# zbMATH — the first resource for mathematics

Viscous fluid flow. (English) Zbl 0946.76001
Boca Raton, FL: CRC Press. xv, 418 p. (2000).
In this textbook, the authors present a good course on viscous flows, most useful to graduate-level students of engineering departments. The material is divided into ten chapters.
Chapter 1 deals with vector and tensor calculus necessary for studying fluid dynamics. The fluid as continuum is introduced in chapter 2. Here the discussion is focussed on the notions of density, mass, volume, linear and angular momentum, viscosity, kinematic viscosity, body and contact forces, mechanical pressure and surface tension. Chapter 3 presents the conservation laws derived by using the Gauss theorem. Static equilibrium of fluids and interfaces in the absence of relative flows are considered in chapter 4.
In chapter 5, the authors derive the full Navier-Stokes equations by employing tensor calculus, and then write these equations in Cartesian, cylindrical and spherical coordinate systems. Then the equations are expressed in the vorticity-velocity form and in other forms. This is followed by a short discussion of different types of boundary conditions. Exact solutions of Navier-Stokes equations are listed in chapter 6. Both steady and unsteady cases in one and two dimension are discussed in different physical situations.
Chapter 7 starts with the presentation of dimensional analysis. Various non-dimensional parameters are introduced and demonstrated in practical problems. Then the authors discuss regular and singular perturbation methods, which is a distinctive feature of this textbook. Usually, one has to study this topic from specialized books by different authors. Hence an advantage of the book under review is that the reader can find in one chapter all standard perturbation methods. As an application of the perturbation methods, the authors derive, in an original manner, the boundary layer equations using a parameter known as Reynolds number. Chapter 8 shows how a partial differential equation for a boundary layer can be converted into an ordinary nonlinear differential equation. The solution of this ordinary differential boundary layer equation is given numerically and by using the von Kármán approximate method. It is known that the solution for a flow past stationary semi-infinite plate is different from the solution for a flow past a continuously moving semi-infinite plate. This special fact is discussed in this chapter, together with some types of potential flows.
Two concluding chapters, 9 and 10, deal with the lubrication under different physical conditions, and with very slow motions of viscous fluid past bodies of different shapes (creeping flows). A good discussion is presented. At the end of each chapter, a number of problems are given, to be solved by the reader, which will help the reader to understand the theory presented in the book.
Since practically all important topics of the viscous flow theory are discussed in the above chapters, the reviewer finds the book certainly useful to both under-graduate and graduate students. However, the reviewer would like to suggest to the authors to include a chapter on heat transfer in a future edition of the book, because the knowledge of the heat transfer in viscous fluids can be very important to engineers. Additionally, the cost of this book seems to be too high in developing countries, and hence it should be expedient to bring out a cheap paperback edition which will be then a more popular book.

##### MSC:
 76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics 76Dxx Incompressible viscous fluids 76M55 Dimensional analysis and similarity applied to problems in fluid mechanics