NUMERICAL ANALYSIS OF THERMAL PERFORMANCE OF AN EXTERNALLY LONGITUDINALLY FINNED RECEIVER FOR PARABOLIC TROUGH SOLAR COLLECTOR

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1 HEFAT 9 h Inenaional onfeence on Hea Tansfe, Flid Mechanics and Themodynamics 6-8 Jly Mala NUMERIAL ANALYSIS OF THERMAL PERFORMANE OF AN EXTERNALLY LONGITUDINALLY FINNED REEIVER FOR PARABOLI TROUGH SOLAR OLLETOR Mwesigye A., Bello-Ochende T.* and Meye J. P. *Aho fo oespondence Depamen of Mechanical and Aeonaical Enneeing Uniesiy of Peoia Peoia Soh Afica * bochende@p.ac.za ABSTRAT A eceie is a cenal componen of he paabolic ogh colleco sysem. Is design and sae gealy affecs pefomance of he enie colleco sysem. In his pape a hee dimensional nmeical model of a eceie wih an eenally londinally finned absobe be was deeloped o sdy he ec of fin dimensions on hea ansfe and flid flow pefomance chaaceisics. Resls show ha eenal londinal fins impoe he pefomance of he eceie. Resls fhe show ha colleco iciency and sefl hea gain will incease as he fin hicness and heigh incease and so do hea losses, glass empeae and maimm absobe empeae. A 6% incease in iciency and a pesse dop of 37.65Pa/m ae obained fo a finned absobe be wih lowe dimensions. cm. cm when compaed o a non-finned be lage in diamee by cm. An incease in iciency of 8% is obained when he same finned absobe be is compaed wih a non-finned be of he same size. INTRODUTION The inceasing concens of climae change and global waming dien by emission of lage amons geenhose gasses ino he amosphee mainly fom ilizaion of fossil based enegy esoces, ogehe wih he inceasing demand fo enegy has led o inceased seach fo icien and clean alenaie enegy soces and echnoloes []. In ode o mae alenaie enewable enegy echnoloes accepable hey ms be icien, eliable, cos ecie and podcing eleciciy a pices compeiie wih ha fom conenional esoces. Of he alenaie enegy esoces, sola enegy is he wold s mos abndan and clean soce of enegy. I has an enomos poenial fo spplying a significan poion of he wold s enegy demand [, 3] and pesens an opponiy fo disibed enegy geneaion as well as meeing he enegy needs of majoiy al poplaions cenly wiho access o moden enegy seices since i is widely aailable. B significan eseach is sill needed o haness his esoce icienly, a compeiie pices and maing i eliable. oncenaed Sola Powe (SP) has gained accepance fo sola hemal eleciciy geneaion wih paabolic ogh collecos he mos commecially and echnically deeloped. The conscion and sccessfl opeaion of he fis plans, he Lz Sola Eleciciy Geneaing Sysems commonly nown as SEGS in alifonia s Majoe Dese was a majo beahogh of paabolic ogh colleco echnology [, 4, and 5]. Wih an insalled capaciy of abo 354MW, he plans hae been in opeaion since ealy 98 s. They opeae wih hea ansfe flid empeaes beween 93 o 39 o. Wih ecen echnology adances he cos of eleciciy fom PTs is said o be appoaching ha of small-medim sized coal powe plans and fhe cos edcions ae possible wih impoed eceie designs, inceased concenao sizes, and impoed hemal soage sysems [6, 7]. Howee, despie sccessfl opeaion of he SEGS plans hee ae sill challenges o he opeaion of paabolic ogh colleco sysems which inclde; inceased hea losses a highe absobe empeaes, acm loss, degadaion of he selecie coaing, glass beaages aibed o he high empeae gadiens along he absobe be cicmfeence and concenaed hea fl hiing he glass o meal seal [4]. Theefoe, eseach is sill needed o addess hese challenges and impoe colleco pefomance. A nmbe of sdies hae been caied o o inesigae paabolic ogh colleco sysem pefomance