Journal of Engineering Science and Technology Review 5 (4) (2012) Special Issue on Renewable Energy Systems.

Transcription

1 Jestr Journal of Engineering Science and ecnology eview 5 (4) (0) Special Issue on enewable Energy Systems esearc Article JONA OF Engineering Science and ecnology eview An Effective Simulation Model to redict and Optimize te erformance of Single and Double Glaze Flat-late Solar Collector Designs S. Kaplanis* and E. Kaplani Mecanical Engineering Dept., ecnological Educational Institute of atras, Greece eceived 8August 0; Accepted 4September 0 Abstract. is paper outlines and formulates a compact and effective simulation model, wic predicts te performance of single and double glaze flat-plate collector. e model uses an elaborated iterative simulation algoritm and provides te collector top losses, te glass covers temperatures, te collector absorber temperature, te collector fluid outlet temperature, te system efficiency, and te termal gain for any operational and environmental conditions. It is a numerical approac based on simultaneous guesses for te tree temperatures, p plate collector temperature and te temperatures of te two glass covers, g. A set of energy balance equations is developed wic allows for structured iteration modes wose results converge very fast and provide te values of any quantity wic concerns te steady state performance profile of any flat-plate collector design. Comparison of te results obtained by tis model for flat-plate collectors, single or double glaze, wit tose obtained by using te Klein formula, as well as te results provided by oter researcers, is presented. Keywords:solar collector simulation, double glaze, losses coefficient, performance prediction, optimization Nomenclature a ambient temperature (K) A c Cb Di Do F collector area (m ) bond conductance tube inner diameter (m) tube outer diameter (m) fin efficiency for straigt fins wit rectangular or tubular profile F collector efficiency factor F collector eat removal factor I global solar radiation intensity on te collector (W/m ) Nu r Nusselt number (dimensionless) randtl number of te air inside te collector (dimensionless) Q " u eat (rate) gain of te collector panel normalized to its surface (W/m ) a aleig number (dimensionless) a aleig number, generalized for tilted layers; a a cos(β) (dimensionless) total energy losses coefficient (W/m K) t top eat losses coefficient (W/m K) fluid inlet temperature (K), fluid outlet temperature (K) g p f o p m glass cover temperature (K) absorber plate temperature (K), absorber plate mean temperature (K) s W equivalent blac body sy temperature (K) distance between te fluid tubes (m) c p specific eat capacity of te fluid in te collector tubes, J/gK fluid eat transfer coefficient inside te tube (W/m K) p convective eat transfer coefficient between absorber plate and glass cover (W/m K) convective eat transfer coefficient between te g inner and outer glass cover (W/m K) * address: aplanis@teipat.gr ISSN: Kavala Institute of ecnology. All rigts reserved.

2 r, p radiative eat transfer coefficient between absorber plate and glass cover (W/m K) r, g a radiative eat transfer coefficient between te outer glass cover and te environment (W/m K) w eat transfer coefficient from te outer glass cover (W/m K) termal conductivity of te collector material (W/mK) a termal conductivity of air (W/mK), g termal conductivity of te glass covers- and - respectively (W/mK) l, l g ticness of te glass cover- and glass cover- (m) l p- air gap between absorber plate and glass cover- (m) l -g air gap spacing between glass cover- and glass cover- (m) m a fluid mass flow rate (g/s) absorber plate absorption coefficient β collector tilt wit respect to orizontal ( ) δ ε p ε g collector absorber plate ticness (m) absorber plate emissivity coefficient glass cover emissivity coefficient η solar collector instant efficiency v air inematic viscosity (m /s) σ Stefan-Boltzman constant (W/ m K 4 ) τ glass cover transmittance. Introduction Flat-plate solar collector modular designs for Domestic Hot Water (DHW) and innovative solar collector type designs for space eating in buildings or oter applications are tecno-economically attractive and effective for energy savings and green buildings, as argued in te scientific articles in [].e performance of solar collectors, especially te flat-plate ones, as been investigated so far by many researcers, starting wit te classical wors [-6], ten proceeding to furter investigations on various parameters in order to improve te solar collector design and performance, [7-] and finally reacing to more detailed experimental and teoretical investigations wit sopisticated simulation models [-8]. e efforts to increase te solar collector gain and its efficiency are continuous [9-3] and focus