Thermal radiation heat transfer

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgments
Authors
List of Symbols
	Greek Symbols
	Subscripts
	Superscripts
Chapter 1 Introduction to Radiative Transfer
	1.1 Thermal Radiation and the Natural World
	1.2 Thermal Radiation in Engineering
	1.3 Thermal Radiation and Thermodynamics
	1.4 Nature of the Governing Equations
	1.5 Electromagnetic Waves vs Photons
	1.6 Radiative Energy Exchange and Radiative Intensity
	1.7 Solid Angle
	1.8 Spectral Intensity
	1.9 Characteristics of Blackbody Emission
		1.9.1 Perfect Emitter
		1.9.2 Radiation Isotropy of a Black Enclosure
		1.9.3 Perfect Emitter for Each Direction and Wavelength
		1.9.4 Total Radiation into a Vacuum
		1.9.5 Blackbody Intensity and Its Directional Independence
		1.9.6 Blackbody Emissive Power: Cosine Law Dependence
		1.9.7 Hemispherical Spectral Emissive Power of a Blackbody
		1.9.8 Planck’s Law: Spectral Distribution of Emissive Power
		1.9.9 Approximations to the Blackbody Spectral Distribution
			1.9.9.1 Wien’s Formula
			1.9.9.2 Rayleigh–Jeans Formula
		1.9.10 Wien’s Displacement Law
		1.9.11 Total Blackbody Intensity and Emissive Power
		1.9.12 Blackbody Radiation within a Spectral Band
		1.9.13 Summary of Blackbody Properties
	1.10 Radiative Energy along a Line-of-Sight
		1.10.1 Radiative Energy Loss due to Absorption and Scattering
		1.10.2 Mean Penetration Distance
		1.10.3 Optical Thickness
		1.10.4 Radiative Energy Gain Due to Emission
		1.10.5 Radiative Energy Density and Radiation Pressure
		1.10.6 Radiative Energy Gain due to In-Scattering
	1.11 Radiative Transfer Equation
	1.12 Radiative Transfer in Enclosures with Nonparticipating Media
	1.13 Probabilistic Interpretation
	1.14 Concluding Remarks
	Homework Problems
Chapter 2 Radiative Properties at Interfaces
	2.1 Introduction
	2.2 Emissivity
		2.2.1 Directional Spectral Emissivity, ελ(θ,φ,T)
		2.2.2 Directional Total Emissivity, ε(θ,ɸ,T)
		2.2.3 Hemispherical Spectral Emissivity, ελ(T)
		2.2.4 Hemispherical Total Emissivity, ε(T)
	2.3 Absorptivity
		2.3.1 Directional Spectral Absorptivity, αλ(θi,φi,T)
		2.3.2 Kirchhoff’s Law
		2.3.3 Directional Total Absorptivity, α(θi,φi,T)
		2.3.4 Kirchhoff’s Law for Directional Total Properties
		2.3.5 Hemispherical Spectral Absorptivity, αλ(T)
		2.3.6 Hemispherical Total Absorptivity, α(T)
		2.3.7 Diffuse-Gray Surface
	2.4 Reflectivity
		2.4.1 Spectral Reflectivities
			2.4.1.1 Bidirectional Spectral Reflectivity, ρλ(θr,ϕr,θi,ϕi)
			2.4.1.2 Reciprocity for Bidirectional Spectral Reflectivity
			2.4.1.3 Directional Spectral Reflectivities, ρλ(θr,ϕr), ρλ(θi,ϕi)
			2.4.1.4 Reciprocity for Directional Spectral Reflectivity
			2.4.1.5 Hemispherical Spectral Reflectivity, ρλ
			2.4.1.6 Limiting Cases for Spectral Surfaces
		2.4.2 Total Reflectivities
			2.4.2.1 Bidirectional Total Reflectivity, ρ(θr,ϕr,θi,ϕi)
			2.4.2.2 Reciprocity for Bidirectional Total Reflectivity
			2.4.2.3 Directional-Hemispherical Total Reflectivity, ρ(θr,ϕr), ρ(θi,ϕi)
			2.4.2.4 Reciprocity for Directional Total Reflectivity
			2.4.2.5 Hemispherical Total Reflectivity, ρ
		2.4.3 Summary of Restrictions on Reflectivity Reciprocity Relations
	2.5 Transmissivity at an Interface
		2.5.1 Spectral Transmissivities
			2.5.1.1 Bidirectional Spectral Transmissivity, τλ(θt,ϕt,θi,ϕi)
			2.5.1.2 Directional Spectral Transmissivities, τλ(θt,ϕt), τλ(θi,ϕi)
			2.5.1.3 Hemispherical Spectral Transmissivity, τλ
