Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 95
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As such, thesespectral regions often show irregular and erratic behavior. Defects and impurities mayvary appreciably from specimen to specimen and even between different points onthe same sample. As an example, the spectral, normal reflectance of silicon at roomtemperature is shown in Fig. 8.10. The strong influence of different types and levels ofimpurities is clearly evident. Therefore, looking up properties for a given material inpublished tables is problematical unless a detailed description of surface and materialpreparation is given.In spectral regions outside Reststrahlen and electronic transition bands the absorptive index of a nonconductor is very small; typically, k < 10−6 for a pure substance.While impurities and lattice defects can increase the value of k, one is very unlikely tofind values of k > 10−2 for a nonconductor outside the Reststrahlen bands.
This implies that Fresnel’s relations can be simplified significantly, and the spectral, normalreflectance may be evaluated asρnλ =n−1n+12(8.36)Therefore, for optically smooth nonconductors the radiative properties may be calculated from refractive index data. Refractive indices for a number of semitransparentmaterials at room temperature are displayed in Fig. 8.11 as a function of wavelength.All of these crystalline materials show similar spectral behavior: the refractive indexdrops rapidly in the visible region, then is nearly constant (declining very gradually)until the midinfrared, where n again starts to drop rapidly.
This behavior is explainedBOOKCOMP, Inc. — John Wiley & Sons / Page 590 / 2nd Proofs / Heat Transfer Handbook / Bejan———Normal PagePgEnds: TEX[590], (18)RADIATIVE PROPERTIES OF SOLIDS AND LIQUIDS123456789101112131415161718192021222324252627282930313233343536373839404142434445591[591], (19)Lines: 655 to 679Figure 8.10 Spectral, normal reflectance of silicon at room temperature. (Redrawn from thedata of Touloukian and DeWitt, 1972.)by the fact that crystalline solids tend to have an absorption band due to electronictransitions near the visible and a Reststrahlen band in the infrared: The first drop inn is due to the tail end of the electronic band; the second drop in the midinfrared isdue to the beginning of a Reststrahlen band.Directional Dependence For optically smooth nonconductors, for the spectralregion between absorption–reflection bands, experiment has been found to closelyfollow Fresnel’s equations of electromagnetic wave theory.
Figure 8.12 shows acomparison between theory and experiment for the directional reflectance of glass(blackened on one side to avoid multiple reflections) for polarized, monochromaticirradiation. Because k 2 n2 , the absorptive index may be eliminated from Fresnel’srelations, and the relations for a perfect dielectric become valid. For unpolarized lightincident from vacuum (or a gas), this leads to222 − sin2 θcosθ−11nnρ + ρ⊥ = 1 − λ = 1 −2 2n2 cos θ + n2 − sin2 θ+cos θ −cos θ +n2 − sin2 θn2 − sin2 θ2 (8.37)Comparison with experiment agrees well with elecromagnetic wave theory for a largenumber of nonconductors.BOOKCOMP, Inc. — John Wiley & Sons / Page 591 / 2nd Proofs / Heat Transfer Handbook / Bejan———7.54106pt PgVar———Normal PagePgEnds: TEX[591], (19)592123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMAL RADIATION[592], (20)Lines: 679 to 679———-0.96301pt PgVar———Normal PagePgEnds: TEX[592], (20)Figure 8.11 Refractive indices for various semitransparent materials.
(From American Institute of Physics, 1972.)Temperature Dependence The temperature dependence of the radiative properties of nonconductors is considerably more difficult to quantify than for metals.Infrared absorption bands in ionic solids due to excitation of lattice vibrations (Reststrahlen bands) generally increase in width and decrease in strength with temperature, and the wavelength of peak reflection–absorption shifts toward higher values.The reflectance for shorter wavelengths depends largely on the material’s impurities.Often, the behavior is similar to that of metals, that is, the emittance increases withtemperature for the near infrared while it decreases with shorter wavelengths.
