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Thermal Radiation Fundamentals

ISBN:
1-56700-203-X (Print)

Thermal Radiation Fundamentals

K. G. Terry Hollands
Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada

Description

This new publication is intended primarily as the chief resource for a graduate course in thermal radiation heat transfer in engineering. The book should also be very useful for researchers and designers of heat transfer equipment. In contrast to existing books, the text takes a holistic view, treating radiation as a volumetric phenomenon, and then treating surface radiation as a special case.

A CD containing a popular engineering software package is included for the expeditious solving of radiation problems, and the smoothed-band model is introduced for handling gaseous exchange.



341 pages, © 2004


Table of Contents:

PREFACE
INTRODUCTION
SYMBOLS
UNITS AND FUNDAMENTAL CONSTANTS
1 NATURE OF THERMAL RADIATION
1.1 Dual Nature of Thermal Radiation
1.2 Thermal Radiation as EM Waves
1.3 Thermal Radiation as Photons
1.4 Relation between Two Interpretations
1.5 Concluding Remarks
1.6 Problems
2 SPECTRAL QUANTITIES, PHOTONIC EQUILIBRIUM
2.1 Spectral Quantities
2.2 Quantifying Thermal Radiation
2.2.1 Source of Thermal Radiation
2.2.2 Energy-Level Probability: The Boltzmann Factor
2.2.3 Transition Probabilities
2.3 Photonic Equilibrium: Planck's Radiation Law
2.3.1 Derivation
2.3.2 Rewriting in Terms of Wave Quantities
2.3.3 Radiation at the Interface: Emitted Radiation
2.4 Concluding Remarks
2.5 Problems
3 DIRECTIONAL QUANTITIES, NONEQUILIBRIUM
3.1 The Solid Angle
3.1.1 Motivation
3.1.2 Definition
3.1.3 Determination
3.2 Directional Quantities and Their Integrals
3.2.1 Directional Quantities
3.2.2 Solid-Angle Integration
3.3 Directional Net Production of Photons
3.3.1 Directional Transition Probabilities
3.3.2 Directional Photonic Equilibrium
3.3.3 Net Photon Generation
3.4 Concluding Remarks
3.5 Problems
4 INTENSITY AND THE RTE
4.1 Intensity
4.1.1 Definition
4.1.2 Relating Intensity to Directional Photon Density
4.1.3 Source Termin Terms of Intensity
4.2 RTE for Nonscattering Media
4.2.1 Derivation
4.2.2 Discussion
4.3 Solutions to the RTE in NSM
4.3.1 For Transparent Media
4.3.2 For Media with Uniform T, n, and αλ.
4.3.3 For Nonuniform Media
4.3.4 Classification of Bodies
4.4 Alternative Statements of the RTE
4.5 Concluding Remarks
4.6 Problems
5 INTEGRATION OVER DIRECTIONS AND AREA
5.1 Intensity Based on a Different Area
5.2 Radiant Heat Flux
5.2.1 Isotropic Radiant Field
5.3 Uniform Isotropic Sources
5.3.1 Point Form Factor
5.3.2 Gaseous Point Form Factor
5.3.3 Average Radiant Fluxes: The Form Factor
5.3.4 Gaseous Form-Factor Function
5.4 Alternative Derivation of the RTE
5.5 Concluding Remarks
5.6 Problems
6 INTEGRATION OVER WAVELENGTH
6.1 General Remarks
6.2 Integrals Over the Blackbody Functions
6.3 Products with Blackbody Functions
6.4 Integration Using Software Codes
6.5 Concluding Remarks
6.6 Problems
7 SCATTERING
7.1 Characterization of Scattering
7.2 Radiative Transfer Equation
7.3 Scattering Terminology and Models
7.3.1 Terminology
7.3.2 Some Phase Function Models
7.4 Sample Solution to the Complete RTE