on te reduction of te coefficient and te increase of te ratio α/ε p wic in turn affects, too, as one moves from conventional absorbing surfaces to selective ones []. ere is, also, a concern for double glaze flat plate collectors, especially, wen te annual meteorological conditions in a site are in favor, suc as ig wind velocity and low ambient temperatures. In te past, attempts to get to a simple expression of Q u as a function of α/ε p considered an absorbing surface, but not a real solar collector as described in [], wile oter attempts described in [3] present a smart set of formulae to predict p and g for any value of α and ε p but for single glass flat-plate collectors. On te oter and, te termal analysis of solar collector designs wit innovative features, suc as vee corrugated collectors [4], double glazing systems, is complicated [5]. It is necessary to incorporate into te model a wole set of proper matematical expressions wic describe suc collector systems and deal wit te most probable to appen pysical penomena wit all te possible modes of eat transfer and radiation taen into consideration. Conclusively, an accurate prediction of te termal performance of any flat-plate solar collector design is a callenge. In te optical analysis concerning te I troug a solar collector glass cover, an improvement was described in [6]. e energy analysis, wit eat transfer and I radiation taen into account may be andled by various models wic are structured on energy balance equations. Suc fundamental approaces are outlined in [,7], wile in [5,6,9] some improved versions are presented. wo families of suc approaces are distinguised, in general. e empirical one, wit representative formulae for te determination of t coefficient as in [4,3] and te numerical one as in [8-0,4,5,8]. Witin tis scope, te numerical tecniques sowed some errors wic resulted from regrouping of te eat convection and I radiative terms. Improved expressions were elaborated to determine te absorber plate and glass cover temperatures for single and double glaze collectors [5,9,30] wit a good accuracy, were te glass cover solar radiation absorption is also taen into account. However, tese papers are concerned only wit te termal analysis of te top losses and te glass cover temperatures for various environmental conditions and do not develop a complete and compact model analysis for flat-plate collectors wit teir fluid properties studied as a wole system. A detailed analysis to answer wen a double glaze collector is preferable vs a single glazed one is a must, especially wen optimization factors do callenge for te most cost-effective solutions. e latter is of ig importance as solar collector type designs embedded into building structures require cost effective innovations to gain competitiveness. A complete and friendly solar collector simulation model to determine te eat losses coefficients, te absorber and glass covers temperatures, te eat gain and te efficiency, taing into account te glass covers radiation absorption, is presented in tis study.. e solar collector simulation model: details and iterative tecniques e numerical simulation model developed for eiter single or double flat-plate collectors considers: a. e geometrical caracteristics of a double glaze flat plate collector: collector area (A c ), te collector plate ticness (δ) te tube diameters (D o, D i ), te spacing between te fluid tubes (W), te absorber plate to cover- and cover- to cover- distances, l p- and l -g respectively, te glass cover ticnesses l, 57

3 t l g, te tilt of te collector wit reference to te orizontal surface β, etc. b. e termo-pysical caracteristics of te material used in te collector suc as: te termal conductivity of te collector material, as well as te glass covers conductivity, g, te collector s fluid specific eat capacity c p, te randtl number, r, te inematic viscosity ν, te air conductivity coefficient a. eir dependence on temperature was also taen into account. e corresponding values of te above quantities r, ν, a, at te boundary layers of te collector two sections, i.e. te absorber plate to cover- zone and cover- to cover- zone, are fitted to a double exponential for a and r, and to a quadratic expression for te inematic viscosity ν, for te range of K. erefore, te program uses a simple self-adequate data retrieval mode, useful in te various iterations of tis algoritm for increased accuracy. c. te ambient temperature α and te fluid inlet temperature f,i, te fluid mass flow rate m, te collector outer surface eat transfer coefficient w, te values of te absorption coefficient α and te emissivity coefficient ε p of te absorbing surface, te glass cover(s) emissivity coefficient ε g, te fluid eat transfer coefficient inside te tubes f,i, calculated according to te formulae in