DEFINITION OF PROPERTIES FOR OPAQUE SURFACES

1. DEFINITION OF PROPERTIES FOR OPAQUE SURFACES • Emissivity • Absorptivity • Reflectivity - ity : intensive, theoretical - ance : extensive, experimental

2. Emissivity blackbody real surface elb el l Black and non-black surfaces

3. il,e fe qe dA Directional spectral emissivity

4. Ex 3-1 From Table A-5,

5. il,e fe qe Since dA Directional total emissivity

6. Ex 3-2 T = 700 K From Table A-5,

7. il,e fe dwe qe dA Hemispherical spectral emissivity

8. Hemispherical total emissivity

9. or

10. Ex 3-3 e and e = ?

11. Summary Directional spectral emissivity Directional total emissivity Hemispherical spectral emissivity Hemispherical total emissivity or

12. Ex • Find: • Hemispherical total emissivity • Total emissive power • Wavelength at which spectral emissive • power will be a max Assumption: Surface is a diffuse emitter.

13. 1) Hemispherical total emissivity il,e fe dwe qe dA

14. From Table A-5 2) Total emissive power

15. elb l 3) Wavelength at which spectral emissive power will be a max. Maximum el may occur in 0 < l ≤ 2 mm or 2 < l ≤ 5 mm. First check where maximum elb occurs.

16. elb From Wien’s displacement law Thus, maximum occurs at l = 1.81 mm orl = 2 mm

17. at l = 1.81 mm From Table A-5, lT = 2898 mm.K at l = 2 mm From Table A-5, lT = 3200 mm.K Maximum spectral emissive power occurs at l = 2 mm.

18. elb elb, el el Peak emission

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

20. blackbody atT ilb dw q il dAatT Kirchhoff’s law absorbed energy emitted energy in equilibrium : no restriction

21. i) when ii) when not function of l Directional total absorptivity directional-gray surface

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

23. i) when ii) when and iii) when Hemispherical total absorptivity : diffuse-gray surface and iv) when

24. Ex 3-6 • Find a • for diffuse incident radiation from a black source at Ti = 1000 K and • 2) for diffuse incident solar radiation 1) Ti = 1000 K incident radiation: absorbed energy:

26. 2) Ti = 5780 K Remark:

27. 30,000 people gathered in Yoido Square to get express bus ticket bounded for Kwangju (noon on Sep. 19, 1982)

28. The road to home town in Thanks Giving Days is far and hard. 100,000 people gathered at Seoul Station (Sep. 29,1985)

29. Heavily crowded people at Seoul Station (early in the morning on Sep. 24)

30. Struggling to get tickets to home town at Seoul Station (Aug. 6, 1992)

31. il,i dwi dwr dA Reflectivity • Spectral reflectivity • bidirectional spectral reflectivity • directional spectral reflectivity • directional-hemispherical spectral reflectivity • hemispherical-directional spectral reflectivity • hemispherical spectral reflectivity dil,r

32. dil,r dwi il,i dA dil,r: contribution of il,i from direction to il,r in direction Bidirectional spectral reflectivity (spectral reflection distribution function) Reciprocity:

33. dwi dwr dA Directional-hemispherical spectral reflectivity il,i dil,r

34. dil,r il,r dwi il,i dA dA Hemispherical-directional spectral reflectivity

35. reciprocity: when is uniform over all incident directions average incident intensity

36. dwr dA Hemispherical spectral reflectivity il,i il,r dwi

38. Hemispherical total reflectivityr

39. a) b) Relations among Reflectivity, Absorptivity, and Emissivity Kirchhoff’s law for a directional-gray surface,

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

41. ir,n= ? Ex 3-9 black hemisphere at Ti = 1500 K dAat 500 K Assumption: The element has a specularly reflecting surface.

42. ir,n= ? black hemisphere at Ti = 1500 K dAat 500 K In the normal direction, incident energy = absorbed energy + reflected energy