IMPLEMENTATION OF AN EARTH TUBE SYSTEM INTO ENERGYPLUS PROGRAM

Transcription

1 IMPLEMENTATION OF AN EARTH TUBE SYSTEM INTO ENERGYPLUS PROGRAM Kwng Ho Lee *, nd Richrd K. Srnd Univeriy of Illinoi Urbn-Chpign, Chpign, IL ( * Correponding uhor e-il ddre: klee56@uiuc.edu) ABSTRACT A new odule w developed for nd ipleened in he EnergyPlu progr for he iulion of erh ube. Thi pper decribe he bic concep, upion, nd lgorih ipleened ino he EnergyPlu progr o predic he perfornce of n erh ube. Uing he new odule, preric nlyi w crried ou o inveige he effec of pipe rdiu, pipe lengh, ir flow re nd pipe deph on he overll perfornce of he erh ube under vriou condiion. Pipe lengh, ir flow re nd pipe deph re prediced o hve ore influence on he perfornce hn pipe rdiu. In ddiion, pipe lengh nd pipe deph urned ou o ffec he overll cooling re of he erh ube, while pipe rdiu nd ir flow re inly ffec erh ube inle eperure. INTRODUCTION The uilizion of geoherl energy o reduce heing nd cooling need in building h received increing enion during he l yer. An erh ube i long, underground el or plic pipe hrough which ir i drwn. A ir rvel hrough he pipe, i give up or receive oe of i he o/fro he urrounding oil nd ener he roo condiioned ir during he cooling nd heing period. Due o he ignificnce of erh ube ye, nuerou reerch udie hve been perfored by Krri l. (995), Puri (986), Lb l. (989), nd Schiller (982). Recenly, ophiiced odel decribing he coplex echni of iulneou he nd rnfer occuring round he erh ube h been developed nd inegred ino TRNSYS by Mihlkkou e l. (994). Neverhele, hoe reerch udie hve focued eiher on he rnfer o/fro he urrounding oil or on he predicion of oil eperure eprely. To de, deiled lgorih clculing he oil eperure vriion round he erh ube direcly fro weher d file h no been encoded wihin he exiing iulion ool. Since n ccure ground eperure predicion i lo n eenil fcor for he iulion of n erh ube, boh he he rnfer occuring round he erh ube nd he oil eperure hould be odeled ogeher in n erh ube odel. Before clculing he oil eperure, he ground urfce eperure bove erh ube hould be prediced by king ino ccoun everl echni occuring on he ground urfce. Bed on he clculed ground urfce eperure, he eperure of he oil urrounding he erh ube nd he rnfer re cn be prediced. The objecive of hi pper i o dicu he developen nd ipleenion of new odule hndling boh he rnfer nd oil eperure lgorih ino he EnergyPlu progr for he iulion of erh ube. Alo, uing he new odel, he effec of four preer, pipe rdiu nd lengh, ir flow re nd pipe deph under he ground urfce on he overll perfornce of he erh ube were quniively eed. Preliinry eing nd preric nlyi reul will lo be dicued in hi pper. EARTH TUBE MODEL DESCRIPTION The iulion progr in which he erh ube odule w ipleened i EnergyPlu. The inegred oluion nger in EnergyPlu coni of hree nger: he urfce he blnce nger, he ir he blnce nger nd he building ye iulion nger. Aong he, n erh ube odule i ipleened he ir he blnce nger level. Due o he coplex echni occuring round he erh ube, everl iplyfying upion were de nd re decribed below: Convecion flow inide he pipe i hydrodyniclly nd herlly developed. Soil eperure in he pipe viciniy cn be clculed uing he oil odel dicued below