		2.5.2 Total Transmissivities
			2.5.2.1 Bidirectional Total Transmissivity, τ(θi,ϕi,θt,ϕt)
			2.5.2.2 Directional Total Transmissivities, τ(θi,ϕi)
			2.5.2.3 Hemispherical-Directional Total Transmissivity, τ(θt,ϕt), τ(θi,ϕi)
			2.5.2.4 Hemispherical Total Transmissivity, τ
	2.6 Relations among Reflectivity, Absorptivity, Emissivity, and Transmissivity
	Homework Problems
Chapter 3 Radiative Properties of Opaque Materials
	3.1 Introduction
	3.2 Electromagnetic Wave Theory Predictions
		3.2.1 Dielectric Materials
			3.2.1.1 Reflection and Refraction at the Interface between Two Perfect Dielectrics (No Wave Attenuation, k → 0)
			3.2.1.2 Reflectivity
			3.2.1.3 Emissivity
		3.2.2 Radiative Properties of Conductors
			3.2.2.1 Electromagnetic Relations for Incidence on an Absorbing Medium
			3.2.2.2 Reflectivity and Emissivity Relations for Metals (Large k)
			3.2.2.3 Relations between Radiative Emission and Electrical Properties
		3.2.3 Extensions to the Theory of Radiative Properties
	3.3 Measurements on Real Surfaces
		3.3.1 Heterogeneity and Surface Coatings
		3.3.2 Surface Roughness Effects
		3.3.3 Variation of Radiative Properties with Surface Temperature
			3.3.3.1 Non-metals
			3.3.3.2 Metals
		3.3.4 Properties of Liquid Metals
		3.3.5 Properties of Semiconductors and Superconductors
	3.4 Selective Surfaces for Solar Applications
		3.4.1 Characteristics of Solar Radiation
		3.4.2 Modification of Surface Spectral Characteristics
		3.4.3 Modification of Surface Directional Characteristics
	3.5 Concluding Remarks
	Homework Problems
Chapter 4 Configuration Factors for Diffuse Surfaces with Uniform Radiosity
	4.1 Radiative Transfer Equation for Surfaces Separated by a Transparent Medium
		4.1.1 Enclosures with Diffuse Surfaces
		4.1.2 Enclosures with Directional (Nondiffuse) and Spectral (Nongray) Surfaces
	4.2 Geometric Configuration Factors between Two Surfaces
		4.2.1 Configuration Factor for Energy Exchange between Diffuse Differential Areas
			4.2.1.1 Reciprocity for Differential Element Configuration Factors
			4.2.1.2 Sample Configuration Factors between Differential Elements
		4.2.2 Configuration Factor between a Differential Area Element and a Finite Area
			4.2.2.1 Reciprocity Relation for Configuration Factors between Differential and Finite Areas
			4.2.2.2 Configuration Factors between Differential and Finite Areas
		4.2.3 Configuration Factor and Reciprocity for Two Finite Areas
	4.3 Methods for Determining Configuration Factors
		4.3.1 Configuration Factor Algebra
			4.3.1.1 Configuration Factors Determined by Symmetry
		4.3.2 Configuration Factor Relations in Enclosures
		4.3.3 Techniques for Evaluating Configuration Factors
			4.3.3.1 Hottel’s Crossed-String Method
			4.3.3.2 Contour Integration
			4.3.3.3 Differentiation of Known Factors
		4.3.4 Unit-Sphere and Hemicube Methods
		4.3.5 Direct Numerical Integration
		4.3.6 Computer Programs for the Evaluation of Configuration Factors
	4.4 Constraints on Configuration Factor Accuracy
	4.5 Compilation of Known Configuration Factors and Their References: Appendix C and Web Catalog
	Homework Problems
Chapter 5 Radiation Exchange in Enclosures Composed of Black and/or Diffuse-Gray Surfaces
	5.1 Introduction
	5.2 Radiative Transfer for Black Surfaces
		5.2.1 Transfer between Black Surfaces Using Configuration Factors
		5.2.2 Radiation Exchange in a Black Enclosure
