M.Tech. / Due to electric (E) and magnetic (H) fields that vary with space (r) and time (t) in the microwave cavity, and due to the inhomogeneous nature of the minerals, heating a mineral in a microwave oven gives an inherently non-uniform temperature distribution. The objective of the project is to introduce a mathematical model that will demonstrate the thermal interaction between ilmenite mineral (FeTiO3) and microwaves. The simulation presents the temperature distribution in the sample based on the conditions imposed on its boundaries. The field distribution in the cavity is simulated, and then the thermal analysis is performed using the lumped thermal capacity model. The temperature distribution in the sample is also simulated using the general heat conduction equation. Finite difference method is used two solve the two-dimensional unsteady heat conduction equation. The simulation of the field distribution in the cavity reveals that there are position of intense electric and magnetic field in the oven. This is demonstrated by experiment 6, where samples are heated at different positions in the oven for the same duration and different temperatures in the samples were measured. Electromagnetic wave propagation was also studied. It became apparent that the electric and magnetic field can not be treated independently from each other, because the changing electric field produces a changing magnetic field and the newly produced changing magnetic field produces a changing electric field, which is an electromagnetic wave. It is also proved that, considering the relationship given by Maxwell's equations, the electric and magnetic fields are not only space out of phase but they are also time out of phase, meaning that the one quantity is leading while the other is lagging. Based on the available mathematical evidence it was suggested to fit the conventional representation of the electromagnetic field, which show the electric field and the magnetic field at right angle to each other and in time phase, to the new representation which would highlight the fact that the electric and magnetic fields are time out of phase. The study of electromagnetic wave propagation has proved that the one-dimensional conventional representation of electromagnetic waves is inadequate. It does not support the fact that there are a number of resonant modes that exists in the cavity which has long been proved and accepted by authors in the field of electromagnetism. This is very much clear when dealing with electromagnetic waves in three dimensional space.

M.Tech. (Mechanical Engineering Technology) / Please refer to full text to view abstract

A coupled electromagnetic/heat transfer model capable of simulating microwave processing of composite materials in a cylindrical resonant cavity was developed. The two-dimensional model simulates processing of axisymmetric material loads in cylindrical resonant cavities operating in the TM₀₁₀ mode. The model consists of an electromagnetic model and a heat transfer model which are coupled by the heat generation term in the heat transfer equation. Heat generation in the process material is due to dielectric loss in the material and is related to the dielectric loss factor ofthe material, the processing frequency, and the magnitude of the electric field. The finite-element method was used to develop both the electromagnetic and heat transfer models. The electromagnetic model, based on Maxwell's equations, allows anisotropic conductivity and permittivity and accounts for resonance. A novel technique for determining resonance was developed for use in the electromagnetic model. The technique can be used to design microwave applicator/material systems. The heat transfer model allows anisotropic thermal conductivity and can be used to simulate heating by microwaves only, by convection only, or by a combination of microwaves and convection. The coupled model can account for the temperature dependence of dielectric properties. The electromagnetic and heat transfer models were verified by comparison to cases for which analytical solutions were available. The coupled model was then used to simulate microwave processing of nylon 66 and composite specimens of S-glass/polycarbonate. Microwave and convective heating were used alone and in combination to heat a thick cylinder of material. Comparisons are made between microwave, convective, and combined processes and the advantages and disadvantages of microwave processing are discussed. / M.S.

Mixture models were studied in an effort to predict the microwave frequency permittivities of unidirectional-fiber-reinforced thermoplastic-matrix composite materials as a function of fiber volume fraction, fiber orientation relative to the electric field, and temperature. The permittivities of the constituent fiber and plastic materials were measured using a resonant cavity perturbation technique at 9.4 GHz and 2.45 GHz. The permittivities of the composite specimens were measured using a reflection cavity technique at 9.4 GHz and 2.45 GHz. Simple" rule of -mixtures II models that use the fiber and plastic permittivities have been found to approximate the complex dielectric properties of the composite for varied fiber volume fractions. The permittivities of oriented composites were successfully modeled at 9.4 GHz using a tensor rotation procedure. Composite permittivities were modeled with temperature up to the glass transition temperature of the thermoplastic matrix. Good agreement was found between the mixture model and experimental results for permittivity as a function of temperature at 9.4 GHz. / Master of Science

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. / Master of Science