1Radiation: Overview Radiation - Emission Radiation - Absorption thermal 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 matterthe 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 matter
2Radiation: Overview Emission Dual Nature emission 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 vacuum
3Radiation: 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 wavelengths
4Radiation: 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, dAn, and propagating in a particular direction (θ,ϕ) is quantified in terms of a differential solid angle associated with the direction, dω.dAn unit element of surface on a hypothetical sphere and normal to the (θ,ϕ) direction
5Radiation: Directional Considerations Solid Anglethe solid angle ω has units of steradians (sr)the solid angle ωhemi associated with a complete hemisphere
6Radiation: 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/m2-sr-μm]
7Radiation: Heat FluxThe 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 directions
8Radiation: Heat FluxThe 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 isotropic
9Radiation: Irradiation electromagnetic 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 (dA1cosθ)
10Radiation: Irradiation Heat Flux 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 power
11Radiation: Radiosity Radiosity Spectral Intensity, Iλ,e+r for 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 radiosity
12Radiation: Black Body Black Body an 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 absorbera black body is defined as a diffuse emitterIsothermal Cavity – Approximation of Black Bodyafter 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 body
13Radiation: Black Body Planck Distribution the spectral emission intensity of a black bodydetermined theoretically and confirmed experimentallyspectral emissive power
14Radiation: Black Body Planck Distribution emitted 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 law
15Radiation: Black Body Stefan-Boltzmann Law the total emissive power of a black body is found by integrating the Planck distributionthe fraction of the total emissive power within a wavelength band(λ1 < λ < λ2) isStefan-Boltzmann Lawthis can be rewritten asthe following function is tabulated
17Example: RadiationAccording 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?
18Example: RadiationThe 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.
19Radiation: 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, τ
20Radiation: Emissivity characterizes 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 directionsa function of direction (angular dependence) averaged over all wavelengthsSpectral, Directional EmissivitySpectral, Hemispherical Emissivity (directional average)Total, Directional Emissivity (spectral average)
21Radiation: Emissivity Total, Hemispherical Emissivity (directional average)to a reasonable approximation, the total, hemispherical emissivity is equal to the total, normal emissivitywhich can be simplified to
22Radiation: Emissivity Representative spectral variationsRepresentative temperature variations
23Radiation: Absorption/Reflection/Transmission Three 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 radiationthe color of an opaque material is based on the spectral dependence of reflection in the visible spectrum
29Radiation: Kirchhoff’s Law spectral, 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 surface
30Radiation: 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??
31Radiation: Gray Surfaces a surface where αλ and ελ are independent of λ over the spectral regions of the irradiation and emissionGray approximation only valid for:
32Radiation: ExampleThe 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?
33Radiation: ExampleA 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.
34Radiation: 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.
35Radiation: 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 dAjthe rate of radiosity (emission + reflection) intercepted by dAjThe view factor is the ratio of the intercepted radiosity to the total radiositythe view factor is based entirely on geometry
36Radiation: View Factor Relations ReciprocitySummationfrom conservation of radiation (energy), for an enclosure
39Radiation: 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 Ai)
40Radiation: 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 isand the driving potential is
41Radiation: Gray Radiation Exchange Net radiation (heat) transfer from surface i due to exchange with all (N) surfaces of an enclosurethus for gray bodies the resistance between two bodies (space or geometrical resistance)and the driving potential isRadiation energy balance on surface i :net energy leaving = energy exchange with other surfaces
42Radiation: Gray Radiation Exchange The equivalent circuit for a radiation network consists of two resistancesresistance at the surfaceresistances between all bodies
43Radiation: 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, …, JNapply the following equation to determine the radiation heat rate qi for each surface of known Ti and Ti for each surface of known qi
44Radiation: Gray Radiation Exchange Special Caseenclosure with an opening (aperture) of area Ai through which the interior surface exchange radiation with large surroundings at temperature TsurTsurAiTreat the aperture as a virtual blackbody surface with area Ai,Ti = Tsur and
45Radiation: 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 exchange
47Radiation: Reradiating Surface idealization 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 surface
48Radiation: 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 yields
49Radiation: 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. enclosure
50Example: 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 = 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.