Radiation: Overview - PowerPoint Presentation

Slide1

Radiation: Overview

Radiation - Emissionthermal radiation is the emission of electromagnetic waves when matter is at an absolute temperature greater than 0 Kemission is due to the oscillations and transitions of the many electrons that comprise the matter the oscillations and transitions are sustained by the thermal energy of the matteremission corresponds to heat transfer from the matter and hence to a reduction in the thermal energy stored in the matterRadiation - Absorptionradiation may also be absorbed by matterabsorption results in heat transfer to the matter and hence to an increase in the thermal energy stored in the matterSlide2

Radiation: Overview

Emissionemission from a gas or semi-transparent solid or liquid is a volumetric phenomenonemission from an opaque solid or liquid is a surface phenomenonemission originates from atoms & molecules within 1 μm of the surfaceDual Naturein some cases, the physical manifestations of radiation may be explained by viewing it as particles (A.K.A. photons or quanta); in other cases, radiation behaves as an electromagnetic waveradiation is characterized by a wavelength λ and frequency ν

which are related through the

speed at which radiation propagates in the medium

of interest (solid, liquid, gas, vacuum)

in a vacuumSlide3

Radiation: Spectral Considerations

Electromagnetic Spectrumthe range of all possible radiation frequenciesthermal radiation is confined to the infrared, visible, and ultraviolet regions of the spectrumSpectral Distributionradiation emitted by an opaque surface varies with wavelengthspectral distribution describes the radiation over all wavelengthsmonochromatic/spectral components are associated with particular wavelengthsSlide4

Radiation: Directional Considerations

EmissionRadiation emitted by a surface will be in all directions associated with a hypothetical hemisphere about the surface and is characterized by a directional distributionDirection may be represented in a spherical coordinate system characterized by the zenith or polar angle θ and the azimuthal angle ϕ.

- The amount of radiation emitted from a surface,

dA

n

, and propagating in a particular direction (

θ,ϕ) is quantified in terms of a differential solid angle associated with the direction, dω.dA

n  unit element of surface on a hypothetical sphere and normal to the (θ

,ϕ) directionSlide5

Solid Angle

Radiation: Directional Considerations

the solid angle

ω

has units of

steradians

(sr) the solid angle ωhemi associated with a complete hemisphereSlide6

Radiation: Spectral Intensity

Spectral Intensity, Iλ,ea quantity used to specify the radiant heat flux (W/m2) within a unit solid angle about a prescribed direction (W/m2-sr) and within a unit wavelength interval about a prescribed wavelength (W/m2-sr-μm) associated with emission from a surface element dA1 in the solid angle dω about θ, ϕ and the wavelength interval

dλ

about

λ

and is defined as:

the rational for defining the radiation flux in terms of the projected area (dA1cosθ

) stems from the existence of surfaces for which, to a good approximation, Iλ,e

is independent of direction. Such surfaces are termed diffuse, and the radiation is said to be isotropic.the projected area is how

dA1 appears

along θ, ϕ

[W

/m

2

-sr-

μm] Slide7

The

spectral heat rate (heat rate per unit wavelength of radiation) associated with emissionThe spectral heat flux (heat flux per unit wavelength of radiation) associated with emissionThe integration of the spectral heat flux is called the spectral emissive powerspectral emission (heat flux) over all possible directionsRadiation: Heat FluxSlide8

The

total heat flux from the surface due to radiation is emission over all wavelengths and directions  total emissive powerIf the emission is the same in all directions, then the surface is diffuse and the emission is isotropicRadiation: Heat FluxSlide9

Radiation: Irradiation

Irradiationelectromagnetic waves incident on a surface is called irradiationirradiation can be either absorbed or reflectedSpectral Intensity, Iλ,ia quantity used to specify the incident radiant heat flux (W/m2) within a unit solid angle about the direction of incidence (W/m2-sr) and within a unit wavelength interval about a prescribed wavelength (W/m2-sr-μm) and the projected area of the receiving surface (d

