Microwave Heating Of Materials Research Articles

On Improving Convergence Characterization to Solve the Electromagnetic–Thermal Model

The electromagnetic (EM)–thermal partial differential equations illuminate the mechanism behind both thermal effect of microwaves on devices and microwave heating of materials. During the transient analysis, the differential equations must be discretized into time steps. Each time step corresponds to the solution of a nonlinear equation system. In order to accelerate convergence, the time steps should be as large as possible and the nonlinear equation system requires an efficient iterative method. In this article, the nodal heat imbalance ratio (NHIBR) is proposed as the basic for the adaptive time-stepping scheme. The normalized weighted mean (NWM) of the NHIBR is introduced to select different accuracy requirements for the temporal discretization and detect the convergence of solution for the steady state. Moreover, the Newton method is used to solve the nonlinear equations for its characterization of superlinear convergence. The finite-element method (FEM) is employed with edge elements for EM fields and node elements for temperature fields. Furthermore, the accuracy and advantages of the proposed analysis scheme are verified by numerical simulations.

Экспериментальная оценка температурной зависимости показателя поглощения порошков оксидов металлов при их нагреве излучением гиротрона с частотой 527 GHz

The temperature dependences of the absorption coefficient of Al2O3, ZnO, TiO2 powders at a frequency of 527 GHz are investigated. A gyrotron with an output power of up to 240 W in CW mode was used as a radiation source for heating the samples. The power absorbed in the samples was measured in the temperature range from 300 to 1000 ° C (for some samples). Compared with experiments at a frequency of 263 GHz, a significant increase (by a factor of 4 - 6) in the absorption coefficient is observed. The results may be of interest to researchers involved in microwave heating of materials.

The Temperature Behavior of Microwave Absorption of Metal Oxide Powders When Heated by a 263-GHz Gyrotron Radiation

In this paper, the temperature dependence of microwave absorption in powders of various metal oxides was studied. The powders of aluminum oxide Al2O3, zinc oxide ZnO, tungsten trioxide WO3, and titanium dioxide TiO2 were the test substances. A subterahertz gyrotron setup with a frequency of 263 GHz and an adjustable output power level from watts to 1 kW was used as a radiation source. In the experiments, the samples of the powders were heated by the radiation of the gyrotron, and at the same time, the temperature of the sample was recorded and the power absorbed in the sample was measured by the calorimetric method. The measurements were carried out in a wide range of temperatures: from several tens up to 1200 °C. The results obtained may be of both fundamental and applied interest for researchers engaged in microwave heating of materials.

A theoretical analysis on the effect of containers on the microwave heating of materials

Microwave heating is generally performed by positioning the sample within a container. The container can reflect, absorb or transmit microwaves based on the dielectric properties and that can influence the microwave heating characteristics of the sample. This work is an attempt to theoretically analyze the alteration of the microwave heating characteristics of materials due to the use of either a low-lossy alumina container or a high lossy SiC container. The heating characteristics have been simulated for the high-lossy beef and low-lossy bread samples of a fixed dimension by solving the coupled energy balance equation and detailed Helmholtz wave propagation equations within the sample-container assembly. It has been shown that the microwave heating characteristics can be significantly altered in the presence of the container based on the relative dielectric properties of the materials. The alumina container has been found to be efficient to enhance the microwave heating efficiency of the high lossy material such as beef, while the rapid microwave heating of the SiC container has been found to be beneficial to enhance the heating of the low lossy material such as bread in some cases.

Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity

A microwave cavity and heating system for microwave processing and in situ dynamic measurements of the complex permittivity of dielectric materials at high temperatures ( $\sim {\hbox{1000}} ^{\circ}{\hbox{C}}$ ) has been developed. The method is based on a dual-mode cylindrical cavity where heating and testing are performed by two different swept frequency microwave sources. A cross-coupling filter isolates the signals coming from both sources. By adjusting the frequency bandwidth of the heating source and the level of coupling to the cavity, an automatic procedure allows for the establishment of a desirable level of heating rate to the dielectric sample to reach high temperatures in short cycles. Dielectric properties of materials as a function of temperature are calculated by an improved cavity perturbation method during heating. Accuracy of complex permittivity results has been evaluated and an error lower than 5% with respect to a rigorous analysis of the cavity has been achieved. The functionality of the microwave dielectric measurement system has been demonstrated by heating and measuring glass and ceramic samples up to ${\hbox{1000}} ^{\circ}{\hbox{C}}$ . The correlation of the complex permittivity with the heating rate, temperature, absorbed power, and other processing parameters can help to better understand the interactions that take place during microwave heating of materials at high temperatures compared to conventional heating.

