JJMIE Jordan Journal of Mechanical and Industrial Engineering

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1 JJMIE Jordn Journl of Mechnicl nd Industril Engineering Volume 10 Number 1, Mrch.2016 ISSN Pges Simultion of Optiml Exergy Efficiency of Solr Flt Plte Collector Subhr Ds (Mukhopdhyy) * Renewble Energy Deprtment, Amity University Hryn, Gurgon, Indi Received 12 Sep 2014 Accepted 25 Sep 2015 Abstrct Exergy nlysis identifies potentil fctors responsible for thermodynmic losses nd leds to efficiency improvements. In the present pper, exergy efficiency is expressed s function of dimensionless mss flow rte nd let fluid temperture. A computer progrm ws developed for determining the optiml performnce prmeters for imum exergy efficiency in flt plte collector. he study ws conducted for six collectors of different res, hving different overll loss coefficient nd het removl fctor. It is observed tht for given vlues of incident solr rdition, inlet fluid temperture nd mbient temperture, the optiml mss flow rte vried from kg/s nd exergy efficiency vried from % for the collectors depending on its gross re, overll het loss coefficient nd het removl fctor Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved Keywords: Optimiztion, Exergy Efficiency, Outlet Fluid emperture, Mss Flow Rte, Flt Plte Collector. Nomenclture A c Gross re of the collector, m 2. A p Absorber plte re, m 2 c p Specific het of the het trnsfer fluid, J/ kgc. F R Het removl fctor of the collector, dimensionless. F Collector efficiency fctor, dimensionless. H Absorbed solr rdition per unit re of the collector, W/m 2. H t Incident solr rdition per unit re, W/m 2. m Mss flow rte, kg/s. M Mss flow number, dimensionless. Ambient temperture, ºC. f, in Inlet fluid temperture, ºC f, Outlet fluid temperture, ºC p Absorber plte temperture, ºC p, Stgntion temperture, ºC s Apprent temperture of Sun, ºC U L Overll het loss coefficient, W/m 2 ºC. Greek Symbols Absorptnce of the bsorber plte, dimensionless. rnsmittnce of the cover, dimensionless. Dimensionless inlet fluid temperture. θ in Mximum collector temperture, dimensionless θ Dimensionless let fluid temperture. θ* Dimensionless optiml let fluid temperture. θ s Dimensionless pprent temperture of Sun. I II 1. Introduction Energy efficiency of collector, dimensionless. Exergy efficiency of collector, dimensionless. Solr flt plte collectors re devices used for low temperture pplictions. he het bsorbed by bsorber is prtly trnsferred from bsorber plte to the fluid flowing in the tubes nd the rest is lost to mbient. Het trnsfer irreversibility decreses with the increse in fluid flow rte but this increses losses due to fluid friction. o optimize het trnsfer to fluid form the bsorber plte, n optiml mss flow rte of the fluid needs to be determined which tkes cre of both het trnsfer irreversibility nd losses due to fluid friction. In recent pst, vrious methods hve been pplied to optimize the design of collector. Anlysis of solr collector ws conducted by Howell nd Bnnerot [1] in order to determine the optimum let temperture for given solr collector tht would imize the work put for vrious idelized het engine cycles. he nlysis demonstrted the effect of the rditive nd convective het losses from the collector. Second lw nlysis for the optimiztion of flt plte solr ir heters ws performed * Corresponding uthor e-mil: nips.subhr@gmil.com.

