284+n δ= sin (single space line, size 10) Figure 1. Schematic for a typical solar collector system 2. BASIC EQUATIONS AND METHODOLOGY

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1 SSN d teratioal Cogress of Mechaical Egieerig (COBEM 2013) November 3-7, 2013, Ribeirão Preto, SP, Brazil Copyright 2013 by ABCM SOLAR COLLECOR PROJEC : EFFEC OF BRAZLAN LOCAONS ON HE WEEKLY PERFORMANCE (SNGLE BLANK LNE SZE 14) Alexadre M. S. Costa Uiversidade Estadual de Marigá, Av. Colombo 5790, bloco 104, DEM, Marigá, PR, amscosta@uem.br Abstract. this work we ivestigate umerically the effect of differet Brazilia geographical locatios o the results of the project selectio procedure for a solar collector. he collector type is plae with geometrical e physical caracteristics similar to existet i Brazilia market. he hot water demad is also typical. Wheever the collector does ot supply the demad a auxiliary source is employed. he hourly diffuse radiatio is calculated by breakig the total hourly horizotal radiatio ito beam ad diffuse compoets usig Erbs correlatio. he estimatio of icidet ad absorbed solar radiatio is doe by the use of the isotropic sky model. Our results poits the effect of climatic data (solar radiatio ad dry bulb temperature) o the storage tak temperature ad i the most feasible collector area. Keywords: solar eergy systems, egieerig desig, reewable eergy 1. NRODUCON the 20 th cetury, idustrial scale productio of solar collector systems wide spread across the globe. However, i Brazil, the techology remais ot accessible to all groups i the society. t is expected that future electricity shortages could revert this tedecy. this paper, we examie a project methodology for solar collector system based o a typical demad. Figure 1 depicts the solar collector system. he et solar eergy from the collector is used to heat the storage water to a adequate temperature at the hot-water outlet. Wheever the et solar eergy is ot eough a auxiliary heater is used. A more detailed aalysis of the system will be effected i sectio BASC EQUAONS AND MEHODOLOGY All equatios will be provided i a stepwise lie: Figure 1. Schematic for a typical solar collector system 284+ δ si (1) Eqs. (1), δ is the su decliatio i degrees from Cooper (1969), is the day of the year (1 365), 7723

2 SSN COSA, A. M. S. Solar Collector Project 360 o cos cos φ cos δ si ω + si φ si δ 365 ( [ ] [ ] [ ] [ ] [ ]) (2) k (3) o Eqs. (2) ad (3), o is the hourly extraterrestrial solar radiatio i MJ/m 2 o a horizotal surface for the hour agle ω cetral to the hour, φ is the locatio latitude i degrees. k is the hour clearess idex. he terrestrial horizotal radiatio for the hour is obtaied from the automatic statios of the Brazilia Natioal stitute of Meteorology (NME, 2013). he ratio of diffuse to total radiatio o a horizotal surface is obtaied from Erbs correlatio (Erbs, 1982) give i eq. (4) k for k d k k (4) k k for 0.22 < k for k Oce, the ratio d / is obtaied, the beam compoet, b, ad diffuse compoet, d, is obtaied from Eq. (5) d b 1 (5) R b d d ( φ+β) ( δ) ( ω ) + ( φ+β) ( δ) cos( φ) cos( δ) cos( ω ) + si ( φ) si ( δ) cos cos cos si si (6) (7) Eq. (7), R b is a geometric factor correspodig to the ratio of beam radiatio o the tilted surface to that o a horizotal surface. this study we cosidered the collector facig the orth, i.e., the surface azimuth is 180 degrees (measured clockwise from south) ad β is the collector tilt agle measured from the horizotal. From the isotropic sky model of solar radiatio (Duffie ad Beckma, 2006) for a tilted surface: the beam, b ; the diffuse, d ; the groud reflected, g ; ad total are give by Eqs. (8), (9), (10) ad (11): R (8) b b b d g ( ) 1+ cos β d 2 1 cos 2 ( β) ρg (9) (10) Eq. (10), ρ g is the terrai albedo. b + d + g (11) he absorbed solar radiatio for the collector plate is give by : Where the τα terms are obtaied by : ( ) ( ) ( ) S τα + τα + τα (12) b b d d g g 7724

