Radiation Chapter 12 L8 (MMV031) Martin Andersson

Transcription

1 Radaton Chapter 12 L8 (MMV031) Martn Andersson

2 Contents Thermal Radaton Gas radaton

3 Thermal radaton Thermal radaton s the electromagnetc radaton a body s emttng due to ts temperature electromagnetc radaton (a wave moton) s 8 progressng wth the speed of lght; 3 10 m/s c ν c speed of lght wavelength ν frequency

4 Thermal radaton - spectrum Termsk strålnng Solstrålnng Sun radaton ν Våglängd (µm) Wave length Frekvens (1/s) Frequency Infraröd Infrared ultravolett Synlga området Vsble range

5 Thermal radaton - notatons E (W/m 2 ) total emtted energy (power) per unt area G (W/m 2 ) ncdent radaton rradance J (W/m 2 ) total radaton from a surface radance J E + ρg I radaton ntensty F vew factor shape factor

6 Thermal radaton - notatons Reflectance ρ - fracton reflected radaton Absorptance α - fracton absorbed radaton Transmttance τ - fracton transmtted radaton Emttance (emssvty) ε rato of emtted radaton from a body and emtted radaton from a smlar black body

7 Thermal radaton nfallande ncdent reflekterat reflected absorberat absorbed ρ + α + τ 1 transmtterat transmtted

8 Thermal radaton opaque surface (τ 0) An opaque surface (τ 0) whch s not reflectng any radaton (ρ 0) s sad to be a black body. It absorbs all ncdent radaton and t s observed as black by the human eye.

9 Thermal radaton E 0 E d E monocromatc radant energy

10 Thermal radaton A perfectly emttng body emts maxmum radant energy for every wavelength at a certan surface temperature. Such a body wll also emt the maxmum total radant energy (see eq. (12-6)) It can easly be shown that a perfect absorber (black body) also s a perfect emtter. Thus a perfect emtter s also sad to be a black body. Propertes/Varables for black bodes are gven a subscrpt B (black body)

11 Thermal radaton 1 / 5 1 B 2 T C e C E Wm C K m C ) ( 1} { ) ( / B 2 T f e T C T E T C

12 Thermal radaton K E π B [ W/cm 2 ] 4000 SYNLIGT SPEKTRUM max T 2898 µm K 1200 K 1600 K 1000 K K Vsble range 600 K Våglängd [µm] wavelength

13 Thermal radaton E B 10 [ W/(m 2 12 /T µ mk 5 5 ] T 10 3 [ µ mk] max T [m]

14 Thermal radaton ( ) 0 / / / 5 1 B 1} { Introduce 1} { x C T C T C e x T dx C T Td dx T x e T C d T d e C E 4 B T E σ Stefan-Boltzmann s lag/law σ W/m 2 K 4

15 Thermal radaton ε 0.06 Fe ε E 0.04 Cu Al E B 0.02 Au Ag µm

16 Thermal radaton 1.0 ε 0.8 lera clay Portland cement ε E 0.6 E B 0.4 kakel vt 0.2 magnesum oxde µm

17 Thermal Radaton grey body E εσ T g 4

18 Thermal radaton 60 o 40 o 20 o 0 o 20 o 40 o 60 o N (polerad) N (matt) Cr Mn Al ε θ

19 Thermal radaton 40 o o 20 o 0 (b) (c) (a) (d) (e) (g) (f) 20 o 40 o (a) våt s wet ce (b) trä wood (c) glas glass (d) papper paper (e) lera clay (f ) kopparoxd copper oxde (g) alumnumoxd alumnum oxde 80 o 60 o o 80 o ε θ

20 Thermal radaton Krchhoff's laws α ε α ε

21 Thermal radaton - Intensty θ dθ da' r I da φ dφ

22 Thermal radaton-sold angle Sold angle dω dω da 2 r

23 Thermal radaton-intensty The radaton ntensty s defned as the radant energy per unt area projected perpendcular to a gven drecton and per sold angle unt vewed from the radatng surface. d( EdA) da I dacosθ dω I dacosθ 2 r

24 Thermal radaton-intensty EdA dω d( EdA) sn θ dθ dφ d( EdA) I dacosθ sn θ dθ dφ EdA 2π 0 π / 2 I da dφ cosθ snθ dθ 0 I daπ E π I

25 Thermal radaton vew factors da 2 A 2 dφ dω 1 I 1 da 1 cosθ 1 n da1 r θ 1 θ 2 n da2 dω 1 da 2 cosθ r 2 2 da 1 A 1

26 Thermal radaton vew factors Φ A A A A 1 2 I cosθ cosθ 1 r 2 2 da da Φ A E 1 1A1 π I1A1 Φ A F Φ 1 A2 12 A1 F 12 1 A 1 A A 1 2 cosθ cosθ 1 π r 2 2 da 1 da 2

