Processing of Ceramic Materials by Microwave and Ohmic Heating

研究者模拟并分析了微波和高温加热陶瓷加工中出现的两类物理问题。这些问题产生了具有挑战性的非线性初始边值问题，其数学陈述涉及一个或多个非线性抛物方程，控制热量的扩散和化学浓度的扩散，麦克斯韦方程的时间谐波版本，以及在欧姆加热的情况下，非线性势问题。这些方程以非线性方式耦合在一起，此外，在表面温度产生显著热辐射的某些应用中需要非线性热平衡。研究者根据一定的物理极限，发展并使用渐近方法对这些物理问题进行数学建模。使用解析和数值方法对这些模型进行分析，以获得对过程的准确描述。利用微波和其他形式的电能对陶瓷进行快速加热，是烧结、纤维涂层、连接和化学蒸汽渗透等几种新兴工业工艺的基础。这些工艺可能能够有效地生产用于高温应用的高质量材料，如热交换器、燃烧衬里、泵和火箭喷嘴。这些有前途的技术的发展和利用仍然受到基本物理过程的阻碍。第一个问题是不均匀加热的出现，它造成了材料性能不均匀的有害影响。第二种，在微波加热的情况下，是热失控的灾难性现象，其中功率的轻微变化导致温度迅速上升到陶瓷的熔点。研究者和他的学生要解决的问题是理解、控制和使用这些现象，以及开发准确有效的数学工具来量化它们。

Kriegsmann0708065 The investigator models and analyzes two classes of physicalproblems arising in ceramic processing by microwave and ohmicheating. These problems give rise to challenging nonlinearinitial boundary value problems, the mathematical statements ofwhich involve one or more nonlinear parabolic equations,governing the diffusion of heat and the diffusion of a chemicalconcentration, the time harmonic version of Maxwell's equations,and in the case of ohmic heating, a nonlinear potential problem. These equations are coupled together in a nonlinear fashion and,in addition, nonlinear heat balances are required in certainapplications where surface temperatures produce significantthermal radiation. The investigator develops and uses asymptoticmethods, dictated by certain physical limits, to mathematicallymodel these physical problems. These models are analyzed, usingboth analytical and numerical methods, to obtain accuratedescriptions of the processes. The rapid heating of ceramics by microwave and other formsof electrical energy is the basis of several emerging industrialprocesses such as sintering, fiber coating, joining, and chemicalvapor infiltration. These processes may be capable of efficientlyproducing high quality materials for use in high temperatureapplications, such as heat exchangers, combustion liners, pumpseals, and rocket nozzles. The development and exploitation ofthese promising technologies remain hindered by the basic physicsof the process. The first problem is the occurrence ofnonuniform heating, which causes the deleterious effect ofnonuniform material properties. The second, in the case ofmicrowave heating, is the catastrophic phenomenon of thermalrunaway, in which a slight change of power causes the temperatureto increase rapidly to the melting point of the ceramic. It isthe understanding, control, and use of these phenomena and thedevelopment of accurate and efficient mathematical tools toquantify them that is addressed by the investigator and hisstudents.