2 beyond priculr dince fro he cener of he pipe (hickne of he nnulu). The eperure profile in he pipe viciniy i no ffeced by he preence of he pipe. A reul, he pipe urfce eperure i unifor in he xil direcion. The oil urrounding he pipe i hoogeneou nd h conn herl conduciviy. Pipe h n unifor cro ecionl re in he xil direcion. Soil eperure clculion Prior o he clculion of oil eperure round erh ube, he ground urfce eperure righ bove erh ube hould be prediced. According o Kuud nd Achenbch (965), he ground urfce eperure ifie he following expreion. iw T = T (0, ) = T + A Re( e ) () ur where T(x,) i he oil eperure profile funcion of deph x nd ie. T nd A re nnul en vlue nd pliude of he ground urfce eperure vriion repecively, which hould be clculed by conidering he convecive he rnfer beween he ir nd ground, he olr rdiion borpion by he ground, he long-wve rdiion eied fro he oil, nd he len he lo due o he oiure evporion he ground urfce. Regrding convecive he rnfer, i cn be clculed fro he following expreion. inolion nd he ir eperure (rd), ϕ, i I clculed by ubrcing he inolion phe ngle fro ir eperure phe ngle. The phe ngle of inolion nd ir eperure i he poin fro he beginning of he yer which he inolion nd ir eperure, repecively, ech reche i iniu vlue ong in he yer. Regrding olr rdiion borpion by he ground, i cn be eied fro he following equion (Krri e l. 995): E olrd = βs (5) The borpion coefficien, β, depend on he oil borpnce nd hding condiion. The coefficien β i pproxiely equl o one inu he oil urfce lbedo. Albedo depend on oil cover nd oiure conen (Krri e l. 995). In iilr wy o ir eperure, horizonl olr rdiion i pproxied by he following equion ( iw+φ +φi ) S( ) = S + S Re[ e ] (6) v The pliude of he olr rdiion (W/ 2 ), S v, cn lo be deerined fro weher d by dividing he difference beween he xiu nd iniu olr rdiion vlue of he enire yer by wo. Regrding he long-wve rdiion eied fro he ground urfce, i cn be pproxied by he expreion (Krri e l. 995): E conv = h T T ) (2) ( ur E longrd = ε R (7) According o McAd(954) he convecive he rnfer coefficien he oil urfce (W/ 2 C), h, cn be pproxied by he following correlion: h = u (3) Wind velociy (/), u, i he nnul verge vlue. The ir eperure vriion i pproxied by he following equion ( iw+φ ) T ( ) = T + T Re[ e ] (4) The nnul ngulr frequency, w, i equl o.992 x 0-7 rd/. The pliude of he ir eperure ( C), T v, cn be evlued by dividing he difference beween he xiu nd iniu ir eperure vlue of he whole yer by wo. The phe ngle beween he v The pproprie vlue of heiphericl eince of he ground urfce, ε, i 0.93~0.96. The rdiion conn (W/ 2 ), R, depend on oil rdiive properie, ir relive huidiy, nd effecive ky eperure. An pproprie vlue of R i 63 W/ 2 (Krri e l. 995). Finlly, regrding he len he lo due o he evporion, i cn be evlued by he following expreion: E = fh [( T + b) r ( T b)] (8) len ur + where = 03 P/ C, b = 609 P Frcion of evporion re, f, depend on he oil cover nd he oil oiure level nd h cn be pproxied by Eq. (3).

