Modeling of energy distribution inside greenhouse using concept of solar fraction with and without re&ecting surface on north wall

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1 Mdeling f energy distributin inside greenhuse using nept f slar fratin with and withut re&eting surfae n nrth wall Ravi Gupta, G.N. Tiwari* Centre fr Energy Studies, Indian Institute f Tehnlgy Delhi, Hauz Khas, New Delhi 6, India Reeived 2 Nvember 23; reeived in revised frm 4 February 24; aepted 29 Marh 24 bstrat nsiderable prtin f the slar radiatin falling n transparent nrth wall/rf inside an east-west-riented greenhuse is lst due t lw-altitude angle f sun during winter mnths. Replaing the transparent nrth wall with a re&eting surfae an inrease slar radiatin n the &r f the greenhuse. Eet f vertial and inlined re&eting nrth wall n distributin f slar radiatin n the &r f greenhuse has been studied fr 2ve dierent latins in India. These latins are Chennai (3 N), Klktta (22.53 N), Jdhpur (26.3 N), Delhi (28.58 N) and Srinagar (34.8 N). Evenspan greenhuse (6 m x 4 m x 3 m) has been nsidered fr the present study. The prpsed mdel an als be used t determine the distributin f slar radiatin fr any ther plae and shape f the greenhuse. Keywrds: Slar radiatin; Greenhuse; Slar fratin; Thermal heating. Intrdutin Slar energy is generally used fr illuminatin and thermal heating f a building/greenhuse []. Sme part f the transmitted slar radiatin falls n nrth wall/rf inside the greenhuse. This radiatin falling n nrth wall /rf further transmits thrugh nrth wall/ rf. Puar [2] has studied the use f re&eting surfae n nrth wall fr mre illuminatin n the &r f the greenhuse. Varius ther attempts have als been made t inrease the illuminatin inside a greenhuse by re&eting the slar radiatin [3-7]. The slar radiatin falling n nrth wall/rf an als be used fr thermal heating f the greenhuse. Eurpean passive slar handbk [8] als desribes the methd fr thermal heating by slar energy. The present wrk analyses the distributin f slar radiatin n &r f the greenhuse after its re&etin by a re&eting nrth wall. The study was mtivated by the fat that the lss f slar radiatin thrugh nrth wall/rf is mre during winter mnths due t lw-altitude angle f the sun. Tiwari [9] has suggested a term alled "slar fratin fr nrth wall" t quantify this lss thrugh nrth wall. "Slar fratin fr nrth wall" is the rati f slar radiatin falling n nrth wall t ttal radiatin transmitted inside the greenhuse. The value f slar fratin (due t nrth wall) will be mre [9] during winter mnths beause f the lw altitude angle f the sun and hene the lsses will be mre. mdel has been develped t alulate "ttal slar fratin". Ttal slar fratin quanti2es the lss f all transmitted slar radiatin ming inside the greenhuse. These lsses take plae frm nrth wall/rf and east/west wall. "Ttal slar fratin" is the rati f ttal slar radiatin lss frm greenhuse t ttal slar radiatin transmitted inside the greenhuse. The slar radiatin n the &r f the greenhuse with and withut re&eting surfae has been evaluated by using the measured inslatin data. The value f ttal slar fratin was mparable fr dierent rientatins f a greenhuse. The maximum lss f slar radiatin takes plae frm nrth wall/rf f the greenhuse fr east-west rientatin. Hwever, when a greenhuse is rtated frm its riginal east-west psitin then the majr lsses f slar radiatin ur frm ther setins f the greenhuse instead f nrth wall/rf. 2. ssumptins. n east-west-riented greenhuse is nsidered. 2. n evenspan greenhuse is divided int six setins (suth wall, suth rf, nrth rf, nrth wall, east wall