A

1

cos

θ

)Slide10

The integration of the

spectral heat flux is called the spectral irradiationspectral irradiation (heat flux) over all possible directionsThe total heat flux to the surface due to irradiation over all wavelengths and directions  total irradiative powerRadiation: Irradiation Heat FluxSlide11

Radiation: Radiosity

Radiosityfor opaque surfacesaccounts for all radiation leaving a surfaceemissionreflectionSpectral Intensity, Iλ,e+ra quantity used to specify emitted and reflected radiation intensityThe integration of the spectral heat flux is called the spectral radiosityspectral emission+reflection (heat flux) over all possible directionsThe total heat flux from

the surface due to irradiation over all wavelengths and directions



total

radiositySlide12

Isothermal Cavity – Approximation of Black Body

after multiple reflections, virtually all radiation entering the cavity is absorbedemission from the aperture is the maximum possible emission for the temperature of cavity and the emission is diffusecumulative effect of emission and reflection off the cavity wall is to provide diffuse irradiation corresponding to emission from a black bodyRadiation: Black BodyBlack Bodyan idealization providing limits on radiation emission and absorption by matterfor a prescribed temperature and wavelength, no surface can emit more than a black body  ideal emittera black body absorbs all incident radiation (no reflection) 

ideal absorber

a black body is defined as a

diffuse emitterSlide13

Radiation: Black Body

Planck Distributionthe spectral emission intensity of a black bodydetermined theoretically and confirmed experimentallyspectral emissive powerSlide14

Radiation: Black Body

Planck Distributionemitted radiation varies continuously with wavelengthat any wavelength, the magnitude of the emitted power increases with temperaturethe spectral region where the emission is concentrated depends on temperaturecomparatively more radiation at shorter wave lengthssun approximated by 5800 K black bodyThe maximum emission power, Eλ,b, occurs at λmax which is determined by Wien’s displacement lawSlide15

Radiation: Black Body

Stefan-Boltzmann Lawthe total emissive power of a black body is found by integrating the Planck distribution the fraction of the total emissive power within a wavelength band (λ1 < λ < λ2) is

Stefan-Boltzmann Law

this can be rewritten as

the following function is tabulatedSlide16

Radiation: Black BodySlide17

Example: Radiation

According to its directional distribution, solar radiation incident on the earth’s surface consists of two components that may be approximated as being diffusely distributed with the angle of the sun θ. Consider clear sky conditions with incident radiation at an angle of 30° with a total heat flux (if the radiation were angled normal to the surface) of 1000 W/m2 and the total intensity of the diffuse radiation is Idif = 70 W/m2-sr. What is the total irradiation on the earth’s surface?Slide18

Example: Radiation

The human eye, as well as the light-sensitive chemicals on color photographic film, respond differently to lighting sources with different spectral distributions. Daylight lighting corresponds to the spectral distribution of a solar disk (approximated as a blackbody at 5800 K) and incandescent lighting from the usual household lamp (approximated as a blackbody at 2900 K). Calculate the band emission fractions for the visible region for each light source. Calculate the wavelength corresponding to the maximum spectral intensity for each light source. Slide19

Radiation: Surface Properties

Real surfaces do not behave like ideal black bodiesnon-ideal surfaces are characterized by factors (< 1) which are the ratio of the non-ideal performance to the ideal black body performancethese factors can be a function of wavelength (spectral dependence) and direction (angular dependence)Non-Ideal Radiation Factoremissivity, εNon-Ideal Irradiationabsorptivity, αreflectivity, ρtransmissivity, τSlide20

Radiation: Emissivity

Emissivitycharacterizes the emission of a real body to the ideal emission of a black body and can be defined in three mannersa function of wavelength (spectral dependence) and direction (angular dependence)a function of wavelength (spectral dependence) averaged over all directions a function of direction (angular dependence) averaged over all wavelengths Spectral, Directional EmissivitySpectral, Hemispherical Emissivity (directional average)Total, Directional Emissivity (spectral average)Slide21

