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(33) Radiation Fundamentals 2

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    FUNDAMENTALS (2)

    Prabal Talukdarssoc a e ro essor

    Department of Mechanical Engineering

    E-mail: [email protected]

    MECH/IITD

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    Irradiation Intensity of incident radiation: It

    which radiant energy ofwavelength is incident from

    e , rec on, per un areaof the intercepting surfacenormal to the direction er unitsolid angle about this direction,and per unit wavelength

    Radiation incident from all

    MECH/IITD

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    Irradiation S ectral irradiation G =

    2/2

    ddsincos,,I

    Total irradiation

    0

    ,

    0

    2m/WdGG

    =0

    MECH/IITD

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    Radiosit

    leaving a surface Emitted and reflected part

    2/2

    dddsincosIJ

    =

    re

    0

    ,

    00

    I +=

    For a surface which is diffuse emitter

    and diffuse reflector

    MECH/IITD

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    Spectral Quantities

    Integration of a

    spectral quantity for

    the total quantity.

    MECH/IITD

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    Blackbod Radiation

    ,

    regardless of wavelength and direction

    wavelength, no surface can emit more

    Although the radiation emitted by a

    ac o y s a unc on o wave eng antemperature, it is independent of direction.

    MECH/IITD

    a s ac o y s a use em er

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    Characteristics of an isothermal

    Complete absorption Diffuse irradiation

    For an interior surfaces

    MECH/IITD

    Diffuse emission from an aperture

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    Planck Distribution

    given by Planck ashc2 20

    = -34

    ]1)kT/hc[exp(,

    0

    5b, =

    , . .

    Boltzmann constants k = 1.3805x10-23 J/K

    speed of light in vacuum c0=2.998x108 m/s

    CTITE 1==

    MECH/IITD

    ]1)T/C[exp( 2,,

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    Planck Distribution

    with wavelengthAt any wavelength the magnitude of the

    emitted radiation increases

    with increasing temperature

    A significant fraction of the radiation emitted

    by the sun, which may be

    approximated as a blackbody at 5800K, is

    in the visible region of the spectrum.

    In contrast, for T

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    Wiens Displacement LawC1==

    Differentiating the above equation with respect to and

    ]1)T/C[exp(,,

    2

    5,,

    setting the result equal to zero, we get

    maxT = 2897.8 m.K

    ,

    power is displaced to shorter wavelengths with increasing

    temperature

    The emission is in the middle of the visible spectrum ( =0.5 m) for solar radiation, since the sun emits

    MECH/IITD

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    Stefan-Boltzmann LawC

    )T,(E5

    1b,

    =

    Total Emissive power

    2

    0 2

    5

    1b d

    ]1)T/C[exp(

    E

    =

    -

    b TE =

    .Since this emission is diffuse, the total intensity

    MECH/IITD

    b b

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    Radiation in certain wavelen th- ,

    under a curve for a giventemperature represents the

    o a ra a on energy em e

    by a blackbody at that

    temperature

    We are often interested in the amount

    of radiation emitted over some

    wavelen th band.

    For example, an incandescentlightbulb is judged on the basis of the

    radiation it emits in the visible range

    MECH/IITD

    rather than the radiation it emits at all

    wavelengths

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    a blackbody per unit area over awavelength band from 0 to is determined from

    MECH/IITD

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    MECH/IITD

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    Surface Emission

    surface to the radiation emitted by a blackbodyat the same temperature

    Spectral directional emissivity ,(,,,T) of a

    surface at the temperature T is the ratio of theintensity of the radiation emitted at the

    wavelength and in the direction of and to

    blackbody at the same values of T and .

    MECH/IITD )T,(I

    ,,,)T,,,(

    b,

    e,

    ,

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    Blackbod and Real Emission

    MECH/IITD

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    Emissivit

    )T,,(IT e

    )T(Ib )T,(E

    Spectral hemispherical

    )T,(E,

    2 2/

    b,

    =

    s ncos,,,

    2 2/

    0 0

    e,

    ,

    2/

    0 0b,

    MECH/IITD

    = s ncos,,0

    ,

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    Total Hemispherical Emissivit Total )T(E)T( =

    emissivityb

    Directional

    distributions of

    total diretctional

    MECH/IITD

    ,

    surfaces to be diffuse emitters with an emissivity equal to the

    value in the normal ( = 0) direction.

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    )T(E)T( =

    b

    MECH/IITD

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    Gra /Real Surface

    A gray surface should emit as much radiation

    as the real surface it represents at the same

    MECH/IITD

    empera ure. ere ore, e areas un er e

    emission curves of the real and gray surfaces

    must be equal.

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    Spectral dependence of

    MECH/IITD

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    The presence of oxide layers may significantly increase the emissivity of metallic

    The emissivity of metallic surfaces is generally small, as low as 0.02 for

    higly polished gold and silver

    .

    MECH/IITD

    The emissivity of non-conductors is comparatively large, generally exceeding 0.6

    The emissivity of conductors increases with increasing temperature; HoweverFor non-conductors it may be both way.


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