3 By conidering ll he four echni decribed bove, he he rnfer re on he ground urfce cn be eied by he following equion: T k x x=0 = E conv E longrd + E olrd E len (9) where, k i herl conduciviy of oil (W/ C). Now, T ur in Eq. (2) nd Eq. (8) cn be replce by he vlue for hi preer hown in Eq. (), nd T in Eq. (2) nd Eq. (8) cn lo be replced by Eq. (4). Siilrly, S in Eq. (5) cn be replced by Eq. (6). T i conn (nnul en vlue) nd i no funcion of deph x nd ie. Therefore, by uing Eq. (2), (5), (7) nd (8) in Eq. (9) nd by only conidering he er h re no funcion of in Eq. (9), he following equion cn be obined: h ( T T fh ( T ) ε R + βs + b r T r b) = 0 (0) Afer he rerrngeen o olve for T, he nnul en ground urfce eperure, T, cn be eied follow: T = ht r ε R+ βs 0.068h fb( r) h e () where e ( ) ( ) h = h + f h = h + r f r The pliude of he oil urfce eperure vriion ( C), A, he phe conn of he oil urfce (ec), 0, nd phe ngle difference beween he ir nd oil urfce eperure (rd), ϕ S, cn be deerined follow (Krri e l. 995): A = ht iφi r v v ( h + δ k ) e β Se φ (2) 0 = 0 + (3) w iφ I ht r v β Sve φ = Arg ( he + δ k) (4) I hould be noed h in Eq. (2) nd (4) h he ybol nd Arg re ued o ignify he odulu nd he rguen of coplex nuber, repecively. The phe conn of he ir (ec), 0, i he ie elped fro he beginning of he yer which he ir eperure reche he iniu vlue in he yer, nd dpening deph (), D, i clculed fro he following equion: 2α D = (5) w The vlue of δ i evlued follow. + i δ = (6) D Auing hoogeneou oil of conn herl diffuiviy, he eperure ny deph z nd ie cn be finlly eied by he following expreion (Lb e l. 989). /2 /2 π 2π z 365 Tz, = T A exp z co 0 365α πα (7) He rnfer nd erh ube inle ir eperure clculion In order o clcule he he rnfer beween he erh ube nd he urrounding oil, he overll he rnfer coefficien hould be deerined uing he following hree herl reince vlue: R R p Rc = (8) 2πr Lhc r + r2 = ln (9) 2 π Lk r p 2 3 = (20) 2 π Lk r + r2 r + r ln + r where R c i herl reince due o convecion he rnfer beween he ir in he pipe nd he pipe inner urfce ( C/W), R p i herl reince due o conducion he rnfer beween he pipe inner nd ouer urfce ( C/W), nd R i herl reince due o conducion he rnfer beween he pipe ouer urfce nd he undiurbed oil ( C/W). The hickne of he nnulu, r 3, i ken being equl o he rdiu of he pipe. The convecive he rnfer coefficien he inner pipe urfce (W/ 2 C), h c, i funcion of Reynold

4 nuber, Re, nd Nuel nuber, Nu nd cn be evlued by he following expreion: Nukir hc = (2) 2r ( f / 2)(Re 000) Pr Nu = (22) / 2 2 / ( f / 2) (Pr ) 2 f = (.58ln Re 3.28) () In ce T > T z, In ce T = T z, In ce T < T z, T + T A ( L) = Tz, e (30) T L) T z, ( = () A ( L) = Tz, e (32) Uing he hree herl reince vlue, R c, R p nd R, overll he rnfer coefficien of erh ube cn be eied follow. U = (24) R c R = R + R + R () Now, he he rnfer beween he oil nd he ir inide he pipe i equl o he oun of he loe ir flow long he pipe (Mihlkkou e l. 989). U dy T [ ( y) T, ] = C [ dt ( y) ] z p (26) The erh ube oule ir eperure i finlly evlued by olving he he rnfer equion bove. The inle ir eperure of ir enering he erh ube (where y = 0) i equl o he bien ir eperure ince oudoor ir iniilly ener he erh ube. By inegring he boh ide of Eq. (26), he following expreion cn be obined: U y = C lnt ( y) Tz, + C () Fro he boundry condiion: T T ( 0) = (28) The conn C cn be deerined fro Eq. () he oil urfce where y = 0: C C ln T Tz, = () By olving for ir eperure inide he pipe, T (y), he following oule ir eperure cn be finlly obined. where C A = ln T T C z, U Tble Decripion of iulion condiion CONDITIONS Locion Spokne, WA - ild nd dry Peori, IL - ild nd we Phoenix, AZ - ho nd dry Key We, FL - ho nd we Run period Suer Deign Dy Vrible Pipe rdiu : 0.05, 0.075, , 0.2 Pipe lengh : 0, 30, 50, 70, 90 Air velociy : 2/, 5/, 8/, /, 4/ Pipe deph :, 2.5, 4, 5.5, 7 PARAMETRIC ANALYSIS L (33) Uing he newly developed erh ube odel, uer cn predic he perfornce of n erh ube under vriou circunce by chnging ech poible inu preer uch he chedule of erh ube operion, volueric ir flow re, rdiu, hickne, lengh, deph nd herl conduciviy of he pipe. Preric udie were crried ou o deerine he effec of four iporn vrible influencing he erh ube oule ir eperure: pipe rdiu, pipe lengh, ir flow re nd pipe deph under he ground urfce. Siulion were perfored on five differen vlue of ech preer while he oher preer were inined he e vlue. In ddiion, four differen locion were eleced which repreen four ypicl cliic condiion in order o inveige he influence of oil eperure nd oil condiion well.