7.5 Concluding Remarks
7.6 Problems
8 ROLE OF RADIATION IN THE ENERGY EQUATION
8.1 Spectral Integration of the Source Term
8.2 Reformulating the Energy Equation
8.3 Joint Solutions
8.4 Example of Radiative Source Calculations
8.5 Radiant Flux Vector and Its Divergence
8.6 Concluding Remarks
8.7 Problems
9 ELECTROMAGNETIC WAVE THEORY
9.1 Maxwell's Equations
9.2 Solutions
9.2.1 Dielectric Medium
9.2.2 Electrically Conducting Medium
9.3 Polarization
9.4 Importance of n and κ.
9.5 Concluding Remarks
9.6 Problems
10 WAVES AT INTERFACES AND PARTICLES
10.1 General Behavior at Smooth Interfaces
10.2 Special Cases
10.2.1 Medium 1 and Medium 2 are Both Dielectrics
10.2.2 Some Aspects of the General Case
10.2.3 Medium 1 is Free Space or a Gas
10.3 EM Theory Applied to Scattering
10.3.1 Rayleigh Scattering
10.4 Concluding Remarks
10.5 Problems
11 OPAQUE SMOOTH SURFACES
11.1 Definition of the Opaque Surface
11.2 Emitted Intensity
11.3 Emissivity and Absorptivity
11.4 Reflected Intensity
11.5 Entire Intensity
11.5.1 Blackbody Surface
11.6 Behavior of ε'λ (θ) for Metals and Dielectrics
11.7 Hemispherical and Total Emission
11.8 Concluding Remarks
11.9 Problems
12 OPAQUE ROUGH SURFACES
12.1 Representative Area
12.2 Emitted Intensity
12.2.1 Reciprocity Considerations
12.2.2 Hemispheric and Total Emission
12.2.3 EmissivityModels
12.3 Reflected Intensity
12.3.1 Bidirectional Reflectivity
12.3.2 Diffusely Reflecting and Specular Surface Models
12.3.3 Reciprocity
12.3.4 Directional-Hemispheric and Hemispheric Reflectivities
12.4 Entire Intensity
12.5 Some Total Energy Considerations
12.6 Concluding Remarks
12.7 Problems
13 PHYSICS OF ROUGH, COMPOSITE SURFACES
13.1 Single-Material Surfaces
13.1.1 Effect of Roughening
13.1.2 Opaque Asperities
13.1.3 Transparent or Partly Transparent Asperities
13.1.4 Wavelength-Dependent Asperities
13.2 Composite Materials
13.2.1 Smooth Films on Smooth Substrates
13.2.2 Paints
13.3 Real SurfaceModels and Spectral Integration
13.3.1 Sources of Data
13.3.2 Data Reduction
13.3.3 Example Problems
13.4 Concluding Remarks
13.5 Problems
14 INTRODUCTION TO THE ENCLOSURE PROBLEM
14.1 Formulation of the Enclosure Problem
14.1.1 Integral Equations
14.1.2 Problem Statement
14.1.3 Terminology
14.1.4 Derivation of Integral Equation
14.1.5 Surface Heat Flux
14.1.6 Surface Heat Flow and Gaseous Heat Flow
14.2 Isothermal Enclosures
14.3 Black-Walled Transparent Enclosure
14.4 Concluding Remarks
14.5 Problems
15 FORM FACTORS AND THEIR EVALUATION
15.1 Interpretation of Form Factors
15.2 Properties of Form Factors
15.3 Self Form Factors
15.4 Net Number of Form Factors
15.4.1 Formula Giving Net Number
15.4.2 Example Problem
15.4.3 Use of Symmetry
15.5 Two-Dimensional Enclosures
15.5.1 Further Example Problems
15.6 Concluding Remarks
15.7 Problems
16 TADD ENCLOSURES AND LUMPED AREAS
16.1 Formulation of the Problem
16.2 The Lumped-Area Approximation
16.2.1 Formulation
16.2.2 Use of Matrices
16.2.3 Example Problem
16.2.4 Exchange Factors
16.2.5 Example Problems
16.3 Gray-Surfaced Enclosures
16.3.1 Example Problems
16.3.2 Discussion
16.4 Concluding Remarks
16.5 Problems
17 MIXED-MODE, NODAL ANALYSIS
17.1 Formulation
17.2 Example Problem