2 64 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) 63-7 Canpy ver transparent t shrt wavelength Refleted shrt wavelength radiatins Fig.. SW Ismerti view f E-W greenhuse ( rientatin) shwing varius setins. and west wall). These setins were named as Setins, 2, 3, 4, 5 and 6, respetively, as shwn in Fig.. 3. The lss f slar radiatin due t absrptin and re&etin at the greenhuse vering material is negleted. 4. Shading by greenhuse strutural mpnents and ndensatin n the vering material is als negleted. 5. The mdel is fr lear sunny day. 6. Useful slar radiatin is available frm 8: am t 4: pm. 3. Thery If the phenmenn f glbal greenhuse eet is taken at the mir level fr a huse having transparent (glass, FRP, plyethylene 2lm) walls/rfs fr maintaining suitable envirnment fr the grwth f plants then this enlsure is alled as greenhuse. Slar radiatin falls n eah setin f the greenhuse. fter transmissin, slar radiatin either falls n the &r r nrth wall/rf r bth f the greenhuse (Figs. 2a and b). re&eting surfae in plae f nrth wall an re&et the transmitted slar radiatin falling n nrth wall twards the &r (Figs. 3 a and b) and by putting an inlined re&eting surfae, slar radiatin lsses urring thrugh nrth rf wall an als be re&eted twards the &r. Inlinatin f the re&eting surfae must be adjusted arding t the lwest altitude angle f sun s that mre and mre re&eted slar radiatin fall n the &r f the greenhuse. Fig. 2. (a) Shrt wave inming slar radiatin ming frm ne setin and ging ut thrugh anther setin and falling n sil surfae utside the greenhuse withut ntributing t greenhuse; (b) shrt wavelength inming slar radiatin ming frm ne setin and ging ut thrugh rf int sky withut ntributing t greenhuse. Fig. 3. Even span greenhuse with vertial (a) and inlined (b) re&eting wall. b) 4. Definitin f slar fratin (F n ) Referring t Fig. 4, the slar fratin fr nrth wall (F n ) an be de2ned as the rati f slar radiatin falling n the nrth wall f the greenhuse (E-W rientatin) t the ttal inming transmitted radiatin inside the greenhuse. The expressin f F n an be written as fllws [6] slar radiatin available n nrth wall inside greenhuse fr a given time slar radiatin measured n the nrth side and &r f the greenhuse at the same time () Fig. 4. Calulatin f the slar fratin (F n ) f uneven span greenhuse fr nrth wall. Fr example, slar radiatin fall n tw setins ( and 2) and mes ut frm Setins 3 and 4 at nn, as shwn in Fig. 4. Slar fratins fr nrth wall due t Setins

3 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) and 2 an be alulated as The length f the prjeted ray after the nrth wall The ttal length f the prjeted ray H 7 G 7 ' The length f the prjeted ray ntributing twards the nrth wall 'C The ttal length f the prjeted ray F n 3 =F n 4 =F n 5 =F n 6 =, (Sine, n radiatin falls n nrth wall frm these setins). Slar fratin (F n ) will vary with the time f the day. Slar fratin fr nrth wall (F n ) will be the average f slar fratins due t eah setin. This an be expressed as fllws: _ (F n + F n 2 + F n 3 + F n 4 + F n 5 + F n 6) n : (4) = 6 The abve equatin an be rewritten as fllws: (2) (3) 6. Calulatin f sun angles The required values f delinatin angle (d), hur angle (!), slar altitude (a) and slar azimuth (y) at dierent time f the day fr a typial day f eah mnth were alulated [] (ppendix ). mputer prgram has been made in MS Exel t alulate varius angles. Fr alulatins, lal time is taken as slar time. 7. Calulatin f ttal energy n the greenhuse fter knwing beam and diuse radiatin n hrizntal surfae, ttal radiatin n a surfae f arbitrary rientatin was alulated by Liu and Jrdan frmula (ppendix B). Ttal slar radiatin n the greenhuse (S t ) = sum ttal f slar radiatin falling n dierent setins f the greenhuse. r where () 5. Definitin f ttal slar fratin (F t ) j= () F = r F t = \- Sum f transmitted slar radiatin falling n eah setin f the greenhuse fr a given time Ttal slar radiatin transmitted inside the greenhuse at the same time Transmitted slar radiatin falling n &r f the greenhuse fr a given time Ttal slar radiatin transmitted inside the greenhuse at the same time (6) (7) 8. Optimizatin f inlinatin f refleted surfae vertial re&eting surfae in plae f nrth wall an be utilize t re&et the transmitted slar radiatin falling n nrth wall as shwn in the Fig. 3 a. T maximize the re&eted slar radiatin n &r f the greenhuse, an inlined surfae is suggested as shwn in the Fig. 3b. The inlinatin f the re&eting surfae, as shwn in Fig. 5, shuld be ptimized fr maximum slar radiatin n the &r f the greenhuse. Fr the purpse f ptimizatin the altitude angle at 8. am was nsidered fr winter mnths beause if an inlinatin r F = (8) where j is the number f setins in a greenhuse reeiving transmitted slar radiatin. Fr the jth setin reeiving transmitted slar radiatin inside the greenhuse, slar fratin in terms f shadw f jth setin an be de2ned as j I I \ f \ J Parallel 3Re fleted ray Inidene ray t grund Nrmal t refleting surfae rea f shadw f the jth setin n hrizntal surfae Ttal shadw area f the greenhuse (9) L' Fig. 5. Shemati representatin f re&etin f beam radiatin t grund with inlined re&eting surfae.

