ε (5) 4. Radiative Heat Transfer 4.1 Fundamentals of thermal radiation (1) W/m / K Stefan-Boltzmann-constant

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1 . Radatve Heat ranfer. Fundamental of thermal radaton 0 ( λ) q I dλ σ () max 8 σ 5,67 0 W/m / K Stefan-Boltzmann-contant λ ( λ) q I dλ () λ 0 emperature q λ / q Sun 6000 K 0, µm Hot materal 600 K 0 µm Envronment 300 K 5 50 µm q (3) σ emvty f( λ) aborptvty a Krchhoff la () λ λ mean emvty ( ) λ 0 ( λ) I( λ,) σ dλ emvty of gae exp( a p ) (5) λ λ Approxmaton A exp( B ) (6) Ga A B p n bar m n K 0,5 p 0. 0, 085 6,7 0 ( p ) 0,0,5 > ( p ) ,00 0,0 0,60 p 0, 0, 5,3 0 ( p ) 0, > p 0. 0,0 0, CO ( ) 6 H O ( ) 5 ( ) 7 ( a p a p ) exp λ CO λh O H O (7) CO (8) CO HO CO HO mean beam length

2 V 0,9 (9) A. Radaton beteen area (ve factor) Lambert la q q co ψ (0) ψ n q π / π q n ψ 0 ϕ 0 co ψ n ψ dψ dϕ π q n dq () σ da dq ϕ dq () coψ coψ ϕ A da da (3) π A A ϕ A ϕ A 0 ϕ for flat or convex urface (no element can ee an other) ϕ 0 for nfnte parallel plate or encloure (all radaton from element meet element k) ϕ k.3 Radaton exchange beteen urface ρ α q reflectvty aborptvty emvty heat flux (reflectance) (aborptance) (emttance) q h b h b radoty rradaton

3 h e e ρ b emon e q σ ρ [ e ( ρ ) h ] N b h k k ϕ k h ρ N k h k ϕ k e (ρ ϕ ) h ρ ϕ h K ρ ϕ h e ρ ϕ h ( ρ ϕ ) h L ρ ϕ h e N N N N N ρ ϕ h ρ ϕ h K ( ρ ϕ ) h N R h e N N N NN N e N R ρϕ ρϕ L ρϕn ρϕ ρϕ L ρϕn M M O M ρn ϕn ρn ϕn ρ L N ϕnn h M h N, h h, e e e. M e N e quaton for h h R e nvere matrx calculaton th commercal program q ρ [ e ( ρ ) h ] Example to parallel nfnte plate ϕ ϕ ϕ ϕ 0 no emon reache on urface h ρ h e

4 ρ h h e h e ρ e ρ ρ ρ q e e ( ) q σ ρ ρ q σ ( ) overall emvty Example for encloure ( ρ ϕ) h ρ ϕ h e ρ h ϕ ( ρ ϕ ) h h e [( ρ ϕ ) e ρ ϕ e ] j jj j j for, j or, j ( ρ ϕ ) ( ρ ϕ ) ρ ρ ϕ ϕ q ϕ ϕ ( ) σ A ϕ A ϕ A A Q σ A ( ) (8) urroundng area A < A

5 ( A A A Q σ ) (9). Radaton held ( 0 q σ ) (0) ( q σ ) () ( q σ ) () Replacng ( q σ ) (3), () ( ) q σ (5) q q 0 (6) : ( ) ( ) q q 0 (7) : q q 0 (8) : 0 q q (9)

6 .5 Heat tranfer by radaton and convecton.5. Radatve heat tranfer q α ( ) σ ( ) ( ) q ( α α ) α ( ) σ ( ) 3 3 α σ 3 3 << α σ 3 / α σ.5. hermocouple (tc) tc ( g tc Q α A ) ( 30) Q A σ tc tc ( ) tc (3) g tc tc tc σ α (3) Q α α A tc σ ( ) tc 3 tc tc (33) (3) tc α g α g α / α (35) α α α / α α / α 0 : tc g meaurng ga temperature accuratvly:. hgh convectve heat tranfer mall dameter of thermocouple Nu 0,66 Re 0,5 Pr 0,33 (36) α d tc d Nu, Re tc (37) λ ν

