-3-D Finite-Element Method for Simulating Cylindrical Induction-Heating Devices

A cylindrically symmetric problem can be simulated by a two-dimensional (2-D) axisymmetric finite-element model by exploiting the symmetry and thus reducing the original 3-D geometry to a 2-D cross section. This is, however, no longer possible when boundary conditions or excitations that violate the geometrical symmetry are applied. To avoid a computationally expensive 3-D simulation, a quasi-3-D finite-element method is developed. The method uses tensor-product shape functions combining standard finite elements in the cross-sectional plane with harmonic functions to account for the azimuthal variation of the field. The method and its convergence are validated against an analytical model. The method is particular useful for cylindrical induction-heating devices with asymmetric cooling effects, as is demonstrated by the example.