anng fom sdies on enie sysem pefomance [8, 9,, and ] o sdies on only he eceie. Ddley [, ] caied o ess on SEGS LS- and Indsial Sola Technology (IST) sola collecos especiely wih diffeen coaings and diffeen configaions in he annls space. Receies wih acm in annls space had speio pefomance oe hose wiho. Odeh and Moison [3] sdied he dependence of hemal losses on ai elociy. Li e al. [4] deeloped an epeimenal plafom fo inesigaing paabolic ogh sola colleco pefomance. Epeimens showed ha colleco iciency inceases wih olme flow ae. Meased iciencies wee in he ange 4 6% and hea losses abo W/m when he empeae diffeence beween absobe and ambien was 8 o. Sdies hae also been caied o on eceie hea loss deeminaion and eceie pefomance monioing. Pince e al. [5] sed a sola blind Infaed camea o monio oe, eceies a he SEGS plans. Glass empeaes beween 3 7 o wee obained depending on: he ype of 59

2 eceie, ime in opeaion and whehe he eceie has hydogen emoes o no. The ceme coaed eceie wih hydogen emoes showed good esls wih glass empeae beween 5 o and o no mae he age and some less han 5 o. Lpfe e al. [6] also sed a sola blind infaed camea o mease empeae along he absobe cicmfeence and compaed esls wih hose fom ay ace mehods. The empeae along he be cicmfeence was fond o ay along be cicmfeence b was nifom along he lengh of he absobe. Lpfe e al. [7], Bholde and Ksche [8, 9] sed laboaoy seady sae ess o mease eceie hea losses. Receie losses wee fond o depend on inciden adiaion and absobe empeae. Fo he Solel UVA3 he eceie losses wee in he ange 5 46W/m depending on absobe empeae and ambien empeae [8]. Foisall [] deeloped a hea ansfe model fo deemining he pefomance of paabolic ogh eceie implemened in Enneeing Eqaion Sole (EES). The pefomance was deied fom enegy balances beween colleco, eceie and ai. The model was in ageemen wih epeimenal esls obained by Ddley []. To ae ino accon he diffeenial hea fl on he absobe be sface, He e al. [] sed Mone-alo ay ace mehods and a finie olme mehod o sdy flow and hea ansfe chaaceisics of he woing flid inside he absobe. Pefomance enhancemen of eceies has eceied consideable aenion in he las wo decades. Hegazy [] analyically consideed possible se of eenal londinal fins on an absobe be and fond ha he iciency of he colleco can be inceased by %. Reddy e al. [3] sed nmeical mehods o pefom hemal analysis on a eceie wih poos and londinal inenal fins. The sdy shows a hea ansfe enhancemen of % wih a poos fin when compaed o a londinal fin. Kma and Reddy [4] eended he analysis done by Reddy e al. [3] o a eceie wih a poos disc oiened a diffeen angles o he absobe ais. A 64.% incease in Nssel nmbe was achieable b wih a pesse dop penaly of 457Pa. Mnoz and Abanades [5] inesigaed an inenally helically finned absobe be wih a iew of eening o he non-nifom absobe cicmfeenial empeaes. Fom he sdy a 3% incease in colleco iciency and 4% edcion in absobe empeae diffeence is achieable while he pesse dop inceased by - 5 % depending on he fin aangemen. The ppose of his sdy is o nmeically inesigae he pefomance of an eenally londinally finned absobe be of a paabolic ogh eceie. Vaiaion of eceie iciency, eceie hea losses, absobe maimm empeae; pesse dop and glass empeae wih fin dimensions ae inesigaed. I is assmed ha he lowe fin and lowe half of he absobe eceie he same concenaed hea fl. PHYSIAL MODEL AND GOVERNING EQUATIONS The paabolic ogh sola colleco is simply made by bending a shee of meal ino a paabolic shape wih a eceie along is focal ais as shown in Fige. The eceie consiss of a seel absobe be enclosed in a glass