	5.3 Radiation Among Finite Diffuse-Gray Areas
		5.3.1 Net-Radiation Method for Enclosures
			5.3.1.1 System of Equations Relating Surface Heating Rate Q and Surface Temperature T
			5.3.1.2 Solution Method in Terms of Radiosity J
		5.3.2 Enclosure Analysis in Terms of Energy Absorbed at Surface
		5.3.3 Enclosure Analysis by the Use of Transfer Factors
		5.3.4 Matrix Inversion for Enclosure Equations
	5.4 Radiation Analysis Using Infinitesimal Areas
		5.4.1 Generalized Net-Radiation Method Using Infinitesimal Areas
			5.4.1.1 Relations between Surface Temperature T and Surface Heat Flux q
			5.4.1.2 Solution Method in Terms of Outgoing Radiative Flux J
			5.4.1.3 Special Case When Imposed Heating q Is Specified for All Surfaces
		5.4.2 Boundary Conditions Specifying Inverse Problems
	5.5 Computer Programs for Enclosure Analysis
	Homework Problems
Chapter 6 Exchange of Thermal Radiation among Nondiffuse Nongray Surfaces
	6.1 Introduction
	6.2 Enclosure Theory for Diffuse Nongray Surfaces
		6.2.1 Parallel-Plate Geometry
		6.2.2 Spectral and Finite Spectral Band Relations for an Enclosure
		6.2.3 Semigray Approximations
	6.3 Directional-Gray Surfaces
	6.4 Surfaces with Directionally and Spectrally Dependent Properties
	6.5 Radiation Exchange in Enclosures with Specularly Reflecting Surfaces
		6.5.1 Representative Cases with Simple Geometries
		6.5.2 Ray Tracing and Image Formation
		6.5.3 Radiative Transfer among Simple Specular Surfaces for Diffuse Energy Leaving a Surface
		6.5.4 Configuration-Factor Reciprocity for Specular Surfaces; Specular Exchange Factors
	6.6 Net-Radiation Method in Enclosures Having Both Specular and Diffuse Reflecting Surfaces
		6.6.1 Enclosures with Planar Surfaces
		6.6.2 Curved Specular Reflecting Surfaces
	6.7 Multiple Radiation Shields
	6.8 Concluding Remarks
	Homework Problems
Chapter 7 Radiation Combined with Conduction and Convection at Boundaries
	7.1 Introduction
	7.2 Energy Relations and Boundary Conditions
		7.2.1 General Relations
		7.2.2 Uncoupled and Coupled Energy Transfer Modes
		7.2.3 Control Volume Approach for One- or Two-Dimensional Conduction along Thin Walls
	7.3 Radiation Transfer with Conduction Boundary Conditions
		7.3.1 Thin Fins with 1D or 2D Conduction
			7.3.1.1 1D Energy Flow
			7.3.1.2 2D Energy Flow
		7.3.2 Multidimensional and Transient Heat Conduction with Radiation
	7.4 Radiation with Convection and Conduction
		7.4.1 Thin Radiating Fins with Convection
		7.4.2 Channel Flows
		7.4.3 Natural Convection with Radiation
	7.5 Numerical Solution Methods
		7.5.1 Numerical Integration Methods for Use with Enclosure Equations
		7.5.2 Numerical Formulations for Combined-Mode Energy Transfer
			7.5.2.1 Finite-Difference Formulation
			7.5.2.2 Finite Element Method Formulation
		7.5.3 Numerical Solution Techniques
		7.5.4 Verification, Validation, and Uncertainty Quantification
			7.5.4.1 Verification
			7.5.4.2 Validation
			7.5.4.3 Uncertainty Quantification
	7.6 Concluding Remarks
	Homework Problems
Chapter 8 Electromagnetic Wave Theory
	8.1 Introduction
	8.2 The Electromagnetic Wave Equations
	8.3 Wave Propagation in a Medium
		8.3.1 EM Wave Propagation in Perfect Dielectric Media
		8.3.2 Wave Propagation in Isotropic Media with Finite Electrical Conductivity
		8.3.3 Energy of an EM Wave
		8.3.4 Polarization
	8.4 Laws of Reflection and Refraction