Radiation: Emissivity

EmissivityTotal, Hemispherical Emissivity (directional average)to a reasonable approximation, the total, hemispherical emissivity is equal to the total, normal emissivitywhich can be simplified toSlide22

Radiation: Emissivity

Representative spectral variationsRepresentative temperature variationsSlide23

Radiation:

Absorption/Reflection/TransmissionThree responses of semi-transparent medium to irradiation, Gλabsorption within medium, Gλ,absreflection from the medium, Gλ,reftransmission through the medium, Gλ,trTotal irradiation balanceAn opaque material only has a surface response – there is no transmission (volumetric effect)The semi-transparency or opaqueness of a medium is governed by both the nature of the material and the wavelength of the incident radiation

the

color

of an opaque material is based on the

spectral dependence of reflection in the visible spectrumSlide24

Radiation: Absorptivity

Spectral, Directional Absorptivity assuming negligible temperature dependenceSpectral, Hemispherical Absorptivity (directional average)Total, Hemispherical AbsorptivitySlide25

Radiation: Reflectivity

Spectral, Directional Reflectivityassuming negligible temperature dependenceSpectral, Hemispherical Reflectivity (spectral average)Total, Hemispherical Reflectivity

diffuse – rough surfaces

specular – polished

surfacesSlide26

Radiation: Reflectivity

Representative spectral variationsSlide27

Radiation: Transmissivity

Spectral, Hemispherical Reflectivityassuming negligible temperature dependenceTotal, Hemispherical TransmissivityRepresentative spectral variationsSlide28

Radiation: Irradiation Balance

Semi-Transparent MaterialsOpaque Materialsand

andSlide29

Radiation: Kirchhoff’s Law

Kirchhoff’s Lawspectral, directional surface properties are equalKirchhoff’s Law (spectral)spectral, hemispherical surface properties are equalfor diffuse surfaces or diffuse irradiationKirchhoff’s Law (blackbodies)total, hemispherical properties are equalwhen the irradiation is from a blackbody at the same temperature as the emitting surfaceSlide30

Radiation: Kirchhoff’s Law

Kirchhoff’s Law (spectral)true if irradiation is diffusetrue if surface is diffuseKirchhoff’s Law (blackbody)true if irradiation is from a blackbody at the same temperature as the emitting surfacetrue if the surface is gray

?

?Slide31

Radiation: Gray Surfaces

Gray Surfacea surface where αλ and ελ are independent of λ over the spectral regions of the irradiation and emission Gray approximation only valid for: Slide32

Radiation: Example

The spectral, hemispherical emissivity absorptivity of an opaque surface is shown below. What is the solar absorptivity?If Kirchhoff’s Law (spectral) is assumed and the surface temperature is 340 K, what is the total hemispherical emissivity?Slide33

Radiation: Example

A vertical flat plate, 2 m in height, is insulated on its edges and backside is suspended in atmospheric air at 300 K. The exposed surface is painted with a special diffuse coating having the prescribed absorptivity distribution and is irradiated by solar-simulation lamps that provide spectral irradiation characteristic of the solar spectrum. Under steady conditions the plate is at 400 K. (a) Find the plate absorptivity, emissivity, free convection coefficient, and irradiation. (b) Estimate the plate temperature if if the irradiation was doubled.Slide34

Radiation: Exchange Between Surfaces

OverviewEnclosures consist of two or more surfaces that envelop a region of space (typically gas-filled) and between which there is radiation transfer. Virtual, as well as real, surfaces may be introduced to form an enclosure.A nonparticipating medium within the enclosure neither emits, absorbs, nor scatters radiation and hence has no effect on radiation exchange between the surfaces. Each surface of the enclosure is assumed to be isothermal, opaque, diffuse and gray, and to be characterized by uniform radiosity and irradiation.Slide35

Radiation: View Factor (Shape Factor)

