Energy Balance of Solar Collector

Transcription

1 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Wecome! Energy Bnce of Sor Coector Mohmd Khrseh

2 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Liuid Ft Pte Coectors. Het Loss from Coector 2. esting of Sor Coectors 2

3 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! sefu Het Gined By he Coector Not of sor rdition hits the soed surfce cn be used: Some sor rdition is refected nd re-emitted wy Some of the gined energy is ost gin to the surrounding u S A u sefu het gined by the coector S Sor Energy bsorbed in bsorber A Are of the bsorber tes Het ost from the coector 3

4 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Losses from Coector he therm osses deends on: he temerture difference between the bsorber te nd the mbient ir he over het oss coefficient, [W/m 2,K] A ( ) m m Men temerture of bsorber tes Ambient ir temerture 4

5 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Losses from Coector Whenever the bsorber te is wrmer thn the mbient ir, het is ost from the coector through: the cover (to), [W] t t A ( ) m the bottom, [W] b b A ( ) m the sides, [W] s s A ( ) m Most of the het osses is through the cover 5

6 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Over Het Loss Coefficient hen, the tot het osses is: t b s Since the het oss eutions re exressed on the bsis of the sme temerture difference, it is then ossibe to evute the over het oss coefficient,, by A ( m ) t b s yic vues of rnges from 2 to 0 W/m 2 K 6

7 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! herm Network for Ft-Pte u 7

8 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Bottom Het Losses Coefficient he het osses coefficient through the bottom is reresented by two series resistors, R 3 nd R 4. It is ossibe to ssume R 4 is zero: b R 3 λ δ b λ therm conductivity of insutor δ b thickness of insuted bottom 8

9 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Side Loss Coefficient Simiry, the het trnsfer coefficient for the coector side is: s 2 L3 L ( L L ) L 2 2 λ δ s L ength of csing L 2 width of csing L 3 height of csing λ therm conductivity of insution δ s thickness of insuted side 9

10 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! o Loss Coefficient t C m N m N f e α ε σ N α 2 2 ( ) ( ) m 2N f m 033. ε ε g N α v or α v or Nu 0 86Re wind wind. / 2 Pr / 3 f ( α 066. α ε ) ( 0. N) C 520 ( β ); 0 β 00 e ( m ) 2 70 N number of covers σ Stefn-Botzmnn constnt ε emissivity of te ε g emissivity of gss (0.88) α convection coefficient of mbient ir (W/m 2 K) ν wind Wind seed of mbient ir (m/sec) β coector tit (degree) 0

11 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! o Loss Coefficient Determine the over oss coefficient for coector, singe gss cover, with the foowing secifiction: Pte emissivity 0.95 Ambient temerture 0 0 C Men te temerture 00 0 C Coector soed nge 45 0 Wind seed 2 m/sec Bck-insution thickness 50 mm insution conductivity W/m.K Coector bnk ength 0 m Coector bnk width 3 m Coector thickness 75 mm Edge insution thickness 25 mm

12 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Bnce of Coector u A ( S ( ) m his exression deends on two fctors:. : is function of the men te temerture, m 2. m : is the men te temerture, which is unknown We need to exress u in terms of known temerture. he ony known temerture is the fuid inet temerture 2

13 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Absorber Cross-section he usefu het gined by the bsorber te cn be divided into:. the het gined from the re bove the tube 2. the het gined from the fin u u tube u fin tube fin W-D o W 3

14 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Gin er unit Length he usefu het trnsfer rte to the fuid in the bsorber cross-section is: u [ F ( W D ) D ] [ S ( )] o o b F: Stndrd Fin Efficiency F tnh m [ m ( W Do )/ 2] ( W D )/ 2 o Hyerboic tngent Where m is : m ( /λ δ ) ½ D o tube outer dimeter W distnce between tubes b oc bsorber temerture bove the bond λ therm conductivity of bsorber te δ thickness of bsorber te 4

15 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Coector Efficiency Fctor, F u [ F ( W D ) D ] [ S ( )] o o b o rete this exression to the oc fuid temerture tht resuts from this het trnsfer, the coector efficiency fctor, F, is introduced: F' 0 W [ F( W D ) D ] πd α o o i f D i tube inner dimeter α f convection coefficient of fuid o over het oss coefficient from fuid to mbient over het oss coefficient from bsorber to mbient 5

