1. RADIATION IN ENCLOSURES WITH SOME SPECULARLY REFLECTING SURFACES Exchange Factor Net Radiation Method Curved Specularly Reflecting Surfaces

2. Scope optical roughness long wavelength (infrared): specular fashion assumptions: 1)Specular reflectivity is independent of incident angle of radiation. 2) All surfaces are gray.

3. A1A1 A2A2 diffuse reflector specular reflector dA 1 Exchange Factor Specular view factor Mirror-image method (Eckert & Sparrow 1965) dA 1(2) dA 1(2) : mirror image of dA 1 through A 2 A 1(2)

4. dA 1 A1A1 A2A2 dA 1(2) When A 2 is a perfect specular reflector : the fraction of radiation energy leaving dA 1 that strikes A 1 after one specular reflection at A 2 : specular reflector diffuse reflector When :

5. A 1(2) dA 1 A1A1 A2A2 diffuse reflector specular reflector dA 1(2) fraction : partial diffuse view factor

6. Ex A2A2 A3A3 A4A4 A1A1 A 4(3) A 2(3) A 1(3) A 1, A 2, A 4 : diffuse A 3 : specular

7. A 1(3) A 1(2,3) Ex A2A2 A3A3 A4A4 A1A1 A 4(3) A 2(3) A 1(2) A 3(2) A 4(2) A 4(2,3)

8. Reciprocity for specular surfaces A 1 black A 2 black A 3, specular A 1(3) A 2(3) isothermal enclosure since

9. A 2 black A 3, specular A 1(3) A 2(3) A 1 black A4A4

10. isothermal enclosure A 2 black A 3, specular A 1(3) A 2(3) A 1 black

11. Net Radiation Method enclosure with n plane surfaces d : diffuse reflecting surfaces n - d : specularly reflecting surfaces for diffuse surfaces: or for specular surfaces: irradiation

13. parallel plates (both specular) Ex -- T 1,  1  -- T 2,  2 

14. spherical vacuum bottle specular: diffuse: specular: diffuse: Ex 9-1 294 K 0.65 cm A2A2 e = 0.02 15 cm A1A1 368 K

15. Ex 9-6 1/A 2 F 23 1/A 1 F 13 1/A 1 F 12 J1J1 eb1eb1 eb2eb2 eb3eb3 q1q1 a) surface 1 : diffuse reflector 45° A3A3 A2A2 A1A1 T 3 = 750 K,  3 = 1 T 2 = 525 K,  2 = 1 T 1 = 525 K,  1 = 0.05

17. b) surface 1 : specular

19. 1) direct: Curved Specularly Reflecting Surface specular tube Ex Let dX 1 dX D

20. 2) one-reflection: 3) n reflection: dX 1 dXdX/2