2 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) by Altfeld et l. [2] where net exergy flow ws imized by minimizing exergy losses by bsorption of rdition t bsorber temperture level. Bsed on this nlysis, optiml designs of the bsorbers nd flow ducts were determined. Hving developed the optiml designs for ir heters, Altfeld et l. [3] conducted sensitivity nlysis to study the influence of vrying opertionl conditions on optiml results. Hepbsli [4] comprehensively reviewed nd evluted the performnce of wide rnge of renewble energy resources nd hd defined exergy efficiency of solr flt plte collector. Luminosu et l. [5] conducted n exergy nlysis of flt plte collector with the ssumption tht the globl solr rdition is equl to solr flux nd inlet fluid temperture is equl to mbient temperture. Optiml opertion mode of flt plte collector ws determined by imizing exergy efficiency of the collector with respect to vrious prmeters. he globl optiml opertion mode of flt plte collector ws clculted considering exergy efficiency s function of mss flow rte nd collector re. Exergy nlysis ws pplied by vrious uthors [6, 7, 8, 9] to judge system nd showed how exergy nlysis provided illuminting nd meningful ssessment of solr therml processes nd cn ssist in improving nd optimizing designs. Klogirou et l. [10] presented review of exergy nlysis of solr therml systems. It includes exergy nlysis of solr collectors like flt plte collectors, hybrid PV/ systems, prbolic trough collectors, prbolic dish collectors nd reported vrious pplictions of solr therml systems. hough exergy nlysis provides vluble informtion b the system but it is very complex to pply. hus, the second lw nlyses which re simplified forms of exergy nlysis re often employed. he Entropy Genertion Minimiztion (EGM) technique ws widely studied by Bejn [11] to optimize system performnce in vrious het trnsfer processes including solr therml pplictions. In the pst, mny uthors used the EGM method to judge nd optimize processes [12, 13, 14]. orres-reyes et l. [15] estblished procedure for the determintion of optiml performnce prmeters for minimum entropy genertion during the collection of solr energy. Doos et l. [16] presented Fuzzy ARMAP neurl network model to improve the process rel-time performnce of power sttion in Al-Dur Refinery for the multi-gent process s clssifying system. Agent bsed fuzzy method hs been employed by vrious uthors in decision mking problems to obtin the optiml solution [17, 18, 19, 20]. A numericl simultion ws employed for the performnce nlysis of Stirling engine cycle by rwneh et l. [21]. F. Jfrkzemi et l. [22] conducted n energetic nd exergetic evlution of flt plte collector. he theoreticl model ws verified experimentlly wherein flt plte collectors were tested in open loop with wter s het trnsfer fluid. he energy nd exergy efficiency of flt plte collector were determined for constnt mss flow rtes of 0.03, 0.04 nd 0.05 kg/s. he theoreticl nd experimentl vlues were compred by computing the root men squre error. he effect of design prmeters on the collector performnce ws lso studied. Khdemi et l. [23] studied the optiml exergy efficiency of flt plte collector by employing Sequentil Qudrtic Progrmming (SQP) nd Genetic Algorithm (GA). Nonliner constrint optimiztion technique ws dopted in the present pper wherein objective function (1 η II ) is minimized w.r.t two inequlity constrints viz. [1 A p 5 nd m 0.1]. Khdemi et l. [23] suggested tht the rte of convergence of SQP [24] ws much higher thn tht of GA, but GA provides results with higher ccurcy for exergy efficiency. hey lso suggested tht the smller collector could lso hve similr nd better performnce compred to the collector with lrger surfce re. SQP lgorithm hs high convergence rte. But the rte of convergence of SQP depends highly on the strting point, first nd second order derivtives of the objective function nd lso it stops in locl optimum points. hese re the weknesses of SQP. GA, on the other hnd, requires n initil popultion for trining nd rte of convergence is lso low. Mukhopdhyy et l. [25] optimized exergy efficiency of flt plte collector to obtin the optiml opertionl mode, i.e., mss flow rte nd let fluid temperture for given collector wheres Khdemi et l. [23] optimized exergy efficiency to determine the optiml design prmeters, i.e., re of collector nd mss flow rte. In the present pper, n nlyticl study [25] is conducted for six different collectors with different surfce re A c, het removl fctor F R nd overll het loss coefficient U L to determine the optiml mode of opertion for which exergy nd energy efficiency would be imum for the fixed vlues of uncontrollble prmeters such s solr rdition nd mbient temperture. he present pper is n extension of our work [25], to present the simultion done to obtin the optiml opertionl mode of flt plte collector. A computer progrm is written bsed on the proposed mthemticl model to solve the nonliner constrined optimiztion problem using Direct Substitution Method (DSM) to obtin the optiml results. DSM to solve nonliner optimiztion problem is simple to implement compred to SQP nd GA. he simultor thus developed requires initil input-specifiction dt of collector (F U L, F τα, A c, F r U L, F R τα, τα), vlues of uncontrollble prmeters (H t,, s ) nd het cpcity of het trnsfer fluid, c p to compute the optiml solution. he simultor is cpble of determining the initil strting solution nd thereby minimizes humn error in its prediction. he optiml solution is obtined in less thn 20 itertions. he development of the computer progrm bsed on the proposed optimiztion technique elimintes the dependency of uthor to use softwre which hs its own limittions nd complexities. 2. Optimiztion of Exergy Efficiency Exergy efficiency of ny process, s defined by Öztürk [6], is the rtio of the exergy trnsfer rte ssocited with the put to the exergy trnsfer rte ssocited with the driving input. Instntneous exergy efficiency of flt plte collector cn be defined s the rtio of the incresed fluid exergy to the exergy of solr rdition. he exergy trnsfer rte ssocited with put (fluid) t given time is given by: Exergy put ssocited with the fluid = Energy put (Entropy genertion in fluid)