16 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Coector Efficiency Fctor, F hus, usefu gin cn be exressed s : u F W [ S ( )] f We eiminted b from the eution nd obtin n exression for usefu gin in term of known dimensions, hysic rmeters nd fuid temerture. 6

17 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Gin in Cross-section We cn exress n energy bnce on the fuid fowing through sign tube of sm ength dy s: Fuid Fow ( m/n) c f(y) ( m/n) c f(y dy) Number of tube in the bsorber te dy y n u dy m c d f m c df dy n F' W [ S ( )] 0 f 7

18 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Gin in Cross-section Soving this differenti eution, we cn determine the fuid temerture t ny osition y: f (y)--s/ - -S/ fi e - nw F' y m c If the coector hs ength L in the fow direction, then the outet fuid temerture fo is found by substituting L for y, note tht n. W. L A fo fi - - -S/ -S/ e AF' - m c 8

19 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Remov Fctor, FR he het remov fctor, which retes the ctu het gin to the mximum het gin, is define s: F R u Actu het gin Mximum het gin u A c( fo fi ) [ S ( )] m fi sing the st eution in the revious side, we cn exress F R tht is indeendent of the outet temerture, fo : F R mc A e A F' m C 9

20 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Het Gin in Cross-section hen the coector het remov fctor times this mximum ossibe usefu energy gin is eu to the ctu usefu energy gin u u A F R [ S ( )] fi 20

21 Gret Ides Grow Better Beow Zero! Renewbe Energy Grou 2 Het Gin in Cross-section sing F R the usefu het gin cn now be determined bsed on the inet temerture. But the over het oss coefficient,, is function of the men te temerture, m m C A F' R e A mc F ( ) [ ] f i o o πd α D D W F W F' 0 ( ) ( ) N ε ε. f N α N. ε σ α f N C N g m m e m m t s b t ( ) [ ] fi R u S F A

22 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Men Pte emerture. Guess first vue of (2 0 W/m 2,K) nd ccute the het gin, u. 2. m cn then be ccuted from the origin het gin eution: u A ( S ( ) m 3. se the ccuted m to derive new. 4. Continue with itertions unti remins roximtey the sme from one ccution to nother. Since is ony vguey deendent on the temerture, one or two reetition shoud be necessry 22

23 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Instntneous Coector Efficiency Coector is exosed to sor rdition whie the fuid fow rte nd temerture increse is mesured. he usefu het gin in coector oerting under stedy stte condition eus the enthy increse of the fuid: ( ) umc fo-fi he instntneous coector efficiency is the rtio of the usefu het gin to the incident sor rdition: mc ( - ) [ S- ( )] u fo fi R i L fi- AI AI I η F 23

24 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Instntneous Coector Efficiency he efficiency curve for coector is otted s function of ( fi )/I [ fi - /I ]0 3 [Km 2 /W] he efficiency curve yieds stright ine since FR, (τα) nd re firy constnt for coector tye when the fow rte is constnt 24

25 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Exme Csing: Length 2.4m Width.2m δb 25mm λb 0.036W/mK Absorber: Length 2.3m Width.5m δ-c 25mm δ 0.5mm λ 237W/mK α 0.9 ε 0. D0 3.4mm Di 2.4mm W 43mm Kδc 0.03 Cover: Mteri: gss N α c ε c 0.84 n 2 /n.526 Het crrier: Fuid: wter m 5kg/h i 293 K h f 205W/m 2 K Ambient: 273 K V 5 m/s 25

26 Renewbe Energy Grou Gret Ides Grow Better Beow Zero! Assignment 2 sefu het gined by the coector nd coector efficiency. Determine the best soe nge of your sor coector, for your region, tht roduces the mximum energy. 2. Annu & monthy vibe sor energy on soed surfce in your region. 3. Annu & monthy usefu het gined by one sure meter of soo coector. 4. Monthy sor coector efficiency. 5. nnu verge sor coector efficiency sing foowing Assumtion: W0.43 m, Do0.034, Di0.023, δb0.05, δs0.025, δ0.00, λinsution0.045, λ237 nd the fow rte is 0,004 kg/s 26

27 Gret Ides Grow Better Beow Zero! Renewbe Energy Grou 27 ( ) ( ) ( ) r d d b b G G τα G τα S ( ) ( ) d ρ α α τ τα ( ) [ ] fi R u S F A m C A F' R e A mc F ( ) [ ] f i o o πd α D D W F W F' 0 ( ) ( ) N ε ε. f N α N. ε σ α f N C N g m m e m m t s b t