3 SSN d teratioal Cogress of Mechaical Egieerig (COBEM 2013) November 3-7, 2013, Ribeirão Preto, SP, Brazil ( τα ) b ( τα ) d ( τα ) g ( ) ( τα ) τα ( τα ) is a collector parameter available from the maufacturer. he ratios, d g ( τα ) surface slope followig Brademuehl ad Beckma (1980). By his tur, the term b icidece agle, cover ad absorber material. b d g are fuctio of depeds o the beam Eq. (16), F R is collector heat removal factor, is the ratio of the actual useful eergy gai of a collector to the useful gai if the whole surface collector were at fluid ilet temperature. F collector efficiecy factor, represets the ratio of the actual useful eergy gai to useful gai that would result if the collector absorbig surface had bee at the local fluid temperature. U L is the collector global heat trasfer coefficiet i W/(m 2 C), m c is the collector fluid flow rate per area i kg/(s m 2 ), c p is the collector fluid specific heat at costat pressure evaluated at the ambiet temperature. (13) (14) (15) m c FU FR 1 exp U m c ' c p L L c p (16) Eq. (17), Q u is the useful eergy delivered from the collector to the storage tak. he max fuctios idicates, wheever the absorbed eergy is greater tha the heat trasfer loss, eergy is trasferred from the collector frame to the storage tak. ( [ ]) Q max 0,A F S U u c R L tak a (17) the above equatio, A c is the collector area ad a is the ambiet temperature where the collector is located. Also, the storage tak temperature, tak, is assumed homogeeous i all the tak., Equatio (18) represets the tak heat loss for the eviromet. ts is assumed that the a, the ambiet temperature where the tak is located ca be differet., Qloss,tak UL,takA tak tak a (18) Eq. (19) the L max is the projected load based o a miimum hot water supply temperature mi. t is assumed the makeup water temperature to the tak mais is kept costat. (19) L m c max L p mi mais From the previous equatio the eergy required from the load Q load i a give hour is calculated from Eq. (20). OOff is a 24 positio vector correspodig to a 24 h period. Whe a give positio is the value 1, the hot water load at mi or above is required. he value 0, implies hot water is ot required. Q OOff mi L, m c load max L p ta k mais (20) the previous equatio, wheever the storage temperature is less tha mi, the auxiliary eergy source supplies sufficiet eergy to heat the water comig from the storage tak to mi. Eq. (21) is based o the eergy balace for the storage tak. he superscript correspod to the curret hour, ad -1 to the previous hour. 7725

4 SSN COSA, A. M. S. Solar Collector Project Q Q Q + 1 u loss,tak load ta k ta k (21) mtakcp he calculatio procedure for a project cosists i solvig equatios (1) to (21) for each hour. A example of calculatio is depicted i the ext sectio. Whe the calculatio is performed for a week, the weekly fractio of the miimum load supplied from the solar collector system F week is obtaied from : F week N hours,week Q 1 7 N L hours load max (22) he variable N hours represets the umber of hours the hot water is required each day. N hours,week is the umber of hours of the week. 3. RESULS AND DSCUSSON espaço simples etre lihas, tamaho 10) he calculatio procedure described i the previous sectio was implemeted for calculatig the eeded collector area A c of a typical orth facig plae solar collector system such as the oe depicted i Figure 1, usig the thermodyamics software EES (Klei, 1993), for differet Brazilia cities. he aalysis was performed for seve Brazilia cities, amely: Maaus, Fortaleza, Rio de Jaeiro, São Paulo, Floriaopolis. he correspodig latitudes i degrees from the equator for the previous cities are give by the vector [-3,-3.7,-22.9,-23.5,-27.6,-30]. able 1 is preseted fixed properties of the solar collector system ad load demad. he parameters β, U L, (τα), m c, F are collector parameters. he storage tak parameters are m tak /A c, U L,tak, (H/D) tak. he load parameters are mais, mi, m L,F week. he load is uiformly distributed over the day from 7 AM to 9 PM, i.e, the vector OOff is [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]. able 1. Baselie parameters. Parameter Value β 40 o U L 4 W/(m 2 C) (τα) 0.77 m 50 kg/(m 2 h) c F 0.95 ρ g 0.2, a m tak /A c 60 kg/m 2 U L,tak 1.05 W/(m 2 C) (H/D) tak 3 mais 25 C mi 45 C m kg/h L F week 0.75 he climate data for performig the calculatios were obtaied from the NME automatic statios from 01/28/2013 to 02/03/2013. he followig values were used:, the total hour solar radiatio icidet o a horizotal surface, ad a, the hourly averaged ambiet temperature. hose values are depicted i Figs. 2 ad 3 for the week cosidered for the project calculatio. 21 C 7726