3 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 53 Exergy mc p ( f put f, f, in ) ln, f, in Exergy trnsfer rte ssocited with solr rdition t given time [7] is: Exergy input 1 A ch t 1 3 s s he instntneous exergy efficiency of the collector is given by: Exergy II Exergy put input f, mc p ( f, f, in ) ln f, in A c H t 1 3 s 3 s Exergy efficiency given in Eq. (3) is expressed in dimensionless form s: M II e in ) ln in (1) (2) (3) ( (4) where mss flow number M mc p ; A H c t exergy frction of solr rdition, (5) 4 1 e 1 3 s 4 3 s Dimensionless let nd inlet fluid temperture respectively re, f, f, in ; in (6) It is evident from Eq. (4) tht the exergy efficiency of given collector is function of mss flow number, M nd dimensionless let fluid temperture θ, for given solr insoltion nd mbient temperture. Outlet fluid temperture for collector cn be computed using the following reltion [26]: f, f, in H H / U / U L L Ac F' U exp mc p In dimensionless form the let fluid temperture in flt plte collector cn be expressed s: ( in F'( ) )exp M ( 1) where is the imum collector temperture in dimensionless form. he imum temperture of the plte ( p, ) clled the stgntion temperture, occurs when the entire solr het trnsfer is lost to the mbient. ht is, when the useful energy gins by the collector is zero. he imum collector temperture is given in dimensionless form s [10]: H p, t 1 (9) U L Eliminting θ from Eq. (4) using Eq. (8) nd differentiting η II with respect to mss flow number M ssuming in nd η e constnt nd equting to zero we obtin: L (7) (8) ln (1 )exp F' ( 1) M F' (1 )exp F' ( 1) ( 1) M M (1 )exp F' ( 1) M + ( 1) 1 exp ' F ( 1 ' 1) F M ( 0 1) M (10) For the computer progrm, the left hnd side of Eq. (10) is denoted by deffdm. Eq. (10) is solved using Bisection Method to find the optiml mss flow number M* for which exergy efficiency is imum for given collector. Substituting M* in Eq. (8) gives the optiml let fluid temperture *. he optiml exergy * efficiency η* II is obtined by substituting M* nd in Eq. (4).

4 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 3. Optimiztion Process he mthemticl model for optimizing exergy efficiency is bsed on the following nonliner constrined optimiztion problem: Mximize M M II e subject to the constrints mc c t in ) ln in ( eq.(4) p eq.(5) A H ( in M 0, 0 F'( ) )exp M ( 1) eq.(8) he Direct Substitution Method ws pplied to solve the optimiztion problem s discussed in Section 2. he optimiztion process is described in the following schemtic digrm, Figure 1. Vrition of the exergy efficiency ws studied s function of mss flow rte with the following ssumptions: For given collector ssume tht the prmeters like re of the collector A c ; het removl fctor, F R ; collector efficiency fctor F nd overll het loss coefficient, U L ; trnsmissivity of cover (τ) nd bsorptnce of plte (α) re constnt. Inlet fluid temperture is ssumed to be equl to mbient temperture, i.e., θ in = f,in / = 1; incident solr rdition on the collector, H t = 800 W/m 2 ; mbient temperture, = 30ºC nd pprent sun temperture, s = 6000 K. Mss flow rte is vried from to kg/s nd the corresponding exergy efficiency nd energy efficiency re clculted for given collector. he flow chrt for the optimiztion process to compute optiml mss flow rte nd let fluid temperture, which imizes exergy efficiency of the collector, is shown in Figures 2-4. Figure 2 represents the process for computing energy nd exergy efficiency for different vlues of mss flow rte. Flow chrt for computing two initil vlues of mss flow rte such tht deffdm tkes positive vlue for one nd negtive vlue for the other, shown in Figure 3. hese two vlues re the initil input for strting bisection method to obtin the optiml mss flow rte. Figure 4 shows the flow chrt for computing the optiml mss flow rte tht optimizes exergy efficiency. Het rnsfer Fluid Output Input Constnts c p, in Uncontrollble prmeters, Constnts - H t, FPC Specifictions F R U L, F R (τα), F U L, F (τα). τα, A c Compute η I & η II Vrible m m Mx. η II = f(m, ) Subject to = g(m ) M= h(m ) Apply DSM η II =f(m) compute dη II dm = 0 m Compute η* I, η* II &* η I & η II M*, m η* I, η* II &* Stge I Energy & Exergy Anlysis Stge II Optiml mss flow rte Stge III Optiml Operting Condition Figure 1. Schemtic Digrm of Optimiztion Process

