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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [Fi [57 Lin 11 —— No * PgE [57 CHAPTER 8 Thermal Radiation MICHAEL F. MODEST College of Engineering Pennsylvania State University University Park, Pennsylvania 8.1 Fundamentals 8.1.1 Emissive power 8.1.2 Solid angles 8.1.3 Radiative intensity 8.1.4 Radiative heat flux 8.2 Radiative properties of solids and liquids 8.2.1 Radiative properties of metals Wavelength dependence Directional dependence Hemispherical properties Total properties Surface temperature effects 8.2.2 Radiative properties of nonconductors Wavelength dependence Directional dependence Temperature dependence 8.2.3 Effects of surface conditions Surface roughness Surface layers and oxide films 8.2.4 Semitransparent sheets 8.2.5 Summary 8.3 Radiative exchange between surfaces 8.3.1 View factors Direct integration Special methods View factor algebra Crossed-strings method 8.3.2 Radiative exchange between black surfaces 8.3.3 Radiative exchange between diffuse gray surfaces Convex surface exposed to large isothermal enclosure 8.3.4 Radiation shields 8.3.5 Radiative exchange between diffuse nongray surfaces Semigray approximation method Band approximation method 573
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574 THERMAL RADIATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [574 Lin -1. —— Nor * PgE [574 8.4 Radiative properties of participating media 8.4.1 Molecular gases 8.4.2 Particle clouds Soot Pulverized coal and fly ash dispersions Mixtures of molecular gases and particulates 8.5 Radiative exchange within participating media 8.5.1 Mean beam length method 8.5.2 Diffusion approximation 8.5.3 P-1 approximation 8.5.4 Other RTE solution methods 8.5.5 Weighted sum of gray gases 8.5.6 Other spectral models Nomenclature References 8.1 FUNDAMENTALS Radiative heat transfer or thermal radiation is the science of transferring energy in the form of electromagnetic waves. Unlike heat conduction, electromagnetic waves do not require a medium for their propagation. Therefore, because of their ability to travel across vacuum, thermal radiation becomes the dominant mode of heat trans- fer in low pressure (vacuum) and outer-space applications. Another distinguishing characteristic between conduction (and convection, if aided by flow) and thermal ra- diation is their temperature dependence. While conductive and convective fluxes are more or less linearly dependent on temperature differences, radiative heat fluxes tend to be proportional to differences in the fourth power of temperature (or even higher). For this reason, radiation tends to become the dominant mode of heat transfer in high-temperature applications, such as combustion (fires, furnaces, rocket nozzles), nuclear reactions (solar emission, nuclear weapons), and others.
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