Page 18 - Bird R.B. Transport phenomena

§0.2 Three Levels At Which Transport Phenomena Can Be Studied 3

ecular structure and intermolecular forces. Generally this is the realm of the theoretical
physicist or physical chemist, but occasionally engineers and applied scientists have to
get involved at this level. This is particularly true if the processes being studied involve
complex molecules, extreme ranges of temperature and pressure, or chemically reacting
systems.
It should be evident that these three levels of description involve different "length
scales": for example, in a typical industrial problem, at the macroscopic level the dimen-
sions of the flow systems may be of the order of centimeters or meters; the microscopic
level involves what is happening in the micron to the centimeter range; and molecular-
level problems involve ranges of about 1 to 1000 nanometers.
This book is divided into three parts dealing with
• Flow of pure fluids at constant temperature (with emphasis on viscous and con-
vective momentum transport)—Chapters 1-8
• Flow of pure fluids with varying temperature (with emphasis on conductive, con-
vective, and radiative energy transport)—Chapters 9-16
• Flow of fluid mixtures with varying composition (with emphasis on diffusive and
convective mass transport)—Chapters 17-24

That is, we build from the simpler to the more difficult problems. Within each of these
parts, we start with an initial chapter dealing with some results of the molecular theory
of the transport properties (viscosity, thermal conductivity, and diffusivity). Then we
proceed to the microscopic level and learn how to determine the velocity, temperature,
and concentration profiles in various kinds of systems. The discussion concludes with
the macroscopic level and the description of large systems.
As the discussion unfolds, the reader will appreciate that there are many connec-
tions between the levels of description. The transport properties that are described by
molecular theory are used at the microscopic level. Furthermore, the equations devel-
oped at the microscopic level are needed in order to provide some input into problem
solving at the macroscopic level.
There are also many connections between the three areas of momentum, energy,
and mass transport. By learning how to solve problems in one area, one also learns the
techniques for solving problems in another area. The similarities of the equations in the
three areas mean that in many instances one can solve a problem "by analogy"—that is,
by taking over a solution directly from one area and, then changing the symbols in the
equations, write down the solution to a problem in another area.
The student will find that these connections—among levels, and among the various
transport phenomena—reinforce the learning process. As one goes from the first part of
the book (momentum transport) to the second part (energy transport) and then on to the
third part (mass transport) the story will be very similar but the "names of the players"
will change.
Table 0.2-1 shows the arrangement of the chapters in the form of a 3 X 8 "matrix."
Just a brief glance at the matrix will make it abundantly clear what kinds of interconnec-
tions can be expected in the course of the study of the book. We recommend that the
book be studied by columns, particularly in undergraduate courses. For graduate stu-
dents, on the other hand, studying the topics by rows may provide a chance to reinforce
the connections between the three areas of transport phenomena.
At all three levels of description—molecular, microscopic, and macroscopic—the
conservation laws play a key role. The derivation of the conservation laws for molecu-
lar systems is straightforward and instructive. With elementary physics and a mini-
mum of mathematics we can illustrate the main concepts and review key physical
quantities that will be encountered throughout this book. That is the topic of the next
section.