4 66 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) 63-7 is suited fr 8: am than it will autmatially be best fr rest f the day. Thugh the altitude angle will be lwest at sunrise but pratially during winter mnths useful slar radiatin will be available nly after 8: am. Fr the purpse f ptimizatin, (ppendix C), length f the re&eted radiatins frm bttm f the re&eted surfae (L'), as shwn in Fig. 5, shuld be less than width f the greenhuse. 9. Determinatin f energy n refleted surfae {E^) The slar radiatin falling n re&eting surfae is the sum f the transmitted slar radiatin falling n nrth wall and sme part f transmitted slar radiatin falling n nrth rf. Slar fratin f re&eting surfae is the sum f slar fratin f nrth wall (Fn nw ) and part f slar fratin f nrth rf (F nnr ). F = F n+ k : Fn; (2) where 'k' is the perentage area f nrth rf vered by re&eting surfae. k = h (3) where 'a' is the linear distane between tp f nrth wall and tp f re&eting surfae and ' Wn r ' is width f nrth rf. Energy n re&eting surfae (S rs ) is given by S r s=f n rss(t) : (4). Mdeling f slar fratin Transmitted beam radiatin falling n eah setin inside the greenhuse makes shadw n the grund. Part f the shadw area verlaps with shadw area f ther setins. The slar fratin f a partiular setin an be evaluated by the rati f shadw area f that setin n grund t the ttal shadw area f greenhuse n grund. Based n the shadw area f the setins, slar fratin f dierent setins is evaluated, frm Eq. (9), by making a prgramme in MS-Exell. The study has been made fr the winter mnths fr the measured slar radiatin data n hrizntal surfae as given in Table. The dimensins f the greenhuse have als been shwn in Table 2.. Results and disussins It has been evaluated using ppendix C that 5 angle f inlinatin fr re&eting surfae is suitable fr the evenspan greenhuse. This is in ardane with the value f Puar [] fr maximum illuminatin. Fig. 6a shws the mnthly variatin f ttal daily slar radiatin falling n different setins f the greenhuse fr all the 2ve latins. Maximum slar radiatin is reeived by suth wall fllwed by suth rf fr all latins. Hwever, slar radiatin reeived by suth rf is nstant fr Chennai thrugh the winter mnths. Nrth wall reeives the minimum slar radiatin fr all the latins and hene it an be replaed by a re&eting surfae. s latitude dereases, slar radiatin reeived by suth wall als dereases and slar radiatin reeived by ther setins inreases. t higher latitudes, slar radiatin reeived by nrth rf is very less and hene it an als be replaed by a re&eting surfae. Fig. 6b shws the hurly variatin f slar radiatin falling n dierent setins f the greenhuse fr a typial day f Deember in Delhi. Majr prtin f the slar radiatin falls n the suth rf f the greenhuse. Fig. 6b als shws the ttal slar radiatin falling n the greenhuse when the nrth wall is replaed by an paque re&eting surfae. Fig. 7a shws the daily variatin f transmitted slar radiatin fr fur mnths f winter. It is evident frm Fig. 7a that fratin f the transmitted slar radiatin falling n the &r f the greenhuse is maximum. Further it is t be nted that remaining part f transmitted slar radiatin (slar fratin) fall n east/ west/nrth wall/rf f the greenhuse. The fratin f transmitted slar radiatin inreases with day f the mnths n &r while it dereases fr the nrth wall as expeted (Fig. 7a). Slar fratin f east and west wall remains same thrugh ut winter mnths. This variatin f transmitted slar radiatin indiates that nrth wall an be used as a re&eting surfae t enhane the slar radiatin n the &r f the greenhuse fr further enhaning illuminatin and thermal heating. Fig. 7b shws the ttal slar radiatin per day n the &r f the greenhuse with and withut re&eting surfae. It is lear that the ttal radiatin f the &r f the greenhuse is inreased due t re&eted radiatin frm the nrth wall. The lss thrugh greenhuse with and withut re&eting surfae has als been shwn in the same 2gure. Fig. 7 shws the hurly variatin f distributin f slar radiatin n the &r f the greenhuse with and withut re&eting surfae fr a typial mnth f Deember fr all latitude under study. Maximum slar radiatin is available at 2 nn. There is lss f slar radiatin withut re&eting surfae and by putting a re&eting surfae these lsses an be minimized mre fr higher latitudes. Slar radiatin reeived by the nrth rf is very lw fr higher latitudes (Fig. 7a), therefre an inlined re&eting surfae is mre suitable fr higher latitudes. Fig. 8 shw the eet f latitude n availability f slar radiatin n &r f the greenhuse. There is a lear relatinship between latitude and availability f slar radiatin. 2. Cnlusins The terms slar fratin and ttal slar fratin quantify the distributin f transmitted slar radiatin inside