jace ha is eacaed o edce conecion hea losses; he glass and be ae sealed wih glass o meal seals and poided wih gee maeial as shown in Fige o absob any hydogen ha infilaes fom he hea ansfe flid. Refleced sola enegy is inciden on he lowe half of he absobe be as in Fige 3 whee mos of i is absobed and condced hogh he absobe be wall and caied by he hea ansfe flid o he hea echanges of he powe bloc while he es is adiaed and condced o he glass enelope and los o he enionmen. Fige Paabolic ogh colleco Theefoe, hea ansfe in he eceie consiss of foced conecion inside he absobe be, condcion wihin he absobe walls and adiaion in he glass enelope when flly eacaed. ombined adiaion and fee molecla condcion will occ in he glass enelop when no flly eacaed o combined adiaion and naal conecion when he glass enelop is boen o non-eisen. Fige Eacaed eceie be Fige 3 Ray ace diagam fo a paabolic ogh colleco The poposed model of he eceie consiss of fins ha ae eenal o he absobe be as shown in Fige 4. Wih his aangemen he absobe diamee can be ep small, lage eceie apee widhs can be sed, hs highe concenaion aios. Moeoe, an almos nifom hea fl on he lowe half of he absobe be can be achieed. Fhe sill, since he eceie s annls is eacaed and absobe sface is sally coaed wih a selecie coaing, naal conecion is sppessed and adiaion losses ae minimised. As a esl mos 6

3 of he inciden sola adiaion on he fin ms be condced o he absobe be impoing pefomance. Fige 4 (a) ompaional domain (b). Finned eceie cosssecion The diamee of he absobe o inecep he enie sola image deied fom ay ace diagam in Fige 3 is en eqaion () [6] fo a ogh of pefec alignmen and shape and consideing sn s shape as pefec. a sin.67 d sin.67 () sin ϕ Wheeas he size of he fla eceie o he diamee of he semi-cicla eceie o inecep he enie sola image is en by eqaion () [6] also deied fom Fige 3 sin.67 a sin.67 W () cos( ϕ.67) sinϕ cos( ϕ.67) Since d is sally ey small absobe diamees beween d and W ae commonly sed mainly o aoid highe local concenaion of sola adiaion on be sface []. Theefoe, combining a small absobe diamee wih eenal fins wold alleiae sch ho spos. The pefomance of he paabolic ogh colleco is qaniaiely epessed in ems of he hea gained by he woing flid and colleco iciency en by eqaions (3) and (4) especiely. q I η A Q m& c T T (3) b o a loss f p ( ) olleco iciency is en by q η (4) I b Aa Hea ansfe in he annls space In he annls eceies ae manfaced wih a high acm (P <.3Pa) [, 7] in ode o aciae he gees ha absob hydogen eleased by he hea ansfe flid and hen diffsing hogh he absobe ino he acm jace. In his highly eacaed gap he hea ansfe is only by adiaion. A modeae acm pesses hea loss is by boh adiaion and molecla condcion since he gas densiy will be oo low o sppo fee conecion. Fo ey low pesses he o in behaio of ai depends on he mean fee pah, χ (m) of he gas molecles defined by eqaion (5) [7] as χ RsT (5) P As he pesse in he annls edces he mean fee pah of he ai molecles becomes lage and he assmpion of a coninm model beas down fo conecion hea ansfe modelling. As sch he mean fee pah needed o mainain he coninm model in he eceie s annls is calclaed o be aboe 3 Pa. Hea loss fo a colleco of lengh (L) is en by eqaions (6) and (7) [, 6]. Hea los by he absobe be is he same as he hea los o he sonding enionmen. Q Q loss loss πλ d ln d o ( T T ) o πd ξ o o LΦ 4 4 ( T T )) o ξ ξ d d o 4 4 ( T T ) π d golhw ( Tgo Tamb ) ξ gπd golφ (7) go sy Whee λ,ai is he ecie condciiy beween he glass coe and he eceie sysem en by eqaion (8) as en by [6] 4 * λ, ai P Ra (8) ma,.386 λ.86 P ai Whee 4 d