Appendix. d. te solar irradiance on te collector I and te effective product of te coefficients τ and α, nown as (τα), estimated by a set of formulae provided in Appendix. e simulation model developed estimates te following quantities: t, p,, g, f,o, Q u and η vs I wit parameters f,,i, α, ε p and w. e numerical approac uses te following set of equations to tae into account eat convection between absorber plate and glass cover-, glass cover- and glass cover- and outer glass to te environment; also, te I radiation excanges between te various zones of te collector, plus te one between te collector surface and te environment and finally, te termal conductivity in te glass covers. e overall energy transfer coefficient from te absorber to te environment is given by te expression: p r, p g r, g w r, g a l l is formula is easily developed by using te electric equivalent circuit for te eat transfer troug te collector were: r, p and r, g σ ( ) ( ) ε ε σ ( ) ( ) g ε g ε g g ( ) ( ) r, g a ε g σ g s g s g g () () (3) s is te sy temperature given by : s 0 a.055( ).5 s and α are bot in Kelvin, as discussed in [7]. Factors: (4) l / and l g / g (5) are defined as te termal resistances wic represent eat conduction troug te glass cover- and cover-, respectively. Finally, te convection eat transfer coefficient w for te outer glass cover is determined wit respect to te wind velocity v w, on te collector surface by te following formulae, in cases te forced flow convection prevails: w v w [9] w.8 3.0v w [30] w 4.5.9v w [3] (6a) (6b) (6c) For cases of natural eat convection, w may be replaced by g-a to be determined by a set of equations provided in [33]. e values of p, and g are generally unnown, wile α and f,i may be measured experimentally along wit te solar irradiance on te collector I. Hence, tey are given as input guess values or as predefined initial parameters in tis algoritm. ecurrence formulae wic relate p, and g can be easily constructed assuming tat te energy flow from te collector s absorber plate to cover- is te same wit te energy flow from cover- to cover- and finally to te environment. Conclusively, steady state conditions and no side losses are considered, wile te temperature difference due to eat conduction in te glass covers is taen into account, along wit te convection and te radiative losses in te various zones te collector consists of. An exercise on te continuity principle for te energy flow wic crosses te solar collector leads to te following recurrence formulae for te collector glass cover- and glass cover- temperatures. t ( p a ) ( ) [ ] p r, p g and t ( p a ) [( ) ] g g r, g However, as p and, g are not nown, t cannot be accurately calculated, and ence eq.(7) cannot be effectively andled. e iteration starts wit a guess for p and, g simultaneously. A fast converging set of various modes of iterations is developed, were te convection eat transfer coefficients p- and -g are calculated from te Nu number according to te following expressions. (7) 58

4 l Nu Nu * p a * g a l p p l a g g l a, (8) Δ p and g Δ g g () l* is te caracteristic lengt wic in tis case is te absorber plate to glass cover- distance l p-, wile l -g is te cover- to cover- distance. e Nu numbers Nu and Nu for tose two zones are calculated from te equations below: Nu * l a a,for 708< a <5900 or Nu 0.9( a ) for9.3 0 > > 5900 Nu 0.57( a ) 0.85 (9a) a or (9b) 4 6 for9.3 0 < a < 0, (9c) were, to cater for te collector inclination β, α is defined by: a a cos β (9d) Detailed discussion on α for various angles of inclination is found in [7,33]. Introducing te corresponding value of l* for te zone investigated, te associated α (ayleig) numbers may be estimated by te expression: g β Δ a ν g β Δ a ν 3 l p g 3 l g g r r, (0) were, te values of α, v, r for te air space witin te collector can be determined from ables at te corresponding boundary layer temperature bl. Generally te values of te above termo-pysical quantities for air and water may be taen from relevant ables [33] and especially in te algoritm developed are estimated by te fitted exponentials or polynomial expressions mentioned above. e program determines automatically te termo-pysical properties of air and water, along wit te oter calculations in eac loop. For gasses, β and bl are interrelated: β and bl ( ) p β bl ( ) g () bl and bl are te temperatures, in K, at te boundary layers of plate to cover- and cover- to cover- zones, respectively. en, te temperature differences are defined by: 59 ese relationsips provide a constraint in te guess process. e, p guessed value sould be different tan te guessed and g as Δ obtained from eq.() must be 0 for te numerical process to tae place witout problems. In case Δ0, ten α0, wic is not true as termal losses do exist. 