Comparison of the heating of ceramic cylinders by 2.45 GHz and 83 GHz beams

Summary form only given. Techniques for processing ceramic materials using microwave or millimeter-wave radiation are being developed as an alternative to the use of conventional furnaces because of several advantages, including more rapid processing, improved material properties, and higher overall efficiency. Although microwave processing has been successfully industrialized, there is a need for better modeling of the heating process. The internal temperature profile of the workpiece during processing can greatly impact its quality, but is more difficult to determine in the case of microwave heating than for conventional furnaces. This is because microwave power deposition depends on wave effects and the workpiece dielectric properties as well as its size, shape, and temperature. In this paper we analyze the heating of ceramic cylinders and tubes by a plane-wave RF beam for frequencies of 2.45 and 83 GHz. In the analysis the workpiece is subdivided into thin concentric tubes in which the temperature, complex dielectric constant, and other material properties are held constant; and the workpiece is assumed to be rotating to provide azimuthal averaging of the power deposition. Maxwell's equations are solved by expanding the RF fields in cylindrical waves. Matching the boundary conditions at the tube interfaces leads to a set of equations for the expansion coefficients. The radial heat-conduction equation is nonlinear and is solved numerically. Both transient and steady-state solutions have been investigated. When solving the heat conduction equation, the tube dielectric and thermal parameters, and the RF field expansion coefficients are recalculated after each time step or iteration. This leads to a self-consistent RF-thermal solution. The frequencies correspond to wavelengths that are large and small, respectively, compared to the workpiece diameter and generally produce different temperature profiles. The power deposition is non-uniform in both cases. The non-uniformity varies with temperature and is caused by wave interference effects, strong beam absorption, internal temperature gradients, and, particularly at 83 GHz, geometrical focusing effects. The results show the importance of averaging the irradiation with respect to workpiece orientation to obtain more uniform heating. In the case of millimeter-wave beam heating this can be achieved by rotating the cylinder, while in a 2.45 GHz furnace it could be approximated by mode stirring. The results demonstrate the utility of hybrid heating especially at 2.45 GHz for materials such as alumina that have a low loss tangent at moderate temperatures