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RADIATIVE PROPERTIES OF REAL MATERIALS. Electromagnetic Theory: ▪ ideal, optically smooth surface ▪ valid for spectral range larger than visible Real Materials: surface condition ▪ contaminants or oxides ▪ surface roughness ▪ thin coating on substrate.

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RADIATIVE PROPERTIES OF

REAL MATERIALS

  • Electromagnetic Theory:

  • ▪ ideal, optically smooth surface

  • ▪ valid for spectral range larger than

  • visible

  • Real Materials: surface condition

  • ▪ contaminants or oxides

  • ▪ surface roughness

  • ▪ thin coating on substrate


  • Material Dependence

  • ▪ opaque nonmetals

  • ▪ opaque metals

  • ▪ selective and directional opaque

  • surfaces

  • ▪ selectively transparent materials

  • Parameter Dependence

  • ▪ spectral and directional variations

  • ▪ variation with temperature

  • ▪ effect of surface roughness

  • ▪ effect of surface impurities


Radiative Properties of

Opaque Nonmetals

Effect of Coating Thickness

Emissivity of zinc oxide coatings on oxidized stainless steel substrate. Surface temperature, 880 ± 8 K


Effect of Substrates

Effect of substrate reflection characteristics on the hemispherical characteristics of a TiO2 paint film for normal incidence: Film thickness, 14.4 mm; volume concentration of pigment 0.017,


Spectral Dependence

Spectral reflectivity of paint coatings. Specimens at room temperature



Variation with Temperature

Effect of surface temperature on emissivity of dielectrics



Effect of Surface Roughness zirconium oxide

Bidirectional total reflectivity of typewriter paper in plane of incidence. Source temperature, 1178 K


Bidirectional total reflectivity for visible light zirconium oxidein plane of incidence for mountainous regions of lunar surface


constant zirconium oxide

q varies from 0° to 90° as the position of the incident energy varies from the center to the edge of the lunar disk

uniform brightness: constant intensity reflected to earth

Reflected energy at full moon


Semiconductor zirconium oxide

Normal spectral emissivity of a highly doped silicon semiconductor at room temperature


follow theoretical trend zirconium oxide

Radiative Properties of Metals

Directional Dependence

EM theory doesn’t hold at shorter wavelengths.

Effect of wavelength on directional spectral emissivity of pure titanium. Surfaceground to 0.4 mm rms


infrared region zirconium oxide

Spectral Dependence

Peak e near the visible region

gray body assumption

Variation with wavelength of normal spectral emissivity for polished metals


Peak appears near the visible region zirconium oxide

H-R relation holds

1.27 mm

Effect of wavelength and surface temperature on hemispherical spectral emissivity of tungsten

X point: iron,1.0 mm; nickel,1.5 mm; copper,1.7 mm; platinum,0.7 mm


Hagen – Rubens zirconium oxide

Variation with Temperature

Effect of temperature on hemispherical total emissivity of several metals and one dielectric


approach to optically zirconium oxide

smooth surface

follow theoretical trend

Effect of Surface Roughness

Precise definition of surface characteristics

geometric shape,

method of preparation,

distribution of size around rms

s0/l > 1: multiple reflection

Roughness effects for small optical roughness, s0/l < 1; effect of surface finish on directional spectral emissivity of pure titanium. Wavelength, 2 mm


behave more like a polished surface zirconium oxide

smoother relative to the incident radiation for large l

Effects of roughness on bidirectional reflectivity in specular direction for ground nickel specimens. Mechanical roughness for polished specimen, 0.015 mm


s zirconium oxide0/l = 2.6

For large q, peak qr shifted to larger angles

Off-specular reflection at larger rough-ness and incident angle

Bidirectional reflectivity in plane of incidence for various incidence angles; material, aluminum (2024-T4), aluminum coated; rms roughness s0 = 1.3 mm; wavelength of incident radiation, l =0.5 mm


0.69 zirconium oxide

0.45

Effect of Surface Impurities

Effect of oxide layer on directional spectral emissivity of titanium. Emission angle, q = 25°; surface lapped to 0.05 mm rms; temperature, 294 K.



