Chapter 11 FUNDAMENTALS OF THERMAL RADIATION

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Chapter 11 Fundamentals of Thermal Radiation11-45 The variations of emissivity of two surfaces are given. The average emissivity, absorptivity, andreflectivity of each surface are to be determined at the given temperature.Analysis For the first surface:1T ( 3 m)(3000 K) = 9000 mK f 0890029 .1The average emissivity of this surface is(T) 1 f (1 f (0.2)(0.890029) (0.9)(1 0.890029) 0.281 21)The absorptivity and reflectivity are determined from Kirchhoff’s law 0.28(at 3000K) 1 1 10.28 0.72For the second surface:1T ( 3 m)(3000 K) = 9000 mK f 0890029 .The average emissivity of this surface is1 0.80.230.90.1, mThen,(T) 1 f (1 f (0.8)(0.890029) (0.1)(1 0.890029) 0.72 1 20.721 1 1 10.72 0.28)(at 3000K)Discussion The second surface is more suitable to serve as a solar absorber since its absorptivity for shortwavelength radiation (typical of radiation emitted by a high-temperature source such as the sun) is high,and its emissivity for long wavelength radiation (typical of emitted radiation from the absorber plate) islow.11-21
Chapter 11 Fundamentals of Thermal Radiation11-46 The variation of emissivity of a surface with wavelength is given. The average emissivity andabsorptivity of the surface are to be determined for two temperatures.Analysis (a) For T = 5800 K: T (5 m)(5800 K) = 29,000 mK f 099534 .1 1The average emissivity of this surface is(T ) f(1 f1 1 2 (0.2)(0.99534) (0.9)(1 0.99534) 0.203(b) For T = 300 K:1) 0.5 T (5 m)(300 K) =1500 mK f 0013754 .and1 1(T) f (0.2)(0.013754) (0.9)(1 0.013754) 0.89(1 f1 1 21)The absorptivities of this surface for radiation coming from sources at 5800 K and 300 K are, fromKirchhoff’s law, 0.203 (at 5800 K) 0.89 (at 300 K)0.25, m11-47 The variation of absorptivity of a surface with wavelength is given. The average absorptivity,reflectivity, and emissivity of the surface are to be determined at given temperatures.Analysis For T = 2500 K:1T ( 2 m)(2500 K) = 5000 mK f 0633747 .1The average absorptivity of this surface is(T ) f(1 f1 1 2 (0.2)(0.633747) (0.7)(1 0.633747) 0.38Then the reflectivity of this surface becomes 1 1 10. 38 0.621) 0.70.2Using Kirchhoff’s law, , the average emissivityof this surface at T = 3000 K is determined to beT ( 2m)(3000 K) = 6000 mK f 0.737818(T) 1 f (1 f1 21 (0.2)(0.737818) (0.7)(1 0.737818) 0.33)2, m11-22
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Chapter 11 FUNDAMENTALS OF THERMAL RADIATION

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