Theory of Periodic Conjugate Heat Transfer

Preface
Contents
Abbreviations
Symbols
List of Figures
List of Tables
1 Introduction
1.1 Heat Transfer Processes Containing Periodic Oscillations
1.1.1 Oscillation Structure of Convective Heat Transfer
1.1.2 Correct Averaging of Heat Transfer Coefficients
1.2 Physical Examples
1.3 Numerical Modeling
1.4 Oscillatory Mechanism of Near-Wall Turbulence
1.4.1 Van Driest Model
1.4.2 Periodic Model of the Reynolds Analogy
1.4.3 Model of Periodical Contacts
1.5 One-Time Thermal Contact Model
1.6 Hydrodynamic Heat Transfer Coefficient
1.7 Previous Investigations
1.8 Analytical Methods
1.9 Summary
References
2 Construction of a General Solution
2.1 Boundary Value Problem for the Heat Conduction Equation
2.1.1 Spatial and Temporal Types of Oscillations
2.2 Interrelation Between the Two Averaged Coefficients of Heat Transfer
2.2.1 Notation of the Boundary Condition (First Form)
2.2.2 Notation of the Boundary Condition (Second Form)
2.3 Dimensionless Parameters
2.4 Factor of Conjugation (Limiting Variants)
2.5 Summary
References
3 Solution of Characteristic Problems
3.1 Construction of the General Solution
3.2 Harmonic Law of Oscillations
3.3 Inverse Harmonic Law of Oscillations
3.4 Delta-Like Law of Oscillations
3.5 Step Law of Oscillations
3.6 Comparative Analysis of the Conjugation Effects
3.7 Particular Exact Solution
3.8 Asymptotic Solution for Thin Wall
3.9 The Method of Separation of Variables
3.10 Summary
References
4 Algorithm of Computation of the Factor of Conjugation
4.1 Smooth Oscillations
4.1.1 Harmonic Law of Oscillations
4.1.2 Inverse Harmonic Law of Oscillations
4.2 Boundary Condition (Series Expansion)
4.3 Derivation of a Computational Algorithm
4.4 Approximate Solution for Smooth Oscillations
4.5 Phase Shift Between Oscillations
4.6 Method of Small Parameter
4.7 Arbitrary Law of Oscillations
4.8 Filtration Property of the Computational Algorithm
4.9 Generalized Parameter of the Thermal Effect
4.10 Advantages of the Computational Algorithm
4.11 Summary
References
5 Solution of Special Problems
5.1 Introduction
5.2 Complex Case of Heating
5.2.1 Linear Interrelation of Fluctuations
5.2.2 Heat Supply from an Ambience
5.2.3 Thermal Contact to Another Body
5.3 Heat Transfer on the Surface of a Cylinder
5.4 Heat Transfer on the Surface of a Sphere
5.5 Parameter of Thermal Effect (Different Geometrical Bodies)
5.6 Overall Averaged True Heat Transfer Coefficient
5.6.1 Overall Experimental Heat Transfer Coefficient
5.6.2 Issues of the Heat Transfer Intensification
5.6.3 Bilateral Spatio-Temporal Periodicity of Heat Transfer
5.7 Step and Nonperiodic Oscillations of the Heat Transfer Intensity
5.7.1 Asymmetric Step Oscillations
5.7.2 Semi-Infinite Body
5.8 Nonperiodic Oscillations
5.9 Summary
References
6 Engineering Applications of the Theory
6.1 Model Experiment
6.2 Dropwise Condensation
6.3 Nucleate Boiling
6.3.1 Labuntsov Theory
6.3.2 Periodic Model
6.4 Wall Turbulent Flows (Conjugate Problem)
6.4.1 Turbulent Flows
6.4.2 The Reynolds Analogy
6.4.3 Turbulent Impulse Transport
6.4.4 Turbulent Heat Transport
6.4.5 Viscous and Conductive Sublayers
6.5 Summary
References
7 Wall Thermal Effect on Hydrodynamic Flow Stability
7.1 Flow of a Liquid with Supercritical Parameters
7.2 Density Wave Instability Phenomena
7.2.1 Theoretical Analysis
7.2.2 Mathematical Description
7.2.3 Type of Instability
7.3 Density Wave Instability Scenario
7.4 Basic Equations
7.5 Wall Thermal Effect
7.6 Analytical Solution
7.6.1 Low-Frequency Perturbations
7.6.2 Analytical Approximations
7.6.3 Advantages of the Analytical Model
7.7 Summary
References
8 Liquid Film Evaporation (Landau Instability)
8.1 Landau Instability
8.2 Problem Statement
8.3 Consistency Conditions
8.4 Stability Analysis
8.4.1 Evaluation of Reynolds Number
8.5 Effect of Hydrodynamic Boundary Condition
8.6 Summary
References
9 Hyperbolic Heat Conduction Equation
9.1 Advanced Topics of Theory of Heat Conduction
9.2 Cattaneo-Vernotte Law
9.3 Mathematical Statement
9.4 Limiting Cases
9.5 Pulse Heating of Surface
9.6 Computational Algorithm
9.7 Telegraph Equation
9.8 Fourier Law and Cattaneo-Vernotte Law (Land-Mark)
9.9 Practical Applications
9.10 Approximate Solution
9.10.1 Algorithm for Approximate Solution
9.10.2 Analysis of the Approximation Solution
9.10.3 Self-Oscillating Systems
9.10.4 Spatially Inhomogeneous Structures
9.10.5 Estimate of the Relaxation Time
9.11 Summary
References
10 Bubbles Dynamics in Liquid
10.1 Introduction
10.2 Generalized Rayleigh Equation
10.2.1 Classical Rayleigh Equation
10.2.2 Bubble Dynamics in a Tube