5 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 55 Strt Initil Dt Controllble Prmeter Initil Dt Uncontrollble Prmeter Input mss flow rte m <= Ac*0.02 rue Compute F, F R, U L, η e, H, θ in Flse Stge II() Compute M, θ, η II, η I, Q u, pm, m=m Print η II, η I Figure 2. Flow Chrt for Energy & Exergy Anlysis

6 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) strt m = m<=a c *0.02 Compute deffdm If deffdm m *deffdm m <0 flse m=m rue Initil Guess for m Initil 1= m Initil2=m Figure 3: Stge II ()- Flow chrt for computing initil vlues of mss flow rte to strt Bisection method

7 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 57 Strt Input from Stge II() Initil1, initil 2 derdiff=100 m= (initil1 +initil2)/2 derdiff > count <500 Flse rue Compute M, deffdm deffdm>0 rue Flse Initil2=m Initil1=Initil1 Initil1=m Initil2=Initil2 Compute der1= deffdm initil1 der2= deffdm initil2 derdiff=bs(der1- der2) counter= counter +1 Optiml vlue of m m*=m Compute M*, θ*, η II *, η I *, *, Print η II *, η I *, *, Figure 4. Flow chrt for computing optiml mss flow rte nd corresponding optiml energy nd exergy efficiency, optiml let temperture

8 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 4. Results nd Discussion A computer progrm in C lnguge ws developed bsed on the method discussed in Section 3 for computing the optiml mss flow rte tht imizes exergy efficiency of flt plte collector. Figures 5 nd 6, respectively, show the vrition of energy nd exergy efficiency of flt plte collector with respect to mss flow rte. From Figure 5, it is observed tht energy efficiency increses exponentilly with the increse in mss flow rte then sturtion begins, the growth slows nd finlly the growth stops nd the energy efficiency remins unchnged with the increse in mss flow rte. Energy efficiency growth curve resembles the logistic curve in 1 st qudrnt. A similr pttern of the growth of energy efficiency with respect to mss flow rte is reported by Jfrkzemi [22]. Exergy efficiency increses rpidly with the increse in mss flow rte; it ttins imum vlue nd then decreses with the further increse in mss flow rte. he optiml operting conditions, i.e., optiml mss flow rte m * nd the corresponding optiml let fluid temperture, the exergy efficiency nd Δ re determined for given flt plte collector. he optiml operting conditions for six different collectors with different collector re, het removl fctor nd n overll het loss coefficient re computed ssuming H t = 800 W/m 2 nd = 30 ºC = f,in nd re tbulted in ble 1. It is observed tht for given vlue of incident solr rdition, inlet fluid temperture nd mbient temperture, optiml mss flow rte vried from kg/s nd exergy efficiency vried from % for the collectors depending on its gross re A c, overll het loss coefficient U L nd het removl fctor F R. Luminosu et l. [5] lso determined the optiml opertionl mode of flt plte collector by exergetic nlysis. hey ssumed tht the exergy flow rte in globl solr rdition is equl to the solr flux (HR) nd defined exergy efficiency for flt plte collector s: II, Lu min osu mc p f ln A ( HR) c, f, in (11) he globl imum points suggested by Luminosu et l. [5] re: A c = 3.3 m 2, mss flow rte = kg/s, II 3.9% nd Δ= 63.3 K. he optiml operting conditions for collector with re A c = 3.12 m 2 s obtined by uthor in this work re optiml mss flow rte = kg/s, exergy efficiency = 8.9%. For the sme collector, Khdemi et l. [23] obtined optiml mss flow rte = kg/s, exergy efficiency = 7.002%. he optiml mss flow rtes obtined in ll the three works bove re lmost equl. A significnt difference in optiml vlues of exergy efficiency is noted in the work of Luminosu et l. which mybe becuse of the simplifying ssumption for sun s exergy flow rte mde by them. Khdemi et l. [23] pplied SQP nd Genetic Algorithm to obtin optiml design criteri for imizing exergy efficiency. Optiml result obtined by Khdemi et l. [22] pplying SQP is: m = kg s, A p = 5m 2, η II = %, f, = K, η I = %. he optiml results obtined by employing GA over popultion of 500 nd 150 genertion re: m = kg s, A p = 3.12 m 2, η II = %, f, = K, η I = %. ble 1. Optiml mss flow rte for different flt plte collectors nd the corresponding optiml exergy efficiency, optiml let fluid temperture nd Δ=* f, - f,in re tbulted where H t = 800 W/m 2, = 303 K= f,in nd c p of wter is considered t the inlet fluid temperture. Collector A c F R U L m * m 2 W/m 2 K kg/s % K K η II * * f, Δ A B C D E F