17.3 Radiant Heat Transfer Coefficient
17.4 Nongray Enclosures
17.4.1 Example Problem
17.5 Prescribed Heat Flux, Gray Surfaces
17.5.1 Formulation
17.5.2 Example Problems
17.6 Concluding Remarks
17.7 Problems
18 SPECULAR TRANSPARENT ENCLOSURES
18.1 Enclosures with One Specular Surface
18.1.1 Evaluation of Specular Form Factors
18.2 Two or More Specular Surfaces
18.2.1 Two Specular Surfaces
18.2.2 More Than Two Specular Surfaces
18.3 Matrix Representation of the Solution
18.3.1 Example Problem
18.4 Nongray Specular Enclosures
18.5 Concluding Remarks
18.6 Problems
19 INFINITESIMAL-AREA ANALYSIS
19.1 Introduction
19.2 Formulation
19.2.1 Assumptions and Terminology
19.2.2 Integral Equations
19.2.3 Reduction to a Single Integral Equation
19.2.4 Generalized Enclosure Representation
19.3 Solving the Integral Equation Numerically
19.4 Infinitesimal-Area Exchange Factors
19.5 Published Solutions
19.6 Errors in the Lumped-Area Method
19.7 Single-Variable Enclosures
19.7.1 The Axi-invariant Enclosure
19.8 One Gray Surface and the Rest Black
19.8.1 Example Problem
19.9 Concluding Remarks
19.10 Problems
20 PROPERTIES OF GASES I: BASICS
20.1 Introduction
20.2 The Emission-Absorption Line
20.2.1 Line-Broadening
20.2.2 Combinations of Broadened Lines
20.3 Vibration-Rotation Bands
20.3.1 Structure
20.3.2 Explanation
20.4 Symmetric Molecules and Transparency
20.5 Concluding Remarks
20.6 Problems
21 PROPERTIES OF GASES II: BAND MODELS
21.1 Statistical Narrow-Band Model
21.2 Exponential Wide-Band Model
21.3 Smoothed or Reordered Band Model
21.4 Evaluation of Model Parameters
21.4.1 Evaluation of S0/δ
21.4.2 Evaluation of β
21.4.3 Evaluation of ω
21.5 Example Problem
21.6 Combining Bands
21.7 Example Problem
21.8 Concluding Remarks
21.9 Problems
22 ENCLOSURES WITH AN ISOTHERMAL GAS
22.1 Formulation of Solution
22.1.1 General Principals
22.1.2 Matrix Formulation
22.2 Implementation
22.2.1 Approximating the Gaseous Form-Factor Function
22.2.2 Example Problem
22.2.3 Methods With Greater Precision
22.2.4 Example Problem
22.3 Special Cases
22.3.1 Single-Surface Enclosure
22.3.2 Enclosure with all Black Surfaces
22.3.3 Example Problem
22.4 k-Distribution and WSGG
22.5 Gases Containing Soot Particles
22.6 Concluding Remarks
22.7 Problems
23 GRAY, STATIONARY, NONISOTHERMAL MEDIA
23.1 Radiative Equilibrium
23.1.1 Definition
23.1.2 Plane-Layer Enclosure Having Black Walls
23.1.3 Plane-Layer Enclosure Having Gray Walls
23.2 Radiation with Conduction in Plane Layers
23.3 Radiative Diffusion Approximation
23.3.1 Derivation of the Differential Equation
23.3.2 Boundary Conditions
23.3.3 Solution
23.3.4 Extension to Conductive Media
23.4 Some Isotropic-Scattering Solutions
23.5 Concluding Remarks
23.6 Problems
A Parametric Representation of Surfaces
A.1 Introduction
A.2 Catalog of Surface Representations
A.3 Application to Radiant Analysis
A.3.1 Solid Angle Evaluation
A.3.2 Point Form-Factor Evaluation
A.3.3 Gaseous Point Form-Factor Evaluation
A.3.4 Form-Factor Evaluation
A.3.5 Gaseous Form-Factor Evaluation
A.4 Representing an Entire Enclosure
B Properties of Sample Surfaces
C Some Form-Factor Formulas
C.1 Point Form Factors
C.2 Form Factors
References, Bibliography, and Further Reading