9R44. Modeling in Materials Processing. - JA Dantzig and CL Tucker III (Dept of Mech and Indust Eng, Univ of Illinois Urbana-Champaign, IL). Cambridge UP, New York. 2001. 363 pp. Softcover (Hardcover ISBN: 0-521-77063-7, $130.00). ISBN 0-521-77923-5. $47.95.

Reviewed by M Foster (Dept of Aeronaut and Astronaut Eng, Ohio State Univ, Columbus OH 43210).

This book represents a combining of materials and approaches generated over a period of years by two faculty members teaching courses in polymer processing and metal solidification at the University of Illinois. I am not able to find any indication by the authors about the level of the course, but based on the informal style of the book and the level of the problems, this book appears to be targeted to advanced undergraduate or lower-level graduate students. The derivations are generally done well, if sometimes wanting a bit in rigor. The authors’ approach is deductive—begin with the basic equations, then specialize them to particular situations—because the authors state in the preface that they are dissatisfied (and rightly so, in this reviewer’s view) with ad hoc approaches to modeling. Hence, they begin with dimensional analysis, which then forms a basis for various approximations in the modeling phase, leading then to “canonical problems” that are solvable analytically. These canonical problems presumably exhibit the essential details of particular physical phenomena, but without unnecessary complexity. The authors have been largely successful in carrying out their stated goals.

A few comments on the overall structure of the book ought to be made. The introductory chapter contains a long (14-page) discussion of modeling issues in 1D traffic flow, done in an interesting way, but it seems to this reviewer wholly out of place in this book. The equations of motion are derived in Chapter 2, in a generally satisfactory fashion using the Reynolds Transport Theorem; there is a very cursory discussion of deformation and stress tensors, which is probably at the right level for the (presumed) target audience. There is a brief, and in this reviewer’s view, ill-considered treatment of irrotational, inviscid flows; the Bernoulli equation; etc. Surely most students taking a course from this book would have already seen this material. After a nice chapter on dimensional analysis and modeling, the authors come to Chapter 4, the bulk of which is a short and out-of-place reiteration of very elementary engineering heat transfer problems: transient 1D heat flow, steady 3D heat transfer. After 20 pages, they finally come to the Stefan problem, which is treated very carefully, and at the right level, over the next 14 pages, balancing effectively between the mathematics and the physics.

Chapters 5–8 then deal with the primary topics of special interest to the authors: Newtonian lubrication theory, non-Newtonian fluids, Hele-Shaw flow, buoyancy-driven flows, flows with free surfaces, and directional solidification. The discussion of interfacial forces, and later, mass transfer at a solidification front, are done quite skillfully, with adequate attention to the underlying physics. Oddly, however, in the midst of these chapters that go to the heart of the subject, is Section 5.4.2: “Flows with significant inertia,” with an altogether inadequate discussion of the Rayleigh problem, developing boundary layers in a pipe (a very dated, Schlichting-like treatment), and separated flows past bluff bodies (also very inadequate and misleading), culminating in a discussion of instability, DNS, and turbulent averaging—all of this in 10 pages! This information is completely out of place in this book. The authors are very good at what they do, but they should leave aerodynamics alone. The buoyancy-driven flow chapter, by contrast, is well organized and insightful. The final chapter includes discussion of the Gulliver-Scheil equation and a long derivation of the Mullins-Sekerka instability at a planar solidification front. The chapter does not, however, make note of the wealth of recent work on solidification modeling and dendritic scaling laws, which has made Scheil’s equation largely irrelevant.

The adoption of Modeling in Materials Processing is certainly recommended for a specialized materials processing course, or perhaps for a first course in non-Newtonian phenomena. This reviewer resonates very much with Dantzig and Tucker’s systematic approach to the subject of modeling materials processing; their interesting examples and vast numbers of problems reinforce their outlook. With so much of our engineering culture now oriented toward numerical schemes for solving “real-world” problems, it is refreshing to encounter a book that emphasizes modeling and the understanding of basic phenomena.