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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 Fall '12
 DrMuzychka
 Heat Transfer, λ, Air India, fij, GλGref, Radia%on00

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