Thermal Radiation Heat Transfer

Transcription

1 Thermal Radiation Heat Transfer FIFTH EDITION John R. Howell Robert Siegel M. Pinar Mengü9 CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

2 Contents Preface to the Fifth Edition... List of Symbols... xxi xxiii Chapter 1 Introduction to Radiative Transfer Importance of Thermal Radiation in Engineering Thermal Energy Transfer Thermal Radiative Transfer Radiative Energy Exchange and Radiative Intensity Solid Angle Spectral Radiative Intensity Characteristics of Emission Perfect Emitter Radiation Isotropy in a Black Enclosure Perfect Emitter in Each Direction and Wavelength Total Radiation into Vacuum Is a Function Only of Temperature Blackbody Intensity and Its Directional Independence Blackbody Emissive Power: Cosine-Law Dependence Hemispherical Spectral Emissive Power of a Blackbody Planck's Law: Spectral Distribution of Emissive Power Approximations for Blackbody Spectral Distribution Wien's Formula Rayleigh-Jeans Formula Wien's Displacement Law Total Blackbody Intensity and Emissive Power Blackbody Radiation within a Spectral Band Summary of Blackbody Properties Radiative Energy Loss and Gain along a Line-of-Sight Radiative Energy Loss due to Absorption and Scattering Mean Penetration Distance Optical Thickness Radiative Energy Gain due to Emission Radiative Energy Gain due to In-Scattering Radiative Transfer Equation Radiative Transfer in Nonparticipating Enclosures Concluding Remarks and Historical Notes Homework Chapter 2 Definitions of Properties at Interfaces Introduction Nomenclature for Properties Notation Emissivity Directional Spectral Emissivity E x (0, T)... 51

3 viii Contents Directional Total Emissivity (04,T) Hemispherical Spectral Emissivity e x (T) Hemispherical Total Emissivity e(t) Absorptivity Directional Spectral Absorptivity a x (0 0 T) Kirchhoff's Law Directional Total Absorptivity a(0 0 T) Kirchhoff's Law for Directional Total Properties Hemispherical Spectral Absorptivity a x (T) Hemispherical Total Absorptivity a(t) Diffuse-Gray Surface Reflectivity Spectral Reflectivities Bidirectional Spectral Reflectivity (i)r, 0,, 4) Reciprocity for Bidirectional Spectral Reflectivity Directional Spectral Refelctivities Reciprocity for Directional Spectral Reflectivity Hemispherical Spectral Reflectivity p x Limiting Cases for Spectral Surfaces Total Reflectivities Bidirectional Total Reflectivity p(0 4 r, 0,, cl),) Reciprocity for Bidirectional Total Reflectivity Directional Total Reflectivity p(0 (1) i ) or 0 11),) Reciprocity for Directional Total Reflectivity Hemispherical Total Reflectivity, p Summary of Restrictions an Reflectivity Reciprocity Relations Transmissivity at an Interface Spectral Transmissivities Bidirectional Spectral Transmissivity T x (0 i,ü1) 0 4) T) Directional Spectral Transmissivities,(0 1, ei) Hemispherical Spectral Transmissivity i r Total Transmissivities Bidirectional Total Transmissivity t(oi, (1)i, O e4 ) Directional Total Transmissivities t(0 4,) Hemispherical-Directional Total Transmissivity (1) Hemispherical Total Transmissivity Relations among Reflectivity, Absorptivity, Emissivity, and Transmissivity Homework Chapter 3 Radiative Properties of Opaque Materials Introduction Electromagnetic Wave Theory Predictions Dielectric Materials Reflection and Refraction at the Interface between Two Perfect Dielectrics (k --> 0) Reflectivity Emissivity Radiative Properties of Metals... 94