3. Iterative rocess: Steps and Iterations A compreensive iterative procedure is sown in Fig. and te steps are briefly outlined below:. p and, g are guessed wit te constraint as required above. An approximate value of t is estimated using eqs.(-6) and eqs.(8-).. e program starts a number of loops to determine a better value of for te guessed values of p and g using eq.(7) and eqs.(-6). 3. e program re-evaluates t from eqs.(-6) for te new value, eeping te previously guessed values p, g for a subsequent correction. 4. en, starts anoter loop to determine a better value of g for te guessed value of p and te value of as estimated before in Step, using eq.(7) and eqs.(-6). 5. aing into consideration te values of, g as resulted from te iteration procedure, i.e. Steps 4, and te initially guessed value of p, te program reevaluates t from eqs.(-6). 6. e program sets t as te purpose is not to calculate but, as said above, to investigate top losses for various environmental and operational conditions. In fact, t approaces since an effective bac and side insulation is placed in te collector frame. It is obvious tat te side and bacwards direction losses could be easily calculated, as discussed in [34]. For tis set of values p, and g, te program calculates Δ, Δ, bl, bl, i.e. β, β and α, α. en, it calculates te eat removal coefficient, F given by te related formulae below, as fully presented in [7]. F m c [ exp( Ac F m c )], were (3) Ac F W [ ( Do ( W Do ) F) ] ( π Di ) Cb (4α) F is te collector efficiency factor, wic provides for te ratio of te eat transfer resistance from te absorber plate to te environment over te eat transfer resistance from te fluid to te environment, and tan F m [ m ( W Do ) ] m ( W Do ), δ (4b) were, F is te fin efficiency for straigt fins wit tubular or rectangular profile [7,8]. C b represents te

5 bond conductance of te fluid tubes attaced on te absorber. C b typical values must be > 30 W/m K. 7. Having estimated t in Step 6 te program calculates Q u, i.e. te eat rate gain, by te energy balance formula of Hottel Willier Bliss and te calorimetric equation as it regards te fluid flow in te collector tubes: " u. [ I ) ( )] ( m c ) ( ) Q F τα f ( a f,0 (5) were, (τα) is te effective product of te solar radiation transmission coefficient of te glass cover(s) system and te absorption coefficient of te collector plate. It is estimated according to te set of formulae provided by Appendix. 8. e program calculates te value of te f,o from te second part of eq.(5) and determines a better value of p from a formula wic provides te absorber plate mean temperature p,m, were we assume p p,m, i.e. " u p " Q p, m F ( F ) (6) Anoter equivalent expression to calculate p is given by: F I ( τα ) a ( F ) ( F ) wic is derived from te obvious identity: [ I ( τα ) ( )] I ) ( ) Q F τα a ( p, m a (7) (8) t C N σ ( p, m a ) ( p, m a ) e ( N f p m a ) w 0.33 ε, ( ε N w ) N ( N f ) ε g, m (0) were, N is te number of te glass covers; in tis case, N. f ( w w ε p )( N) (0a) C 50( β ) for 0<β<70 o (0b) wile, for 70 o <β <90 o te eq.(0b) is used wit β70 ο e 0.43(-00/Τ p,m ) (0c) According to eq.(0), only te p as to be given wen te Klein empirical formula is cosen for te estimation of t. is is done wit a little cost in te accuracy, as to be discussed below. In tis approac α is estimated directly using eqs.(9a-), wile and g may be determined in tis mode using te Klein formula for t via eq. (7), provided te t value by te Klein formula is introduced into te iteration procedure, just described before. However, in tis approac p is arbitrarily given wereas it is straigtly associated to te I and to f,i plus te parameters α, ε p and w. sing te Hottel-Willier-Bliss equation and te calorimetry one, see eq.(8), te program estimates a new p,m and f,o for a given I. e iteration is repeated until p,m does not cange significantly. is is te version of te program wic provides results based on te Klein formula. 9. Substituting p,m for p te program repeats once again te first set of loops, see Step, to determine a better value for and ten for g, as described before. 0. en, te program repeats all te above steps as before until te new p,m differs from te previous one by a preset value according to te accuracy required. An improved version of tis set of iterations was tested, were te separate iterations associated wit te determination of eac one of te tree parameters p,, g,are andled in parallel witin te same loop, see flowcart in Fig.. is procedure is muc faster and te results converge witin 9-3 iterations, regardless of te initial guess values given to p,, g. e convergence is set to te 3rd decimal point, so tat te iteration ends wen te tree temperatures p,, g do not differ more tan 0.00 o C from teir corresponding values in te previous iteration. e above iterations give as outputs te required p and, g values, necessary for te calculations of te performance indicators for te solar collectors. It, also, provides f,o, Q u and finally, te solar collector efficiency, η, wic is determined by: ηq u / I (9) e results of tis simulation tecnique for t wit te guessed temperatures p and, g are compared wit te ones obtained by using te Atar & Mullic model [5] and te generalized formula proposed by Klein [4]: Fig. Flow cart of te proposed simulation model 60

