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