Microwave Absorption of Barium Borosilicate, Zinc Borate, Fe-Doped Alumino-Phosphate Glasses and Its Raw Materials

This study presents microwave absorption of raw materials used in barium borosilicate, Fe-doped alumina phosphate and zinc borate glass. Microwave absorption was investigated for the raw materials SiO2, Na2CO3, BaCO3, BPO4, Al(PO3)3, Mg(PO3)2, Al(OH)3, TiO2. The study shows that SiO2 could be heated directly above 1000 °C within 30 min at 1.5 kW microwave output (MW) power and 0.8 kW MW power is necessary to initiate heating (from 260 °C). Microwave heating of material with low dielectric loss has been investigated by increasing MW power. Microwave absorption of above glass systems has also been investigated. Dielectric properties such as loss tangent of glass as a function of temperature are presented. Glass melting under direct microwave heating was demonstrated for the studied glass systems. Temperature-Microwave power-Time (T-P-t) profiles for the three glasses indicate maximum MW output power ~1 kW, 0.65 kW and ~1 kW for barium borosilicate, zinc borate glass and alumino-phosphate glass for 60 g glass melting.

Effects of the Susceptor Dielectric Properties on the Microwave Sintering of Alumina

Microwave sintering of alumina has been carried out using SiC and Y‐ZrO2 based susceptors. The microstructure of the sintered samples has been rigorously compared and correlated to the heating behaviour of the susceptor used. It was found that the nature of the susceptor highly influences the sintering behaviour of alumina. The results show that at high temperatures, the electrical conductivity of the SiC susceptor tends to screen the incident electric field, thus resulting in a surface heating of the alumina sample material. When using ZrO2 susceptor, the microstructure analysis of the sintered alumina samples reveals a volumetric heating, which is a signature of the microwave dielectric loss mechanism. This could be explained by the lower ZrO2 electrical conductivity compared to the SiC one. The simulation results confirm this behaviour, particularly showing that in the presence of ZrO2, the intensity of the electric field within the sample is higher than the one when SiC susceptor is used. Basically, the results of the simulation data are in good agreement with our experimental results. Although the SiC based susceptor is usually used in the microwave heating of materials, the ZrO2 based susceptor presents numerous advantages over the SiC one, especially in term of direct microwave heating contributions.

Spatial observation and quantification of microwave heating in materials

An electromagnetic exposure chamber was designed to safely deliver electromagnetic power in the range of microwaves between 0.8 and 4.2 GHz to a thin cylindrical materials. This instrumentation is unique because the diagnostics not only measure sample heating with a response time of 1.3 ms, but also energy transmitted and reflected. Energy absorption at different frequencies was quantified via electromagnetic heating using an infrared camera. This in situ IR imaging of the spatial distribution of temperature during microwave exposure coupled with sensors for determining transmitted and reflected energy enables novel new microwave energy experiments. Samples were exposed to a portion of both the electric and magnetic fields inside a waveguide and based on sample dimensions, the field strengths were assumed uniform across the sample. Three materials were examined: two were borosilicate, first coated with graphite paint and a second without the coating; and, the third was a compressed sample of flake graphite pressed to 69% of its bulk density. Results are in agreement with the theories of microwave heating and verify the functionality of this experimental design. This diagnostic will be important in future tests where a variety of different materials can be exposed to weak electromagnetic waves and their efficiency in coupling to the microwaves can be examined.

Role of convective heat removal and electromagnetic field structure in the microwave heating of materials

The temperature distributions arising in a low-loss dielectric sample in the process of microwave heating have been studied by means of numerical simulation. The convective heat removal has been demonstrated to play the determining role in the energy balance of the sample. The obtained temperature distributions have been compared with the results of a purposely designed microwave heating experiment with multi-channel temperature measurement. The temperature on the surface of the sample agreed well to the simulation accounting for convective heat removal. The temperature measured inside the sample was higher than predicted by simulation. The electrodynamic calculations have shown that due to diffraction effects the electromagnetic field inside the sample is inhomogeneous even if the sample is irradiated by microwaves isotropically. Thus, it is concluded that in order to simulate the microwave heating process accurately, it is necessary to account for air convection and calculate the structure of electromagnetic field inside the sample.

Role of ceramic supports on microwave heating of materials

A detailed analysis has been carried out to study efficient heating due to microwaves for one-dimensional samples placed on ceramic supports (Al2O3, SiC). The greater effects on microwave heating of samples have been illustrated via average power within a sample versus sample thickness diagram for various cases. The maxima in power, also termed as “resonances,” is observed for specific sample thicknesses and the two consecutive maxima in average power are termed as R1 and R2 modes. The greater heating effects leading to hot spots would occur in water samples during both-sides incidence when the sample is kept on Al2O3 support. SiC support may be recommended for water samples due to uniform heating throughout the sample. In contrast, SiC support could cause local hot spots or thermal runaway for oil samples. The localized hot spots are more pronounced for the samples exposed to microwaves on both faces. The choice of support may not be trivial due to the complex dielectric response of sample-support assembly. Current analysis has been illustrated for low- and high-dielectric materials (water and oil) and a representative case study has also been shown for beef samples. Based on such observations, a generalized heating strategy for materials due to uniform plane waves has been derived.

