Transport Phenomena, Second Edition

R. Byron Bird
Warren E. Stewart
Edwin N. Lightfoot
Chemical Engineering Department
University of Wisconsin-Madison

1. Fluid dynamics. 2. Transport theory.

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 914 p
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 19,338 KB
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 2002 John Wiley & Sons, Inc 

While momentum, heat, and mass transfer developed independently as branches of
classical physics long ago, their unified study has found its place as one of the fundamental
engineering sciences. This development, in turn, less than half a century old, continues
to grow and to find applications in new fields such as biotechnology,
microelectronics, nanotechnology, and polymer science.
Evolution of transport phenomena has been so rapid and extensive that complete
coverage is not possible. While we have included many representative examples, our
main emphasis has, of necessity, been on the fundamental aspects of this field. Moreover,
we have found in discussions with colleagues that transport phenomena is taught
in a variety of ways and at several different levels. Enough material has been included
for two courses, one introductory and one advanced. The elementary course, in turn, can
be divided into one course on momentum transfer, and another on heat and mass transfer,
thus providing more opportunity to demonstrate the utility of this material in practical
applications. Designation of some sections as optional (0) and other as advanced (a)
may be helpful to students and instructors.

Long regarded as a rather mathematical subject, transport phenomena is most important
for its physical significance. The essence of this subject is the careful and compact
statement of the conservation principles, along with the flux expressions, with emphasis
on the similarities and differences among the three transport processes considered. Often,
specialization to the boundary conditions and the physical properties in a specific problem
can provide useful insight with minimal effort. Nevertheless, the language of transport
phenomena is mathematics, and in this textbook we have assumed familiarity with
ordinary differential equations and elementary vector analysis. We introduce the use of
partial differential equations with sufficient explanation that the interested student can
master the material presented. Numerical techniques are deferred, in spite of their obvious
importance, in order to concentrate on fundamental understanding.

Citations to the published literature are emphasized throughout, both to place transport
phenomena in its proper historical context and to lead the reader into further extensions
of fundamentals and to applications. We have been particularly anxious to
introduce the pioneers to whom we owe so much, and from whom we can still draw
useful inspiration. These were human beings not so different from ourselves, and perhaps
some of our readers will be inspired to make similar contributions.
Obviously both the needs of our readers and the tools available to them have
changed greatly since the first edition was written over forty years ago. We have made a
serious effort to bring our text up to date, within the limits of space and our abilities, and
we have tried to anticipate further developments. Major changes from the first edition
-transport properties of two-phase systems
-use of "combined fluxes" to set up shell balances and equations of change
-angular momentum conservation and its consequences
-complete derivation of the mechanical energy balance
-expanded treatment of boundary-layer theory
-Taylor dispersion
-improved discussions of turbulent transport
-Fourier analysis of turbulent transport at high Pr or Sc
-more on heat and mass transfer coefficients
-enlarged discussions of dimensional analysis and scaling
-matrix methods for multicomponent mass transfer
-ionic systems, membrane separations, and porous media
-the relation between the Boltzmann equation and the continuum equations
-use of the "Q+W convention in energy discussions, in conformity with the leading textbooks in physics and physical chemistry

However, it is always the youngest generation of professionals who see the future most
clearly, and who must build on their imperfect inheritance.
Much remains to be done, but the utility of transport phenomena can be expected to
increase rather than diminish. Each of the exciting new technologies blossoming around
us is governed, at the detailed level of interest, by the conservation laws and flux expressions,
together with information on the transport coefficients. Adapting the problem formulations
and solution techniques for these new areas will undoubtedly keep engineers
busy for a long time, and we can only hope that we have provided a useful base from
which to start.

Each new book depends for its success on many more individuals than those whose
names appear on the title page. The most obvious debt is certainly to the hard-working
and gifted students who have collectively taught us much more than we have taught
them. In addition, the professors who reviewed the manuscript deserve special thanks
for their numerous corrections and insightful comments: Yu-Ling Cheng (University of
Toronto), Michael D. Graham (University of Wisconsin), Susan J. Muller (University of
California-Berkeley), William B. Russel (Princeton University), Jay D. Schieber (Illinois
Institute of Technology), and John F. Wendt (Von Kdrm6n Institute for Fluid Dynamics).
However, at a deeper level, we have benefited from the departmental structure and traditions
provided by our elders here in Madison. Foremost among these was Olaf Andreas
Hougen, and it is to his memory that this edition is dedicated.
Madison, Wisconsin

