Developing and analyzing mathematical models that physically describe microwave processing of ceramics is the focus of research by Gregory Kriegsmann, distinguished professor of mathematics and Foundation Chair of applied mathematics.
Because of their high hardness, fracture strength, wear resistance and melting point, new ceramic materials have emerged as leading candidates for use in high-temperature structural components of automotive turbochargers, jet engines, nozzles, tank armor and cutting tools. In ceramics manufacturing, microwave heating is an attractive alternative to conventional heating methods for sintering (densification), annealing and joining of ceramics to other materials. Microwave processing can significantly reduce both forming and drying times, thereby reducing energy consumption and production time.
With funding from both the National Science Foundation, he is working toward a mathematical understanding of the basic physical mechanisms that make the microwave process work, as well as developing the asymptotic, numerical and other approximate methods required to obtain this understanding. Under a grant from the U.S. Department of Energy, he is addressing the physical modeling and analysis of several specific applications, including problems that arise in fiber processing, in the control of temperature, and in the fabrication of ceramic composites.
The mathematical models to the left represent a ceramic slab heated by microwaves. As the power is increased, the heating becomes increasingly localized. The image at the bottom right a concentration that would result in hole burned through the middle of the slab.