5 Tble 2 Soil reled preer Key We Peori Phoenix Spokne SOIL CONDITION Hevy nd oi Hevy nd oi Hevy nd dry Hevy nd dry T M (AVERAGE) A S (AMPLITUDE) 24.3 C 5.0 C 0.0 C 8.8 C.0 C 9.4 C 9.9 C 8.5 C Teperure (C) Tie (hr) Oudoor Tep Zone Tep (no erhube) Zone Tep (wih erhube) 33 Figure2 Indoor eperure decree (Peori) 32 Teperure (C) Tie (hr) Oudoor Tep Zone Tep (no erhube) Zone Tep (wih erhube) Figure Indoor eperure decree (Key We) Aug. 2 i choen uer deign dy for Key We nd Spokne, nd Jul. 2 i choen for Peori nd Phoenix. The xiu dry bulb eperure were e 30.6 C, 30.4 C, 35.7 C nd 28.3 C for Key We, Peori, Phoenix nd Spokne, repecively. Tble how he deil of preric udie. The ndrd vlue of ech vrible were e : for pipe rdiu, 30 for pipe lengh, 5/ for ir velociy, nd 2.5 for pipe deph. In oher word, when chnging only one vrible every iulion proce for preric udie, he oher vrible were kep hoe vlue. Tble 2 decribe he inpued oil condiion nd preer for ech locion. The nnul verge ground urfce eperure, T, nd pliude of he oil urfce eperure vriion, A, re clculed by uiliy progr h i provided wih EnergyPlu. A hree-zone reidenil building w choen for hi preric udy. The building coni of living pce, n ched grge nd ic bove living pce nd grge hving floor re of pproxiely 40 2, 37 2, nd 76 2, repecively. In hi udy, he living pce will be nlyzed, which i loced on he norhern ide of he building wih he ceiling heigh of The inernl he gin for ligh nd. Teperure (C) Teperure (C) Tie (hr) Oudoor Tep Zone Tep (no erhube) Zone Tep (wih erhube) Figure 3 Indoor eperure decree (Phoenix) Tie (hr) Oudoor Tep Zone Tep (no erhube) Zone Tep (wih erhube) Figure 4 Indoor eperure decree (Spokne) equipen were e 5.4W/ 2 nd wo people were plced in he living pce during he iulion Infilrion w e 0. ACH nd he erh ube w e o run connly he e volueric flow re of /h during he whole running period. DISCUSSION AND RESULT ANALYSIS Indoor eperure decree due o erh ube Fig. hrough fig. 4 illure he indoor eperure

6 ErhTube Inle Tep (C) Pipe Lengh () Key We Peori Phoenix Spokne Figure5. Influence of pipe lengh on inle eperure. ErhTube Inle Tep (C) Pipe Deph () Key We Peori Phoenix Spokne Figure 6. Influence of pipe deph on inle eperure. decree due o he cooling poenil of he erh ube in four differen locion. The higher zone eperure i he ce when he erh ube i hu down, while he lower zone eperure i he ce when he erh ube w opered under he e condiion during he whole dy. In hee ce, he inpu vrible were e he ndrd vlue wih for pipe rdiu, 30 for pipe lengh, 5/ for ir velociy, nd 2.5 for pipe deph. A cn be een in he figure bove, he erh ube h he cooling poenil o reduce he indoor eperure nd herefore reduce he cooling need in building. However, he exen of eperure decree due o erh ube were differen in four locion becue of differen oil condiion. The eperure decree were 2.6 C nd.8 C in Peori nd Spokne repecively, while eperure decree were.0 C nd 0.7 C in ce of Key We nd Phoenix repecively. Thi indice h he ho weher of he ler wo locion lo hd increed oil eperure nd, reul, he cooling