9 ηii ηi 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) m [kg/s] Figure 5. Vrition of energy efficiency with respect to mss flow rte for collector of re Ac = 2.13 m2, FR =0.805, UL =5.76 W/m2K, Ht = 800 W/m2 nd = 30 ºC m [kg/s] Figure 6. Vrition of exergy efficiency with respect to mss flow rte for collector of re A c = 2.13 m 2, F R =0.805, U L =5.76 W/m 2 K, H t = 800 W/m 2 nd = 30 ºC = f,in. 5. Vlidtion of Computer Code o vlidte the computer code, optiml opertion mode is determined for flt plte collector with design prmeters considered by Khdemi et l. [23] s input for the proposed model. he optiml results re compred with those reported by Khdemi et l.. bles 2 nd 3 respectively presents comprison of the optiml results obtined in the present work with those obtined by Khdemi et l. using Genetic Algorithm nd SQP. From bles 2 nd 3, it is evident tht the error in computing the optiml exergy efficiency, optiml mss flow rte nd optiml let temperture using the proposed method is smll in both cses. One of the sources of error my be the input solr rdition which is considered to be 800W/m 2 in the present work nd is tken to be constnt. Khdemi et l. [23] did not report explicitly the vlue of input solr rdition used for computing the optiml design conditions. ble 2. Comprison of optiml results obtined by using proposed model with tht obtined by Khdemi [23] using Genetic Algorithm; Number of itertion is 15 for proposed model. Input η*ii m* * Applying Present Erro Applying Present Applying Present Erro Ac in U L Q u η I Error GA work r GA work GA work r m 2 K W/m 2 K W/m 2 K 4.97E ble 3. Comprison of optiml results obtined by using proposed model with tht obtined by Khdemi [23] using SQP; Number of itertion is 17 for proposed model nd 9 for SQP. Input η*ii m* * A Applying Present Erro Applying Present Applying Present in U c L Q u η I Error Error SQP work r SQP work SQP work m W/m 2 2 K W/m K 2 K E