ln o d Ra i ( ) Ra (9) 5 3 L d 3 5 i d 3 5 o And g ( T ) 3 o T L P RaL β () Fo ey low acm pesses λ,ai appoaches zeo and only adiaion hea ansfe shold be consideed. Ai hemal condciiy fo low pesses has been deemined fom eqaion () [8] () λai λai, o d g P T Whee d g is he glass coe-absobe be spacing The sy empeae has been calclaed fom he elaion by [9].5 T.55T () sy amb While he emissiiy of glass is en as ξ.86 [8, ] and he absobe emissiiy aies wih wall empeae. Fo cemen selecie coaing is absobe emissiiy is en by [] as ξ o.3t o.6 (3) The aeage wind hea ansfe coicien h w was esimaed sing he epession en by [9] as h (4) w 4 w w (6) 6

4 Themal analysis of flow and hea ansfe inside he absobe be Deeminaion of Reynolds nmbes fo flow in he absobe be fo elociies aboe.5m/s indicaes ha he flow is blen. Theefoe, Reynolds Aeaged Naie Soes (RANS) eqaions ae sed o model hea ansfe and flow in he absobe be. Fo seady sae, incompessible, blen, aisymmeic flow he RANS eqaions fo coniniy, momenm and enegy ae en by eqaions (5 8) [3, 3]. oniniy eqaion ) ( (5) Aial momenm d dp (6) Radial componen p (7) The Enegy eqaion assming no iscos heaing by he hea ansfe flid is en by T T T T c p λ λ (8) Whee λ is he ecie flid hemal condciiy and fo he sandad - and ealizable model is en by [3] as p c P λ λ (9) Becase RANS eqaions pesen a close poblem addiional eqaions ae needed o obain all he nnowns. Tblence modelling is sally sed o emedy sch a poblem. Of he aailable blen models he - model and is impoemens of - RNG (Renomalizaion gop) and he - Realizable models ae he mos widely sed and alidaed models fo mos flows [3]. The RNG and Realizable - models ae impoemens of he sandad - model. In his sdy he Realizable - model was sed. The - models hae wo eqaions fo he blen enegy () and dissipaion ae (). The anspo eqaions fo he Realizable - model ae en by eqaions ( -3) [3]; - Eqaion σ σ G () ɛ- Eqaion ν σ σ S () G, he geneaion of blen ineic enegy is en by S G () σ is he blen Pandl nmbe fo, σ ɛ is he blen Pandl nmbe fo ɛ and G is he geneaion of blen ineic enegy de o he mean elociy gadiens en as [3, 33]. The model consans ae.9, σ, σ.. Fo Realizable - model is no consan and is deemined as deailed in [3, 33] Eddy iscosiy calclaion fo he ealizable model is en by (3) is a fncion of he mean sain and oaion enso whose deailed deeminaion is en in [33] Tblen models do no esole he flow chaaceisics in eons nea walls since in hese eons iscos foces ae eihe eqal in magnide o ineia foces o lage. Nea he wall elociy changes apidly, solion gadiens ae ey high, flow is inflenced by he iscos ecs and is independen of he paamees fa fom he wall. In ANSYS Flen sandad wall fncions based on he wos of Lade and Spalding [33] and ae widely sed fo mos flows. The nea wall node is modelled by laws of he wall [33] The law of he wall fo mean elociy yields ) ln( * * y E U κ (4) Whee; κ is he Von Kàmàn onsan.487and E is an empiical consan The dimensionless wall elociy U * is en by τ w p p U U 4 * (5) And he dimensionless disance fom he wall y * p p y y 4 * (6) Whee, p is he blen enegy fo he nea wall node, y p is he disance fom he wall o nea wall node and U p is mean elociy fo he nea wall node. The lowe limi fo se of wall fncions is abo y * 5 and he ppe limi depends songly on he Reynolds nmbe. Below he lowe limi he accacy of he solion canno be mainained ecep when scalable wall fncions ae sed. In his sdy scalable wall fncions wee sed and hey help when he d is efined sch ha y * < [33]. They foce he sage 6