10.2.3 Derivation of the Generalized Rayleigh Equation
10.2.4 Physical Analogies
10.2.5 Collapse of a Bubble in a Long Tube
10.2.6 Practical Applications
10.3 Homogeneous Nucleation (Quantum–Mechanical Model)
10.3.1 Homogeneous Nucleation
10.3.2 Classical Theory
10.3.3 Quantum–Mechanical Model
10.3.4 Limiting Frequency of Homogeneous Nucleation
10.4 Thermally Controlled Vapor Bubble Growth
10.4.1 Vapor Bubble Growth in a Superheated Liquid
10.4.2 Problem Statement
10.4.3 Solution of the Problem
10.4.4 Asymptotics Analysis
10.4.5 Approximation of the Scriven Integral
10.4.6 A Refined Approximation
10.4.7 Bubble Dynamics on a Rigid Surface
10.5 Summary
References
11 Taylor Bubble (Rise Velocity and Geometric Characteristics)
11.1 Solutions of Prandtl and Taylor
11.2 Velocity Potential
11.3 Problem Statement
11.3.1 Elementary Flows
11.3.2 Flow Parameters
11.3.3 Stagnation Point Flow
11.4 Analytical Solution
11.4.1 Collocation Method
11.4.2 Asymptotical Solution
11.5 Plane Taylor Bubble
11.6 Summary
References
12 Periodical Model of Turbulent Heat Transfer
12.1 Introduction
12.2 Quasi-Ordered Structures of Wall Turbulence
12.3 Surface Rejuvenation Model
12.3.1 Bursting Effect
12.3.2 Variable Thermophysical Properties
12.4 Method of Relative Correspondence
12.5 Mathematical Description
12.5.1 The Main Equation
12.5.2 Universal Parameter
12.6 Laminar Boundary Layer
12.7 Solving the Main Equation
12.7.1 Exact Solution
12.7.2 Approximate Analytical Solution
12.7.3 Solution Validation (Laminar Boundary Layer)
12.8 Turbulent Supercritical Flow
12.8.1 Modes of Turbulent Supercritical Flow
12.8.2 Relative Law of Heat Transfer
12.8.3 Heat Transfer Regimes
12.9 Mass Transfer Through the Interfacial Surface
12.9.1 Reynolds and Chilton-Colburn Analogies
12.9.2 Locally Isotropic Turbulence
12.9.3 Small-Scale Turbulence Modeling
12.9.4 Turbulent Flow in a Tube
12.9.5 Effective Dissipation Value
12.9.6 Mass Transfer Through the Interface
12.9.7 Periodic Model
12.9.8 Mass Transfer in Channel Flow
12.9.9 Bubble Flow
12.10 Internal Heat Generation
12.10.1 The Molten Salt Reactor
12.10.2 Thermal Perturbation Front
12.10.3 Heat Source
12.10.4 Heat Sink
12.10.5 Definition of the Source Parameter
12.11 Summary
References
13 Variable Heat Transfer Coefficient (Heat Conduction Problem)
13.1 Introduction
13.2 Method of Separation of Variables
13.3 Integral Laplace Transform
13.4 Boundary Value Problem of Heat Conduction
13.5 Picard Method
13.6 The Cauchy Problem
13.7 Proof of the Convergence of the Series
13.8 Representative Examples
13.9 Green Function Method
13.10 Representative Functions
13.11 Approximation of the Analytical Solution
13.12 Almost Periodic and Quasiperiodic Functions
13.13 Quasiperiodic Heat Transfer Problem
13.14 Factor of Conjugation
13.15 Summary
References
14 Model of the Evaporating Meniscus
14.1 Introduction
14.2 Hydrodynamics of the Moving Film
14.2.1 Statement of the Problem
14.2.2 Method of the Solution
14.2.3 The Effect of Microfilm Thickness
14.2.4 Generalized Solution
14.3 Thermohydrodynamics of the Evaporating Meniscus
14.3.1 Theoretical Investigation
14.3.2 Method of the Solution
14.4 Mathematical Description of the Problem
14.4.1 System of Equations
14.4.2 Mathematical and Physical Difficulties
14.5 Analytical Solution
14.5.1 Reduction of Order
14.5.2 Method of Small Parameter
14.5.3 Meniscus Profile
14.5.4 Nanoscale Film
14.5.5 The Heat Transfer Coefficient
14.6 Conjugate Heat Transfer Problem
14.6.1 Averaging the Heat Transfer Coefficient
14.6.2 Boundary Condition q = const
14.7 Nucleate Boiling
14.7.1 Nucleate Boiling Model
14.7.2 Simulation of the Conjugate Problem
14.7.3 Empirical Model of Nucleate Boiling Heat Transfer
14.8 Summary
References
Appendix A Proof of the Basic Levels
A.1 Proof of the First Basic Level
A.2 Proof of the Second Basic Level
A.3 Proof of the Basic Levels in the General Case
Appendix B Functions of Thickness
B.1 Definition of Functions of the Wall Thickness
B.2 Spatial Type of Oscillations
B.3 Temporal Type of Oscillations
B.4 Functions of Thickness for Special Problems
Appendix C Infinite Continued Fractions
C.1 Fundamental Theorems of Khinchin
C.2 Generalization of the Third Theorem of Khinchin
Appendix D Proof of Divergence of Infinite Series
D.1 Spatial Type of Oscillations
D.2 Temporal Type of Oscillations
Appendix E Correction of Approximate Solutions
E.1 Harmonic Law of Oscillations
E.2 Inverse Harmonic Law of Oscillations
E.3 Step Law of Oscillations
Appendix F Heat Balance Integral Method
F.1 Classical Solution
F.2 Thermal Perturbation Front
References
Appendix G Periodical Self-Oscillations
References