6 4.esults e proposed model wit its sets of formulae, as outlined in tis paper was developed in MAAB. Functions were also developed to elaborate results based on bot te Atar & Mullic model and te Klein empirical formula. is model was executed systematically to provide results for η, f,o, Q u, t, p,, g for any environmental conditions, as it regards te ambient temperature α, and te wind velocity v w for various values of I, f,i and te coefficients α, ε p and w. e purpose was first to investigate te accuracy of its results compared wit te ones obtained by te Klein formula [4] and also by te Atar & Mullic model [5]. Bot of tese models require as inputs te value of p wic is I dependent, wereas te model proposed in tis paper is complete and compact only taing as input data te I, w, α, f,i wic mae up a realistic set of solar collector operation variables. e results provided by te above tree models for t vs I, are sown in Figs.-5 for te case of double glaze solar collector for various sets of parameter values f,i, α, ε p and w. It is obvious from tose figures tat tis model provides t results wic are very close to te ones by te Atar & Mullic approac. ey differ less tan % in all cases. It sould be noted tat te results sown for te Atar & Mullic s approac are based on teir formula using α instead of s, oterwise te results obtained for teir model deviated significantly from normal especially for low I values. On te oter and, in te proposed model s was calculated by eq.(4). As it concerns te Klein formula results, tey differ to tis model by about -3 % for low I values. is difference is lower tan te uncertainty in t obtained by te Klein formula, as it is discussed by Duffie & Becman [7]. As I increases, tis difference becomes muc lower and Klein model results get close to tis model. Generally, te Klein formula underestimates t for low ε p values. However, as ε p increases Klein formula provides an overestimation in te t results and for ig w and f,i values tis overestimation reaces around 3-4% compared to te ones from tis model and te model in [5]. Fig.3. Heat losses coefficient t, vs I for a double glaze flat-plate collector as estimated by te proposed model and compared to Klein model [4] and model [5], for α0 o C, ε p0.95, w5 W/m K, wit f,i0 o C and f,i50 o C. Fig.4. Heat losses coefficient t, vs I for a double glaze flat-plate collector as estimated by te proposed model and compared to Klein model [4] and model [5], for α0 o C, ε p0., w0 W/m K, wit f,i0 o C and f,i50 o C. Fig.5. Heat losses coefficient t, vs I for a double glaze flat-plate collector as estimated by te proposed model and compared to Klein model [4] and model [5], for α0 o C, ε p0.95, w0 W/m K, wit f,i0 o C and f,i50 o C. Fig.. Heat losses coefficient t, vs I for a double glaze flat-plate collector as estimated by te proposed model and compared to Klein model [4] and model [5], for α0 o C, ε p0., w5 W/m K, wit fi0 o C and fi50 o C. Fig.6 sows te t results provided by te 3 approaces for single glaze flat-plate collectors. In tis type of collector, te Klein formula provides results wic are systematically iger tan te ones provided by te oter two approaces. However, tis difference is not iger tan 5-8% for te worst cases, tat is, for ig w and ig ε p values displayed in Fig.6. It is evident tat te last two coefficients affect greatly te t profile. 6

7 ε p0., w5 W/m K. e predicted values of and g by tis model and by [5] almost coincide. Fig.6. Heat losses coefficient t, vs I for a single glaze flat-plate collector, as estimated by tis model and te ones of [4,5], for α0 o C, f,i 0 o C and various ε p and w values. As said, te model provides te values of te p, and g temperatures vs te solar irradiation on te collector I and tese results are compared wit tose obtained by te formulae described in [5]. It obvious from Figs.7-0 tat, for all environmental conditions tis model was tested, te results compared to tose by te model [5] almost coincided; te difference was less tan 0. o C in a scale of 00 o C. o get results from [5] wit coincidence to tis model te s value was set equal to α. e efficiency of te flat-plate collectors, η vs ( f,i - α )/ I or η vs ( p - α )/ I for eiter single or double glaze collectors was investigated for various w, α and ε p values, as sown in Figs.