Physical and Computational Aspects of Convective Heat Transfer

497 Pages·1984·11.016 MB·English

by  Tuncer Cebeci, Peter Bradshaw (auth.)

Physical and
Computational Aspects of
Convective Heat Transfer
Tuncer Cebeci
Peter Bradshaw
Physical and
Computational Aspects of
Convective Heat Transfer
With 180 Figures
[Sl
Springer-Verlag Berlin Heidelberg GmbH
Tuncer Cebeci Peter Bradshaw
Douglas Aircraft Company Department of Aeronautics
3855 Lakewood Boulevard Imperial College of Science
Long Beach, California 90846 and Technology
V.S.A. Prince Consort Road
London SW7 2BY
and
England
Department of Mechanical Engineering
California State Vniversity, Long Beach
Long Beach, California 90840
V.S.A.
Library of Congress Cataloging in Publication Data
Cebeci, Tuncer.
Physica1 and computational aspects of convective heat
transfer.
Bibliography: p.
1. Heat-Convection. 2. Fluid dynamics. 1. Bradshaw,
P. (Peter), 1935- II. Title.
TJ260.C35 1984 536'.25 83-17002
©1984 by Springer-Verlag Berlin Heidelberg
Origina1ly published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1984
Softcover reprint ofthe hardcover Ist edition 1984
AlI rights reserved. No part of this book may be translated or
reproduced in any form without written permission from
Springer-Verlag Berlin Heidelberg GmbH.
Typeset by Science Typographers, Inc., Medford, New York.
9 8 7 6 5 4 3 2 1
ISBN 978-3-662-02413-3 ISBN 978-3-662-02411-9 (eBook)
DOI 10.1007/978-3-662-02411-9
In memory of our fathers
Orner Zihni Cebeci
and
Joseph William Newbold Bradshaw
Preface
This volume is concerned with the transport of thermal energy in flows of
practical significance. The temperature distributions which result from
convective heat transfer, in contrast to those associated with radiation heat
transfer and conduction in solids, are related to velocity characteristics and
we have included sufficient information of momentum transfer to make the
book self-contained. This is readily achieved because of the close relation
ship between the equations which represent conservation of momentum and
energy: it is very desirable since convective heat transfer involves flows with
large temperature differences, where the equations are coupled through an
equation of state, as well as flows with small temperature differences where
the energy equation is dependent on the momentum equation but the
momentum equation is assumed independent of the energy equation.
The equations which represent the conservation of scalar properties,
including thermal energy, species concentration and particle number density
can be identical in form and solutions obtained in terms of one dependent
variable can represent those of another. Thus, although the discussion and
arguments of this book are expressed in terms of heat transfer, they are
relevant to problems of mass and particle transport. Care is required,
however, in making use of these analogies since, for example, identical
boundary conditions are not usually achieved in practice and mass transfer
can involve more than one dependent variable.
The book is intended for senior undergraduate and graduate students of
aeronautical, chemical, civil and mechanical engineering, as well as those
studying relevant aspects of the environmental sciences. It should also be of
value to those engaged in design and development. The format has been
vii
viii Preface
arranged with this range of readers in mind. Thus, it is readily possible to
find answers to specific heat-transfer problems by reference to correlations
or to results presented in graphical form. Those wishing to understand the
physical processes which form the basis of the results and their limitations
should read the corresponding derivations and explanations.
Many of the results presented in graphical form have been obtained with
the numerical procedure described in Chapters 13 and 14. This stems from
many years of research and is presented in a manner suitable, even for those
with little training in the numerical solution of equations, for the solution of
problems described by boundary-layer equations. This aspect of the book is
of particular significance in view of the rapidly increasing application of
numerical techniques and the present method is described in Chapter 13 in
sufficient detail for the reader to use it. These two chapters can also serve as
a basis for an independent graduate course on the numerical solution of
parabolic linear and nonlinear partial-differential equations with emphasis
on problems relating to fluid mechanics and heat transfer.
We have used Chapters 13 and 14, and various combinations of the
material of other chapters, as the basis for graduate courses at California
State University, Long Beach and at Imperial College, and have learned
that, with access to computers which range from personal microprocessors
to mainframe machines, students are able to reinforce their understanding
of classical and practical material of previous chapters and to apply the
numerical procedures to the solution of new problems. For simplicity, the
descriptions are confined to two-dimensional equations and, for turbulent
