Lecture 26 Radiation

Lecture 26 Radiation - 1 MECE 4364 Heat Transfer Prof. Dong...

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MECE 4364 Heat Transfer Prof. Dong Liu Department of Mechanical Engineering University of Houston 1 Lecture 26 – Nov 18, 2010 Lecture 26 Radiation 2
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Lecture 26 ± Solid Angle measures how large an object appears to an observer looking from a point which is subtended by the object. ± A small object nearby may subtend the same solid angle as a larger object farther away ± Example: The eclipse!! Solid Angle 3 2 sin n dA r d d θθφ = 2 sin n dA dd d r ω == Lecture 26 Spectral Intensity ± Spectral radiation intensity, I λ ,e ( λ , θ , φ ) ± The rate at which radiant energy is emitted at the wavelength λ in the ( θ , φ ) direction ² per unit area of the emitting surface normal to this direction ² per unit solid angle about this direction ² per unit wavelength interval d λ about λ ± the rate at which emission from dA 1 passes through dA n ( )( ) ,1 ,, c o s e dq I dA d d λ λθφ θ ω λ = 4 Consider the rate at which emission from dA 1 passes through dA n where 1 cos n dA dA θ = This is how dA 1 appears along θ , φ Unit: W/m 2 -sr- μ m
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Lecture 26 ± The integration of the spectral heat flux is called the spectral, hemispherical emissive power ± spectral emission (heat flux) over all possible directions from a surface per unit wavelength ± The spectral radiation rate Radiation Heat Flux dq λ = dq d = I , e , θ , φ () cos dA 1 d ω 5 ± The spectra l radiation flux d q = dq d dA 1 = I , e , , cos d = I , e , , cos sin d d () ( ) 22 00 e qE I d d π λλ λθφ θ θ φ == ∫∫ / '' , ,, c o s s i n Lecture 26 ± The total heat flux from the surface due to radiation is emission over all wavelengths and directions Î total hemispherical emissive power ± If the emission is the same in all directions, then the surface is diffuse and the emission is isotropic Radiation Heat Flux q = E = I , e , , cos sin d d d 0 2 0 2 = E d 0 0 W m 2 q = E = I , e d cos sin d d 0 2 0 2 = I , e d 0 = I e 0 W m 2 6
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Lecture 26 Irradiation ± Irradiation ± Radiation incident on a surface is called irradiation ± Spectral Intensity, I λ ,i ( λ , θ , φ ) ± a quantity used to specify the incident radiant heat flux (W/m 2 ) within a unit solid angle about the direction of incidence (W/m 2 -sr) and within a unit wavelength interval about a prescribed wavelength (W/m 2 -sr- μ m) and the projected area of the receiving surface (dA 1 cos θ ) 7 Emitted radiation, I λ ,e v.s. Lecture 26 ± The integration of the spectral heat flux is called the spectral irradiation ± spectral irradiation (heat flux) over all possible directions ± The total heat flux to the surface due to irradiation over all wavelengths and directions Î total irradiative power ± If the incident radiation is diffusive, I λ ,I is independent of θ an φ Irradiation Heat Flux q λ = G () = I , i , θ , φ cos sin d d 0 π 2 0 2 W m 2 μ m q = G = I , i , , cos sin d d d 0 2 0 2 = G d 0 0 W m 2 8 0 i GGd I λπ ==
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Lecture 26
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Lecture 26 Radiation - 1 MECE 4364 Heat Transfer Prof. Dong...

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