5 of he log-law in conjncion wih sandad wall fncions appoach. Hea ansfe and flid flow inside he absobe be can be chaaceized in ems of pesse dop and Nssel nmbe. The pesse dop along he absobe be deemines how mch powe ms be sed o foce he flid hogh he be. Pesse dop ( P) is elaed o ficion faco f by eqaion. (7). L U P f D (7) Whee D is he hydalic diamee en by he aion of aea and weed peimee (p w ) as D 4A p w The eqied pmping powe W & o oecome he pesse pmp dop is en by & V & P (8) W pmp Fo smooh bes he ficion faco f is en by Peho fis eqaion en in [34] p fowad by Peho in 97. f (.79 ln Re.64) (9) Re is he dimensionless Reynolds nmbe en by UD Re The hea ansfe is en in ems of he Nssel Nmbe (N) which is en as hd N and he hea ansfe coicien h, is en as q h (3) T w T ef Fo a consan hea fl along he absobe be cicmfeence, Nssel nmbe, Reynolds nmbe and Pandl nmbe ae coelaed by he Gnielinsi coelaion en by eqaion (3) as was p fowad by Gnielinsi in 976 [34] as an impoemen of Peho s second eqaion [34] wih all popeies ealaed a bl empeae. f ( Re ) P 8 (3) N.5 / 3.7 f ( P ) 8 Fo.5 P and 3 3 < Re < 5 6 The bonday condiions sed in he sdy fo he annls space and absobe be ae en as; Receie Annls d d o A, P in 4 bas T in T amb Wall bonday condiions A mied conecion and adiaion bonday condiion is sed fo glass coe oe sface. d d o A L, A zeo pesse gadien a he annls ole is sed Absobe be A he inle;,, in T T in Wall bonday condiions d i d i, -9 o θ 9 o A, L, a no-slip bonday condiion eiss On he oe sface of he absobe be a nifom hea fl is assmed as in [3, 5] en as; A d o, o θ 9 o q τ g I b d o, -9 o θ o q A η RIb whee a R A A a is he apee aea pojeced on a hoizonal plane and A is he coesponding absobe aea, I b is he diec sola adiaion aen as 933W/m. A he ole ( L, applied d i ) a zeo pesse gadien is On he symmey plane, hee is a zeo nomal elociy and zeo nomal gadiens of all aiables. Theefoe, no conecion and diffsion fles acoss he symmey plane Maeial Popeies Fo his sdy, he absobe is made of sainless seel wih Specific Hea capaciy.5 J/g o and densiy 8 g/cm 3 [35] while he hemal condciiy aies wih empeae accoding o λ T [8]. The glass coe is aen as boosilicae Pye whose popeies wee aen o be consan simila o hose cen eceies [,, 5 and 8]. Ai is aen as he annls flid wih is densiy calclaed by he Incompessible ideal gas law, he hemal condciiy aying accoding o eqaion () and he es of he popeies calclaed sing ineic heoy as en in ef. [33]. Sylhem 8 is sed as he absobe be hea ansfe flid sed whose popeies ae inp as fncions of empeae accoding o polynomial fncions eqaions (3-35) en by[]. c p.78t.7798 (J/ g K) (3) λ T T.9 - (W/m - K) (33) T.57 3 (g m -3 ) (34) T T 3.388T T (Pa s) (35) 63

6 Geomeic paamees A eceie wih dimensions simila o hose of he cen SEGS- plans Ddley [] was sed in his sdy. Receie dimensions ae en in Table. Table : Geomeical paamees Validaion Base case simlaions Receie inne.5.5 diamee(cm) Absobe inne diamee (cm) Absobe hicness (cm).. Receie lengh (m) oncenaion aio 7 7 Opical Efficiency (%) Fie diffeen cases of he finned eceie wee compaed agains he base case. Fin hicness is ep consan in all cases he same as he absobe hicness i.e. ase A. cm. cm, ase B.6 cm. cm, ase. cm. cm, ase D.4 cm. cm and case E.8 cm. cm. ase F consideed a lage non-finned be of absobe inne diamee 7.7cm and eceie inne diamee 3.5cm. Only he lowe fin was aied since i is he one deemed o inflence eceie pefomance. SOLUTION PROEDURE The nmeical solion of he goening eqaions was implemened in a commecial hee dimensional pacage ANSYS 3.. The geomey bil in ANSYS Design Modele and he d in ANSYS meshing. The mesh is efined wih a fine mesh