Temperature dependence of the total, normal emissivity e n of selected materials

1. Temperature dependence of the total, normal emissivity en of selected materials

2. Representative values of total, normal emissivity en

3. Absorptivity dependence on the directional and spectral distributions of the incident radiation, thus not a material property except fi qi dA Directional spectral absorptivity

4. Ilb dw Il Kirchhoff’s law blackbody atT q dAatT absorbed energy emitted energy in equilibrium : no restriction

5. when not function of l Directional total absorptivity absorbed energy at l and (qi, fi) directional-gray surface

6. when only: ii) when independent of direction Hemispherical spectral absorptivity diffuse irradiation diffuse-spectral surface

7. i) when Hemispherical total absorptivity : diffuse-gray surface

8. Relations among reflectivity, absorptivity, and emissivity a) b) Kirchhoff’s law for a directional-gray surface,

9. c) d) for a diffuse-spectral surface, for a diffuse-gray surface,

10. Example 12.7 • Find: • Spectral distribution of reflectivity rl • Hemispherical total absorptivity a • Nature of surface temperature change

11. 1)Spectral reflectivity

12. = 5000 W/m2 2)Hemispherical total absorptivity a incident radiation in W at l: absorbed energy: Why is the value of a(= 0.76) closer to unity ?

13. Since , the surface temperature will increase with time. 3)Nature of surface temperature change Does the surface temperature increase or decrease?

14. Environmental Radiation extraterrestrial solar irradiation Solar rays q Gs,o Sc Earth atmosphere Earth surface Sc: solar constant (flux of solar energy incident on a surface oriented normal to the sun’s rays, when the earth is at its mean distance from the sun) f : correction factor to account for the eccentricity of the earth’s orbit about the sun q : incident angle of solar irradiation

15. Spectral distribution of solar radiation

16. Directional distribution of solar radiation at earth’s surface actual diffuse

17. Scattering of solar radiation in the earth’s atmosphere

18. Find: • Useful heat removal rate per unit area, • Efficiency h of the collector. Example 12.11 flat-plate solar collector : useful heat removal • Assumptions: • steady-state • absorber surface diffuse

19. : useful heat removal 1)Useful heat removal rate

20. Comments: • Since the spectral range of Gsky is entirely different • from that of GS, it would be incorrect to assume that • asky = aS . • 2) With a convection coefficient , the useful heat flux and the efficiency are reduced to • and . A cover plate can contribute significantly to reducing convection (and radiation) heat loss from the absorber plate. : useful heat removal 2)The collector efficiency

22. Reflectivity Il,i dwi dIl,r dwr dA Directional-hemispherical spectral reflectivity

23. Il,r Il,i dA dA

24. Il,r Il,i dA dA Hemispherical-directional spectral reflectivity average incident intensity

25. Reciprocity: when is uniform over all incident directions

26. dwi Il,r Il,i dwr dA Hemispherical spectral reflectivity

27. Hemispherical total reflectivity

28. A transmitting Layer with Thickness L >l 1 r r3 (1-r)t3(1-t) r (1-r)t(1-t) (1-r)(1-t) r2(1-r)t2(1-t) 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

29. 1 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

30. the amount of radiation energy streaming out through a unit area perpendicular to the direction of propagation , per unit solid angle around the direction w, per unit wavelength around l, and per unit time about t. the amount of radiation energy intercepted by dA2 per unit wavelength, per unit time [W/mm]