7 α ~ d... 0,5 tc d tc. lo radatv heat tranfer radaton held for thermocouple.5.3 Secondary radaton Q Q Q Q g Q g (38) adabatc all (39) Q Q Q g g α α g g A A σ A ( ) g ( ) g ( ) (0) () () from Eq. (39) th () and () Lnearzaton of radaton Q α A ( ) (3) α g g () α g α α Q α / αg α g A ( g ) (5) α / α g α α 0 e.g. 0 / g Q Q g α e.g. hgh /α g Q Q g

8 .6 Radatve heat tranfer beteen ga and old ( ) Q σ A g g g (6) g g (7) a g (8) a g a emvty of ga for g emvty of ga for emvty of all.7 Radatve heat tranfer beteen ga, old and all Q g g σ ( g ) A (9) g g ( g ) A Q σ (50) ( ) A Q σ (5) Q Q g Q (5) Q adabatc all (53) g Q g g g A A / A / A (5) Q g ( g ) A A σ (55) g A

9 Materal Metal th polhed and brght urface Ag, Al, Cr, Cu, Fe, Hg, Pb, Sn, Zn, bra Metal th reacted urface oxdzed, galvanzed, carburzed, ruty teel, cat ron Inorganc non-metallc materal concrete, gla, ceramc, porcellan, clay, brck, refractore, ce Organc materal Platc, pant, paper, rubber, ood Graphte ab. -: Approxmate value for emvte at ambent temperature Geometry of ga volumne nfnte lab, thckne t cube, length a retangular, man length a phere, dameter d long cylnder, dameter d long half cylnder, dameter d Mean beam length.8 t 0.6 a 0.9 a 0.6 d 0.9 d 0.6 d ab. -: Approxmate value for mean beam length

10 Formeln Kaptel E G AGe G. (.) H E ρ B W W W B H ϕ H ϕ τ H W G GW W WW GW G E G W. (.), (.3) (.) G q GW q WG GW e G e W (.5) α GW GW α W GW GW W GW σ G W (. (.6) Q A ) (.7) GW W G Q H B E H S. (.8) ( ) ( ) S S S S S ρs H E ρ B S S S S, W W W B H ϕ H ϕ τ H ϕ τ S G GS S SS GS W WS GW. (.9) H E ρ B (.0) W, (.a) B H ϕ H ϕ τ H ϕ τ W G GW S SW GS W WW GW. (.b) H S E SρS AS e G H SϕSSτ GS H WϕWSτGW, (.a) H W E W ρw AW e G H SϕSWτ GS H WϕWWτGW, (.b) S H W S, H W (.3) ϕ ρ τ ϕ ρ τ ϕ ϕ ρ ρ τ τ (.) ( ) ( ) SS S GS WW W GW WS SW S W GS GW ( ) ( S E S ϕww ρw τ GW E W ϕws ρs τ GW AS e G ρs ρw τgw ϕsw ϕ WW ), (.5a) ϕ ρ τ ( ϕ ρ τ ) ρ ρ τ ( ϕ ϕ ) W E S SW W GS E W SS S GS AW e G W S GS WS SS. (.5b) Q A ( K e K e K e ) S S S G G W W S S (.6) K G G [ ρwτgw( ϕsw ϕ WW)]

11 K W ϕswwτ GW, ( ) ( ) KS ϕssτgs ϕwwρwτgw ϕswϕwsρwτgsτ GW (.7a) (.7b) (.7c) τ GW τ GS : τ G G und ϕ SS 0 (.8) S Q S AS σ( KG G KWW KS S) (.0) ( ) ( ) KG G ϕwsρwτ G, K W Wτ G, K S ρ W τ G ϕ WS G, (.) [ ( ρ τ ϕ ρ τ )]. (.) W G WS S G Q H H. (.3) S W WS W S S W ρs ρw H E ϕ ρ τ (.) W S W WS S GW W S Q WS AW ϕws ( τgw e W τgs e S). (.5) Q Q Q. (.6) GW WS W W Q W AW { [( ϕss ρs τgs) ( ϕww τgw) ϕsw ϕws ρs τgs τgw ] e W ϕ τ e ϕ ϕ ρ τ e. [ ( ) ] WS S GS S WS SS S GS G G W Q GW AW {[ ( ϕws ϕss) ρ Sτ GS] G e G α ρ τ ϕ α ρ τ ϕ e [ ( ) ] GW S GS SS GS S GW WS W } }. (.7) (.8) S Q GS AS {[ ( ϕsw ϕww) ρw τgw ] G e G α ρ τ ϕ α ρ τ ϕ e [ ( ) ] GS W GW WW GW W GS SW S }. (.9) W S G Q τ WS AW WS σ( W S ) mt WS (.30) G W WS S G Q ( ϕ ρ τ ) GW AW GW σ( G W ) mt GW (.3)