5 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) Table Measured slar radiatin data n hrizntal surfae a (Kw=m 2 ) Time Nvember Deember January February Ttal Diuse Ttal Diuse Ttal Diuse Ttal Diuse Chennai 8. am 9. am am 2. am Klkta 8. am 9. am am 2. am Jdhpur 8. am 9. am am 2. am Delhi 8. am 9. am am 2. am Srinagar 8. am 9. am am 2. am a The values at,, 9, 8, 7 & 6 am rrespnds t, 2, 3, 4, 5 <? i, 6 pm, respetively. Table 2 Dimensins f even span greenhuse under nsideratin Length Width Height f suth wall P angle f suth wall Height f nrth wall ji angle f nrth wall Central height P angle f suth rf P angle f nrth rf 6. m 4. m 8 m 9 8 m 9 3 m Width f Setin (suth wall) rea f Setin (suth wall) Width f Setin 2 (suth rf) and 3(nrth rf) rea f Setin 2 (suth rf) rea f Setin 3 (nrth rf) rea f Setin 4 (nrth wall) rea f Setin 5 (east wall) rea f Setin 6 (west wall) Ttal area f anpy ver 8 m : 8 m m 3 : 9 m 2 3 : 9 m 2 : 8 m 2 9 : 6 m 2 9 : 6 m 2 68 : 78 m 2 the greenhuse and als tells abut the lss f slar radiatin frm the greenhuse. Fr the given dimensin f a greenhuse, higher latitude shwed higher slar fratin and hene less slar radiatin is available fr thermal heating f the greenhuse. It has been nluded that nrth wall an be replaed by a re&eting surfae t maximize