		8.4.1 Reflection and Refraction at the Interface between Perfect Dielectrics
		8.4.2 Reflection and Refraction at the Interface of a Perfect Dielectric and a Conducting Medium
	8.5 Classical Models for Optical Constants
		8.5.1 Lorentz Model (Non-conductors)
		8.5.2 Drude Model (Conductors)
	8.6 EM Wave Theory and the Radiative Transfer Equation
	Homework Problems
Chapter 9 Properties of Participating Media
	9.1 Introduction
	9.2 Propagation of Radiation in Absorbing Media
	9.3 Spectral Lines and Bands for Gas Absorption and Emission
		9.3.1 Physical Mechanisms
		9.3.2 Local Thermodynamic Equilibrium (LTE)
		9.3.3 Spectral Line Broadening
			9.3.3.1 Natural Broadening
			9.3.3.2 Doppler Broadening
			9.3.3.3 Collision Broadening and Narrowing
			9.3.3.4 Stark Broadening
		9.3.4 Absorption or Emission by a Single Spectral Line
			9.3.4.1 Property Definitions along a Path in a Uniform Absorbing and Emitting Medium
			9.3.4.2 Weak Lines
			9.3.4.3 Lorentz Lines
		9.3.5 Band Absorption
			9.3.5.1 Band Structure
			9.3.5.2 Types of Band Models
			9.3.5.3 Databases for the Line Absorption Properties of Molecular Gases
	9.4 Band Models and Correlations for Gas Absorption and Emission
		9.4.1 Narrow-Band Models
			9.4.1.1 Elsasser Model
			9.4.1.2 Goody Model
			9.4.1.3 Malkmus Model
		9.4.2 Wide Band Models
		9.4.3 Probability Density Function-Based Band Correlations
			9.4.3.1 k-Distribution Method
			9.4.3.2 Correlated-k Assumption
			9.4.3.3 Full Spectrum k-Distribution Methods
			9.4.3.4 Effect of Temperature and Concentration Gradients in the Medium
		9.4.4 Weighted Sum of Gray Gases
	9.5 Gas Total Emittance Correlations
	9.6 Absorption Coefficient Neglecting Induced Emission
	9.7 Definitions and Use of Mean Absorption Coefficients
		9.7.1 Use of Mean Absorption Coefficients
		9.7.2 Definitions of Mean Absorption Coefficients
		9.7.3 Approximate Solutions of the Radiative Transfer Equation Using Mean Absorption Coefficients
	9.8 Radiative Properties of Translucent Liquids and Solids
	Homework Problems
Chapter 10 Absorption and Scattering by Particles and Agglomerates
	10.1 Overview
	10.2 Absorption and Scattering: Definitions
		10.2.1 Background
		10.2.2 Absorption and Scattering Coefficients, Cross-Sections, Efficiencies
		10.2.3 Scattering Phase Function
	10.3 Scattering by Spherical Particles
		10.3.1 Scattering by a Large Specularly Reflecting Sphere
		10.3.2 Reflection from a Large Diffuse Sphere
		10.3.3 Large Ideal Dielectric Sphere with n ≈ 1
		10.3.4 Diffraction by a Large Sphere
		10.3.5 Geometric Optics Approximation
	10.4 Scattering by Small Particles
		10.4.1 Rayleigh Scattering by Small Spheres
		10.4.2 Cross-Section for Rayleigh Scattering
		10.4.3 Phase Function for Rayleigh Scattering
	10.5 The Lorenz–Mie Theory for Spherical Particles
		10.5.1 Formulation for Homogeneous and Stratified Spherical Particles
		10.5.2 Cross-Sections for Specific Cases
	10.6 Approximate Anisotropic Scattering Phase Functions
		10.6.1 Forward Scattering Phase Function
		10.6.2 Linear-Anisotropic Phase Function
		10.6.3 Delta-Eddington Phase Function
		10.6.4 Henyey–Greenstein Phase Function
	10.7 Prediction of Properties for Irregularly Shaped Particles
		10.7.1 Integral and Differential Formulations
		10.7.2 T-Matrix Approach
		10.7.3 Discrete Dipole Approximation
		10.7.4 Finite-Element Method
		10.7.5 Finite-Difference Time-Domain Method
	10.8 Dependent Absorption and Scattering