4 Contents ix Electromagnetic Relations for Incidence an an Absorbing Medium Reflectivity and Emissivity Relations for Metals (Large k) Relations between Radiative Emission and Electrical Properties Extensions of the Theory for Radiative Properties Measured Properties of Real Dielectric Materials Variation of Total Properties with Surface Temperature Effect of Surface Roughness Properties of Semiconductors and Superconductors Measured Properties of Metals Directional and Spectral Variations Effect of Surface Temperature Effect of Surface Roughness Effect of Surface Impurities Molten Metals Selective and Directional Opaque Surfaces Characteristics of Solar Radiation Solar Constant Solar Radiating Temperature Modification of Surface Spectral Characteristics Modification of Surface Directional Characteristics Concluding Remarks Homework Chapter 4 Configuration Factors for Diffuse Surfaces with Uniform Radiosity Radiative Transfer Equation for Surfaces Separated by a Transparent Medium Enclosures with Diffuse Surfaces Enclosures with Directional (Nondiffuse) and Spectral (Nongray) Surfaces Geometric Configuration Factors between Two Surfaces Configuration Factor for Energy Exchange between Diffuse Differential Areas Reciprocity for Differential-Element Configuration Factors Sample Configuration Factors between Differential Elements Configuration Factor between a Differential Area Element and a Finite Area Reciprocity Relation for Configuration Factor between Differential and Finite Areas Configuration Factors between Differential and a Finite Areas Configuration Factor and Reciprocity for Two Finite Areas Methods for Determining Configuration Factors Configuration-Factor Algebra Configuration Factors Determined by Use of Symmetry Configuration-Factor Relations in Enclosures

5 x Contents Techniques for Evaluating Configuration Factors Hottel's Crossed-String Method Contour Integration Differentiation of Known Factors Unit-Sphere and Hemicube Methods Direct Numerical Integration Computer Programs for Evaluation of Configuration Factors Constraints an Configuration Factor Accuracy Compilation of Known Configuration Factors and Their References Appendix C and Web Catalog Homework Chapter 5 Radiation Exchange in Enclosures Composed of Black and/or Diffuse-Gray Surfaces Approximations and Restrictions for Analysis of Enclosures with Black and/or Diffuse-Gray Surfaces Radiative Transfer for Black Surfaces Transfer Between Black Surfaces by Use of Configuration Factors Radiation Exchange in a Black Enclosure Radiation Between Finite Diffuse-Gray Areas Net-Radiation Method for Enclosures System of Equations Relating Surface Heating Q and Surface Temperature T Solution Method in Terms of Radiosity J Enclosure Analysis in Terms of Energy Absorbed at Surface Enclosure Analysis by Use of Transfer Factors Matrix Inversion for Enclosure Equations Radiation Analysis Using Infinitesimal Areas Generalized Net-Radiation Method Using Infinitesimal Areas Relations between Surface Temperature T and Surface Heat Flux q Solution Method in Terms of Outgoing Radiative Flux J Special Case When Imposed Heat Flux q Is Specified for All Surfaces Methods for Solving Integral Equations Numerical Integration Analytical Solutions Exact Solution of Integral Equation for Radiation from a Spherical Cavity General Boundary Conditions that Provide Inverse Problems Computer Programs for Enclosure Analysis Homework Chapter 6 Exchange of Thermal Radiation among Nondiffuse Nongray Surfaces Introduction Enclosure Theory for Diffuse Nongray Surfaces Parallel-Plate Geometry

