12b Mod
12b Mod
12b Mod
Properties
Surface Radiative Properties
Chapter 12
Sections 12.4 through 12.7
Presented by R. Ben-Mansour
Emissivity
Surface Emissivity
• Radiation emitted by a surface may be determined by introducing a property
(the emissivity) that contrasts its emission with the ideal behavior of a blackbody
at the same temperature.
Note:
Low emissivity of polished metals and increasing emissivity for unpolished
and oxidized surfaces.
Comparatively large emissivities of nonconductors.
Emissivity (cont)
Note decreasing ,n with increasing for metals and different behavior for nonmetals.
Why does n increase with increasing for tungsten and not for aluminum oxide?
Abs, Ref & Trans
Radiation balance
G G ,ref G ,abs G ,tr
What may be said about reflection for a white surface? A black surface?
Note shift from semitransparent to opaque conditions at large and small wavelengths.
, ,
Why are there no restrictions on use of the foregoing equation?
Diffuse/Gray Surfaces
Diffuse/Gray Surfaces
• With 02 0 / 2 , cos sin d d
2 / 2
0 0 cos sin d d
• With
E d
0 ,b
E b T
and G d
0
G
Under what conditions may we equate to ?
FIND: (a) Solar absorptivity, (b) Total, hemispherical emissivity for T s = 340K.
Problem: Surface Emissivity and Absorptivity (cont)
SCHEMATIC:
ASSUMPTIONS: (1) Surface is opaque, (2) = , (3) Solar spectrum has G = G,S
proportional to E,b (, 5800K).
Hence,
S 0 0.0355 0.9 0.8805 0.0335 0.11 0.8805 0.774.
(b) The total, hemispherical emissivity for the surface at 340K may be
expressed as
E ,b , 340K d / E b 340K .
0
With = , the integral can be written in terms of the F(0 ) function. However, it is readily
recognized that since
F 01.5 m,340K 0.000 at T 1.5 340 510 m K
It follows that
0.1
COMMENTS: The assumption = is satisfied if the surface is
irradiated diffusely or if the surface itself is diffuse. Note that for this
surface under the specified conditions of solar irradiation and surface
temperature, S . Such a surface is spectrally selective.
Problem: Energy Balance for an Irradiated Surface
Ein Eout 0
G T 4 h T T L 0
s s
where, from Table 12.1, with ,Ts 1m 400 K 400 mK, F(0-T) 0.000.
Problem: Energy Balance for an Irradiated Surface (cont)
Plate absorptivity: With the spectral distribution of simulated solar irradiation proportional to
emission from a blackbody at 5800 K,
where, from Table 12.1, with 1Ts 5800 mK, F(0 -T) 0.7202.
Estimating the free convection coefficient, h : Using the Churchill-Chu correlation with
properties evaluated at Tf (Ts + T )2 350 K,
g Ts T L3
Ra L
2
0.387Ra L1/ 6
Nu L 0.825 =377.6
8 27
1 0.492 Pr 9 16
G 1052 W m2