Microwave Thawing of Cylinders zy B. J. Pangrle, K. zyxwvuts G. Ayappa, and H. T. Davis zyxw Dept. of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 E. A. Davis and J. Gordon Dept. of Food Science and Nutrition, University of Minnesota, St. Paul, MN 55108 zyx The finite element method was used to model microwave thawing zyx of pure-water and 0. I-M NaCI cylinders. The electromagnetic field was described by Maxwell’s equations with temperature-dependent dielectricproperties, while the heat equation, coupled with the Stefan and Robin conditions, was used to describe the thawing process. An additional equation for the frozen volume fraction was used, when necessary, to account for the presence of a mushy region. Two microwave fre- quencies, 915 MHz and zyxwvu 2,450 MHz, were examined and the microwave radiation was assumed to be radially isotropic and normal to the surface of the cylinder. Results show that a two-phase mushy region may exist, and an additional thawing front may appear at the center of the cylinder. Salt cylinders have a higher dielectric zy loss than pure-water cylinders and therefore thaw more quickly. Internal resonance occurs when the wavelength of the radiation is a harmonic of the cylinder radius. Resonance increases power deposition and expedites the thawing process. The onset of resonance alters thawing times and complicates the development of heuristic rules f o r microwave thawing. introduction Heating lossy dielectric media by electromagnetic (EM) ra- diation has found widespread use in commercial and industrial applications. These applications rely on internal heat gener- ation produced from interactions between the media and the EM radiation. Many governments have imposed strict regu- lations on which frequencies may be used for industrial, sci- entific and medical use (Varey, 1990). In North America the microwave frequencies of 915 MHz and 2,450 MHz are avail- able and in the British Isles 896 MHz and 2,450 MHz, while there is no frequency allocated near 900 MHz in continental Europe (Pearce, 1990). In theU.S., 915 MHzis used commonly in industrial ovens and 2,450 MHz in household ovens. Heating is different at these two frequencies. The longer wavelength (915 MHz) radiation penetrates deeper into the sample and distributes power more evenly. The shorter wavelength (2,450 MHz) radiation allows for more node/antinode formation within the oven capacity and sample. At a node the electric field is zero and no power is deposited, whereas at an antinode there is a peak in the power deposition. A process common to industry and household applications is microwave thawing. The EM phenomenon associated with ice/water systems is also a concern to scientists studying the AIChE Journal December 1991 cryosphere (Vant et al., 1978; Matzler and Wegmuller, 1987) and attenuation of radar signals in the atmosphere (Sihvola, 1989;Klassen, 1990). Thawing rates for frozen samples depend on the sample’s material properties and dimensions and the magnitude and frequency of the electromagnetic radiation. For example, consider a frozen cylinder placed in an environment whose temperature is above the cylinder’s freezing point. At first, the phase-change front moves inward from the surface. Exposing this thawing cylinder to a radially symmetric EM field accelerates the progress of the phase-change front. Ad- ditionally, another phase-change front may appear at the cyl- inder’s center (due to the presence of an antinode or focusing), and/or thawing of the frozen region may occur resulting in a heterogeneous region of frozen and thawed phases. This region is commonly referred to as a “mushy” region. Most classical solutions to phase-change or “Stefan” prob- lems do not consider internal heat generation or mushy regions. If a “mushy” region exists, it is usually due to impurities that cause the phase change to occur over a temperature range. In some instances, the mushy region can be ignored and replaced by a sharp moving interface that is at a discrete transition temperature (Ozisik, 1980). The validity of this simplification Vol. zyxwv 37, No. 12 1789