Energy Transfers by Radiation

351 Pages·2019·10.155 MB·English

by  Benallou, Abdelhanine

Energy Transfers by Radiation

Energy Engineering Set
coordinated by
Abdelhanine Benallou
Volume 4
Energy Transfers
by Radiation

Abdelhanine Benallou
First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-277-9
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
vi Energy Transfers by Radiation
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
Contents vii
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
viii Energy Transfers by Radiation
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