Mathematical Modeling of Manufacturing Processes

Abstract

The importance of heat and mass transfer and of the associated fluid flow and material transformations, including chemical conversion, in a wide range of materials processing techniques is stressed in this chapter. In many circumstances, such as melting and solidification that are encountered in casting and crystal growing, the heat transfer to and from the material is at the very core of the process, since it determines the rate of phase change. In addition, the temperature distribution and the buoyancy-driven flows that arise in the molten material due to temperature and concentration differences affect the characteristics of the solid-liquid interface and the microstructure of the product. In processes like food extrusion, hot rolling, thermal spray coating, and soldering, the thermal transport again determines the rate of fabrication and the characteristics of the final product. Thus, it is necessary to develop mathematical models for these processes in order to understand the basic mechanisms and thereby lay the foundation for analysis, numerical simulation, and experimentation. Computational models are developed on the basis of the mathematical models. Numerical solution techniques are generally needed since complexities that arise in common materials processing systems make it very difficult to obtain analytical results, which are applicable largely for very idealized and simplified systems. Mathematical models also guide the design of relevant experiments and the selection of relevant data to be obtained. They help in generalizing the experimental and numerical results, ultimately leading to greater insight into the basic processes involved and the framework to use the results for improving existing processes and for developing new ones. These aspects are presented in detail in this chapter.