Processing of Ceramic Materials by Microwave and Ohmic Heating

Kriegsmann0708065研究人员模拟并分析了微波和欧姆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边值问题，其数学表述涉及一个或多个控制热扩散和化学浓度扩散的非线性抛物型方程、麦克斯韦方程的时间调和形式，以及在欧姆加热的情况下的非线性势能问题。这些方程以一种非线性的方式耦合在一起，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。研究人员开发并使用了受某些物理限制的渐近方法来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。微波和其他形式的电能对陶瓷的快速加热是几种新兴工业过程的基础，如烧结、纤维涂层、连接和化学气相渗透。这些工艺可能能够高效地生产用于高温应用的高质量材料，例如热交换器、燃烧衬里、泵和火箭喷嘴。这些前景看好的技术的开发和利用仍然受到这一过程的基础物理的阻碍。第一个问题是不均匀加热的发生，它导致材料性质不均匀的有害影响。第二，在微波加热的情况下，是灾难性的热失控现象，在这种现象中，功率的微小变化会导致温度迅速上升到陶瓷的熔点。研究人员和他的学生致力于理解、控制和使用这些现象，并开发准确而有效的数学工具来量化这些现象。

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.