Inside industrial furnaces and combustion chambers, energy is essentially exchanged by radiation. It is through the same mechanism that the energy emitted by the Sun spreads through different media to reach the Earth.
Developing a sound understanding of the laws underlying energy exchanges by radiation is therefore essential, not only for establishing design equations for industrial equipment, but also for an optimal harvesting of solar energy and a better understanding of climate change phenomena such as the greenhouse effect.
Energy Transfers by Radiation establishes the basic laws and equations which support the quantification of energy fluxes transferred between surfaces for situations similar to those usually encountered in industrial processes or in solar energy applications.
Table of Contents
Preface xi
Introduction xiii
Chapter 1. Origin of Radiation 1
1.1. Introduction 1
1.2. The Niels Bohr model. 2
1.2.1. Illustration: excitation of the neon atom 3
1.2.2. Illustration: mercury vapor lamps 5
1.3. Nature of the radiating energy 7
1.3.1. Reminders regarding the characterization of electromagnetic waves 7
1.3.2. Electromagnetic spectrum and position of thermal radiation 8
Chapter 2. Magnitudes Used in Radiation 11
2.1. Introduction 11
2.2. Monochromatic, total, directional and hemispherical magnitudes 11
2.3. Absorption, reflection and transmission 13
2.3.1. Opaque materials 14
2.3.2. Transparent materials 14
2.4. Total intensity of a source in one direction 15
2.5. Total luminance of a source in one direction 15
2.6. Illuminance of a receiving surface 16
2.7. Examples of monochromatic magnitudes and explanation of the greenhouse effect 16
2.7.1. Terrestrial greenhouse effect, transmissivity of atmosphere is incriminated 18
2.7.2. The terrestrial greenhouse effect, a natural temperature controller 19
2.7.3. The terrestrial greenhouse effect, both an asset and a risk 19
2.8. Relations between magnitudes 20
2.8.1. Illuminance and luminance 20
2.8.2. Lambert’s law 21
2.8.3. Emittance and luminance in the case of isotropic emissions 22
Chapter 3. Analysis of Radiative Energy Transfers: Black-body Radiation 25
3.1. Introduction 25
3.2. Definition of a black body 25
3.3. Physical creation of the black body 26
3.4. Black-body radiation 27
3.4.1. Planck’s law 27
3.4.2. Stefan-Boltzmann law 28
3.4.3. Illustration: calculating the energy emitted by a black surface 29
3.4.4. Wien laws 30
3.4.5. Illustration: emittance as a function of wavelength 31
3.4.6. Evaluating emittance in a given wavelength band 33
3.4.7. Illustration: calculating the energy radiated in the infrared 34
3.4.8. Useful spectrum 35
3.4.9. Illustration: determining a useful spectrum 36
Chapter 4. Radiant Properties of Real Surfaces 39
4.1. Introduction 39
4.2. Emissivity of a real surface 39
4.2.1. Total emissivity 40
4.2.2. Monochromatic emissivity 40
4.2.3. Emissivity data 41
4.3. Gray body 43
4.3.1. Density of flux emitted by a gray body 43
4.3.2. Illustration: calculating the energy emitted by an electric heater 43
4.4. Effective temperature of a real surface 44
4.4.1. Calculating the effective temperature of a real surface 44
4.4.2. Illustration: calculating the effective temperature of a gray surface 45
4.5. Luminance of a real surface 45
4.6. Kirchhoff’s law 46
4.6.1. Consequences for gray bodies 46
4.6.2. Consequences for black bodies 46
4.6.3. Illustration: simple radiation balances 46
Chapter 5. Radiation Balances between Real Surfaces Separated by a Transparent Medium 49
5.1. Introduction 49
5.2. The angle factor 50
5.3. Expressing the shape factor 51
5.4. Relations between shape factors 53
5.4.1. Reciprocity relations 53
5.4.2. Transfer function 54
5.4.3. Angle factors for convex or concave surfaces 54
5.4.4. Property of the sum of the shape factors 55
5.5. Reducing the number of shape factors to be calculated 55
5.5.1. Reducing using symmetry 56
5.5.2. Illustration: shape factors between the surfaces of a cylinder 57
5.5.3. Illustration: shape factors of the surfaces forming a cube 59
5.5.4. Illustration: using relations between shape factors 61
5.6. Superposition principle 64
5.6.1. Illustration: shape factors of complementary surfaces 65
5.7. Crossed-string method: very long surfaces 66
Chapter 6. Practical Determination of Shape Factors 69
6.1. Introduction 69
6.2. Methods of practical determination of shape factors 69
6.2.1. Surfaces under total influence 70
6.2.2. Illustration: angle factors for concentric spheres 71
6.2.3. Illustration: infinite coaxial cylinders 71
6.2.4. Illustration: shape factors for a half-sphere covering a disc 71
6.2.5. Illustration: half-cylinder covering a rectangular plane 72
6.3. Shape factors for standard geometric configurations 73
6.3.1. Configuration 1: equal area parallel planes, centered on an axis 73
6.3.2. Configuration 2: two infinite parallel planes of the same width and with the same axis 74
6.3.3. Configuration 3: two infinite parallel planes of different widths but with the same axis 74
6.3.4. Configuration 4: two rectangular perpendicular planes with a side in common 75
6.3.5. Configuration 5: two planes of the same dimensions, with a side in common 76