6 68 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) 63-7 (/) -i X x X Chennai - Klkata Jdhpur Delhi Shrinagar (a) suth wall suth rf nrth rf nrth wall mnth/setin west wall east wall SW -B- SR - -NR -*- WW Ttal with RS -e-nw EW 5. (b) 2 3 Time f the day Fig. 6. (a) Mnthly variatin f ttal daily slar radiatin falling f dierent setins f evenspan greenhuse; (b) hurly variatin f slar radiatin falling n dierent setins f greenhuse (fr Deember, Delhi). the slar radiatin n &r f the greenhuse. n inlined re&eting surfae has als been fund t be mre suitable fr utilizing slar radiatin transmitting ut thrugh bth nrth wall/rf. The ptimum angle f inlinatin fr the inlined re&eting surfae is 5 fr all the latins. Inlined re&eting surfae has been fund mre useful fr higher latitudes than fr lwer latitudes. Results indiate that re&eting surfae n nrth side nsiderably inrease the available slar radiatin fr thermal heating f greenhuse. It is als nluded that even an inlined re&eting surfae annt redue lss f slar radiatin t zer, sme slar radiatin lsses will always ur. vailability f ttal slar radiatin and re&eted slar radiatin n &r f the greenhuse dereases with inrease in the latitude f the plae. knwledgements Finanial supprt f Cunil fr Sienti2 and Industrial Researh, Pusa, New Delhi fr preparatin f the researh paper is duly aknwledged. ppendix. Evaluatin f slar angles Further, the required values f delinatin (8), hur (!), slar altitude (a) and slar azimuth (y) angles at dierent time fr typial days f eah mnths have been alulated by using the fllwing expressins: "36.(284 + n) 8 = 23 : 45 sin (.) 365 : CO=5 (4lar-2.), sin a = s s 8 s! + sin 8 sin r a = sin (s s 8 s! + sin 8 sin ) ; sin a sin sin 8 sy = s a s r _] f sin a sin sin 8~\ y = s s a s Fr alulatins lal time is taken as slar time. (.2) (.3) (.4) (.5)

7 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) I 5 is u 2 «(a).7 -I OM De Jan Flr Feb Nv De Jan Feb nrth wall ->-_y-_,* Nv i Febl nrth rf mnth/setins -Bi W W De Jan Feb west wall Chennai - Klkata Jdhpur Delhi Shrinagar De Jan Feb east wal g 24 -, S I s 2. (b) > Z i LJ_ withut refleting surfae energy n flr > O Z O LJ_ with refleting surfae energy n flr > O Z mnth/mde -3 L_ lss withut refleting surfae > O Z Chennai Klkata Jdhpur Delhi Shrinagar ~3 LJ_ lss with refleting surfae I 6 Z.5 it () M Chennai with RS. 3 Klkata with RS Jdhpur with RS Delhi with RS Shrinagar with RS Time f the day R S Chennai withut RS w ith R S Klkata withut RS R SJdhpur withut RS hrsdelhi withut RS R SShrinagar withut RS Fig. 7. (a) Mnthly variatin f daily fratin f transmitted slar radiatin and its distributin inside the greenhuse; (b) mnthly variatin f daily ttal slar radiatin n &r and its lss thrugh greenhuse with and withut re&eting surfae; () hurly variatin f fratin f slar radiatin n &r with and withut re&eting surfae(rs) fr the mnth f Deember. ppendix B. Slar radiatin n inlined surfae (Liu and Jrdan frmula, 962) fter knwing beam and diuse radiatin n hrizntal surfae, Liu and Jrdan (963) have given a frmula t evaluate ttal radiatin n a surfae f arbitrary rientatin. h = IbRb + IdRd + prv(lb + Id) (B.) where Rb, Rd and R r are knwn as nversin fatrs fr beam, diuse and re&eted mpnents, respetively, and p is the refletin effiient f the grund (=.2 and.6 fr rdinary and snw vered grund, respetively). Rb is de2ned as the rati f &ux f beam radiatin inident n an inlined surfae t that n a hrizntal surfae. s( s 9 Z ; (B.2) where d z and, are the angles f inidene n the hrizntal and inlined surfaes respetively. Rd: It is de2ned as the rati f the &ux f diuse radiatin falling n the tilted surfae t that n the hrizntal surfae. Rd= +^ S^ (B.3)

