Energy Transfers by Radiation

Abdelhanine Benallou has diverse experience in engineering education. He has also managed several companies in solar energy and energy efficiency. He has served as president of the International Solar Energy Network and as a member of the board of the World Energy Efficiency Association

• Preface xiIntroduction xiiiChapter 1. Origin of Radiation 11.1. Introduction 11.2. The Niels Bohr model. 21.2.1. Illustration: excitation of the neon atom 31.2.2. Illustration: mercury vapor lamps 51.3. Nature of the radiating energy 71.3.1. Reminders regarding the characterization of electromagnetic waves 71.3.2. Electromagnetic spectrum and position of thermal radiation 8Chapter 2. Magnitudes Used in Radiation 112.1. Introduction 112.2. Monochromatic, total, directional and hemispherical magnitudes 112.3. Absorption, reflection and transmission 132.3.1. Opaque materials 142.3.2. Transparent materials 142.4. Total intensity of a source in one direction 152.5. Total luminance of a source in one direction 152.6. Illuminance of a receiving surface 162.7. Examples of monochromatic magnitudes and explanation of the greenhouse effect 162.7.1. Terrestrial greenhouse effect, transmissivity of atmosphere is incriminated 182.7.2. The terrestrial greenhouse effect, a natural temperature controller 192.7.3. The terrestrial greenhouse effect, both an asset and a risk 192.8. Relations between magnitudes 202.8.1. Illuminance and luminance 202.8.2. Lambert’s law 212.8.3. Emittance and luminance in the case of isotropic emissions 22Chapter 3. Analysis of Radiative Energy Transfers: Black-body Radiation 253.1. Introduction 253.2. Definition of a black body 253.3. Physical creation of the black body 263.4. Black-body radiation 273.4.1. Planck’s law 273.4.2. Stefan-Boltzmann law 283.4.3. Illustration: calculating the energy emitted by a black surface 293.4.4. Wien laws 303.4.5. Illustration: emittance as a function of wavelength 313.4.6. Evaluating emittance in a given wavelength band 333.4.7. Illustration: calculating the energy radiated in the infrared 343.4.8. Useful spectrum 353.4.9. Illustration: determining a useful spectrum 36Chapter 4. Radiant Properties of Real Surfaces 394.1. Introduction 394.2. Emissivity of a real surface 394.2.1. Total emissivity 404.2.2. Monochromatic emissivity 404.2.3. Emissivity data 414.3. Gray body 434.3.1. Density of flux emitted by a gray body 434.3.2. Illustration: calculating the energy emitted by an electric heater 434.4. Effective temperature of a real surface 444.4.1. Calculating the effective temperature of a real surface 444.4.2. Illustration: calculating the effective temperature of a gray surface 454.5. Luminance of a real surface 454.6. Kirchhoff’s law 464.6.1. Consequences for gray bodies 464.6.2. Consequences for black bodies 464.6.3. Illustration: simple radiation balances 46Chapter 5. Radiation Balances between Real Surfaces Separated by a Transparent Medium 495.1. Introduction 495.2. The angle factor 505.3. Expressing the shape factor 515.4. Relations between shape factors 535.4.1. Reciprocity relations 535.4.2. Transfer function 545.4.3. Angle factors for convex or concave surfaces 545.4.4. Property of the sum of the shape factors 555.5. Reducing the number of shape factors to be calculated 555.5.1. Reducing using symmetry 565.5.2. Illustration: shape factors between the surfaces of a cylinder 575.5.3. Illustration: shape factors of the surfaces forming a cube 595.5.4. Illustration: using relations between shape factors 615.6. Superposition principle 645.6.1. Illustration: shape factors of complementary surfaces 655.7. Crossed-string method: very long surfaces 66Chapter 6. Practical Determination of Shape Factors 696.1. Introduction 696.2. Methods of practical determination of shape factors 696.2.1. Surfaces under total influence 706.2.2. Illustration: angle factors for concentric spheres 716.2.3. Illustration: infinite coaxial cylinders 716.2.4. Illustration: shape factors for a half-sphere covering a disc 716.2.5. Illustration: half-cylinder covering a rectangular plane 726.3. Shape factors for standard geometric configurations 736.3.1. Configuration 1: equal area parallel planes, centered on an axis 736.3.2. Configuration 2: two infinite parallel planes of the same width and with the same axis 746.3.3. Configuration 3: two infinite parallel planes of different widths but with the same axis 746.3.4. Configuration 4: two rectangular perpendicular planes with a side in common 756.3.5. Configuration 5: two planes of the same dimensions, with a side in common 766.3.6. Configuration 6: two planes of different dimensions, with a side in common 766.3.7. Configuration 7: two perpendicular rectangles 776.3.8. Configuration 8: two parallel, off-center rectangles of arbitrary dimensions 