6 Contents xi Spectral and Finite Spectral Band Relations for an Enclosure Semigray Approximations... Directional-Gray Surfaces... Surfaces with Directionally and Spectrally Dependent Properties... Radiation Exchange in Enclosures with Some Specularly Reflecting Surfaces Some Situations with Simple Geometries Ray Tracing and the Construction of Images Radiative Transfer by Means of Simple Specular Surfaces for Diffuse Energy Leaving a Surface Configuration-Factor Reciprocity for Specular Surfaces; Specular Exchange Factors Net-Radiation Method in Enclosures Having Specular and Diffuse Reflecting Surfaces Enclosures with Planar Surfaces Curved Specular Reflecting Surfaces Multiple Radiation Shields Concluding Remarks Homework Chapter 7 Radiation Combined with Conduction and Convection at Boundaries Introduction Energy Relations and Boundary Conditions General Relations Uncoupled and Coupled Energy Transfer Modes Control Volume Approach for One- or Two-Dimensional Conduction along Thin Walls Radiation Transfer with Conduction Boundary Conditions Thin Fins with One- or Two-Dimensional Conduction One-Dimensional Heat Flow Two-Dimensional Heat Flow Multidimensional and Transient Heat Conduction with Radiation Radiation with Convection and Conduction Thin Radiating Fins with Convection Channel Flows Free Convection with Radiation Numerical Solution Methods Numerical Integration Methods for Use with Enclosure Equations Trapezoidal Rule Simpson's Rule Other Integration Methods Numerical Formulations for Combined-Mode Energy Transfer Finite-Difference Formulation Finite-Element Method Formulation Shape Function Galerkin Form for the Energy Equation Numerical Solution Techniques Successive Substitution Methods Simple Successive Substitution (SSS)

7 xii Contents Successive Underrelaxation (SUR) Regulated Successive Underrelaxation (RSUR) Newton-Raphson-Based Methods for Nonlinear Problems Modified Newton-Raphson (MNR) Accelerated Newton-Raphson (ANR) Applications of the Numerical Methods Monte Carlo Method Definition of Monte Carlo Method Fundamentals of the Method Random Walk Choosing from Probability Distributions Random Numbers Evaluation of Uncertainty Application to Thermal Radiative Transfer Model of the Radiative Exchange Process Useful Functions Forward Monte Carlo Reverse Monte Carlo Results for Radiative Transfer Literature an Radiation Exchange among Surfaces Radiative Transmission through the Inside of a Channel Extension to Directional and Spectral Surfaces Application of Monte Carlo Methods to Combined-Mode Problems Concluding Remarks Verification Validation Uncertainty Quantification Homework 400 Chapter 8 Inverse Problems in Radiative Heat Transfer Introduction to Inverse Problems Inverse Design and Data Analysis Direct Inverse Solutions General Inverse Solution Methods Regularization Optimization Deterministic (Quasi-Newton) Approach Metaheuristic Approaches Simulated Annealing Comparison of Methods for a Particular Problem Solution by Direct Inversion TSVD Solution Method Tikhonov Solution Method CGR Solution Optimization Techniques Metaheuristic Results Simulated Annealing Comparison of Selected Results

8 Contents xiii 8.4 Application of Metaheuristic Methods Unresolved Problems Inverse Problems Involving Participating Media Concluding Remarks Homework Chapter 9 Absorption and Emission in Participating Media Introduction Spectral Lines and Bands for Absorption and Emission of Gases Physical Mechanisms Condition of Local Thermodynamic Equilibrium (LTE) Spectral Line Broadening Natural Broadening Doppler Broadening Collision Broadening and Narrowing Stark Broadening Absorption or Emission by a Single Spectral Line Property Definitions for a Path in a Uniform Absorbing and Emitting Medium Weak Lines Relations for Lorentz Lines Band Absorption Band Structure Types of Band Models Spectral Line-by-Line Databases Band Models and Correlations for Gas Absorption and Emission Narrow-Band Models Elsasser Model Goody Model Malkmus Model Wide-Band Models and Correlations Contemporary Band Correlations k-distribution Method Correlated-k Method Weighted Sum of Gray Gases Total Gas-Total Emittance Correlations Mean Absorption Coefficients Planck Mean Absorption Coefficient Rosseland Mean Absorption Coefficient Patch Mean Absorption Coefficient True Absorption Coefficient Radiative Properties of Translucent Liquids and Solids Homework Chapter 10 Radiative Transfer Relations in Simple Systems Introduction Energy Equation and Boundary Conditions for a Translucent Medium with Radiation

