Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 96
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Dielectric materials, on the other hand,have small k’s, and their relatively strong emission and absorption take place over avery thick surface layer. The addition of a thin, different dielectric layer cannot significantly alter their radiative properties (Bennett et al., 1963; Dunkle and Gier, 1953).Figure 8.13 shows the spectral, normal emittance (or absorptance) of aluminum fora surface prepared by the ultrahigh vacuum method and for several other aluminumsurface finishes. While ultrahigh vacuum aluminum follows the Drude theory forλ > 1 µm, polished aluminum (clean and optically smooth for large wavelengths)has a much higher absorptance over the entire spectrum. Still, the overall level of absorptance remains very low, and the reflectance remains rather specular. As Fig.
8.13shows, the absorptance is much larger still when off-the-shelf commercial aluminumBOOKCOMP, Inc. — John Wiley & Sons / Page 594 / 2nd Proofs / Heat Transfer Handbook / Bejan[594], (22)Lines: 687 to 698———0.0pt PgVar———Normal PagePgEnds: TEX[594], (22)RADIATIVE PROPERTIES OF SOLIDS AND LIQUIDS123456789101112131415161718192021222324252627282930313233343536373839404142434445595[595], (23)Lines: 698 to 704———12.721pt PgVarFigure 8.13 Spectral, normal emittance for aluminum with different surface finishes.
(FromBennett et al., 1963; Dunkle and Gier, 1953.)is tested, probably due to a combination of roughness, contamination, and slight atmospheric oxidation. Deposition of a thin oxide layer on aluminum (up to 100 Å)appreciably increases the emittance only for wavelengths less than 1.5 µm. Thisclearly is not true for thick oxide layers, as evidenced by Fig. 8.13: Anodized aluminum (electrolytically oxidized material with a thick layer of alumina, Al2O3) nolonger displays the typical trends of a metal, but rather, shows the behavior of thedielectric alumina. The effects of thin and thick oxide layers have been measured formany metals, with similar results. As a rule of thumb, clean metal exposed to air atroom temperature grows oxide films so thin that infrared emittances are not affectedappreciably.
On the other hand, metal surfaces exposed to high-temperature oxidizingenvironments (furnaces, laser heating) generally have radiative properties similar tothose of their oxide layer.Although most severe for metallic surfaces, the problem of surface modification isnot unknown for nonmetals. For example, it is well known that when exposed to airat high temperature, silicon carbide (SiC) forms a layer of silica (SiO2) on its surface,resulting in a reflection band around 9 µm.
Nonoxidizing chemical reactions can alsosignificantly change the radiative properties of dielectrics. For example, the strongultraviolet radiation in outer space (from the sun) as well as gamma rays (from insideEarth’s van Allen belt) can damage the surface of spacecraft-protective coatings suchas white acrylic paint or titanium dioxide epoxy coating, and similar results can beexpected for ultraviolet laser irradiation.BOOKCOMP, Inc. — John Wiley & Sons / Page 595 / 2nd Proofs / Heat Transfer Handbook / Bejan———Normal PagePgEnds: TEX[595], (23)123456789101112131415161718192021222324252627282930313233343536373839404142434445596THERMAL RADIATION8.2.4Semitransparent SheetsFor an optically smooth semitransparent sheet of thickness L substantially larger thanthe laser wavelength, L λ, radiative properties are readily determined throughgeometric optics and raytracing.
Accounting for multiple reflections, the absorptanceT slab of an absorbing layer with complexAslab, reflectance R slab, and transmittance√index of refraction m = n − ık(ı = −1) are given by(1 − ρ)2 τ2(8.38)Rslab = ρ 1 +1 − ρ 2 τ2Tslab =(1 − ρ)2 τ1 − ρ2 τ2(8.39)Aslab =(1 − ρ)(1 − τ)1 − ρτ(8.40)andLines: 704 to 832Aslab + Rslab + Tslab = 1(8.41)In these relations ρ is the reflectance of both sheet–air interfaces and τ is the transmittance of the sheet, as given for a nonscattering material (one without defects, inclusions, bubbles) byτ = e−κLSummaryReflectance and absorptance for many materials have been compiled in a number ofbooks and other publications, notably the handbooks by Touloukian et al.
(Touloukianand DeWitt, 1970, 1972; Touloukian et al., 1973). These tabulations show largeamounts of scatter, and radiative properties for opaque surfaces, when obtained fromtabulations and figures in the literature, should be taken with a grain of salt. Unlessdetailed descriptions of surface purity, preparation, and treatment are available, thedata may not give any more than an order-of-magnitude estimate. One should alsokeep in mind that the properties of a surface may change during a process or overnightBOOKCOMP, Inc.
— John Wiley & Sons / Page 596 / 2nd Proofs / Heat Transfer Handbook / Bejan———4.06808pt PgVar———Normal PagePgEnds: TEX(8.42)where κ = 4πk/λ is the absorption coefficient of the material, which is related to theabsorptive index k as shown.If the thickness of the semitransparent sheet is on the order of the wavelength ofthe irradiation (thin film), interference effects need to be accounted for because phasedifferences between first- and second-surface reflected light make film reflectance astrongly oscillating function of wavelength, with near-zero reflectance at some wavelengths and very substantial reflectances in between.