786.3.9. Configuration 9: linear strip whose plane is parallel to a rectangle 796.3.10. Configuration 10: narrow linear strip whose plane is perpendicular to a rectangle 806.3.11. Configuration 11: narrow linear source whose plane intersects a rectangular plane with an angle θ 816.3.12. Configuration 12: elementary surface placed on the normal to a plane 826.3.13. Configuration 13: elementary surface placed on a plane perpendicular to a rectangle 836.3.14. Configuration 14: two parallel discs with the same axis 846.3.15. Configuration 15: elementary source placed on the normal of a disc 846.3.16. Configuration 16: two infinite cylinders with parallel axes 856.3.17. Configuration 17: two infinite coaxial cylinders 856.3.18. Configuration 18: finite coaxial cylinders 866.3.19. Configuration 19: elementary source of arbitrary length, parallel to an infinite cylinder 876.3.20. Configuration 20: spherical point source and sphere of radius R 886.3.21. Configuration 21: elementary plane and sphere of radius R 886.3.22. Configuration 22: elementary plane whose tangent passes through the center of a sphere 896.3.23. Configuration 23: sphere and disc with the same axis 896.3.24. Configuration 24: prism of infinite length and triangular cross-sectional area 906.3.25. Illustration: calculating the angle factors of two planes intersecting at 45° 916.3.26. Illustration: calculating the angle factors of parallel discs 926.3.27. Illustration: parallel planes, with the same axis and surface area 936.3.28. Illustration: calculating the angle factor for two perpendicular, rectangular planes with a side in common 946.3.29. Illustration: development of charts for inclined planes of different dimensions 96Chapter 7. Balances of Radiative Energy Transfers between Black Surfaces 997.1. Introduction 997.2. Establishing balance equations 1007.3. Solving radiation balances for black surfaces 1017.3.1. Surfaces with imposed fluxes 1027.3.2. Surfaces at imposed temperatures 1027.3.3. Case where certain fluxes and certain temperatures are imposed 1027.3.4. Illustration: radiation transfers in a baking oven 1027.3.5. Illustration: design of an industrial furnace with imposed temperatures 110Chapter 8. Balances on Radiative Energy Transfers between Gray Surfaces 1198.1. Introduction 1198.2. Reminder of the radiative properties of real surfaces 1198.3. Radiosity 1208.4. Balances on gray surfaces 1218.4.1. Establishing the balance on Si 1218.4.2. Simplifying the balance equation 1238.5. Solving the radiation balance equations between gray surfaces 1238.5.1. Surfaces with imposed fluxes 1248.5.2. Surfaces at imposed temperatures 1258.5.3. Scenario where certain fluxes and certain temperatures are imposed 1268.5.4. Illustration: industrial furnace with gray adiabatic walls 128Chapter 9. Electrical Analogies in Radiation 1359.1. Introduction 1359.2. Analogies for black surfaces 1359.2.1. Electrical analog representing emittances 1369.2.2. Electrical analog representing temperatures 1379.2.3. Electrical analog representing the flux density 1379.2.4. Illustration: calculating the flux density by electrical analogy 1389.3. Electrical analogies for heat transfer between gray surfaces 1399.3.1. Electrical analog representing radiosities 1399.3.2. Electrical analogy representing temperatures 1409.3.3. Illustration: determining net fluxes in an industrial furnace 1429.4. Gray shape factor 1459.5. Illustration: gray shape factor of the industrial furnace with adiabatic walls 146Chapter 10. Reduction of Radiating Energy Transfers through Filtering 15310.1. Introduction 15310.2. Expressing the flux density for a filterless transfer 15410.3. Reducing the flux through filtering 15610.4. Comparing q0 and qm 15810.5. Scenario where plates S0 and Sn have the same emissivity 15910.5.1. Situation without filter (m = 0) 15910.5.2. Situation with m filters (m ≠ 0) with emissivities equal to ε 15910.5.3. Illustration: reducing radiative energy transfers through filtration 160Chapter 11. Radiative Energy Transfers in Semi-transparent Media 16311.1. Introduction 16311.2. Radiation in semi-transparent gases 16411.2.1. Beer’s law 16511.2.2. Alternative expression of Beer’s law 16611.2.3. Transmissivity of semi-transparent gases 16711.2.4. Transmission of energy between surfaces separated by a semi-transparent medium 16711.2.5. Spectral absorptivity of a semi-transparent gas 17011.2.6. Spectral emissivity of a semi-transparent gas 17111.2.7. Practical determination of parameters and radiative fluxes of semi-transparent gases 17111.2.8. Radiative behavior of an optically thick gas 17211.3. Illustration: calculating the flux radiated by combustion gases 17311.4. Reading: discovery of the Stefan-Boltzmann law 174Chapter 12. Exercises and Solutions 179Appendix 247References 309Index 323