8 7 R. Gupta, G.N. Tiwari/Building and Envirnment 4 (25) 63-7 day with refleting surfae energy n flr > Ttal energy (withut nrth wall) fr withut refleting surfae energy n flr atii per Kw) 5 re Slar (a) Latitude (degrees) > 25 - re Y Slar radia (b) CD O -* O O O O d d d Chennai3. ' ' ' i ' ' ' ' i ' ' ' ' I ' ' ' ^ ^ ~~~~"^-x2253 S^tja ^xx26.3 Jdhpur De l h i ^ > 34.8 ^X/^V. Shrinagar Nv De Jan.Feb Mnth Fig. 8. (a) Eet f latitude n daily ttal available slar radiatin and radiatin falling n &r f greenhuse with and withut re&eting surfae; (b) ttal energy falling n all setins f greenhuse (exept nrth wall). R r : The re&eted mpnent mes mainly frm the grund and ther surrunding bjets. -sp where p is the inlinatin (slpe) f the surfae. (B.4) ppendix C. Optimizatin fr angle f inlinatin f refleted surfae s shwn in the Fig. 4, sum f angles in a triangle is 8, therefre 2 = 8O O - (9 + p\ r ) - W, (C.) H a = Sm(6»2 ) (C.5) Sine p\ r is 2xed fr a greenhuse, therefre shuld be suh that:- Cnditin; a 6 length f the rf Length f the re&eting surfae = 63 = W + (a + f){ lternate angles f a line interseting tw parallel lines are equal} ; = 9 -^, (C.6) (C.7) (C.8) 9 2 = 9 - (p\ r + W). rding t Sine Law f triangle Ha Sm(9 +p\ r ) Sin( 2 ) Sin(W)' H = Sin(2 ) (C.2) (C.3) (C.4) {sum f angles in a triangle is 8 }, (C.9) 5 = 8 - {(9 - fi n ) + (a + 2W)}, (C.) 5 = 8-9 +fl ST -a-2t, (C.) 5=9 -(f + a + 2'P), (C.2)

9 R. Gupta, G.N. Tiwari / Building and Envirnment 4 (25) u Sin( 5 ) Sin( 3 ) Sm(a Sin( 3 )' x Sin( 5 ), x Sm(9 - (P SI + a + 2W)). (C.3) (C.4) (C.5) Fr all the re&eted radiatin t fall inside the greenhuse Cnditin; L' 6 W. Referenes [] Tiwari GN. Greenhuse tehnlgy fr ntrlled envirnment. England: lpha Siene Internatinal Ltd.; 23. [2] Puar M. Parameters f planning and designing f glass-vered spae as an element f bilimati arhiteture. PhD thesis, Begrad, 999. [3] Kurata K. Studie n imprvement f the light envirnment in greenhuse. (i) ppliatin f a Fresnel prism t greenhuse vering. Jurnal f griultural Methds 983;39(2): 3-6. [4] Kurata K. Studie n imprvement f the light envirnment in greenhuse. (ii) Utilizatin f re&etive blinds. Jurnal f griultural Methds 983;39(3): [5] Critten DL. The use f re&etr in venetian blinds t enhane irradiane in greenhuse. Slar Energy 985;34(): [6] Critten DL. Light enhanement using re&etrs arranged n a venetian blind n2guratin. Slar Energy 986;37(6): [7] ndrews B, Bailey J, Cttn RF. The eet f glasshuse light transmissin f vering the walls and &r with plasti materials. Div. Nte DN/222, Natinal Institute f griulture and Engineering, Silse, 982. [8] hard P, Giquel R. Eurpean passive slar handbk. Brussels: Cmmissin f the Eurpean Cmmunities; 986. [9] Tiwari GN, mita G, Ravi G. Evaluatin f slar fratin n nrth partitin wall fr varius shapes f slarium by ut-cd. Energy and Building 22;56:-8. [] Tiwari GN. Slar energy fundamentals, design, mdeling and appliatin. New Delhi: Narsa Publishing Huse; and Ba Ratn, US: CRC Press; 23. [] Puar M. Enhanement f grund radiatin in greenhuses by re&etin f diret sunlight. Renewable Energy 22;26:56-86.

Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References

Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References Khmelnik. I. Lrentz Fre, Ampere Fre and Mmentum Cnservatin Law Quantitative. Analysis and Crllaries. Abstrat It is knwn that Lrentz Fre and Ampere fre ntradits the Third Newtn Law, but it des nt ntradit