RADIATIVE HEAT TRANSFER

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1 RADIATIVE HEAT TRANSFER Second Edition Michael F. Modest The Pennsylvania State University ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo

2 Preface to the Second Edition List of Symbols xiv xvii 1 Fundamentals of Thermal Radiation Introduction The Nature of Thermal Radiation Basic Laws of Thermal Radiation Emissive Power SolidAngles Radiative Intensity Radiative Heat Flux Radiation Pressure Visible Radiation (Luminance) Introduction to Radiation Characteristics of Opaque Surfaces Introduction to Radiation Characteristics of Gases Introduction to Radiation Characteristics of Solids and Liquids Introduction to Radiation Characteristics of Particles Outline of Radiative Transport Theory 26 References 27 Problems 28 2 Radiative Property Predictions from Electromagnetic Wave Theory Introduction The Macroscopic Maxwell Equations Electromagnetic Wave Propagation in Unbounded Media Polarization Reflection and Transmission Theories for Optical Constants 57 References 60 Problems 60 vn

3 3 Radiative Properties of Real Surfaces Introduction Definitions Predictions from Electromagnetic Wave Theory Radiative Properties of Metals Radiative Properties of Nonconductors Effects of Surface Roughness Effects of Surface Damage and Oxide Films Radiative Properties of Semitransparent Sheets Special Surfaces Experimental Methods 107 References 121 Problems View Factors Introduction Definition of View Factors Methods for the Evaluation of View Factors Area Integration Contour Integration View Factor Algebra The Crossed-Strings Method The Inside-Sphere Method The Unit Sphere Method 156 References 158 Problems 15? 5 Radiative Exchange Between Gray, Diffuse Surfaces Introduction Radiative Exchange Between Black Surfaces Radiative Exchange Between Gray, Diffuse Surfaces Electrical Network Analogy Solution Methods for the Governing Integral Equations 17S References 185 Problems 19C 6 Radiative Exchange Between Partially-Specular Gray Surfaces Introduction Specular View Factors 20C 6.3 Enclosures with Partially-Specular Surfaces Electrical Network Analogy 2\t 6.5 Radiation Shields 21" 6.6 Semitransparent Sheets (Windows) 21S 6.7 Solution of the Governing Integral Equation Concluding Remarks 22f References 22( Problems 22"

4 ix 7 Radiative Exchange Between Nonideal Surfaces Introduction Radiative Exchange Between Nongray Surfaces Directionally Nonideal Surfaces Analysis for Arbitrary Surface Characteristics 246 References 247 Problems Surface Radiative Exchange in the Presence of Conduction and Convection Introduction Conduction and Surface Radiation Fins Convection and Surface Radiation 254 References 258 Problems The Equation of Radiative Transfer in Participating Media Introduction Radiative Intensity in Vacuum Attenuation by Absorption and Scattering Augmentation by Emission and Scattering The Equation of Transfer Formal Solution to the Equation of Transfer Boundary Conditions for the Equation of Transfer Radiation Energy Density Radiative Heat Flux Divergence of the Radiative Heat Flux Integral Formulation of the Equation of Transfer Overall Energy Conservation Solution Methods for the Equation of Transfer 282 References 284 Problems Radiative Properties of Molecular Gases Fundamental Principles Emission and Absorption Probabilities Atomic and Molecular Spectra Line Radiation Spectral Models for Radiative Transfer Calculations Narrow Band Models Narrow Band ^-Distributions Wide Band Models Total Emissivity and Mean Absorption Coefficient Experimental Methods 346 References 352 Problems 356