-. In tis case, te potential of te proposed model is clear as it provides answers about te collector efficiency for any environmental conditions. e effect of ig I, were ig p temperatures are reaced, is evident from te cange of te η curve. e efficiency curve from its initial linear beaviour, wen te convection losses in te collector prevail, taes a curved profile of nd degree, as in tis case te I radiation losses prevail. e curved sape in te efficiency is prominent wen te efficiency is given vs ( p - α )/I. is is more realistic diagram, as it is te absorber plate wic is eated by te I absorbed and tis affects greatly te wole energy performance of te collector. In Fig. te effect of te parameters α, ε p and w is obvious. Also, Fig. sows a comparison between a single flat-plate solar collector efficiency against te double glaze one. e region of te environmental conditions te one type of collector is preferable over te oter is clear. Figs. 3 and 4 provide te η values vs I eeping as parameter te fluid inlet temperature f,i. As expected, η decreases as f,i increases, wile te efficiency increases wit I for constant f,i. For iger f,i values η reaces to its saturation value for iger I values, around 500 W/m, compared to te cases of low f,i. e effect of te ε p in te collector efficiency is obvious by comparing te results in Figs. 3 and 4. Fig.8 Absorber plate and glass covers temperatures for a double glaze flat-plate collector as estimated by tis model for α0 o C, f,i 0 o C ε p0.95, w5 W/m K. e predicted values of and g by tis model and by [5] almost coincide. Fig.9 Absorber plate and glass covers temperatures for a double glaze flat-plate collector as estimated by tis model for α0 o C, f,i 0 o C ε p0., w0 W/m K. e predicted values of and g by tis model and by [5] almost coincide. Fig.7 Absorber plate and glass covers temperatures for a double glaze flat-plate collector as estimated by tis model for α0 o C, f,i 0 o C, Fig.0 Absorber plate and glass covers temperatures for a double glaze flat-plate collector as estimated by tis model for α0 o C, f,i 0 o C ε p0.95, w0 W/m K. e predicted values of and g by tis model and by [5] almost coincide. 6

8 Fig.4. Flat-plate solar collector efficiency, η, vs I wit parameter te f,i. α0 o C, ε p0.95 and w0 W/m K. Fig. e efficiency of a double glaze flat-plate collectors, η vs ( f,i - α)/ I eeping α0 o C and I 600 W/m. e effect of te parameters ε p and w is obvious. Fig. e efficiency of te flat-plate collectors, η vs ( p - α)/ I for bot single and double glaze flat-plate collectors under te same conditions of α, ε p and w. Fig.3. Flat-plate solar collector efficiency, η, vs I wit parameter te f,i. α0 o C, ε p0. and w0 W/m K. 5. Discussion e results obtained by tis model, also, by te model outlined in [5] and te Klein formula [4] for a large set of environmental conditions sow a consistency to eac oter. e predicted and g by tis model and te one of [5] almost coincide, as te difference between tem is of te order of o C at a range of 80 o C 30 o C. On te oter and, tis model provides te p values, too, wic are not determined by [4, 5]. e tree models provide te t coefficient. e results obtained by tis model and te one of [5] for te case of double glaze flat-plate collectors sow a difference of -%, wile te empirical Klein formula provides for t results wic differ by 3-4% for te cases of ig w and f,i values. is difference gets smaller for low w and f,i values. However, tis difference for single glaze collectors reaces up to 5-8% for te worst conditions, tat is for ig w and ε p values. Generally speaing te Klein formula gives an underestimation in t for low ε p values. However, as ε p increases t is overestimated; see Figs. 3 and 5. Finally, te model provides te efficiency η of te flatplate solar collectors. e results provided vs ( f,i - α )/ I or η vs ( p - α )/ I for eiter single or double glaze collectors were investigated for various w, α and ε p values, as sown in Figs.-3. At ig I values wic imply iger p values, tan for low I, te efficiency curve, η vs ( p - α )/ I deviates from linearity as te I radiation excanged between te collector and te environment increases fast wit ( p 4 s 4 ). is model may serve as a dynamic tool to provide te energy performance, of a solar flat-plate collector, identified by η, Q u, t, p,, g, f,o. ese results elp for decisions to be taen over te environmental and operational conditions tat te double glaze flat-plate collector is preferable against a single glaze one for te same conditions. Finally, tis model requires 3 guessed values p,, g and results are provided very fast converging to te 3rd decimal point. is model may be executed on any platform. e equations used, accept any combination of input data for te estimation of double glaze solar flat plate collector s efficiency and eat gain.e initial guess values of p, and g sould differ in order to let te program run. It is important to point out tat watever guessed values for p, and g are taen and wit any set of α, f,,i values, te program runs efficiently and converges fast, as said above. 63