The Electromagnetic Field Modeling As A Tool In The Microwave Heating Feasibility Studies

The electromagnetic field modeling of a loaded microwave applicator can help in choosing the proper conditions to successfully organize feasibility studies, allowing savings of time and money, which are usually wasted during “blindfold” tests. As a matter of fact, when microwave heating of materials is performed, the pronounced nonhomogeneity of the field distribution in multi-mode applicators can produce contradictory experimental results, leading to erroneous conclusions regarding the main variables controlling the process. This is particularly true considering the microwave heat treatment of low thermal conductivity materials. Two different applications in the ceramic field, comparing the results of “blindfold” and modeling-aided experimental conditions, are presented: de-binding of technical ceramics and asbestos inertization and/or vitrification. Thanks to a better knowledge of the electromagnetic field in the applicators, it has been possible to succeed in applications that, at a first glance, did not seem promising at all.

A DRBEM model for microwave heating problems

Due to the speed of processing, the microwave heating of materials is becoming industrially important. One of the major difficulties in using this technology is the occurrence of “hot spots,” which are localized areas of high temperature that develop as the material is being irradiated. It is of great practical significance to predict the condition under which hot spots arise so that their occurrence can be avoided or utilized. For example, hot spots are desirable in smelting since they quicken the process and undesirable in sintering ceramics since they can lead to damage.

Microwave heating of materials with impurities

The microwave heating of materials is important in many industrial processes. For example, it is used for the smelting of metals and the sintering of ceramics. Hot-spots (localised areas of high temperature) can develop in the material being heated or in the microwave oven itself, with disastrous consequences. Impurities in the material or in a component of the microwave oven can have different electromagnetic and thermal properties to the surrounding material. Different rates of heating occur at these sites, which gives rise to differential heating, which can lead to the generation of hot-spots. The generation of hot-spots by this mechanism is considered for a finite one-dimensional slab with a single impurity at its centre. A fixed-temperature boundary condition is applied at both ends of the slab and one end of the slab is irradiated by microwaves of constant amplitude. The heat absorption at the impurity is assumed to have a power-law dependence on temperature (hence hot-spot generation can occur via thermal runaway). Depending on the electrical and thermal properties of the material there are two possibilities; either a hot-spot occurs or a steady-state solution occurs due to a balance between heat absorption in the material and heat loss through the boundaries. These steady-state solutions are found for both linear and non-linear thermal absorptivity and constant and decaying electric-field amplitude. If possible the region of parameter space in which they occur (in the rest of the parameter space hot-spots occur) is also found. In addition, numerical solutions are developed to verify the steady-state solutions and to investigate cases where analytical solutions are difficult to derive, such as for materials with multiple impurities.

Microwave heating of materials with temperature-dependent wavespeed

The microwave heating of a one-dimensional, semi-infinite material with temperature-dependent material properties is studied. The governing equations, Maxwell's equations and the forced heat equation, are considered in the limit of high-frequency radiation and small thermal diffusivity. Particular power-law dependencies are chosen for the material parameters and an uniformly valid asymptotic solution is derived, using the techniques of strained coordinates and multiple scales. The asymptotic solution is compared with numerical solutions and an example involving the development of a hot-spot (a localised area of very high temperature) is examined.

Microwave heating of materials with power law temperature dependencies

The time-dependent microwave heating of a semi-infinite material, which is governed by a coupled system of Maxwell's equations and the forced heat equation, is considered. The dielectric properties of the material are assumed to be temperature-d ependent, with this dependence being of a power law form. Asymptotic solutions of the governing equations are found in the high-frequency geometric-optics limit. These solutions are compared with numerical solutions of the governing equations, and good agreement is found.

Microwave Heating of Materials with Nonohmic Conductance

The microwave heating of a material with temperature-dependent, nonohmic con-ductance is considered both analytically and numerically. In the case when the microwave amplitude is small, it is shown using a multiple scales expansion that the heating is governed by a Ginzburg–Landau type equation. This equation does not possess the solitary wave solutions of the full Ginzburg–Landau equation. Approximate solutions in the form of a slowly varying soliton and a front are found in certain parameter limits; these solutions compare very well with numerical solutions of the full governing equations. Initial-boundary value and initial value problems are considered numerically with particular emphasis on the structure of fronts.

Microwave heating of materials with low conductivity

The microwave heating of a one-dimensional, semi-infinite material with low conductivity is considered. Starting from Maxwell’s equations, it is shown that this heating is governed by a coupled system consisting of the damped wave equation and a forced heat equation with forcing depending on the amplitude squared of the electric field. For simplicity, the conductivity of the material and the speed of microwave radiation in the material are assumed to have power law dependencies on temperature. Approximate analytical solutions of the governing equations are found as a slowly varying wave. These solutions and the slow equations from which they are derived are found to give criteria for when ‘hotspots' (regions of very high temperature relative to their surroundings) can form. The approximate analytical solutions are compared with numerical solutions of the governing equations.