12 G S WS W G Q ( ϕ ρ τ ) GS AS GS σ( G S ) mt GS, (.3) W ( ) WS S GS G G WS GS S S ϕ ρ τ ϕ τ ( ) τ ϕ ρ τ GW WS S GS. (.33) W GW G WS WS S ϕ ϕ GW WS WS. (.3) G GW W WS GS S ϕ ϕ GW WS GS. (.35) [ ] H E ρ A e H ϕ τ H ϕ τ S S S S G S SS GS W WS GW, (.36a) H A e H ϕ τ H ϕ τ W W G S SW GS W WW GW, (.36b) S Q GWS A S σ{ G [ ( ϕsw ϕww ) τgw] G SS GS WW GW SW WS GS GW S [( ϕ τ ) ( ϕ τ ) ϕ ϕ τ τ ] } (.37) ( ) ( ) ϕ ρ τ ϕ τ ϕ ϕ ρ τ τ. (.38) SS S GS WW GS SW WS S GS GW ( ) GWS S GWS σ G S. (.39) Q A ( ϕ τ) S G WS G GWS. (.0) G ϕ WS ( ρ S τ G) τg GWS GS ϕws WS GW. (.) Q W Q S. (.) Q E W ( ) W W W ρw H, Q S SH SE S ρs ( ). (.3) ρ H ρ H ρ E ρ E S W W W S S S W W S. (.) [ ( )] [ ( )] ϕ ρ ρ τ ϕ ϕ H ϕ ρ ρ τ ϕ ϕ H WS S W GW SW WW W SW W S GS WS SS S (.5) ϕ ρ E ϕ ρ E WS S W SW W S.

13 {[ ( ) ] [ ( ) } Q ϕ A SW S W WGS S σ ϕsw ϕww τgw W ϕws ϕss τgs] S, (.6) WS S [ ( SW WW) W GW] SW W [ ( WS SS) S GS (.7) ϕ ϕ ϕ ρ τ ϕ ϕ ϕ ρ τ ] Q A ) (.8) WGS S WGS σ W S ( WGS. (.9) ϕws ϕws ϕws τg S W Q ( E H ), Q S ( SH SE S ) (.50) ρ ρ ( ) WGS S WGS σ S (.5) Q A WGS ϕs τ ϕ τ S S G G S. (.5)

14 Fg..: Mono chromatc Intenty of black radaton Fg..: Spectral fracton of radaton Fg..3: Prncple profle of emvty

15 Fg..: Spectral emvty of alumnum and hte pant Fg..5: Spectral emvty of ome metal

16 Fg..6: Mean emvty of ome metal

17 Fg..7: Spectral emvty of ome refractore Fg..8: Mean emvty of ome refractore

18 Fg..9: Aborptvty of elected materal n dependence on temperature of emttent Fg..0: Spectral tranmon of gla

19 Fg..: Spectral emvty of CO and H O Fg..: Mean emvty of CO

20 Fg..3: Mean emvty of H O emvty 0,6 0,5 0, 0,3 0, , 0 0 0,5,5,5 3 (p CO p HO )* n bar*m Fg..: Emvty of combuton ga of natural ga

21 Fg..5: Emvty of oot Fg..6: Emvty of dut

22 Fg..7: Mean beam length Fg..8: Lambert la Fg..9: Hemphere radaton

23 Fg..0: Radaton beteen to fnte area Fg..: Fg..: Ve factor Fg..3: Radaton exchange beteen element

24 Fg..: Radaton held / h π π emperature n K Fg..5: Radatve heat tranfer coeffcent

25 Fg..6: Meaurng ga temperature nfluenced by encloure Fg..7: Secondary radaton Fg..8: Heat tranfer beteen ga and encloure

26 Fg. -3: emperature dependency of knematc vcoty for organc lqud

27 Fg. -3: hermal phycal properte for mneral ol