On theBOOKCOMP, Inc. — John Wiley & Sons / Page 592 / 2nd Proofs / Heat Transfer Handbook / BejanRADIATIVE PROPERTIES OF SOLIDS AND LIQUIDSBlack Glass: n = 1.517, = 0.546 mElectromagnetic theoryExperimentReflectance, ⬘123456789101112131415161718192021222324252627282930313233343536373839404142434445593⊥⬘[593], (21)Lines: 679 to 687Angle of incidence (degrees)Figure 8.12 Spectral, directional reflectance of blackened glass at room temperature. (FromBrandenberg, 1963.)other hand, the emittance of amorphous solids (solids without a crystal lattice) tendsto be independent of temperature.8.2.3Effects of Surface ConditionsUp to this point, the present discussion of radiative properties has assumed that thematerial is pure and homogeneous, and that its surface is isotropic and opticallysmooth.
Very few real material surfaces come close to this idealization. In usuallyhostile industrial environments, even an initially ideal material will have its surfacecomposition and quality altered: Heating of the material may be accompanied bystrong oxidation or other chemical reaction, producing an opaque surface layer ofa material quite different from the substrate.
Similar statements can be made aboutmaterials exposed to corrosive atmospheres for extended periods of time. In addition,very few surfaces have an optically smooth finish when new; exposing them to heatand/or corrosive atmospheres is generally accompanied by further roughening of thesurface finish.Surface Roughness A surface is optically smooth if the average length scaleof surface roughness is much less than the wavelength of the electromagnetic wave.Therefore, a surface that appears rough in visible light (λ 0.5 µm) may well beoptically smooth in the intermediate infrared (λ 50 µm). This difference is theprimary reason why results from electromagnetic wave theory cease to be valid forvery short wavelengths.BOOKCOMP, Inc.
— John Wiley & Sons / Page 593 / 2nd Proofs / Heat Transfer Handbook / Bejan———-5.903pt PgVar———Normal PagePgEnds: TEX[593], (21)594123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMAL RADIATIONThe character of roughness may be very different from surface to surface, depending on the material, method of manufacture, and surface preparation, and classification of this character is difficult. A common measure of surface roughness is givenby the root-mean-square (rms) roughness, σm . The rms roughness can be measuredreadily with a profilometer (a sharp stylus that traverses the surface, recording theheight fluctuations). Unfortunately, σm alone is woefully inadequate to describe theroughness of a surface.
Surfaces of identical σm may have vastly different frequencies of roughness peaks, as well as different peak-to-valley lengths; in addition, σmgives no information on second-order (or higher) roughness superimposed onto thefundamental roughness.In general terms it may be stated that surfaces will become less reflective, and thebehavior of reflection will become less specular and more diffuse as surface roughness increases. This behavior may be explained through geometric optics by realizingthat, for a rough surface, incoming radiation hitting the surface may undergo two ormore reflections off local peaks and valleys (resulting in increased absorption), after which it leaves the surface into an off-specular direction.
Simple models predictsharp reflection peaks in the specular direction, and lesser reflection into other directions, with the strength of the peak depending on the surface roughness. This was alsofound to be true experimentally for most cases as long as the incidence angle was nottoo large. For large off-normal angles of incidence, experiment has shown that thereflectance has its peak at polar angles greater than the specular direction, and forlarger incidence angles, rough surfaces tend to display off-specular peaks, apparentlydue to shadowing of parts of the surface by adjacent peaks.Surface Layers and Oxide Films Even optically smooth surfaces have a surface structure that is different from the bulk material, due to either surface damageor the presence of thin layers of foreign materials.
Surface damage is usually causedby the machining process, particularly for metals and semiconductors, which distortsor damages the crystal lattice near the surface. Thin foreign coats may be formedby chemical reaction (mostly oxidation), absorption (coats of grease or water), orelectrostatics (dust particles). All of these effects may have a severe impact on theradiation properties of metals and may cause considerable changes in the propertiesof semiconductors. Because metals have large absorptive indices k and thus high reflectances, a thin, nonmetallic layer with small k can significantly decrease the composite’s reflectance (and raise its absorptance).
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