Thermal runaway and bistability in microwave heated slabs, cylinders, and spheres

This study analyzes the runaway of microwave (2450 MHz) heated slabs, cylinders, and spheres in free space. It is shown that the phenomenon can be described with an S-shaped response curve of steady-state temperature versus microwave power at any position within the sample. The analysis demonstrates that the direct influence of the temperature dependent loss factor in the absorption of electromagnetic energy is canceled by the attenuation constant. Runaway can be understood from the behavior of the waves within the sample. In foodstuffs the small decrease of the phase constant with increasing temperature causes resonance at certain temperature, which can be considered as the physical origin of runaway. So characteristic dimension of food samples have to be smaller than a quarter of the temperature dependent wavelength to prevent runaway. The investigation of a slab of alumina demonstrates that thermal runaway in ceramics with a dielectric loss factor exponentially increasing with increasing temperature is caused by the strongly increasing attenuation constant at high temperatures. This means that only relatively thick ceramic objects will not be damaged by the runaway. The physical and mathematical aspects of bistability are investigated for a system with a microwave power directly proportional to time.</p