a he absobe annls ineface and a glass ambien ineface as well as along he eceie s aial diecion as shown in Fige 5. The solion is obained in ANSYS FLUENT which ses a Finie Volme mehod fo soling he goening coniniy, momenm, enegy and - model eqaions. The compaional domain was disceized sing heahedal and qadilaeal elemens. Second ode pwind scheme was employed fo inegaing he goening eqaions ogehe wih he bonday condiions oe he compaional domain and SIMPLE algoihm was sed fo copling pesse and elociy. Radiaion hea ansfe in he annls is modelled sing he discee odinaes model wih ai aen as a adiaiely non-paicipaing medim. onegence was obained wih scaled esidals of mass, momenm, blen ineic enegy () and blence dissipaion ae () less han -4 while he enegy esidals wee less han -6 and when monios of he conegence hisoy of he absobe ole empeae and glass empeae hae flaened fo moe han sccessie ieaions. Mesh independence sdies fo seeal efinemens of he mesh wee caied o wih he eceie hea losses and hea gain as monioed qaniies i i q q.and q l ql. Whee i is he ale i i q q i l i befoe mesh efinemen and i is he ale afe mesh efinemen. Fige 5 Mesh sed in he sdy: Radial and aial diecions RESULTS AND DISUSSION The Nmeical model was alidaed sing he es esls of Ddley [] fo hea gain and es esls fom Bholde and Ksche [8] fo hea losses. Moeoe, hea ansfe was alidaed sing Nssel Nmbe and flid flow by ficion faco. Peho second eqaion and Gnielinsi coelaions [34] wee sed fo Nssel nmbe compaisons wheeas Peho s fis eqaion (9) was sed fo pesse dop alidaion. Tempeae gain ( o K) Receie losses (W/m) Pesen wo Ddley [] Deiaion (%) T_inle ( o K) Fige 6 Validaion of empeae gain Pesen sdy adiaion losses Bholde and Ksche Tabsobe-Tambien ( o ) Fige 7 Validaion of eceie hea losses Deiaion (%) 64

7 Tempeae gain esls wee wihin less han % of epeimenal esls obained by Ddely [] as shown in Fige 6. The coelaion obained by Bholde and Ksche [8] which elaes hea losses o he diffeence beween absobe empeae and ambien empeae was sed o alidae hea losses. The pesen sdy coelaes well wih he epeimenal daa as shown in Fige 7 when only adiaion losses ae consideed. Nssel nmbe and ficion faco also compae well wih coelaion daa. Nssel nmbe was wihin less han 8% of boh Peho s second eqaion and Gnielinsi coelaions as shown in Fige 8. heigh inceases. Fo all cases he aeage glass empeae emains wihin he nomal opeaing ange less han o [5]. Nssel nmbe 5 5 Base ase ase A ase ase B ase D ase E ase F Nssel nmbe Gnielinsi Peho Pesen sdy Reynolds nmbe Fige 8 Validaion of Nssel nmbe Effec of eenal fins on pesse dop and hea ansfe coicien Eenal fin dimensions hae no o neglible ec on he pesse dop and hea ansfe chaaceisics fo he same diamee of he absobe be. When compaed wih he a nonfinned absobe of diamee eqal o finned absobe diamee pls he fin heigh hee is some pesse dop penaly. As wold be epeced an incease in he flow ae o Reynolds nmbe inceases boh he pesse dop and Nssel nmbe. Fige 9 shows he ec of eenal fins on Nssel nmbe. Fo a lage be, he Nssel nmbe inceases as a esl of inceased diamee of he be and no as a esl of inceased hea ansfe coicien. Effec of eenal fins on glass empeae and maimm absobe empeae Fige shows ha as he heigh of he eenal fins inceases he glass empeae also inceases. Addiion of eenal fins on he absobe implies ha some hea ms be ansfeed fom he fin o he absobe by condcion while some of i is adiaed o he space beween he absobe and he glass coe. This ansfe of hea is consained by he fac ha hee is a limi on he amon of hea ha can be ansfeed by he hea ansfe flid deemined