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 m; volume concentration of pigment 0.017,

Spectral Dependence

Spectral reflectivity of paint coatings. Specimens at room temperature

Normal spectral emissivity of some nonmetal samples.

Variation with Temperature

Effect of surface temperature on emissivity of dielectrics

Effect of surface temperature on normal total emissivity of zirconium oxide

Effect of Surface Roughness

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

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

Reflected energy at full moon

varies from 0° to 90° as the position of the incident energy varies from the center to the edge of the lunar diskuniform brightness: constant intensity reflected to earthcos consta

nt

Semiconductor

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

Radiative Properties of Metals

Effect of wavelength on directional spectral emissivity of pure titanium. Surface ground to 0.4 m rms

Directional Dependence

follow theoretical trend

EM theory doesn’t hold at shorter wavelengths.

Spectral Dependence

Variation with wavelength of normal spectral emissivity for polished metals

gray body assumption

Peak near the visible region

infrared region

1.27 m

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

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

H-R relation holds

Peak appears near the visible region

Variation with Temperature

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

er T

Hagen – Rubens

Effect of Surface Roughness

Roughness effects for small optical roughness, 0/ < 1; effect of surface finish on directional spectral emissivity of pure titanium. Wavelength, 2 m

follow theoretical trend

approach to optically smooth surface

Precise definition of surface characteristics geometric shape, method of preparation, distribution of size around rms

0/ > 1: multiple reflection

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

behave more like a polished surface

smoother relative to the incident radiation for large

Bidirectional reflectivity in plane of incidence for various incidence angles; material, aluminum (2024-T4), aluminum coated; rms roughness 0 = 1.3 m; wavelength of incident radiation, = 0.5 m

For large , peak r shifted to larger anglesOff-specular reflection at larger rough-ness and incident angle

/= 2.6

Effect of Surface Impurities

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

0.690.45

Effect of oxidation on normal spectral emissivity of Inconel X

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

Effect of oxide coating on hemispherical total emissivity of copper

Effect of oxide thickness on normal total emissivity of copper at 369 K

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

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

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 SurfacesModification of Surface Spectral

Characteristics

Characteristics of some spectrally selective surfaces

c: cutoff wavelength

c

Ex 5-1

An ideal selective surface with a cutoff wavelength c = 1 m

21353 W/miq

eq ?T

Energy balance

in out g stE E E E in outE E

inE : absorbed energy

outE : emitted energy

arriving from the sun at Ts = 5780 K

1 0 , 0 c c

4 2 162

2 22

5.67 57.8 6.95 10= 1358 W/m

1.5 10

sunearth

TS = 5780 K

ib,s d

L = 1.50 × 1011 m

R = 6.95 × 108 m

, cosc b sS i d 4 2

2 (cos 1)ST R

L

An ideal selective surface with a cutoff wavelength c = 1 m

21353 W/miqarriving from the sun at Ts = 5780 K

eq ?T

0( )cosi b sq Ci T d d

4

sC T 21353 W/m

4 4 25.67 (57.8) 63,284,000 W/msT

0( ) ( )cosb s eqCi T T d d

inE 0

( ) ( )coseq b sT Ci T d d

For diffuse irradiation

in 0( ) ( )cosb s eqE Ci T T d d

,

,

cos

cos

i i i

i i i

i d

i d

eq( )cosT d

in 0( ) ( )eq b sE C T i T d

0( ) ( )eq b sC T e T d

0

( )c

b sC e T d

4

40

( )c b ss

s

e TC T d

T

0 c si Tq F

eq eq0( ) ( )cosbi T T d d

eq eq0

1( ) ( )cosbi T T d d

eq eq0( ) ( )bT e T d

For diffuse irradiation

eq eq( ) ( )T T

out eq0( )

c

bE e T d

eq

40eq cTFT

eqe4

0q 0 c c siT TF q FT oreq

040eq

c s

c

i TTT

q FF

outE eq eq0

( ) ( )cosbT i T d d

By trial and erroreq 1334 KT

Cutoff wavelengt

h c, m

0.6

0.8

1.0

1.2

1.5

∞

Equilibrium temperatur

e Teq, K

1811

1523

1334

1210

1041

393

Ex 5-3,n

Wavelength

approximation

SiO-Al selective surface

21353 W/miq

Solar energy absorberat TA = 393 K1. extracted energy for use in a

power- generating cycle

?pq

2. for the black surface at the same

temperature

pq

0.95

0.051.5

in out g stE E E E

Energy balance

in , aE qout peE q q

p a eqq q

aq 0 00.95 0.05 1c s c si T Tq F F

21139 W/m

eq 40 00.95 0.05 1

c A c AA T TT F F

267.63 W/m

21139 68 1071 W/mpq

For black surface

(79% of )iq

4 21353 W/me A iq T q

No energy available

,n

Wavelength

approximation

SiO-Al selective surface

0.95

0.051.5

Reflectivity of white paint coating on aluminum

reflect well at short wavelengths

radiate well at long wavelengths

Selective Transmission

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

c c

ordinary glasses: typically two strong cutoff wavelengths

A transmitting Layer with Thickness L >

Reflectance

2 22 2

2 2 2 2

111 1 1

1 1

Transmittance

22 2 2 4 4

2 2

11 1

1T

1-

(1-)

(1-)2

(1-)

(1-)2

(1-)22

2(1-)2

(1-)3

2 (1-)23

3 (1-)3

3 (1-)4

3 (1-)24

(1-)(1-) (1-)(1-)

(1-)2(1-)

3 (1-)3(1-)

4 (1-)4

2 2 2 2 4 41 1 1R

2 2 3 3 1 11 1 1

1A

spectral transmittance 2

2 2

1

1T

2

2 20

1

1G d

G

,trG T G

total transmittance

Absorptance

1-

(1-)(1-)

(1-)

(1-)2

(1-)

(1-)(1-)

(1-)2

(1-)22

2(1-)2

(1-)2(1-)

(1-)3

2 (1-)23

3 (1-)3

3 (1-)3(1-)

3 (1-)4

3 (1-)24

4 (1-)4

,tr ,G

G

0T G d

G

,tr0

0

G dT

G d

R + T + A =1

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

Transmittance depends on thickness.95% of solar energy can be trapped.

Emittance of sheets of window glass at 1000°C

01 11

1A

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

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

Modification of Surface Directional Characteristics

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 m