This phenomenon is commonlyexploited by putting antireflection coatings onto optical components, optimized tominimize the reflectance of the optical elements at desired wavelengths.8.2.5[596], (24)[596], (24)597RADIATIVE PROPERTIES OF SOLIDS AND LIQUIDS123456789101112131415161718192021222324252627282930313233343536373839404142434445TABLE 8.2Total Emittance and Solar Absorptance of Selected SurfacesTemperature(°C)Total, NormalEmittanceSolarAbsorptance−250.800.28202020−25225–57510010040200–60095–50035–26035–370150370600150370600750.040.0250.0250.840.039–0.0570.090.180.055–0.070.11–0.190.20–0.310.28–0.310.93–0.940.180.210.300.900.880.820.34−25−25 to 750−2595–42540–3152250–350200–600100–320320–50095–270250–51040–11002080115200–600800–11001075–1275260–540225–6250.950.930.890.81–0.800.100.060.220.61–0.590.76–0.750.75–0.710.9520.980.08–0.360.030.0180.0230.570.66–0.540.16–0.130.95–0.850.018–0.035Alumina, flame-sprayedAluminum foilAs receivedBright dippedAluminum, vacuum-depositedHard-anodizedHighly polished plate, 98.3% pureCommercial sheetRough polishRough plateOxidized at 600°CHeavily oxidizedAntimony, polishedAsbestosBerylliumBeryllium, anodizedBismuth, brightBlack paintParson’s optical blackBlack siliconeBlack epoxy paintBlack enamel paintBrass, polishedRolled plate, natural surfaceDull plateOxidized by heating at 600°CCarbon, graphitizedCandle sootGraphite, pressed, filed surfaceChromium, polishedCopper, electroplatedCarefully polished electrolytic copperPolishedPlate heated at 600°CCuprous oxideMolten copperGlass, pyrex, lead, and sodaGold, pure, highly polishedBOOKCOMP, Inc.
— John Wiley & Sons / Page 597 / 2nd Proofs / Heat Transfer Handbook / Bejan0.100.100.92[597], (25)Lines: 832 to 8320.77———0.19804pt PgVar———Normal PagePgEnds: TEX0.9750.940.950.47(continued)[597], (25)598123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMAL RADIATIONTABLE 8.2Total Emittance and Solar Absorptance of Selected Surfaces (Continued)GypsumInconel X, oxidizedLead, pure (99.96%), unoxidizedGray oxidizedOxidized at 150°CMagnesium, polishedMagnesium oxideMercuryMolybdenum, polishedNickel, electroplatedPolishedPlatinum, pure, polishedSilica, sintered, powdered, fused silicaSilicon carbideSilver, polished, pureStainless steelType 312, heated 300 h at 260°CType 301 with Armco black oxideType 410, heated to 700°C in airType 303, sandblastedTitanium, 75A75A, oxidized 300 h at 450°CAnodizedTungsten, filament, agedZinc, pure, polishedGalvanized sheetTemperature(°C)Total, NormalEmittance20−25125–2252520035–260275–825900–17050–10035–260540–1370275020100225–62535150–65040–6250.9030.710.057–0.0750.280.630.07–0.130.55–0.200.200.09–0.120.05–0.080.10–0.180.290.030.0720.054–0.1040.840.83–0.960.020–0.03295–425−25359595–42535–425−2527–3300225–3251000.27–0.320.750.130.420.10–0.190.21–0.250.730.032–0.350.045–0.0530.21SolarAbsorptance0.90[598], (26)0.22Lines: 832 to 8370.080.890.760.680.800.51(by oxidation and/or contamination).
A representative list of total normal emittancesand total normal absorptances (= 1− reflectance) for solar irradiation is given inTable 8.2 for a number of metals and nonmetals, which may be enlisted for a grayanalysis. All values are for stated temperature ranges and stated surface conditions:As explained earlier, these values may change significantly with temperature, surfaceroughness, and oxidation.8.3RADIATIVE EXCHANGE BETWEEN SURFACESIn many engineering applications the exchange of radiative energy between surfacesis virtually unaffected by the medium that separates them. Such (radiatively) nonparticipating media include vacuum as well as monatomic and most diatomic gasesBOOKCOMP, Inc.
— John Wiley & Sons / Page 598 / 2nd Proofs / Heat Transfer Handbook / Bejan———-10.08395pt PgVar———Normal PagePgEnds: TEX[598], (26)RADIATIVE EXCHANGE BETWEEN SURFACES123456789101112131415161718192021222324252627282930313233343536373839404142434445599(including air) at low to moderate temperature levels (i.e., in the absence of ionizationand dissociation). Examples include spacecraft heat rejection systems, solar collectorsystems, radiative space heaters, illumination problems, and so on. This implies thatphotons will travel unimpeded from surface to surface, possibly over large distances.To account for all the radiative energy arriving at a point in space from all directions,the analysis has to be carried out over a complete enclosure of opaque surfaces.
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