by he flow ae and he amon ha can be adiaed deemined he absobe wall selecie coaing emissiiy. This will affec he maimm empeae in he absobe be and glass empeae as fin Reynolds nmbe Fige 9 Vaiaion of Nssel nmbe wih Reynolds nmbe Glass empeae ( o ) Base ase ase A ase B ase ase D ase E Reynolds nmbe Fige Vaiaion of eceie glass empeae Glass empeae edces as he hea ansfe flid flow ae incease. As he fin heigh inceases he absobe maimm empeae also inceases. I will appoach he maimm opeaion empeae of sainless seel nde coninos opeaion abo 43 o K [35] as he inle empeae and concenaion aio incease. Table Effec of concenaion aio and inle empeae on maimm wall empeaes R T inle ( o K) Mass flow ae (g/s) T i, ma ( o K) T o,ma ( o K) T abs_ae ( o K) Fo all cases consideed he maimm absobe empeae is lowe han he maimm woing empeae and he meling poin of sainless seel 673 o K [35]. As he concenaion aio and inle empeae incease boh glass 65

8 empeae and absobe maimm empeae ae epeced o incease. Table shows some of he daa fo he ec of inceasing inle empeae and concenaion aio on he absobe inne and oe wall empeaes (T i and T o ). Effec of Eenal Fins on Hea Gain and Efficiency The hea gained by he woing flid and colleco iciency ae obseed o incease as he Reynolds nmbes inceases and hen becoming nealy consan a Reynolds nmbes of he ode fo boh finned and non-finned absobe bes. A low Reynolds nmbes he iciency incease slighly by abo 3% and hen becomes nealy consan as he Reynolds nmbes incease as shown in Fige. This is becase hea gained by he hea ansfe flid no longe inceases significanly as he Reynolds nmbe inceases. As fin heigh inceases he iciency coninally inceases. Fo he cen flow aes sed in he SEGS- plans he colleco iciency inceases by abo.6 % fom 45% o 56.6% when a finned absobe be is compaed wih same size non- finned be and by 3.6% when a finned be is compaed wih a lage non-finned be fo a fin of heigh.8 cm by hicness. cm. The lage absobe be es a low iciency since he concenaion aio is slighly edced. Effec of eenal fins on hea losses Fige shows ha as he fin heigh inceases he eceie hea losses also incease. The incease is moe pononced a low Reynolds nmbes. A highe Reynolds nmbes hea ansfe coiciens ae highe and moe hea is caied by he hea ansfe flid. A lowe ales of fin heigh he incease in losses is smalle and becomes lage as he fin heigh inceases since mos of he hea will no be condced o he absobe be. Fo smalle fin heighs he hea losses ae lowe han fo a lage non-finned absobe be. The lage non-finned be has a lage hea loss aea. Een hogh he eenal fins incease iciency of he eceie i shold be noed ha hee ae limiing facos o hei se. These inclde: he empeae of he absobe be oe wall cenly limied o abo 4 o o aoid degadaion of he absobe be s selecie coaing; he empeae of he absobe be inne wall o aoid degadaion of he hea ansfe flid whose cen opeaion empeaes ae limied o 4 o [4]. Theefoe, fin dimensions shold be seleced sch ha hey impoe pefomance wiho compomising he life of he eceie. Hea losses (W/m) Base ase ase A ase B ase ase D ase E Reynolds nmbe Fige Vaiaion of hea losses wih fin dimensions and Reynolds nmbe Fom he sdy, wih he assmed consan hea fl (DNI 933W/m ) he absobe wall inside empeae emains lowe han 673 o K fo all fin heighs and concenaion aios 7, 8, 9 and poided he inle empeae does no eceed 6 o K and hea ansfe flid mass flow aes ae ep highe han 6.9 g/s. Fo flow aes aboe 6.9 g/s and inle empeae less han 55 o K he maimm oe absobe empeae is ep wihin less han 673 o K a a concenaion aio of 7. Fo a fin of dimensions cm. cm he iciency