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Although radiaon emiced by a blackbody is a funcon of

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Unformatted text preview: problems we assume that surfaces behave in a diffuse manner. 7 Radia%on Heat Transfer •  Blackbody Radia%on: we now consider the special case of a blackbody. A blackbody is defined as: –  A body which absorbs all incident radia%on regardless of wavelength and direc%on •  For a prescribed temperature and wavelength, no surface can emit more energy than a black body. •  Although radia%on emiCed by a blackbody is a func%on of temperature and wavelength, it is independent of direc%on, i.e. a diffuse emiCer. 8 Radia%on Heat Transfer •  The emissive power of a blackbody is defined using Planck’s spectral distribu%on: C1 E λ ,b ( λ, T ) = 5 λ [exp(C2 / λT ) − 1] € 2 C1 = 2πhc o = 3.742 × 10 8 W ⋅ µm / m 2 and C2 = hc o / kB = 1.439 × 10 4 µm⋅ K •  h = 6.26 x 10 ­34 Js and kB = 1.381 x 10 ­23 J/K are the Planck and Boltzmann constants, € respec%vely. co is the speed of light in a vacuum. 9 Radia%on Heat Transfer •  Spectral Emissive Power 10 Radia%on Heat Transfer •  General Observa%ons: –  Emission varies con%nuously with wavelength –  At any wavelength, as T increases, the emissive power increases –  The peak emission is shieed to the lee (shorter wavelengths) as T increases. •  Wien’s Displacement Law –  Defines the locus of maximum emission λmax T = 2898 µm⋅ K •  Note that temperature is in absolute [K] and wavelength in µm. Don’t Forget!!!!! € 11 Radia%on Heat Transfer •  Stefan ­Boltzmann Law –  If we integrate the spectral distribu%on over the en%re bandwidth, we obtain the total emissive power of a blackbody [W/m2]: ∞ Eb = ∫ 0 C1dλ = σT 4 λ5 [exp(C2 / λT ) − 1] •  The constant σ = 5.67 x 10 ­8 W/m2K4 is the € Stefan ­Boltzmann constant. •  The above integra%on is...
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