Table of Contents
Preface 52.4 Flow through an Annulus 53
52.5 Flow of Two Adjacent Immiscible Fluids 56
Chapter 0 The Subject of Transport 52.6 Creeping Flow around a Sphere 58
Phenomena 1 Ex. 2.6-1 Determination of Viscosity from the
Terminal Velocity of a Falling Sphere 61
Questions for Discussion 61
Part I Momentum Transport
Chapter 1 Viscosity and the Mechanisms of
Momentum Transport 11
51.1 Newton's Law of Viscosity (Molecular Momentum
Transport) 11
Ex. 1.1-1 Calculation of Momentum Flux 15
1 . 2 Generalization of Newton's Law of Viscosity 16
1 . 3 Pressure and Temperature Dependence of
Viscosity 21
Ex. 1.3-1 Estimation of Viscosity from Critical
Properties 23
~1.4' Molecular Theory of the Viscosity of Gases at Low
Density 23
Ex. 1.4-1 Computation of the Viscosity of a Gas
Mixture at Low Density 28
Ex. 1.4-2 Prediction of the Viscosity of a Gas
Mixture at Low Density 28
51.5' Molecular Theory of the Viscosity of Liquids 29
Ex. 1.5-1 Estimation of the Viscosity of a Pure
Liquid 31
51.6' Viscosity of Suspensions and Emulsions 31
1 . 7 Convective Momentum Transport 34
Questions for Discussion 37
Problems 37
Chapter 2 Shell Momentum Balances and Velocity
Distributions in Laminar Flow 40
Problems 62
Chapter 3 The Equations of Change for
Isothermal Systems 75
3 . 1 The Equation of Continuity 77
Ex. 3.1-1 Normal Stresses at Solid Surfaces for
Incompressible Newtonian Fluids 78
53.2 The Equation of Motion 78
g3.3 The Equation of Mechanical Energy 81
53.4' The Equation of Angular Momentum 82
53.5 The Equations of Change in Terms of the
Substantial Derivative 83
Ex. 3.5-1 The Bernoulli Equation for the Steady
Flow of Inviscid Fluids 86
53.6 Use of the Equations of Change to Solve Flow
Problems 86
Ex. 3.6-1 Steady Flow in a Long Circular
Tube 88
Ex. 3.6-2 Falling Film with Variable
Viscosity 89
Ex. 3.6-3 Operation of a Couette Viscometer 89
Ex. 3.6-4 Shape of the Surface of a Rotating
Liquid 93
Ex. 3.6-5 Flow near a Slowly Rotating
Sphere 95
53.7 Dimensional Analysis of the Equations of
Change 97
~xr3.7-1 Transverse Flow around a Circular
Cylinder 98
Ex. 3.7-2 Steady Flow in an Agitated Tank 101
2 . Shell Momentum Balances and Boundary Ex. 3.7-3 Pressure Drop for Creeping Flow in a
Conditions 41 Packed Tube 103
52.2 Flow of a Falling Film 42 Questions for Discussion 104
Ex. 2.2-1 Calculation of Film Velocity 47 Problems 104
Ex. 2.2-2 Falling Film with Variable
Viscosity 47 Chapter 4 Velocity Distributions with More than
52.3 Flow Through a Circular Tube 48 One Independent Variable 114
Ex. 2.3-1 Determination of Viscosity from Capillary - ,
Flow Data 52 1 Time-Dependent Flow of Newtonian Fluids 114
Ex. 2.3-2 Compressible Flow in a Horizontal Ex. 4.1-1 Flow near a Wall Suddenly Set in
Circular Tube 53 Motion 115
vi Contents
Ex. 4.1-2 Unsteady Laminar Flow between Two
Parallel Plates 117
Ex. 4.1-3 Unsteady Laminar Flow near an
Oscillating Plate 120
54.2' Solving Flow Problems Using a Stream
Function 121
Ex. 4.2-1 Creeping Flow around a Sphere 122
54.3' Flow of Inviscid Fluids by Use of the Velocity
Potential 126
Ex. 4.3-1 Potential Flow around a Cylinder 128
Ex. 4.3-2 Flow into a Rectangular Channel 130
Ex. 4.3-3 Flow near a Corner 131
54.4' Flow near Solid Surfaces by Boundary-Layer
Theory 133
Ex. 4.4-1 Laminar Flow along a Flat Plate
(Approximate Solution) 136
Ex. 4.4-2 Laminar Flow along a Flat Plate (Exact
Solution) 137
Ex. 4.4-3 Flow near a Corner 139
Questions for Discussion 140
Problems 141
Chapter 5 Velocity Distributions in
Turbulent Flow 152
Comparisons of Laminar and Turbulent
Flows 154
Time-Smoothed Equations of Change for
Incompressible Fluids 156
The Time-Smoothed Velocity Profile near a
Wall 159
Empirical Expressions for the Turbulent
Momentum Flux 162
Ex. 5.4-1 Development of the Reynolds Stress
Expression in the Vicinity of the Wall 164
Turbulent Flow in Ducts 165
Ex. 5.5-1 Estimation of the Average Velocity in a
Circular Tube 166
Ex. 5.5-2 Application of Prandtl's Mixing Length
Fomula to Turbulent Flow in a Circular
Tube 167
Ex. 5.5-3 Relative Magnitude of Viscosity and Eddy
Viscosity 167
~ 5 . 6Tu~rb ulent Flbw in Jets 168
Ex. 5.6-1 Time-Smoothed Velocity Distribution in a
Circular Wall Jet 168
Questions for Discussion 172
Problems 172
Chapter 6 Interphase Transport in
Isothermal Systems 177
6.1 Definition of Friction Factors 178
56.2 Friction Factors for Flow in Tubes 179
Ex. 6.2-Pressure Drop Required for a Given Flow
Rate 183


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