inceases by 6% and 8% when compaed o he wo non-finned cases especiely fo an inle empeae of 53 o K. The smalle be es an addiional pesse dop of 37.65Pa/m (3.7W/m addiional pmping powe) when compaed wih he lage non-finned be and an incease in hea gain of 444. W/m 7 6 Base ase ase A ase B ase ase D ase E Efficiency (%) Reynolds nmbe Fige Vaiaion of colleco iciency (a).5 cm. cm fin (b).4 cm. cm fin Fige 3 onos of empeae a absobe ole a Reynolds nmbe.44 4, R 7, DNI 933W/m fo.5 cm. cm and.4 cm. cm finned absobe bes As he concenaion aio, inle empeaes and fin heigh incease he maimm empeae inside and oside he absobe be will incease and eceed 673 o K. The maimm empeae is concenaed on he lowe fin as shown in he conos of empeae in Figes 3 and 4. Using highe flow aes is one way of deceasing he maimm absobe wall empeaes. ombining he oe fins wih 66

9 inne fins is liely o significanly edce he maimm oe absobe maimm inne absobe empeae. (a).5 cm. cm fin (b).4 cm. cm fin Fige 4 onos of annls empeae a a Reynolds nmbe.44 4, R 7, DNI 933W/m fo.5 cm. cm and.4 cm. cm finned absobe ONLUSION A nmeical model o ealae he pefomance of an eenally finned paabolic ogh eceie was deeloped. Fom he sdy i can be conclded ha inclding eenal fins on he absobe be impoes pefomance of eceie. The longe he fin, he moe is he hea gain, he highe he iciency b also he highe he hea losses, glass empeae and absobe be maimm empeae. Fo concenaion aios beween 7 and flow aes highe han 6.9g/s he maimm absobe inne wall empeae will eceed 673 o K when inle empeaes geae han 6 o K ae sed. The maimm absobe oe wall empeae eceeds 673 o K when inle empeaes highe han 55 o K ae sed. A combinaion of eenal fins and inenal fins can be sdied o ealae he ec of diffeen fin configaions on he pefomance and he possible edcion of absobe be maimm empeaes. AKNOWLEDGEMENT The ahos acnowledge he sppo eceied fom Depamen of Mechanical and Aeonaical Enneeing, Uniesiy of Peoia, Peoia, Soh Afica NOMENLATURE A [m ] Aea a [m] olleco apee widh c p [Jg - K - ] Specific hea capaciy R [-] oncenaion aio d [m] Absobe be diamee D [m] Hydalic diamee DNI [W/m ] Diec Nomal Iadiaion f [-] Ficion faco f p [m] Focal lengh g [m/s ] Acceleaion de o gaiy h [W/m K] hea ansfe coicien I b [W/m ] Diec sola adiaion [m /s ] Tblen ineic enegy L [m] Reciee lengh m& [g/s] Flid mass flow ae f N [-] Nssel nmbe P [Pa] Pese P [-] Pandl nmbe q [W] Hea gain Q loss [W] Hea loss q " [W/m ] Hea fl Ra [-] Raleigh nmbe Re [-] Reynolds nmbe R s [Jg - K - ] Specific gas consan [cm] Thicness T [ o K] Tempeae U [m/s] Mean elociy, [m/s] Velociy componens V & [m 3 /s] Volme flow ae W [m] Fla eceie widh, [m] Spaial coodinaes Gee lees Φ [Wm K 4 ] Sefan Bolzman onsan β [ o - ] oicien of hemal epansion [m /s 3 ] Tblen dissipaion ae ξ [-] Emissiiy η [%] Efficiency η [%] Opical iciency [g/m 3 ] Densiy [m] olleco im adis τ g [-] Glass coe ansmissiiy τ w [N/m ] Wall shea sess λ [Wm - K - ] Themal condciiy φ [degees] olleco im angle [Pa s] Viscosiy ν [m /s] Kinemaic iscosiy χ [m] Molecla mean fee pah Sbscips Amb ef go in L o p i o sy Ambien sae Effecie ale Refeence ale Glass inne side Glass oe side Inle Lengh Ole Nea wall node Absobe Absobe inne Absobe oe Sy Tblen Spe scips ˉ Time aeaged ale REFERENES [] IEA, Wold Enegy Oloo Eecie smmay, Inenaional Enegy Agency Pblicaions, [] Kaloo S., Sola Enegy Enneeing: Pocesses and Sysems, s Ed., Elseie, Ofod U.K. 9 [3] DESERTE., lean powe fom deses he DESERTE concep fo Enegy, Wae and limae seciy he Whie boo 4 h Ediion 9. 67

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