9 xiv Contents 10.3 Radiative Transfer and Source Function Equations Radiative Transfer Equation Source Function Equation Radiative Flux and Its Divergence within a Medium Radiative Flux Vector Divergence of Radiative Flux without Scattering (Absorption Alone) Divergence of Radiative Flux Including Scattering Summary of Relations for Radiative Transfer in Absorbing, Emitting, and Scattering Media Energy Equation Radiative Energy Source Source Function Radiative Transfer Equation Relations for a Gray Medium Net-Radiation Method for Enclosures Filled with an Isothermal Medium of Uniform Composition Definitions of Spectral Geometric-Mean Transmission and Absorption Factors Definitions of Spectral Geometric-Mean Transmission and Absorption Factors Matrix of Enclosure-Theory Equations Energy Balance in a Medium Spectral Band Equations for an Enclosure Gray Medium in a Gray Enclosure Evaluation of Spectral Geometric-Mean Transmittance and Absorptance Factors Mean Beam-Length Approximation for Spectral Radiation from an Entire Volume of a Medium to All or Part of Its Boundary Mean Beam Length for a Medium between Parallel Plates Radiating to Area on Plate Mean Beam Length for Sphere of Medium Radiating to Any Area on Its Boundary Radiation from Entire Medium Volume to Its Entire Boundary for Optically Thin Medium Correction to Mean Beam Length When Medium Is Not Optically Thin Exchange of Total Radiation in an Enclosure by Use of Mean Beam Length Total Radiation from Entire Medium Volume to All or Part of its Boundary Exchange between Entire Medium Volume and Emitting Boundary Homework Chapter 11 Energy Transfer in Plane Layers and Multidimensional Geometries: Participating Media with and without Conduction Introduction Equations for Radiative Intensity, Flux, Flux Divergence, and Source Function in a Plane Layer

10 Contents xv Radiative Transfer Equation and Radiative Intensity for a Plane Layer Local Radiative Flux in a Plane Layer Divergence of the Radiative Flux Radiative Energy Source Equation for the Source Function in a Plane Layer Relations for Isotropic Scattering Diffuse Boundary Fluxes for a Plane Layer with Isotropic Scattering Gray Plane Layer of Absorbing and Emitting Medium with Isotropic Scattering Gray Plane Layer in Radiative Equilibrium Energy Equation Absorbing Gray Medium in Radiative Equilibrium with Isotropic Scattering Isotropically Scattering Medium with Zero Absorption Gray Medium with dqrldx = 0 between Opaque Diffuse-Gray Boundaries Solution for Gray Medium with dqrldx = 0 between Black or Diffuse-Gray Walls at Specified Temperatures Gray Medium between Black Walls Gray Medium between Diffuse-Gray Walls Radiation Combined with Conduction Energy Balance Plane Layer with Conduction and Radiation Absorbing-Emitting Medium without Scattering Absorbing-Emitting Medium with Scattering Multidimensional Radiation in a Participating Gray Medium with Isotropic Scattering Radiation Relations in Three Dimensions Two-Dimensional Transfer in a Rectangular Region Rectangular Region with Conduction and Radiation One-Dimensional Transfer in a Cylindrical Region Additional Information an Nonplanar and Multidimensional Geometries Transient Solutions Including Conduction Discussion of Solution Procedures Simultaneous Solution of Energy and Radiative Transfer Relations Outline of Solution Methods for the Radiative Transfer Equation Solution Methods for the Differential RTE Solution Methods for the Integral RTE Homework Chapter 12 Optically Thin and Thick Limits for Radiative Transfer in Participating Media Introduction Optically Thin and Cold Media Nearly Transparent Optically Thin Medium Optically Thin Media with Cold Boundaries or Small Incident Radiation; the Emission Approximation Cold Medium with Weak Scattering