View Factor, Fijgeometrical quantity corresponding to the fraction of the radiation leaving surface i that is intercepted by surface jGeneral expressionconsider radiation from the differential area dAi to the differential area dAj the rate of radiosity (emission + reflection) intercepted by dAj The

view factor

is the ratio of the

intercepted

radiosity

to the total radiosity

the view factor is based

entirely

on geometrySlide36

Radiation: View Factor Relations

ReciprocitySummationfrom conservation of radiation (energy), for an enclosureSlide37

Radiation: View Factors

2-D GeometriesSlide38

Radiation: View Factors

3-D GeometriesSlide39

Radiation: Blackbody Radiation Exchange

For a blackbody there is no reflection (perfect absorber)Net radiation exchange (heat rate) between two “blackbodies”net rate at which radiation leaves surface i due to its interaction with j ORnet rate at which surface j gains radiation due to its interaction with iNet radiation (heat) transfer from surface i due to exchange with all (N) surfaces of an enclosure

(heat loss from

A

i

)Slide40

Radiation: Gray Radiation Exchange

General assumption for opaque, diffuse, gray surfacesEquivalent expressions for the net radiation (heat) transfer from surface ithus for gray bodies the resistance at the surface is

and the driving potential is Slide41

Radiation: Gray Radiation Exchange

Net radiation (heat) transfer from surface i due to exchange with all (N) surfaces of an enclosure thus for gray bodies the resistance between two bodies (space or geometrical resistance)and the driving potential is

Radiation

energy balance

on surface

i

:

net energy

leaving

= energy exchange with other surfacesSlide42

Radiation: Gray Radiation Exchange

The equivalent circuit for a radiation network consists of two resistancesresistance at the surfaceresistances between all bodiesSlide43

Radiation: Gray Radiation Exchange

Methodology of an enclosure analysisapply the following equation for each surface where the net radiation heat rate qi is knownapply the following equation for each remaining surface where the temperature Ti (and thus Ebi) is knowndetermine all the view factorssolve the system of N equations for the unknown radiosities J1, J2, …, JN

apply the following equation to determine the radiation heat rate

q

i

for each surface of known

Ti and Ti

for each surface of known qi

Slide44

Radiation: Gray Radiation Exchange

Special Caseenclosure with an opening (aperture) of area Ai through which the interior surface exchange radiation with large surroundings at temperature Tsur

T

sur

A

i

Treat the aperture as a

virtual blackbody surface

with area

A

i

,

T

i

=

T

sur

andSlide45

Radiation: Two Surface Enclosures

Simplest enclosure for which radiation exchange is exclusively between two surfaces and a single expression for the rate of radiation transfer may be inferred from a network representation of the exchangeSlide46

Radiation: Two Surface Enclosures

Special CasesSlide47

Radiation: Reradiating Surface

Reradiating Surfaceidealization for which GR = JR hence qR = 0 and JR = Eb,Rapproximated by surfaces that are well insulated on one side and for which convection is negligible on the opposite (radiating) sideThree-surface enclosure with a reradiating surfaceSlide48

Radiation: Reradiating Surface

The temperature of the reradiating surface TR may be determined from knowledge of its radiosity JR. With qR = 0 a radiation balance on the surface yieldsSlide49

Radiation: Multimode Effects

In an enclosure with conduction and convection heat transfer to/from one or more surface, the foregoing treatments of the radiation exchange may be combined with surface energy balances to determine thermal conditionsConsider a general surface condition for which there is external heat addition (e.g., electrically) as well as conduction, convection and radiationappropriate analysis for N-surface, two-surface, etc. enclosureSlide50

Example: Radiation Exchange

A cylindrical furnace for heat treating materials in a spacecraft environment has a 90-mm diameter and an overall length of 180 mm. Heating elements in the 135 mm long section maintain a refractory lining at 800 °C and ε = 0.8. the other linings are insulated but made of the same material. The surroundings are at 23 °C. Determine the power required to maintain the furnace operating conditions.