10 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 6. Conclusions Exergetic optimiztion of flt plte collectors is crried to evlute the performnce of flt plte collector depending on mss flow rte nd let fluid temperture. It is observed tht decresing the flow rte below optiml vlue increses the temperture of the fluid but decrese in the exergy efficiency occurs. On the other hnd, incresing the flow rte bove the optiml vlue increses the energy efficiency but decrese in the exergy efficiency nd fluid temperture occurs. hus, it cn be concluded tht the exergy nlysis of the solr flt plte collectors llows the pre-determintion of the optiml opertionl conditions for collector for given vlues of controlled or uncontrolled prmeters. he simultor developed bsed on the proposed mthemticl model cn be used to determine the optiml opertionl mode of flt plte collector for given environmentl conditions. he rte of convergence of the proposed method is high nd the ccurcy of the result is lso high. he results obtined re comprble to those reported by Khdemi et l. [23] with n error of 0.8 for computing optiml exergy efficiency, error of the order of 10-3 for computing the optiml mss flow rte nd error of for computing the optiml let fluid temperture when results were compred with those obtined by using SQP. When results were compred with results obtined by Genetic Algorithm, error in computing the optiml exergy is 1.9, error is of the order of 10-4 for computing the optiml mss flow rte nd n error of 6.83 for computing the optiml let fluid temperture is observed. It is observed tht the error in computing the optiml opertionl mode using the proposed model is less when compred to the optiml solution obtined by Genetic Algorithm thn SQP. Khdemi et l. [23] reported tht the results of GA represent more ccurcy of lgorithm. Hence, the simultor developed to solve the nonliner constrint optimiztion problem bsed on direct substitution method gives n optiml result with considerbly good ccurcy. References [1] J. R. Howell, R. B. Bnnerot, Optimum solr collector opertion for imizing cycle work put. Solr Energy, 19 (1977), [2] K. Altfeld, W. Leiner, M. Fiebig, Second lw optimiztion of flt plte solr ir heters. Solr Energy, Vol. 41(1988) No. 2, [3] K. Altfeld, W. Leiner, M. Fiebig, Second lw optimiztion of flt plte solr ir heters. Prt 2: Results of optimiztion nd nlysis of sensibility to vritions of operting conditions. Solr Energy, Vol. 41 (1988) No. 4, [4] A. Hepbsli, A key review on exergetic nlysis nd ssessment of renewble energy resources for sustinble future. Renewble nd Sustinble Energy Reviews, Vol. 12 (2008), [5] I. Luminosu, L. Fr, Determintion of the optiml opertion mode of flt solr collector by exergetic nlysis nd numericl simultion. Energy, Vol. 30 (2005) issue 5, [6] H. H. Öztürk, Experimentl determintion of energy nd exergy efficiency of the solr prbolic-cooker. Solr Energy, Vol.77 (2004), [7] R. Petl, Exergy nlysis of the solr cylindricl-prbolic cooker. Solr Energy, Vol.79 (2005), [8] M. A. Rosen, Second-Lw of Anlysis: Approch nd Impliction. Interntionl Journl of Energy Reserch, Vol. 23 (1999), [9] S. Frht, F. Srhddi, H. Ajm, Exergetic optimiztion of flt plte solr collectors. Renewble Energy, Vol 34 (2009) No.4, [10] S. A. Klogirou, S. Krells, V. Bdescu, K. Brimkis, Exergy nlysis on solr therml systems: A better understnding of their sustinbility. Renewble Energy XXX (2015) 1-6, In press. [11] A. Bejn. Entropy genertion minimiztion. CRC press. Inc., 1996, p [12] D. K. Mhnt, S. K. Sh, Internl irreversibility in wter heting solr flt plte collector. Energy Conversion nd Mngement, Vol. 43 (2002), [13] S. K. Sh, D. K. Mhnt, hermodynmic optimiztion of solr-plte collector. Renewl Energy, Vol. 23 (2001), [14] S. K. Sh, K. K. Dtt Gupt, hermodynmic optimiztion of solr therml collectors. Proceedings of Ntionl Solr Energy Society of Indi, Integrted Renewble Energy for Rurl Development, [15] E. orres-reyes, J. G. Cervntes-De Gortri, B. A. Ibrr- Slzr, M. Picon-Nuñez, A design method of flt plte solr collectors bsed on minimum entropy genertion. Exergy Interntionl, Vol. 1 (2001) [16] Q. M. Doos, Z. Al-Doud, S. M. Al-hr, Agent Bsed Fuzzy ARMAP Neurl Network for Clssifying the Power Plnt Performnce. Jordn Journl of Mechnicl nd Industril Engineering, Vol. 2, (2008) No. 3, [17] Vivek Kumr, S. Srinivsn, S. Ds, Optiml Solution for Supplier Selection bsed on SMAR Fuzzy Cse Bse Approch. 7th IEEE Interntionl Conference on Soft Computing nd Intelligent Systems, flgship interntionl conference of Soft Computing in Asi, Fukuok, JAPAN, [18] Vivek Kumr, S. Srinivsn, S. Ds, Multi-Agent bsed Decision Support System using Dt Mining, Cse Bsed Resoning nd Fuzzy in Supply Chin Mngement. Interntionl Conference on e-commerce, e-administrtion, e-society, e-eduction, nd e-echnology Fll Session (e- CASE & e-ech 2014 Fll Session), okyo, JAPAN [19] Vivek Kumr, S. Srinivsn, S. Ds, A Fuzzy Agent-bsed Architecture for Supplier Selection. Journl of Computing, Vol 3, (2011) Issue 5. [20] Vivek Kumr, S. Srinivsn, S. Ds, A Multi-Agent System for Mngement of Supplier Selection Process in Fuzzy Supply Chin. Interntionl Journl of Computer Appliction, Vol.23 (2011) No. 6, [21] M. rwneh, F. Al-Ghthinb, M. A. Nwflehc, N.Al- Kloub, Numericl Simultion nd Performnce Evlution of Stirling Engine Cycle. Jordn Journl of Mechnicl nd Industril Engineering, Vol. 4 (2010) No. 5, [22] F. Jfrkzemi, E. Ahmdifrd, Energetic nd exergetic evlution of flt plte solr collectors. Renewble Energy, Vol. 56 (2013) [23] M. Khdemi, F. Jfrkzemi, E. Ahmdifrd, S. younesnejd, Optimizing Exergy Efficiency of Flt Plte Solr Collectors Using SQP nd Genetic Algorithm, Applied Mechnics nd Mterils, Vols (2013) [24] P. Boggs, J. W. olle. Sequentil Qudrtic Progrmming, Act Numeric (1996) [25] S. Mukhopdhyy, B. Bndyopdhyy, S. K. Sh, hermodynmic Optimiztion of the Performnce of Flt Plte Collector. Proceedings of Interntionl Conference on Issues nd Chllenge in Energy Conversion nd Mngement, BHU, Indi 2009 [26] J. A. Duffie, W. A. Beckmn. Solr Engineering of herml Process. 2nd ed. New York : Wiley Interscience, 1991.

