Microwave Processing of Ceramic Materials

New Jersey Institute Of Technology, Newark NJ

Investigators

Abstract

The investigator will model and analyze a class of physical problems arising in microwave processing of ceramics. These problems give rise to challenging nonlinear initial boundary value problems for partial differential equations. Their mathematical formulation involves one or more nonlinear parabolic equations, governing the diffusion of heat and the diffusion of a chemical concentration, and the time harmonic version of Maxwells equations, governing the propagation of electromagnetic waves. These equations are coupled together in a nonlinear fashion and, in addition, nonlinear heat balances are required in certain applications where surface temperatures produce significant thermal radiation. Kriegsmann will develop and use asymptotic methods, dictated by certain physical limits, to simplify the mathematical systems and develop and use numerical methods to solve the reduced problems. The goals of the work supported with this award are twofold. The first is the mathematical understanding of the basic physical mechanisms which make microwave processing work. Such an understanding will give scientists and engineers involved in microwave processing of ceramics more basic scientific underpinnings to judge and interpret their experimental findings. The second goal is the development and application of asymptotic, numerical, and other approximate methods required to obtain an accurate description of more realistic and complicated processes. The successful completion of the planned research will allow engineers and scientists to design more efficient sintering and joining processes for ceramics which will allow them to produce higher quality materials. It will also help in the design and implementation of microwave assisted vapor deposition processes which are highly promising in the construction of composite ceramic materials