Conjugate Problems in Convective Heat Transfer

456 Pages·2009·6.65 MB·English

by  Abram S. Dorfman

Conjugate Problems
in Convective
Heat Transfer
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H T
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Conjugate Problems
in Convective
Heat Transfer
Abram S. Dorfman
Boca Raton London New York
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Library of Congress Cataloging-in-Publication Data
Dorfman, A. Sh. (Abram Shlemovich)
Conjugate problems in convective heat transfer / Abram S. Dorfman.
p. cm. -- (Heat transfer)
Includes bibliographical references and index.
ISBN 978-1-4200-8237-1 (hardcover : alk. paper)
1. Heat--Transmission. 2. Heat--Convection. 3. Fluid dynamics. I. Title.
TJ260.D64 2009
621.402’25--dc22 2009018850
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In Memory
In memory of our dearest, lovely,
loving daughter, Ella Fridman.
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Contents
List of Examples ....................................................................................................xi
Preface .................................................................................................................xvii
Acknowledgments .............................................................................................xxi
The Author ........................................................................................................xxiii
Introduction .......................................................................................................xxv
Nomenclature ..................................................................................................xxvii
Part I: Approximate Solutions
Chapter 1
Analytical Methods for the Estimation of Heat Transfer from
Nonisothermal Walls ............................................................................................3
1.1 Basic Equations...............................................................................................3
1.2 Self-Similar Solutions of the Boundary Layer Equations ........................4
1.3 Solutions of the Boundary Layer Equations in the Power Series ...........5
1.4 Integral Methods ............................................................................................7
1.5 Method of Superposition ............................................................................12
1.6 Solutions of the Boundary Layer Equations in the Series
of Shape Parameters ....................................................................................16
References ...............................................................................................................18
Chapter 2
Approximate Solutions of Conjugate Problems in Convective
Heat Transfer ........................................................................................................21
2.1 Formulation of a Conjugate Problem of Convective
Heat Transfer ................................................................................................21
2.2 The Case of Linear Velocity Distribution across the Thermal
Boundary Layer ............................................................................................22
2.3 The Case of Uniform Velocity Distribution across the Thermal
Boundary Layer (Slug Flow) .......................................................................28
2.4 Solutions of the Conjugate Convective Heat Transfer Problems
in the Power Series .......................................................................................35
2.5 Solutions of the Conjugate Heat Transfer Problems by Integral
Methods .........................................................................................................46
References ...............................................................................................................50
vii
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viii Contents
Part II: Theory and Methods
Chapter 3
Heat Transfer from Arbitrary Nonisothermal
Surfaces in a Laminar Flow ...............................................................................55
3.1 The Exact Solution of the Thermal Boundary Layer Equation
for an Arbitrary Surface Temperature Distribution ...............................55
3.2 Generalization for an Arbitrary Velocity Gradient
in a Free Stream Flow ..................................................................................62
3.3 General Form of the Influence Function of the
Unheated Zone: Convergence of the Series..............................................64
3.4 The Exact Solution of the Thermal Boundary Layer
Equation for an Arbitrary Surface Heat Flux Distribution ....................69
3.5 Temperature Distribution on an Adiabatic Surface in an
Impingent Flow ............................................................................................73
3.6 The Exact Solution of an Unsteady Thermal Boundary Layer
Equation for Arbitrary Surface Temperature Distribution ....................75
3.7 The Exact Solution of a Thermal Boundary Layer Equation for
a Surface with Arbitrary Temperature in a Compressible Flow ...........78
3.8 The Exact Solution of a Thermal Boundary Layer
Equation for a Moving Continuous Surface with Arbitrary
Temperature Distribution ...........................................................................79
3.9 The Other Solution of a Thermal Boundary Layer Equation
for an Arbitrary Surface Temperature Distribution ...............................83
3.9.1 Non-Newtonian Fluid with a Power Law Rheology ..................83
3.9.2 The Effect of Mechanical Energy Dissipation .............................86
3.9.3 Axisymmetric Streamlined and Rotating Bodies .......................87
3.9.4 Thin Cylindrical Bodies ..................................................................89
References ...............................................................................................................91
Chapter 4
Heat Transfer from Arbitrary Nonisothermal Surfaces
in Turbulent Flow ................................................................................................95
4.1 Basis Relations for the Equilibrium Boundary Layer .............................95
4.2 Solution of the Thermal Turbulent Boundary Layer Equation
for an Arbitrary Surface Temperature Distribution ...............................99
4.3 Intensity of Heat Transfer from an Isothermal Surface:
Comparison with Experimental Data .....................................................104
4.3.1 Reynolds Analogy .........................................................................104
4.3.2 Relations for Heat Transfer from an Isothermal
Surface in Gradientless Flow ........................................................105
4.3.3 Relations for Heat Transfer from an Isothermal
Surface in Gradient Flows.............................................................109
4.4 The Effect of the Turbulent Prandtl Number on Heat Transfer
on Flat Plates ...............................................................................................111
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Contents ix
4.5 Coefficients g of Heat Flux Series for Nonisothermal Surfaces .........112
k
4.6 Approximate Relations for Heat Flux in a Transition Regime ............116
References .............................................................................................................118
Chapter 5
General Properties of Nonisothermal and Conjugate Heat Transfer ........121
5.1 The Effect of Temperature Head Distribution on Heat Transfer
Intensity .......................................................................................................121
5.1.1 The Effect of the Temperature Head Gradient ..........................122
5.1.2 The Effect of Flow Regime ............................................................132
5.1.3 The Effect of Pressure Gradient ...................................................137
5.2 Gradient Analogy and Reynolds Analogy ............................................137
5.3 Heat Flux Inversion ...................................................................................141
5.4 Zero Heat Transfer Surfaces .....................................................................148
5.5 Examples of Optimizing Heat Transfer in Flow over Bodies..............150
References .............................................................................................................158
Chapter 6
Analytical Methods for Solving Conjugate Convective Heat
Transfer Problems ..............................................................................................161
6.1 A Biot Number as a Criterion of the Conjugate Heat
Transfer Rate ...............................................................................................161
6.2 General Boundary Condition for Convective Heat Transfer
Problems: Errors Caused by Boundary Condition of the Third Kind ....162
6.3 Reduction of a Conjugate Convective Heat Transfer Problem
to an Equivalent Heat Conduction Problem ..........................................166
6.4 Temperature Singularities on the Solid–Fluid Interface ......................179
6.4.1 Basic Equations...............................................................................179
6.4.2 Examples of Singularities for Different Flow Regimes
and Conditions ...............................................................................181
6.4.3 Estimation of Accuracy of the Assumption of a
Thermally Thin Body ....................................................................183
6.5 Universal Functions for Solving Conjugate Heat Transfer
Problems — Solution Examples ...............................................................183
6.6 Reducing the Unsteady Conjugate Convective Heat Transfer
Problem to an Equivalent Heat Conduction Problem ..........................198
6.6.1 Validity of Quasi-Steady Approximation — The Luikov
Number as a Conjugate Criterion in Unsteady Heat Transfer .....199
6.6.2 Universal Eigenfunctions for Unsteady Conjugate Heat
Transfer Problems ..........................................................................201
6.7 Integral Transforms and Similar Methods ............................................206
6.8 Solutions in Asymptotic Series in Eigenfunctions ...............................210
6.9 Superposition and Other Methods ..........................................................220
6.10 Green’s Function and the Method of Perturbation ...............................224
References .............................................................................................................227
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