An improved finite-element model for simulating microwave processing of polymers and polymer-composites in a cylindrical resonant cavity

Abstract

A two-dimensional axisymmetric finite-element model developed to simulate the microwave processing of polymers and polymer-matrix composites in a cylindrical resonant cavity was improved. The model consists of two submodels: the electromagnetic submodel and the heat transfer submodel. These two models are coupled together by the heat generation term arising due to the microwave energy. A single finiteelement program was written to implement the two submodels. The heat generation term arising due to exothermic chemical reactions was added to the heat conduction equation. The model can now handle thermosetting resins as well as amorphous thermoplastic polymers. The governing equations for the electromagnetic submodel are the complex, time-harmonic Maxwell's equations. Since an axisymmetric model was developed, the material needs to be axisymmetric and centered in the cavity. The material can have anisotropic conductivity and permittivity. A separate eigenvalue code was developed to compute the resonant frequency for given cavity dimensions. This eigenvalue code can account for non-homogenous material properties. The heat transfer model is governed by the unsteady heat conduction equation with the addition of heat generation terms accounting for exothermic reactions and microwave energy. All three types of heating: microwave only, convection only, and combined microwave and convection heating can be simulated by the electromagnetic and the heat transfer models. Several test cases were run to validate the programs. The results of the eigenvalue code were compared to those published in the literature. Simple test cases for which analytical expressions are available were run to verify the electromagnetic and heat transfer submodels. Excellent agreement was obtained in all of the comparisons. Once the programs were validated, several simulations were done to study microwave processing and/or convective heating of polymers and polymer-matrix composites. The materials considered were nylon 66, S-glass/polycarbonate composite, and S2-glass/epoxy composite. To study the advantages and disadvantages of microwave processing over conventional processing, comparisons were'made between the simulations of the two processes.