	Homework Problems
Chapter 11 Fundamental Radiative Transfer Relations and Approximate Solution Methods
	11.1 Introduction
	11.2 Energy Equation and Boundary Conditions for a Participating Medium
	11.3 Radiative Transfer and Source-Function Equations
		11.3.1 Radiative Transfer Equation
		11.3.2 Source-Function Equation
	11.4 Radiative Flux and Its Divergence within a Medium
		11.4.1 Radiative Flux Vector
		11.4.2 Divergence of Radiative Flux without Scattering (Absorption Alone)
		11.4.3 Divergence of Radiative Flux Including Scattering
	11.5 Summary of Relations for Radiative Transfer in Absorbing, Emitting, and Scattering Media
		11.5.1 Energy Equation
		11.5.2 Radiative Energy Source
		11.5.3 Source Function
		11.5.4 Radiative Transfer Equation
		11.5.5 Relations for a Gray Medium
	11.6 Treatment of Radiation Transfer in Non-LTE Media
	11.7 Net-Radiation Method for Enclosures Filled with an Isothermal Medium of Uniform Composition
		11.7.1 Definitions of Spectral Geometric-Mean Transmission and Absorption Factors
		11.7.2 Matrix of Enclosure Theory Equations
		11.7.3 Energy Balance on a Medium
		11.7.4 Spectral Band Equations for an Enclosure
		11.7.5 Gray Medium in a Gray Enclosure
	11.8 Evaluation of Spectral Geometric-Mean Transmittance and Absorptance Factors
	11.9 Mean Beam Length Approximation for Spectral Radiation from an Entire Volume of a Medium to All or Part of Its Boundary
		11.9.1 Mean Beam Length for a Medium between Parallel Plates Radiating to Area on Plate
		11.9.2 Mean Beam Length for the Sphere of a Medium Radiating to Any Area on Its Boundary
		11.9.3 Radiation from the Entire Medium Volume to Its Entire Boundary for Optically Thin Media
		11.9.4 Correction to Mean Beam Length When a Medium Is Not Optically Thin
	11.10 Exchange of Total Radiation in an Enclosure by Use of Mean Beam Length
		11.10.1 Total Radiation from the Entire Medium Volume to All or Part of Its Boundary
		11.10.2 Exchange between the Entire Medium Volume and the Emitting Boundary
	11.11 Optically Thin and Cold Media
		11.11.1 Nearly Transparent Medium
		11.11.2 Optically Thin Media with Cold Boundaries or Small Incident Radiation: The Emission Approximation
		11.11.3 Cold Medium with Weak Scattering
	Homework Problems
Chapter 12 Participating Media in Simple Geometries
	12.1 Introduction
	12.2 Radiative Intensity, Flux, Flux Divergence, and Source Function in a Plane Layer
		12.2.1 Radiative Transfer Equation and Radiative Intensity for a Plane Layer
		12.2.2 Local Radiative Flux in a Plane Layer
		12.2.3 Divergence of the Radiative Flux: Radiative Energy Source
		12.2.4 Equation for the Source Function in a Plane Layer
		12.2.5 Relations for Isotropic Scattering
		12.2.6 Diffuse Boundary Fluxes for a Plane Layer with Isotropic Scattering
	12.3 Gray Plane Layer of Absorbing and Emitting Medium with Isotropic Scattering
	12.4 Gray Plane Layer in Radiative Equilibrium
		12.4.1 Energy Equation
		12.4.2 Absorbing Gray Medium in Radiative Equilibrium with Isotropic Scattering
		12.4.3 Isotropically Scattering Medium with Zero Absorption
		12.4.4 Gray Medium with dqR/dx = 0 between Opaque Diffuse-Gray Boundaries
		12.4.5 Solution for Gray Medium with dqr/dx = 0 between Black or Diffuse-Gray Boundaries at Specified Temperatures
			12.4.5.1 Gray Medium between Black Boundaries
			12.4.5.2 Gray Medium between Diffuse-Gray Boundaries