flow, to simple turbulence and heat-transfer models. These limitations can
readily be removed, but the treatment as it stands is likely to be enough for
most undergraduate and graduate courses. The computer programs de
scribed in Chapters 13 and 14 are available together with sample calcula
tions and, in some cases, additional detail. Requests should be addressed to
the first author at the California State University, Long Beach.
Some teachers of undergraduate and graduate courses may prefer to
exclude the use of numerical methods due to lack of available time. In this
case, Chapters 1-8 will form the basis for a useful one semester course for
senior undergraduates and Chapters 1-9 a comprehensive and longer course
for senior undergraduates or graduate students. The derivations of the
equations provided in Chapter 2 may be omitted in an undergraduate
course and emphasis placed on the boundary-layer equations of Chapter 3,
their solution and related applications.
In the preparation of this text, we have benefited from the advice and
assistance of many people. We are especially grateful to Professors Keith
Stewartson and Jim Whitelaw for their constant advice and helpful contri
butions. The book could not have been written without the considerable
assistance of Nancy Barela, Sue Schimke, Kalle Kaups, A. A. Khattab and
K. C. Chang. Finally, it is a pleasure to acknowledge the help rendered by
our families.
TuNCER CEBECI
PETER BRADSHAW
Contents
1 Introduction 1
1.1 Momentum Transfer 3
1.2 Heat and Mass Transfer 7
1.3 Relations between Heat and Momentum Transfer 9
1.4 Coupled and Uncoupled Flows 13
1.5 Units and Dimensions 14
1.6 Outline of the Book 15
Problems 17
References 18
2 Conservation Equations for Mass, Momentum, and Energy 19
2.1 Continuity Equation 20
2.2 Momentum Equations 21
2.3 Internal Energy and Enthalpy Equations 25
2.4 Conservation Equations for Turbulent Flow 31
2.5 Equations of Motion: Summary 37
Problems 38
References 40
3 Boundary-Layer Equations 41
3.1 Uncoupled Flows 42
3.2 Estimates of Density Fluctuations in Coupled Turbulent Flows 48
3.3 Equations for Coupled Turbulent Flows 53
3.4 Integral Equations 58
3.5 Boundary Conditions 62
ix
x Contents
3.6 Thin-Shear-Layer Equations: Summary 66
Problems 67
References 70
4 Uncoupled Laminar Boundary Layers 71
4.1 Similarity Analysis 72
4.2 Two-Dimensional Similar Flows 78
4.3 Two-Dimensional Nonsimilar Flows 88
4.4 Axisymmetric Flows 99
4.5 Wall Jets and Film Cooling 105
Problems 113
References 123
5 Uncoupled Laminar Duct Flows 124
5.1 Fully Developed Duct Flow 125
5.2 Thermal Entry Length for a Fully Developed Velocity Field 132
5.3 Hydrodynamic and Thermal Entry Lengths 136
Problems 142
References 148
6 Uncoupled Turbulent Boundary Layers 150
6.1 Composite Nature of a Turbulent Boundary Layer 153
6.2 The Inner Layer 156
6.3 The Outer Layer 168
6.4 The Whole Layer 170
6.5 Two-Dimensional Boundary Layers with Zero Pressure
Gradient 172
6.6 Two-Dimensional Flows with Pressure Gradient 184
6.7 Wall Jets and Film Cooling 201
Problems 208
References 213
7 Uncoupled Turbulent Duct Flows 216
7.1 Fully Developed Duct Flow 216
7.2 Thermal Entry Length for a Fully Developed Velocity Field 227
7.3 Hydrodynamic and Thermal Entry Lengths 230
Problems 233
References 236
8 Free Shear Flows 238
8.1 Two-Dimensional Laminar Jet 239
8.2 Laminar Mixing Layer between Two Uniform Streams at
Different Temperatures 246
8.3 Two-Dimensional Turbulent Jet 249
8.4 Turbulent Mixing Layer between Two Uniform Streams at
Different Temperatures 252
Contents xi
8.5 Coupled Flows 254
Problems 259
References 261
9 Buoyant Flows 263
9.1 Natural-Convection Boundary Layers 267
9.2 Combined Natural-and Forced-Convection Boundary Layers 280
9.3 Wall Jets and Film Heating or Cooling 284
9.4 Natural and Forced Convection in Duct Flows 288
9.5 Natural Convection in Free Shear Flows 294
Problems 297
References 299
10 Coupled Laminar Boundary Layers 301
10.1 Similar Flows 306
10.2 Nonsimilar Flows 312
10.3 Shock-WavejShear-Layer Interaction 315
10.4 A Prescription for Computing Interactive Flows with Shocks 325
Problems 328
References 330
11 Coupled Turbulent Boundary Layers 333
11.1 Inner-Layer Similarity Analysis for Velocity and Temperature
Profiles 335
11.2 Transformations for Coupled Turbulent Flows 340
11.3 Two-Dimensional Boundary Layers with Zero Pressure
Gradient 343
11.4 Two-Dimensional Flows with Pressure Gradient 355
11.5 Shock- Wave jBoundary-Layer Interaction 365
References 369
12 Coupled Duct Flows 372
12.1 Laminar Flow in a Tube with Uniform Heat Flux 376
12.2 Laminar, Transitional and Turbulent Flow in a Cooled Tube 381
References 384
13 Finite-Difference Solution of Boundary-Layer Equations 385
13.1 Review of Numerical Methods for Boundary-Layer Equations 386
13.2 Solution of the Energy Equation for Internal Flows with Fully
Developed Velocity Profile 395
13.3 Fortran Program for Internal Laminar and Turbulent Flows
with Fully Developed Velocity Profile 398
13.4 Solution of Mass, Momentum, and Energy Equations for
Boundary-Layer Flows 406
13.5 Fortran Program for Coupled Boundary-Layer Flows 415
References 427