11 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 61 Appendix Computer Code Developed for Exergetic Optimiztion of Flt Plte Collectors //**************************************************************** File Nme : Efficiency.cpp PURPOSE : Optimiztion of Second Lw Efficiency w.r.t. mss flow rte *****************************************************************/ // ********************* HEADER FILES **************************** #include<stdio.h> #include<iostrem.h> #include<fstrem.h> #include<mth.h> void min() // ********* DECLARAION AND INIIALIZAION ************* double F_Ul = 4.86; // F'UL double F_owAlph = 0.722; // F'(ow)(Alph) double Ac = 2.13; // Gross Are of the Collector double s = 6000; // Aprent emp of the Solr Rdition double FrUl = 4.66; // FRUL double FrowAlph = 0.688; // FR(ow)(Alph) double owalph = 0.855; // (ow)(alph) double Ht = 800; double = 303; double cp = 4179; // Solr Insoltion on the Collector Plne (W/m*m) // Ambient emp. (in Kelvin) // Specific Het Cpcity of Wter (J/kg-K) int i,j,counter; double tow,lph,fdsh,fr,ul; double in,,h,thetin, thetmx,qu; double ete,m,md,eff2,deffdm; double et1,thetout,tpm,delt; double temp,minitil1,minitil2; double mdlower, mdupper, mdmiddle, mdoptimum; double der1, der2, derdiff; ofstrem result("result.txt",ios::pp); int slopsign1, slopsign2; double initil1 = -1000; double initil2 = -1000; int flgfound = 0; int flgstrt = 1; // ********** CALCULAION ***************** Fdsh = F_owAlph/owAlph; // Fdsh: Collector Efficiency Fctor Fr = FrowAlph/owAlph; // Fr: Collector Het removl fctor

12 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) Ul = FrUl/Fr; // Ul: Overll Loss Coefficient (W/m*m-K) H = owalph*ht; // H: Absorbed Solr Rdition (W/m*m) in = ; // in: Inlet Fluid emp. (K) thetin = in/; // thetin: Dimensionless Inlet fluid temp. thetmx = 1 + H/(Ul*); // thetmx: Dimensionless plte temp. ete = 1 + pow((/s),4)/3-4*(/s)/3; // ete: Exergy Frction of Solr rdition printf("fdsh:%f\n",fdsh); printf("fr:%f\n",fr); printf("ul:%f\n",ul); printf("h:%f\n",h); printf("in:%f\n",in); printf("thetin:%f\n",thetin); printf("thetmx:%f\n",thetmx); printf("cp:%f\n",cp); printf(":%f\n",); printf("ht:%f\n",ht); printf("ac:%f\n",ac); printf("ete:%f\n",ete); result<<"m-dot"<<" "<<"M"<<" "<<"Eff 2"<<" "<<"Derivtion"<<" "<<"Eff 1"<<" "<<"pm"<<" "<<"Delt-"<<endl; // ***CALCULAION OF ENERGY EFFICIENCY AND EXERGY EFFICIENCY OF COLLECOR & INIIAL GUESS FOR BISECION MEHOD********* // md: Mss Flow rte (kg/s) // M: Mss Flow Number // eff2: Second Lw Efficiency // deffdm: Derivtive of Second Lw Efficiency w.r.t M // et1: First Lw Efficiency // tpm: Men Plte temp.(k) // delt: Difference between Outlet nd Inlet fluid temp (K) minitil1 = -1000; minitil2 = -1000; for(md = ; md<= Ac*0.02 ; md=md ) M = md*cp*/(ac*ht); eff2 = (M*(thetMx - 1)/etE)*(1 - exp(-f_owalph/(m*(thetmx-1)))) - (M/etE)*log(thetMx + (1 - thetmx)*exp(-f_owalph/(m*(thetmx-1))));