			12.4.5.3 Extended Solution for Optically Thin Medium between Gray Boundaries
	12.5 Multidimensional Radiation in a Participating Gray Medium with Isotropic Scattering
		12.5.1 Radiation Transfer Relations in Three Dimensions
		12.5.2 Two-Dimensional Transfer in an Infinitely Long Right Rectangular Prism
		12.5.3 One-Dimensional Transfer in a Cylindrical Region
		12.5.4 Additional Information on Non-planar and Multidimensional Geometries
	Homework Problems
Chapter 13 Numerical Solution Methods for Radiative Transfer in Participating Media
	13.1 Introduction
	13.2 Series Expansion and Moment Methods
		13.2.1 Optically Thick Media: Radiative Diffusion
			13.2.1.1 Simplified Derivation of the Radiative Diffusion Approximation
			13.2.1.2 General Radiation–Diffusion Relations in a Medium
		13.2.2 Moment-Based Methods
			13.2.2.1 Milne–Eddington (Differential) Approximation
			13.2.2.2 General Spherical Harmonics (PN) Method
			13.2.2.3 Simplified PN (SPN) Method
			13.2.2.4 MN Method
	13.3 Discrete Ordinates (SN) Method
		13.3.1 Two-Flux Method: The Schuster–Schwarzschild Approximation
		13.3.2 Radiative Transfer Equation with SN Method
		13.3.3 Boundary Conditions for the SN Method
		13.3.4 Control Volume Method for SN Numerical Solution
			13.3.4.1 Relations for 2D Rectangular Coordinates
			13.3.4.2 Relations for 3D Rectangular Coordinates
		13.3.5 Ordinate and Weighting Pairs
		13.3.6 Results Using Discrete Ordinates
	13.4 Other Methods That Depend on Angular Discretization
		13.4.1 Discrete Transfer Method
		13.4.2 Finite Volume Method
		13.4.3 Boundary Element Method
	13.5 Zonal Method
		13.5.1 Exchange Area Relations
		13.5.2 Zonal Formulation for Radiative Equilibrium
		13.5.3 Developments for the Zone Method
			13.5.3.1 Smoothing of Exchange Area Sets
			13.5.3.2 Other Formulations of the Zone Method
			13.5.3.3 Numerical Results from the Zone Method
	13.6 Additional Solution Methods
		13.6.1 Reduction of the Integral Order
		13.6.2 Spectral Methods
		13.6.3 Finite Element Method (FEM) for Radiative Equilibrium
		13.6.4 Lattice-Boltzmann Method
		13.6.5 Additional Information on Numerical Methods
	13.7 Comparison of Results for the Methods
	13.8 Benchmark Solutions for Computational Verification
	Homework Problems
Chapter 14 The Monte Carlo Method
	14.1 Introduction
	14.2 Fundamentals of the Monte Carlo method
		14.2.1 Monte Carlo as an Integration Tool
		14.2.2 Sampling from a Probability Density
		14.2.3 Markov-Chain Monte Carlo
		14.2.4 Uncertainty Quantification
	14.3 Monte Carlo for Surface-to-Surface Radiation Exchange
		14.3.1 Radiation between Black Surfaces
		14.3.2 Radiation between Nonblack Surfaces
		14.3.3 Wavelength-Dependent Properties
		14.3.4 Ray-Tracing
	14.4 Monte Carlo for Enclosures Containing Participating Media
		14.4.1 Relations for Absorption and Scattering within the Medium
		14.4.2 Net Radiative Energy Transfer between Volume and Surface Elements
		14.4.3 Treatment of Wavelength-Dependent Properties
	14.5 Variance Reduction Methods
		14.5.1 Energy Partitioning
		14.5.2 Importance Sampling
		14.5.3 Reciprocity
		14.5.4 Quasi-Monte Carlo
	14.6 Backwards (Reverse) Monte Carlo
	14.7 The Null-Collision Technique
	14.8 Sensitivities and Nonlinear Monte Carlo
	14.9 Summary and Outlook
	Homework Problems
Chapter 15 Conjugate Heat Transfer in Participating Media
	15.1 Introduction
	15.2 Radiation Combined with Conduction
		15.2.1 Energy Balance