Effect of surface condition and oxidation on normal total emissivity of stainless steel type 18-8




At low source temperature, incident radiation in long wavelength region

→ Barely influenced by the thin oxide layer on the anodized surface

→Acts like a bare metal

Approximate directional total absorptivity of anodized aluminum at room temperature relative to value for normal incidence


Hemispherical spectral reflectivity for normal incident beam on aluminum coated with lead sulfide. Coating mass per unit surface area, 0.68 mg/cm2


Selective and Directional Opaque Surfaces on aluminum coated with lead sulfide. Coating mass per unit surface area,

Modification of Surface Spectral Characteristics

lc: cutoff wavelength

lc

Characteristics of some spectrally selective surfaces


Ex 5-1 on aluminum coated with lead sulfide. Coating mass per unit surface area,

arriving from the sun at Ts = 5780 K

An ideal selective surface with a cutoff wavelength lc = 1 mm

Energy balance

: absorbed energy

: emitted energy


d on aluminum coated with lead sulfide. Coating mass per unit surface area, w

ib,s

R = 6.95 × 108 m

earth

sun

L = 1.50 × 1011 m

TS = 5780 K


arriving from the sun at on aluminum coated with lead sulfide. Coating mass per unit surface area, Ts = 5780 K

An ideal selective surface with a cutoff wavelength lc = 1 mm


For diffuse irradiation on aluminum coated with lead sulfide. Coating mass per unit surface area,


For diffuse irradiation on aluminum coated with lead sulfide. Coating mass per unit surface area,

or


Cutoff wavelength on aluminum coated with lead sulfide. Coating mass per unit surface area, lc, mm

0.6

0.8

1.0

1.2

1.5

Equilibrium temperatureTeq, K

1811

1523

1334

1210

1041

393

By trial and error


approximation on aluminum coated with lead sulfide. Coating mass per unit surface area,

0.95

0.05

1.5

  • extracted energy for use in a power-

  • generating cycle

  • for the black surface at the same

  • temperature

Ex 5-3

SiO-Al selective surface

Wavelength l

Solar energy absorber

at TA = 393 K


0.95 on aluminum coated with lead sulfide. Coating mass per unit surface area,

0.05

1.5

approximation

Energy balance

SiO-Al selective surface

Wavelength l

For black surface

No energy available


reflect well at short wavelengths on aluminum coated with lead sulfide. Coating mass per unit surface area,

radiate well at long wavelengths

Reflectivity of white paint coating on aluminum


l on aluminum coated with lead sulfide. Coating mass per unit surface area, c

lc

Selective Transmission

ordinary glasses: typically two strong cutoff wavelengths

Normal overall spectral transmittance of glass plate (includes surface reflection) at 298 K


1 on aluminum coated with lead sulfide. Coating mass per unit surface area,

r

r3 (1-r)t3(1-t)

r (1-r)t(1-t)

(1-r)(1-t)

r2(1-r)t2(1-t)

A transmitting Layer with Thickness L >l

r (1-r)2t2

r3 (1-r)2t4

1-r

r2(1-r)t2

r3 (1-r)t4

r4 (1-r)t4

r (1-r)t2

(1-r)t

r (1-r)t

r2 (1-r)t3

r3 (1-r)t3

(1-r)2t

r2 (1-r)2t3

Reflectance

Transmittance


1 on aluminum coated with lead sulfide. Coating mass per unit surface area,

r

r (1-r)2t2

r3 (1-r)2t4

1-r

r2(1-r)t2

r3 (1-r)t4

r4 (1-r)t4

r (1-r)t2

r3 (1-r)t3(1-t)

r (1-r)t(1-t)

(1-r)(1-t)

r2(1-r)t2(1-t)

(1-r)t

r (1-r)t

r2 (1-r)t3

r3 (1-r)t3

(1-r)2t

r2 (1-r)2t3

Absorptance

R + T + A =1

spectral transmittance

total transmittance


Transmittance depends on thickness. on aluminum coated with lead sulfide. Coating mass per unit surface area,

95% of solar energy can be trapped.

Effect of plate thickness on normal overall spectral transmittance of soda-lime glass (includes surface reflection) at 298 K


Emittance of sheets of window glass at on aluminum coated with lead sulfide. Coating mass per unit surface area, 1000°C


Selectively transparent coating may also be useful in the collection of solar energy.

Transmittance and reflectance of 0.35-mm-thick film of Sn-doped In2O3 film on Corning 7059 glass. Also shown is the effect on Tl of an antireflection coating of MgF2


Modification of Surface Directional Characteristics collection of solar energy.

Directional emissivity of grooved surface with highly reflecting specular side walls and highly absorbing base; d/D = 0.649. Results in plane perpendicular to groove direction; data at 8 mm


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