After some years of teaching separate courses on metal solidification and polymer processing, we realized that the two subjects shared a substantial base of common material. All the models started with the same basic equations and were built by using the same general procedure. We began to teach a single course on materials processing, and we found that our unified treatment gave students a better overall perspective on modeling. We also discovered that we needed a new book, as existing texts were almost all devoted exclusively to polymers, or to metals, or to ceramics. In this book, we treat metal and polymer processing problems together, building around the transport equations as a unifying theme.

We were also dissatisfied with ad hoc model development, in which terms were arbitrarily dropped from the governing equations, or simplifications were made without a clear explanation. Simplifying the general governing equations is a critical step in modeling, but it is a skill, not an art. In this text we introduce scaling analysis as a systematic way to reduce the governing equations for any particular problem. Scaling provides a way for both novices and experts to simplify a model, while ensuring that all of the important phenomena are included.

fter deriving the governing equations in their general form and introducing scaling analysis, we examine physical phenomena such as heat conduction and fluid flow. We work out many problems that include only a few of these phenomena – problems that can be solved analytically.