		15.2.2 Plane Layer with Conduction and Radiation
			15.2.2.1 Absorbing–Emitting Medium without Scattering
			15.2.2.2 Absorbing–Emitting Medium with Scattering
		15.2.3 Rectangular Region with Conduction and Radiation
		15.2.4 PN Method for Radiation Combined with Conduction
		15.2.5 Approximations for Combined Radiation and Conduction
			15.2.5.1 Addition of Energy Transfer by Radiation and Conduction
			15.2.5.2 Diffusion Method for Combined Radiation and Conduction
	15.3 Transient Solutions Including Conduction
	15.4 Combined Radiation, Conduction, and Convection in a Boundary Layer
		15.4.1 Optically Thin Thermal Boundary Layer
		15.4.2 Optically Thick Thermal Boundary Layer
	15.5 Numerical Solution Methods for Combined Radiation, Conduction, and Convection in Participating Media
		15.5.1 Finite-Difference Methods
			15.5.1.1 Energy Equation for Combined Radiation and Conduction
			15.5.1.2 Radiation and Conduction in a Plane Layer
			15.5.1.3 Radiation and Conduction in a 2D Rectangular Region
			15.5.1.4 Boundary Conditions for Numerical Solutions
		15.5.2 Finite-Element Method
			15.5.2.1 FEM for Radiation with Conduction and/or Convection
			15.5.2.2 Results from Finite-Element Analyses
		15.5.3 Pitfalls of Iterative Methods
	15.6 Results for Combined Radiation, Convection, and Conduction Heat Transfer
		15.6.1 Forced Convection Channel Flows
		15.6.2 Natural Convection Flow, Radiative Energy Transfer, and Stability
		15.6.3 Radiative Transfer in Porous Media and Packed Beds
		15.6.4 Radiation Interactions with Turbulence
		15.6.5 Additional Topics with Combined Radiation, Conduction, and Convection
	15.7 Inverse Multimode Problems
	15.8 Verification, Validation, and Uncertainty Quantification
	Homework Problems
Chapter 16 Near-Field Thermal Radiation
	16.1 Introduction
	16.2 Electromagnetic Treatment of Thermal Radiation and Basic Concepts
		16.2.1 Near-Field versus Far-Field Thermal Radiation
		16.2.2 Electromagnetic Description of Near-Field Thermal Radiation
		16.2.3 Near-Field Radiative Energy Flux
		16.2.4 Density of Electromagnetic States
		16.2.5 Spatial and Temporal Coherence of Thermal Radiation
	16.3 Evanescent and Surface Waves
		16.3.1 Evanescent Waves
		16.3.2 Surface Waves
	16.4 Near-Field Radiative Energy Flux Calculations
		16.4.1 Near-Field Radiative Energy Transfer in 1D Layered Media
		16.4.2 Near-Field Radiative Energy Transfer between Two Bulk Materials Separated by a Vacuum Gap
	16.5 Computational Studies of Near-Field Thermal Radiation
	16.6 Experimental Studies of Near-Field Thermal Radiation
		16.6.1 Earlier Work
		16.6.2 Experimental Determination of Near-Field Radiative Transfer Coefficient
		16.6.3 Near-Field Effects on Radiative Properties and Metamaterials
	16.7 Concluding Remarks
	Homework Problems
Chapter 17 Radiative Effects in Translucent Solids, Windows, and Coatings
	17.1 Introduction
	17.2 Transmission, Absorption, and Reflection for Windows
		17.2.1 Single Partially Transmitting Layer with Thickness D ≫ λ (No Wave Interference Effects)
			17.2.1.1 Ray-Tracing Method
			17.2.1.2 Net-Radiation Method
		17.2.2 Multiple Parallel Windows
		17.2.3 Transmission through Multiple Parallel Glass Plates
		17.2.4 Interaction of Transmitting Plates with Absorbing Plate
	17.3 Enclosure Analysis for Partially Transparent Windows
	17.4 Effects of Coatings or Thin Films on Surfaces