27 Thermal radaton vew factors F 21 1 A 2 A A 1 2 cosθ cosθ 1 π r 2 2 da 1 da 2 A 1F12 A2 F21 j n j 1 F j F 1 + F F n 1

28 Thermal radaton- exchange black surfaces k J G Q A J EB A G ( J G ) Ak J k Fk k k A J k F k

29 Thermal radaton- exchange black surfaces ) ( k k k J F J A Q ) ( ) ( B B k k k k k k E E F A J J F A Q

30 Thermal radaton exchange nonblack surfaces k J G Q A ( J G ) J EB ε + ρ G ρ 1 ε

31 Thermal radaton exchange nonblack surfaces Q A ε 1 ε ( E B J ) Q A F ( J J ) k k k

32 Gas radaton

33 Gas radaton (Partcpatng meda) Elementary gases lke H2 O2 and N2 emt almost no thermal radaton and are almost transparent (τ 1) for radatve transfer. In engneerng applcatons CO 2 and H 2 O-steam are most mportant as these are good emtters and usually are present n hgh concentratons. CO SO2 and CH4 are also good emtters but are usually present n small concentratons only.

34 Gas radaton; absorptance CO 2 α % [µm] (1) 5 cm gasskkt (2) 3 cm gasskkt (3) 6.3 cm gasskkt (4) 100 cm gasskkt (1) 5 cm gas layer (2) 3 cm gas layer (3) 6.3 cm gas layer (4) 100 cm gas layer

35 Gas radaton; absorptance H 2 O - steam α % a (a) 127 o C gasskkt 109 cm (b) 127 o C gasskkt 104 cm (c) 127 o C gasskkt 32.4 cm (d) 81 o C gasskkt 32.4 cm (e) rumstemperatur gasskkt 220 cm a a a a a e c b c d (a) C 109 cm gas layer (b) C 104 cm gas layer (c) C gas layer 32.4 cm (d) 81 0 C gas layer 32.4 cm (e) room temperature gas layer 220 cm

36 Gas radaton; absorpton n a gas layer I 0 I x dx di a I dx

37 Gas radaton; absorpton n a gas layer a depends on pressure and temperature If pressure and temperature are unform.e. constant n the gas layer one has I I 0e a x Beer's lag/law

38 Gas radaton; absorpton n a gas layer τ a e x Commonly one as ρ 0 whch means α 1 a x e

39 Gas radaton; mean beam length equvalent beam length Beam lengths are dfferent average needed L 3. 6V A

40 Gas radaton emttance for steam p H2O L 6x10 5 Pa m 3x10 5 ε H2 O x10 4 3x x x10 3 4x10 3 3x x x Temperature [ K ]

41 Gas radaton; emttance for steam pressure correcton p H2O L 1.5x10 3 Pa m 8x x10 4 3x10 4 8x x10 5 3x10 5 C H2 O (p tot +p H2O )/2

42 Gas radaton emttance for CO p CO2 L 10 5 Pa m 0.1 6x10 4 ε CO2 3x x x Temperature [ K ]

43 Gas radaton emttance for CO 2 pressure correcton C CO p CO2 L8x10 4 Pa m 3x x10 4 8x10 3 4x x Totaltryck atm total pressure atm

44 Gas radaton; emttance for a mxture of H 2 O steam and CO 2 ε total ε H + ε 2O CO2 ε ε T g 400 K T g 811 K T g >1200 K p CO2 L+p H2O L1.5x10 5 Pa m x10 4 5x10 4 3x x10 4 p CO2 L+p H2O L1.5x10 5 Pa m p CO2 L+p H2O L1.5x10 5 Pa m x10 4 3x10 4 3x x x p H2O /(p H2O +p CO2 ) p H2O /(p H2O +p CO2 ) p H2O /(p H2O +p CO2 ) 10 4

45 Gas radaton; heat exchange between a gas and a chamber wth black surfaces Black surface T w Gas T g Q A emtted gas radaton absorbed wall radaton

46 Gas radaton; radatve exchange between a gas and a chamber wth black surfaces Q A 4 g Tg ) σ Tg α g ( Tw ) ε ( σ T 4 w ε g ( T g ) s determned at T g α (T ) α CO + α H O g w 2 2 α depends on both T g och/and T w

47 Gas radaton; radatve exchange between gas and a chamber wth black surfaces α α 0.65 Tg CO C 2 CO ε 2 CO2 Tw 0.45 Tg H2O H2O H2O C ε Tw α ε at T w p CO 2 L T T ) p O L ( Tw Tg ) ( w g H 2