6.3.6. Configuration 6: two planes of different dimensions, with a side in common 76
6.3.7. Configuration 7: two perpendicular rectangles 77
6.3.8. Configuration 8: two parallel, off-center rectangles of arbitrary dimensions 78
6.3.9. Configuration 9: linear strip whose plane is parallel to a rectangle 79
6.3.10. Configuration 10: narrow linear strip whose plane is perpendicular to a rectangle 80
6.3.11. Configuration 11: narrow linear source whose plane intersects a rectangular plane with an angle θ 81
6.3.12. Configuration 12: elementary surface placed on the normal to a plane 82
6.3.13. Configuration 13: elementary surface placed on a plane perpendicular to a rectangle 83
6.3.14. Configuration 14: two parallel discs with the same axis 84
6.3.15. Configuration 15: elementary source placed on the normal of a disc 84
6.3.16. Configuration 16: two infinite cylinders with parallel axes 85
6.3.17. Configuration 17: two infinite coaxial cylinders 85
6.3.18. Configuration 18: finite coaxial cylinders 86
6.3.19. Configuration 19: elementary source of arbitrary length, parallel to an infinite cylinder 87
6.3.20. Configuration 20: spherical point source and sphere of radius R 88
6.3.21. Configuration 21: elementary plane and sphere of radius R 88
6.3.22. Configuration 22: elementary plane whose tangent passes through the center of a sphere 89
6.3.23. Configuration 23: sphere and disc with the same axis 89
6.3.24. Configuration 24: prism of infinite length and triangular cross-sectional area 90
6.3.25. Illustration: calculating the angle factors of two planes intersecting at 45° 91
6.3.26. Illustration: calculating the angle factors of parallel discs 92
6.3.27. Illustration: parallel planes, with the same axis and surface area 93
6.3.28. Illustration: calculating the angle factor for two perpendicular, rectangular planes with a side in common 94
6.3.29. Illustration: development of charts for inclined planes of different dimensions 96
Chapter 7. Balances of Radiative Energy Transfers between Black Surfaces 99
7.1. Introduction 99
7.2. Establishing balance equations 100
7.3. Solving radiation balances for black surfaces 101
7.3.1. Surfaces with imposed fluxes 102
7.3.2. Surfaces at imposed temperatures 102
7.3.3. Case where certain fluxes and certain temperatures are imposed 102
7.3.4. Illustration: radiation transfers in a baking oven 102
7.3.5. Illustration: design of an industrial furnace with imposed temperatures 110
Chapter 8. Balances on Radiative Energy Transfers between Gray Surfaces 119
8.1. Introduction 119
8.2. Reminder of the radiative properties of real surfaces 119
8.3. Radiosity 120
8.4. Balances on gray surfaces 121
8.4.1. Establishing the balance on Si 121
8.4.2. Simplifying the balance equation 123
8.5. Solving the radiation balance equations between gray surfaces 123
8.5.1. Surfaces with imposed fluxes 124
8.5.2. Surfaces at imposed temperatures 125
8.5.3. Scenario where certain fluxes and certain temperatures are imposed 126
8.5.4. Illustration: industrial furnace with gray adiabatic walls 128
Chapter 9. Electrical Analogies in Radiation 135
9.1. Introduction 135
9.2. Analogies for black surfaces 135
9.2.1. Electrical analog representing emittances 136
9.2.2. Electrical analog representing temperatures 137
9.2.3. Electrical analog representing the flux density 137
9.2.4. Illustration: calculating the flux density by electrical analogy 138
9.3. Electrical analogies for heat transfer between gray surfaces 139
9.3.1. Electrical analog representing radiosities 139
9.3.2. Electrical analogy representing temperatures 140
9.3.3. Illustration: determining net fluxes in an industrial furnace 142
9.4. Gray shape factor 145
9.5. Illustration: gray shape factor of the industrial furnace with adiabatic walls 146
Chapter 10. Reduction of Radiating Energy Transfers through Filtering 153
10.1. Introduction 153
10.2. Expressing the flux density for a filterless transfer 154
10.3. Reducing the flux through filtering 156
10.4. Comparing q0 and qm 158
10.5. Scenario where plates S0 and Sn have the same emissivity 159
10.5.1. Situation without filter (m = 0) 159
10.5.2. Situation with m filters (m ≠ 0) with emissivities equal to ε 159
10.5.3. Illustration: reducing radiative energy transfers through filtration 160
Chapter 11. Radiative Energy Transfers in Semi-transparent Media 163
11.1. Introduction 163
11.2. Radiation in semi-transparent gases 164
11.2.1. Beer’s law 165
11.2.2. Alternative expression of Beer’s law 166
11.2.3. Transmissivity of semi-transparent gases 167
11.2.4. Transmission of energy between surfaces separated by a semi-transparent medium 167
11.2.5. Spectral absorptivity of a semi-transparent gas 170
11.2.6. Spectral emissivity of a semi-transparent gas 171
11.2.7. Practical determination of parameters and radiative fluxes of semi-transparent gases 171
11.2.8. Radiative behavior of an optically thick gas 172
11.3. Illustration: calculating the flux radiated by combustion gases 173
11.4. Reading: discovery of the Stefan-Boltzmann law 174
Chapter 12. Exercises and Solutions 179
Appendix 247
References 309
Index 323