		17.4.1 Coating without Wave Interference Effects
			17.4.1.1 Nonabsorbing Dielectric Coating on Nonabsorbing Dielectric Substrate
			17.4.1.2 Absorbing Coating on Metal Substrate
		17.4.2 Thin Film with Wave Interference Effects
			17.4.2.1 Dielectric Thin Film on Dielectric Substrate
			17.4.2.2 Absorbing Thin Film on a Metal Substrate
		17.4.3 Films with Partial Coherence
	17.5 Refractive Index Effects on Radiation in a Participating Medium
		17.5.1 Effect of Refractive Index on Intensity Crossing an Interface
		17.5.2 Effect of Angle for Total Reflection
		17.5.3 Effects of Boundary Conditions for Radiation Analysis in a Plane Layer
			17.5.3.1 Layer with Nondiffuse or Specular Surfaces
			17.5.3.2 Diffuse Surfaces
		17.5.4 Emission from a Translucent Layer (n > 1) at Uniform Temperature with Specular or Diffuse Boundaries
	17.6 Multiple Participating Layers with Heat Conduction
		17.6.1 Formulation for Multiple Participating Plane Layers
		17.6.2 Translucent Layer on a Metal Wall
		17.6.3 Composite of Two Translucent Layers
			17.6.3.1 Temperature Distribution Relations from the Energy Equation
			17.6.3.2 Relations for Radiative Energy Flux
			17.6.3.3 Equation for the Source Function
			17.6.3.4 Solution Procedure and Typical Results
	17.7 Light Pipes and Fiber Optics
	17.8 Final Remarks
	Homework Problems
Chapter 18 Inverse Problems in Radiative Transfer
	18.1 Introduction
	18.2 Inverse Analysis and Ill-Posed Problems
	18.3 Mathematical Properties of Inverse Problems
		18.3.1 Linear Inverse Problems
		18.3.2 Nonlinear Inverse Problems
	18.4 Solution Methods for Inverse Problems
		18.4.1 Linear Regularization
		18.4.2 Nonlinear Programming
		18.4.3 Metaheuristics
		18.4.4 Bayesian Methods
		18.4.5 Artificial Neural Networks
		18.4.6 Is Least-Squares Minimization an Inverse Technique?
	18.5 Inverse Design Problems
		18.5.1 Linear Inverse Design Problems
		18.5.2 Nonlinear Inverse Design Problems
	18.6 Parameter Estimation Problems
		18.6.1 Problems Involving 1D Participating Media
		18.6.2 Tomography
		18.6.3 Light-Scattering by Droplets and Particles
		18.6.4 Inverse Crimes
	18.7 Summary
	Homework Problems
Chapter 19 Applications of Radiation Energy Transfer
	19.1 Introduction
	19.2 Solar Energy
		19.2.1 Solar Energy Conversion
			19.2.1.1 Central Solar Power Systems
			19.2.1.2 Photovoltaic (PV) Conversion
			19.2.1.3 Solar Enhanced HVAC Systems
		19.2.2 Radiation Transfer, Architecture, and Visual Comfort
		19.2.3 Astronomy, Astrophysics, and Atmospheric Radiation
		19.2.4 Solar Energy, Global Warming, and Climate Change
	19.3 Radiation from Combustion
		19.3.1 Radiation from Non-Sooting Flames
		19.3.2 Radiation from Sooting Flames
		19.3.3 Modeling of Furnaces and Burners
	19.4 Radiation in Porous Media and Packed Beds
		19.4.1 CSP Absorbers Using Porous Media
		19.4.2 Porous Media Burners
	19.5 Aerospace Applications
		19.5.1 Spacecraft Thermal Control
		19.5.2 Radiation Energy Transfer in Rocket Nozzles
	19.6 Advanced Manufacturing and Materials Processing
		19.6.1 Radiation Transfer in Process Industries
	19.7 Biomedical Applications of Thermal Radiation
	19.8 Conclusions
	Homework Problems
Appendix A: Conversion Factors, Radiation Constants, and Blackbody Functions
Appendix B: Radiative Properties
Appendix C: Catalog of Selected Configuration Factors
Appendix D: Exponential Integral Relations and Two-Dimensional Radiation Functions
References
Index