11 xvi Contents 12.3 Optically Thick Medium : Radiative Diffusion Simplified Derivation of the Radiative Diffusion Approximation General Radiation-Diffusion Relations in a Medium Rosseland Diffusion Equation for Local Radiative Flux Emissive Power Jump Boundary Condition in the Limit without Heat Conduction Gray Stagnant Medium between Parallel Gray Walls Other Radiative Diffusion Solutions for Gray Media without Heat Conduction Approximations for Combined Radiation and Conduction Addition of Energy Transfer by Radiation and Conduction Diffusion Method for Combined Radiation and Conduction Approximate Solutions for Combined Radiation, Conduction, and Convection in a Boundary Layer Optically Thin Thermal Layer Optically Thick Thermal Layer Use of Mean Absorption Coefficients Definitions of Mean Absorption Coefficients Approximate Solutions of the Radiative Transfer Equations Using Mean Absorption Coefficients Curtis-Godson Approximation Homework Chapter 13 Solution of Radiative Transfer in Participating Media Introduction Differential Methods Milne-Eddington (Differential) Approximation General Spherical Harmonics (P N) Method Boundary Conditions for the P N Method P N Method for Radiation Combined with Heat Conduction Simplified P N (SP N) Method SP i Solution SP I Boundary Conditions Higher-Order Solutions SP 3 Solution Boundary Conditions for Higher-Order SP N Solutions Discrete Ordinates (S N) Method Two-Flux Method: The Schuster-Schwarzschild Approximation Radiative Transfer Equation with Discrete Ordinates Method Boundary Conditions for the Discrete Ordinates Method Control Volume Method for Discrete Ordinates Numerical Solution Relations for Two-Dimensional Rectangular Coordinates Relations for Three-Dimensional Rectangular Coordinates Results Using Discrete Ordinates

12 Contents xvii 13.4 Other Methods That Depend on Angular Discretization Discrete Transfer Method Finite Volume Method Boundary Element Method Numerical Solution Methods for Combined Radiation, Conduction, and Convection in Participating Media Finite-Difference Methods Energy Equation for Combined Radiation and Conduction Radiation and Conduction in a Plane Layer Radiation and Conduction in a Two-Dimensional Rectangular Region Finite-Element Method (FEM) FEM for Radiative Equilibrium (No Conduction and/or Convection) Radiation with Conduction and/or Convection Results from Finite-Element Analyses Zonal Method Exchange Area Relations Zonal Formulation for Radiative Equilibrium Developments for the Zonal Method Smoothing of Exchange Area Sets Other Formulations of the Zonal Method Numerical Results from Zone Method Monte Carlo Technique for Radiatively Participating Media Discussion of the Computational Method Monte Carlo Results for Radiation through Gray Gases Infinite Parallel Walls Cylindrical Geometry Consideration of Radiative Property Variations Parallel Processing and Other Computational Improvements Monte Carlo in Combined-Mode Problems Reverse Monte Carlo in Participating Media Numerical Boundary Conditions and Additional Solution Methods Boundary Condition for Numerical Solutions Exponential Kernel Approximation Reduction of the Integral Order YIX Method Additional Information on Numerical Methods Results for Combined Convection, Conduction, and Radiation Forced Convection Channel Flows Free Convection Flow, Heat Transfer, and Stability Radiative Transfer in Porous Media and Packed Beds Additional Topics with Combined Radiation, Conduction, and Convection Benchmark Solutions for Computational Validation Inverse Problems Involving Participating Media Solution Using Commercially Available and Other Codes Verification, Validation, and Uncertainty Quantification Homework