9 6. Conclusions Nu f,i D H / f 0.03 e 0.8 r /3 (A.3) e simulation model developed is friendly to te user, parameterized and equipped wit functions to determine (τα) and te f,i values, as provided in te Appendices. e software built provides values of any quantity related to te flat-plate collector eiter of single or double glazing, given te operation caracteristics, te material used, te fluid flow mass flow rate and its inlet temperature, along wit te I values. Finally, te solar radiation absorption by te glass covers, may be easily tacled as a second small eat source using te superposition principle. e contribution of tis effect seems to be insignificant as te term q*(l g /) / g [33,34], wic determines te max increase in g due to te radiation absorption by te glass cover, provides an increase of less tan o C. Note tat, q* is te eat rate generated per volume (W/m 3 ) in te glass cover due to solar radiation absorption. As it is clearly sown from te results in Fig. te decision to use a double glaze flat plate collector depends on te region of ( f,i - α )/I in wic it will operate, and also on te ε p and w values, wic prevail in te region. e simulation program developed is easy to implement on any platform, wile te results converge in 9-3 iterations wit an accuracy to te 3rd decimal point, regardless of te initial values given to p, and g.e proposed algoritm was developed in MAAB, wile additional functions for te model outlined in [5] and te Klein formula were also incorporated for comparison reasons. e software developed may also determine te, g and p values for any I, ε p, w and f,i using te t value as obtained by te Klein formula. e model considers all possible modes of eat and energy transfer, suc as conduction in te glass covers, convection in te air in te collector zones and in te fluid witin te tubes, for laminar or turbulent flow, solar radiation absorption by te glass covers and te possible modes of energy transfer from te outer glass to te environment. Appendix Determination of fluid flow convection eat transfer coefficient f,i inside a tube. e convection eat transfer coefficient f,i for te fluid flow inside te absorber tubes is obtained by: Nu f,i D H / f.86(erd H /) /3 (µ b /µ bl ) 0.4 for laminar fluid flow pattern wic is developed wen, e<00 and 00> e r D H /> 0, (A.) were D H is te ydraulic diameter of te tube and is te lengt of te tube. µ b is te fluid dynamic viscosity coefficient at te bul temperature b. µ bl is te fluid dynamic viscosity coefficient at te boundary layer temperature bl, were, bl ( b p )/ [ ( f,o f,i )/ p ]/ (A.) For te case wen e >6000 ten, flow is turbulent and olds, wit all te termo-pysical properties estimated at te mean bul temperature ( f,o f,i )/, unless it is specified to be estimated at te boundary layer temperature bl. For cases were, < Gr/e <0 and /D H >50, were te fluid undergoes a transition pase from laminar to turbulent, ten as discussed in [35]: Nu f,i D H / f.75(µ b /µ bl ) 0.4 {(erd H /) 0.0(Gr /3 e, DH rd H /) 4/3 } (A.4) Appendix Determination of (τα) for single and double glaze solar collectors. et us consider te normal incidence of solar radiation on te collector plane as te calculations are elaborated wit I wic implies te normal component on te glass cover. et a glass cover wit refractive index n.53 and ticness 3 mm. et, also, te extinction coefficient K4m -. According to Snell aw te reflectance r is determined by, r ((n-)/(n)) (A.) Substitution of te values of te parameters to formula (A.) above gives, r e transmittance of te solar ligt intensity, I troug N covers is provided by, τ!!!!!!!!!!!!!!!!!!!!!!! (A.) r! and r represent te beam components polarised at normal and parallel to te medium of propagation. Assuming tat te polarized beam components, normal and parallel to te glass, are of equal strengt, ten, r! r. For N, tat is for double glaze collector te above formula becomes, τ r (-r)/((3n-)r) (A.3) In tis case, eq.(a.3) gives, τ r e transmittance wic taes into account te absorption τ α, for normal incidence of te solar radiation, is given by, τ a (0) exp(-k l ) (A.4) Generally, te transmittance τ equals to τ τ a τ r. For a double glaze collector for normal incidence τ a (0) may be determined by: τ a (0)I/I o exp(-k(l l g )) (A.5) Finally, te total transmittance, τ τ a (0)τ r Wen te above results are substituted into te equation above, it gives, τ τ a (0)τ r exp(-4x0.006)x