5 11 Radiative Properties of Particulate Media Introduction Absorption and Scattering from a Single Sphere Radiative Properties of a Particle Cloud Radiative Properties of Small Spheres (Rayleigh Scattering) Rayleigh-Gans Scattering Anomalous Diffraction Radiative Properties of Large Spheres Absorption and Scattering by Long Cylinders Approximate Scattering Phase Functions Experimental Determination of Radiative Properties of Particles 39C Radiation Properties of Combustion Particles 394 References 405 Problems 41C 12 Radiative Properties of Semitransparent Media Introduction Absorption by Semitransparent Solids Absorption by Semitransparent Liquids 41( 12.4 Experimental Methods 41? References 421 Problems 42: 13 Exact Solutions for One-Dimensional Gray Media 42: 13.1 Introduction 42: 13.2 General Formulation for a Plane-Parallel Medium 42^ 13.3 Radiative Equilibrium of a Nonscattering Medium 42i 13.4 Radiative Equilibrium of a Scattering Medium 43! 13.5 Plane Medium with Specified Temperature Field 43' 13.6 Radiative Transfer in Spherical Media 43( 13.7 Radiative Transfer in Cylindrical Media 44( 13.8 Numerical Solution of the Governing Integral Equations 44' References 44: Problems 44i 14 Approximate Solution Methods for One-Dimensional Media 44! 14.1 The Optically Thin Approximation 45' 14.2 The Optically Thick Approximation (Diffusion Approximation) The Schuster-Schwarzschild Approximation 45' 14.4 The Milne-Eddington Approximation (Moment Method) The Exponential Kernel Approximation 46 References 46 Problems The Method of Spherical Harmonics (/V-Approximation) 46: 15.1 Introduction Development of the General flv-approximation Boundary Conditions for the Pv-Method The Pi-Approximation 47

6 Xi 15.5 Pj- and Higher-Order Approximations Enhancements to the P\-Approximation 483 References 492 Problems The Method of Discrete Ordinates (5V-Approximation) Introduction General Relations The One-Dimensional Slab One-Dimensional Concentric Spheres and Cylinders Multidimensional Problems The Finite Volume Method Other Related Methods Concluding Remarks 530 References 530 Problems The Zonal Method Introduction Surface Exchange No Participating Medium Radiative Exchange in Gray Absorbing/Emitting Media Radiative Exchange in Gray Media with Isotropic Scattering Radiative Exchange through a Nongray Medium Determination of Direct Exchange Areas 561 References 561 Problems The Treatment of Collimated Irradiation Introduction Reduction of the Problem The Modified Pi-Approximation with Collimated Irradiation Short-Pulsed Collimated Irradiation with Transient Effects 574 References 577 Problems The Treatment of Nongray Extinction Coefficients Introduction The Mean Beam Length Method Semigray Approximations The Stepwise-Gray Model (Box Model) General Band Model Formulation The Weighted-Sum-of-Gray-Gases (WSGG) Model ^-Distribution Models The Full-Spectrum ^-Distribution (FSK) Method 617 References 637 Problems 641

7 Xii CONTENTS 20 The Monte Carlo Method for Thermal Radiation Introduction Numerical Quadrature by Monte Carlo Heat Transfer Relations for Radiative Exchange Between Surfaces Random Number Relations for Surface Exchange Surface Description Ray Tracing Heat Transfer Relations for Participating Media Random Number Relations for Participating Media Overall Energy Conservation Efficiency Considerations Backward Monte Carlo Example Problems 673 References 676 Problems Radiation Combined with Conduction and Convection Introduction Combined Radiation and Conduction Melting and Solidification with Internal Radiation Combined Radiation and Convection in Boundary Layers Combined Radiation and Free Convection Combined Radiation and Convection in Internal Flow Combined Radiation and Combustion Interfacing Between Turbulent Flow Fields and Radiation Interaction of Radiation with Turbulence 710 References 715 Problems Inverse Radiative Heat Transfer Introduction Solution Methods The Levenberg-Marquardt Method The Conjugate Gradient Method Inverse Surface Radiation Inverse Radiation in Participating Media 736 References 739 Problems 742 A Constants and Conversion Factors 743 B Tables for Radiative Properties of Opaque Surfaces 745 References 758 C Blackbody Emissive Power Table 759 D View Factor Catalogue 762 References 773

8 Xlii E Exponential Integral Functions 779 References 781 F Computer Codes 782 References 788 Acknowledgments 789 Author Index 792 Subject Index 808

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