5 SSN d teratioal Cogress of Mechaical Egieerig (COBEM 2013) November 3-7, 2013, Ribeirão Preto, SP, Brazil Figure 2 Hour terrestrial horizotal radiatio. ( espaço simples etre lihas, tamaho 10) Figure 3. Hour temperature data for differet locatios 7727

6 SSN COSA, A. M. S. Solar Collector Project he solutio is obtaied iteratively by trial ad error. t is ecessary to guess both the collector area A c ad the iitial tak temperature ad see if the desired F week is reached ad if a steady periodic solutio is reached for the tak temperature, i.e., the fial tak temperature equal to the iitial temperature. able 2 shows the results obtaied for the collector area. he greatest required area was for Maaus, whereas Floriaopolis requires the smallest. he results correlate well with the umber of peak levels i Fig. 2, i.e., cities with more peak solar itesities closer to the maximum result i a lower required area. By his tur, from Eq. (17), lower air temperatures reduce the useful delivered solar eergy to the load, icreasig the required area. From Fig. 3, although Fortaleza ad Maaus had the greatest air temperature profile for the week, the solar radiatio profile was iferior to Floriaopolis ad Rio de Jaeiro. this sese, the results poit to more sesitivity of collector area to the solar itesity tha air temperature. t is also worthwhile to metio a basic premise of the simulatio is that the week is a represetative sample of the seaso durig which the load is required. able 2. Collector Area City A c [m 2 ] Maaus 5 Fortaleza 2.2 Rio de Jaeiro 1.9 Sao Paulo 3.8 Floriaopolis CONCLUSON espaço simples etre lihas, tamaho 10) A calculatio procedure for specifyig the size of collector of a typical solar system was preseted. Week data for 5 differet Brazilia cities were used. he results poit to more sesitivity of the collector area to the solar radiatio itesity profile tha ambiet temperature. 5. REFERENCES espaço simples etre lihas, tamaho 10) Brademuehl, M. J., Beckma, W. A., 1980, rasmissio of Diffuse Radiatio through CPC ad Flat-Plate Collector Glazigs, Solar Eergy, 24, pp Cooper, P.,, 1969, he absorptio of solar radiatio i solar stills, Solar Eergy, Vol. 12, No. 3, pp Duffie, J. A., Beckma, W. A., 2006, Solar Egieerig of hermal Processes, Wiley; 3 rd editio, 928p. Erbs, D. G., S. A. Klei, Duffie, J. A., 1982, Estimatio of the diffuse radiatio fractio for hourly, daily, ad mothly average global radiatio, Solar Eergy, 28, pp NME, Estação Meteorológica de Observação de Superfície Automática. 1 Ja < Klei, S. A., 1993, Developmet ad itegratio of a equatio-solvig program for egieerig thermodyamics courses, Computer Applicatios i Egieerig Educatio, vol. 1(3), pp RESPONSBLY NOCE he author is the oly resposible for the prited material icluded i this paper. 7728