Page 22 - Bird R.B. Transport phenomena

§0.4 Concluding Comments 7

The conservation laws as applied to collisions of monatomic molecules can be ob-
tained from the results above as follows: Eqs. 0.3-1, 0.3-2, and 0.3-4 are directly applica-
ble; Eq. 0.3-6 is applicable if the internal energy contributions are omitted; and Eq. 0.3-8
may be used if the internal angular momentum terms are discarded.
Much of this book will be concerned with setting up the conservation laws at the mi-
croscopic and macroscopic levels and applying them to problems of interest in engineer-
ing and science. The above discussion should provide a good background for this
adventure. For a glimpse of the conservation laws for species mass, momentum, and en-
ergy at the microscopic and macroscopic levels, see Tables 19.2-1 and 23.5-1.

§0o4 CONCLUDING COMMENTS
To use the macroscopic balances intelligently, it is necessary to use information about in-
terphase transport that comes from the equations of change. To use the equations of
change, we need the transport properties, which are described by various molecular the-
ories. Therefore, from a teaching point of view, it seems best to start at the molecular
level and work upward toward the larger systems.
All the discussions of theory are accompanied by examples to illustrate how the the-
ory is applied to problem solving. Then at the end of each chapter there are problems to
provide extra experience in using the ideas given in the chapter. The problems are
grouped into four classes:
Class A: Numerical problems, which are designed to highlight important equa-
tions in the text and to give a feeling for the orders of magnitude.
Class B: Analytical problems that require doing elementary derivations using
ideas mainly from the chapter.
Class C: More advanced analytical problems that may bring ideas from other chap-
ters or from other books.
Class D: Problems in which intermediate mathematical skills are required.
Many of the problems and illustrative examples are rather elementary in that they in-
volve oversimplified systems or very idealized models. It is, however, necessary to start
with these elementary problems in order to understand how the theory works and to de-
velop confidence in using it. In addition, some of these elementary examples can be very
useful in making order-of-magnitude estimates in complex problems.
Here are a few suggestions for studying the subject of transport phenomena:

• Always read the text with pencil and paper in hand; work through the details of
the mathematical developments and supply any missing steps.
• Whenever necessary, go back to the mathematics textbooks to brush up on calculus,
differential equations, vectors, etc. This is an excellent time to review the mathemat-
ics that was learned earlier (but possibly not as carefully as it should have been).
• Make it a point to give a physical interpretation of key results; that is, get in the
habit of relating the physical ideas to the equations.
• Always ask whether the results seem reasonable. If the results do not agree with
intuition, it is important to find out which is incorrect.
• Make it a habit to check the dimensions of all results. This is one very good way of
locating errors in derivations.
We hope that the reader will share our enthusiasm for the subject of transport phe-
nomena. It will take some effort to learn the material, but the rewards will be worth the
time and energy required.