10 e effective product of τ and α tat is te (τα) is given by, ρ d τ a - τ r (Α.7) (τα) τ α/(-(- α)ρ d ) (A.6) were, ρ d represents te reflectance of te diffuse radiation and it is estimated by: In tis case, ρ d τ a - τ r sually, ρ d taes values in te region ( ). eferences. e integration of enewable energy systems into te buildings structures roc. International Conference 7-0 July 005, atras, Greece, ISBN Edit. S. Kaplanis.. H.C. Hottel and B.B. Woertz e performance of flat-plate solar eat collectors rans. of ASME 64, 94 (Feb), W. Bliss Jr. e derivations of several "plate-efficiency factors" useful in te design of te flat-plate solar eat collector, Solar Energy 3(4), 959, pp S.A. Klein Calculation of flat plate loss coefficients Solar Energy 7, 975, pp A. Malotra, H..Garg and A.alit Heat loss calculation of flat plate solar collectors Journal of ermal Engineering (Journal of te Indian Society of Mecanical Engineers (), 98, pp S.C. Mullic and S.K. Sambarsi An improved tecnique for computing te top eat loss factor of flat plate collector wit a single glazing ASME Journal of solar energy Engineering 0, 988, pp Amed Y. El-Assy and Jon A. Clar, ermal analysis of a flatplate collector in multipase flows, including supereat. Solar Energy 40(4), 988, pp Y. Bong, K.C. Ng, and H. Bao ermal performance of flatplate eat-pipe collector array Solar Energy 50(6), 993, pp D. Wolf, A.I. Kudis and A.N. Sembira Dynamic simulation and parametric sensitivity studies on a flat-plate solar collector Energy, Vol.6(98)pp E. Hane arameter effects on design and performance of flat plate collectors Solar Energy 34(6), 985, pp A.H.Fanney ermal erformance comparisons for solar ot water systems subjected to various collector and eat excanger flow rates Solar Energy 40(), 988, pp. -.. Abbas Arif, Solcrome solar selective coatings-an effective way for solar water eaters globally. enewable Energy,9, 000, p N.Atar and S.C.Mullic Approximate metod for computation of glass cover temperature and top eat loss coefficient of solar collectors wit single glazing Solar Energy 66(5), 999, pp J.M.Gordon and Y. Zarmi An analytic model for te long-term performance of solar termal systems wit well mixed storage Solar Energy 35(), 985, pp G.H.Amer, J.K.Naya and G.K.Sarma ransient test metods for flat-plate collectors: eview and experimental evaluation Solar Energy Vol.60, No 5 (997) pp D.E. rapas et al esponse function for solar-energy collectors Solar Energy 40(4), 988, pp X.A.Wang and.g.wu Analysis and performance of flat-plate solar collector arrays Solar Energy 45(), 990, pp S. A. Kalogirou Solar termal collectors and applications rogress in Energy and Combustion Science, 30 (004) pp M. Koui, S. Muruyama eoretical approac of a flat-plate solar collector taing into account te absorption and emission witin glass cover layer Solar Energy 80(006) H. Dagdougui et al ermal analysis and performance optimization of a solar water eater flat plate collector: Application to etouan (Morroco) enewable and Sustainable energy eviews 5(0) A.Alvarez et al Experimental and numerical investigation of a flatplate solar collector Energy 35 (00) Zenquian Cen et al A numerical study on eat transfer of ig efficient solar flat-plate collectors wit energy storage International Journal of Green Energy, 7 (00) Cung-Feng Jeffrey Kuo et al sing te aguci metod and grey relational analysis to optimize te flat-plate collector process wit multiple quality caracteristics in solar energy collector manufacturing Energy 36 (0) Cawi Maboud, Noureddine Moummi Calculation of te glass cover temperature and te top eat loss coefficient for 60o vee corrugated solar collectors wit single glazing Solar Energy 86(0) N. Atar, S.C. Mullic Computation of glass-cover temperatures and top eat loss coefficient of flat-plate solar collectors wit double glazing, Energy 3(007), pp J.D. Garrison A program for calculation of solar collector energy collection by fixed and tracing collectors Solar Energy Vol. 73 No.4 (00) J.A. Duffie and W.A. Becman Solar engineering and termal processes Jon Wiley & Sons, NY, H.. Garg and G. Dutta e top loss calculation of flat-plate solar collectors Solar Energy 3(984) W.C. McAdams Heat ransmission 3rd Edn McGraw-Hill, NY, J.H. Watmuff, W.W.S. Carters, D.roctor Solar and wind induced external coefficients solar collectors nd Quarter evue Internationale d`heliotecnique, 977, p J. und, Solar termal engineering, Jon Wiley & Sons, N.Atar, S.C. Mullic Effect of absorption of solar radiation in glass cover(s) on eat transfer coefficients in upward eat flow in single and double glazed flat-plate collectors International Journal of Heat and Mass ransfer 55 0) pp Introduction to Heat ransfer Fran. Incropera, David. DeWitt, Jon Wiley & Sons, NY, enewable Energy Systems: eory, Innovations and Intelligent Applications Eds. S. Kaplanis, E. Kaplani, NOVA Science ublisers, NY, Fran Kreit, Jane F. Kreider rinciples of Solar Engineering, McGraw-Hill Boo Co., NY, 978.