13 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 63 // Output results for Et1, pm thetout = thetmx + (thetin - thetmx)*exp(-f_owalph/(m*(thetmx-1))); et1 = M*(thetOut - thetin); Qu = Ac*Ht*et1; tpm = in + (Qu*(1-Fr))/(Ac*FrUl); = *thetout; delt = - in; // o Find the Initil Guess for Bisection Method temp = F_owAlph/(thetMx - 1); deffdm = log(thetmx + (1-thetMx)*exp(-temp/M)) +(temp*(1-thetmx)*exp(- temp/m))/(m*(thetmx + (1-thetMx)*exp(- temp/m))) - (thetmx-1)*(1-exp(-temp/m)*(1+(temp/m))); if (flgstrt==1) if (deffdm>0) slopsign1 = 1; else slopsign1 = -1; initil1 = md; initil2 = md ; flgstrt = 0; else if (flgfound == 0) if (deffdm>0) slopsign2 = 1; der1= deffdm; else slopsign2 = -1; der2= deffdm;

14 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) if (slopsign1*slopsign2 < 0) flgfound = 1; else initil1 = md; initil2 = md+ 0.02; // End of Else printf("m:%f M:%f Eff:%f Derivtive:%f Et1:%f pm:%f delt:%f\n",md,m,eff2,deffdm,et1,tpm,delt); result<<md<<" "<<M<<""<<eff2<<" "<<deffdm<<" "<<et1<<" "<<tpm<<" "<<delt<<endl; // End of for (md) printf("\ninitil 1: %f Initil 2: %f\n",minitil1,minitil2); //** CALCULAION OF OPIMUM MASS FLOW RAE BY BISECION MEHOD **/ mdlower = minitil1; mdupper = minitil2; mdmiddle = (minitil1 + minitil2)/2; derdiff = 100; counter = 0; temp = F_owAlph/(thetMx - 1); while(derdiff> && counter < 500) M = mdmiddle*cp*/(ac*ht); deffdm = log(thetmx + (1-thetMx)*exp(-temp/M)) + (temp*(1-thetmx)*exp(-temp/m))/(m*(thetmx + (1- thetmx)*exp(-temp/m))) - (thetmx-1)*(1-exp(-temp/m)*(1+(temp/m))); if(deffdm > 0) mdupper = mdmiddle; else mdlower = mdmiddle; M = mdlower*cp*/(ac*ht); der1 = log(thetmx + (1-thetMx)*exp(-temp/M)) + (temp*(1-thetmx)*exp(-temp/m))/(m*(thetmx + (1- thetmx)*exp(-temp/m))) - (thetmx-1)*(1-exp(-temp/m)*(1+(temp/m)));

15 2016 Jordn Journl of Mechnicl nd Industril Engineering. All rights reserved - Volume 10, Number 1 (ISSN ) 65 M = mdupper*cp*/(ac*ht); der2 = log(thetmx + (1-thetMx)*exp(-temp/M)) + (temp*(1-thetmx)*exp(-temp/m))/(m*(thetmx + (1- thetmx)*exp(-temp/m))) - (thetmx-1)*(1-exp(-temp/m)*(1+(temp/m))); mdmiddle = (mdupper + mdlower)/2; derdiff = fbs(der1 der2); counter++; // End of while() // **** CALCULAE HE OPIMUM VALUES *************** mdoptimum = mdmiddle; M = mdoptimum*cp*/(ac*ht); eff2 = (M*(thetMx - 1)/etE)*(1 - exp(-f_owalph/(m*(thetmx-1)))) - (M/etE)*log(thetMx + (1 - thetmx)*exp(-f_owalph/(m*(thetmx-1)))); // Output results for Et1, pm thetout = thetmx + (thetin - thetmx)*exp(- F_owAlph/(M*(thetMx-1))); et1 = M*(thetOut - thetin); Qu = Ac*Ht*et1; tpm = in + (Qu*(1-Fr))/(Ac*FrUl); = *thetout; delt = - in; printf("optimum m:%f Eff2:%f Et1:%f pm:%f delt:%f\n",mdoptimum,eff2,et1,tpm,delt); result<<endl; result<<"****** OPIMUM VALUES ***********"<<endl; result<<"optimum Mss Flow rte:"<<mdoptimum<<endl; result<<"2nd lw Efficiency:"<<eff2<<endl; result<<"1st lw Efficiency:"<<et1<<endl; result<<"pm:"<<tpm<<endl; result<<"delt :"<<delt<<endl; result.close(); // End of min()