13 xviii Contents Chapter 14 Electromagnetic Wave Theory Introduction EM-Wave Equations Wave Propagation in a Medium EM-Wave Propagation in Perfect Dielectric Media Wave Propagation in Isotropic Media with Finite Electrical Conductivity Energy of an EM Wave Laws of Reflection and Refraction Reflection and Refraction at the Interface between Perfect Dielectrics (k 0) Reflection and Refraction at the Interface of an Absorbing Medium (k # 0) Amplitude and Scattering Matrices EM-Wave Theory and the Radiative Transfer Equation Homework Chapter 15 Absorption and Scattering by Particles and Agglomerates Introduction Absorption and Scattering: Definitions Background Absorption and Scattering Coefficients, Cross Sections, Efficiencies Scattering Phase Function Scattering by Large Spherical Particles Scattering by a Large Specularly Reflecting Sphere Reflection from a Large Diffuse Sphere Large Ideal Dielectric Sphere with n Diffraction from a Large Sphere Geometric Optics Approximation Scattering by Small Particles Rayleigh Scattering by Small Spheres Scattering Cross Section for Rayleigh Scattering Phase Function for Rayleigh Scattering Lorenz-Mie Theory for Spherical Particles Formulation for Homogeneous and Stratified Spherical Particles Cross Sections for Specific Cases Prediction of Properties for Irregularly Shaped Particles Integral and Differential Formulations T-matrix Approach Discrete Dipole Approximation Finite Element Method Finite Difference Time Domain Method Approximate Anisotropic Scattering Phase Functions Forward-Scattering Phase Function Linear-Anisotropic Phase Function Delta Eddington Phase Function Henyey Greenstein Phase Function

14 Contents xix 15.8 Dependent Absorption and Scattering Homework Chapter 16 Near-Field Thermal Radiation Introduction Electromagnetic Treatment of Thermal Radiation and Basic Concepts Near-Field Thermal Radiation versus Far-Field Thermal Radiation Electromagnetic Description of Thermal Radiation Near-Field Radiative Heat Flux Density of Electromagnetic States Spatial and Temporal Coherence of Thermal Radiation Evanescent and Surface Waves Evanescent Waves and Total Internal Reflection Surface Waves Near-Field Radiative Heat Flux Calculations Near-Field Radiative Heat Flux in One-Dimensional Layered Medium Near-Field Radiative Heat Transfer between Two Bulk Materials Separated by a Vacuum Gap Experimental Studies of Near-Field Thermal Radiation Historical Overview Experimental Determination of Near-Field Radiative Transfer Coefficient Near-Field Effects on Radiative Properties Concluding Remarks Homework Chapter 17 Radiative Effects in Translucent Solids, Windows, and Coatings Introduction Transmission, Absorption, and Reflection of Windows Single Partially Transmitting Layer with Thickness D» X (No Wave Interference Effects) Ray-Tracing Method Net-Radiation Method Multiple Parallel Windows Transmission through Multiple Parallel Glass Plates Interaction of Transmitting Plates with Absorbing Plate Enclosure Analysis with Partially Transparent Windows Effects of Coatings or Thin Films on Surfaces Coating without Wave Interference Effects Nonabsorbing Dielectric Coating on Nonabsorbing Dielectric Substrate Absorbing Coating on Metal Substrate Thin Film with Wave Interference Effects Nonabsorbing Dielectric Thin Film on Nonabsorbing Dielectric Substrate Absorbing Thin Film on a Metal Substrate Films with Partial Coherence

15 xx Contents 17.5 Refractive Index Effects on Radiation in a Participating Medium Effect of Refractive Index on Intensity Crossing an Interface Effect of Angle for Total Reflection Interface Conditions for Radiation Analysis in a Plane Layer Layer with Nondiffuse or Specular Surfaces Diffuse Surfaces Emission from a Translucent Layer (n > 1) at Uniform Temperature with Specular or Diffuse Boundaries Multiple Participating Layers with Heat Conduction Formulation for Multiple Participating Plane Layers Translucent Layer on a Metal Wall Composite of Two Translucent Layers Temperature Distribution Relations from Energy Equation Relations for Radiative Flux Equation for the Source Function Solution Procedure and Typical Results Light Pipes and Fiber Optics Homework 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 Appendix E: List of References Index