poenil of erh ube w reduced. Key We nd Phoenix hve nnul verge oil urfce eperure 0 C higher hn hoe of Peori nd Spokne (Tble 2). Therefore, he erh ube ye hould be plced ore deeply in hoe ho weher condiion o obin cooling poenil h i iilr o he le exree clie. Alhough erh ube cn reduce he cooling need in building o cerin degree, i hould be noed h i did no pper o be ble o replce he convenionl ir-condiioning ye copleely, ince he indoor eperure doe no inin herlly coforble ir eperure by only eploying he erh ube under ho weher condiion. Influence of pipe lengh Fig. 5 preen he effec of pipe lengh on he erh ube inle ir eperure he highe bien ir eperure. A he pipe lengh incree, he inle ir eperure decree, regrdle of he locion. Thi i due o he fc h he longer pipe provide longer ph over which he rnfer beween he pipe nd he urrounding oil cn ke plce given he e overll he rnfer coefficien of erh ube. Therefore, longer pipe hould be ued if he renching co i no prohibiive. However, he eperure rnge nd rnge of decree in er of pipe lengh were differen ong ech locion. A he pipe lengh incree fro 0 o 90, he inle ir eperure decree by 2.9 C, 0. C, 5.2 C nd 8.5 C in Key We, Peori, Pheonix nd Spokne, repecively. Thi i due o he differen oil condiion, bien ir eperure nd oil eperure in hee locion, indicing h he weher condiion which ffec he oil condiion nd eperure of priculr locion hould be conidered when deciding on wheher or no o ipleen n erh ube. I cn be een fro Fig. 5 h oe lengh he iproveen begin o level off. Influence of pipe deph Fig. 6 how he influence of pipe deph under he ground urfce on he erh ube inle ir eperure. A he pipe deph incree, he inle ir eperure decree, regrdle of he locion, indicing h erh ube hould be plced deeply poible. However, he renching co nd oher fcor hould be conidered when inlling erh ube. Like he ce of pipe lengh, he eperure rnge nd decree re wih pipe deph were differen ech locion due o differen oil condiion. A he pipe deph w chnged fro o 7, he inle ir eperure decreed by.8 C, 9.3 C, 4.0 C nd 7.9 C in Key We, Peori, Pheonix nd Spokne,

7 ErhTube Inle Tep (C) Air Velociy (/) Key We Peori Phoenix Spokne Figure 7. Influence of ir velociy on inle eperure. ErhTube Inle Tep (C) Pipe Rdiu () Key We Peori Phoenix Spokne Figure 8. Influence of pipe rdiu on inle eperure. repecively. Bed on hee reul, pipe deph pper o hve lrge of n influence on erh ube perfornce pipe lengh. Influence of ir velociy inide pipe Fig. 7 preen he effec of ir velociy inide he pipe on he erh ube inle ir eperure. A he ir flow re incree he inle ir eperure incree in ll locion, indicing h n erh ube wih lower ir velociy will perfor beer ince he ir pend ore ie in he ube nd hu in conc wih he lower oil eperure. Thi cn be een in he erh ube odeling equion ince ccording o Eq. (30) nd Eq. (33) higher ir flow re cue higher flow re nd higher ir eperure. Likewie, he rnge nd re of incree of he inle ir eperure funcion of ir velociy inide he pipe were differen ech locion. A he ir velociy incree fro 2 / o 4 /, he inle ir eperure incree by.9 C, 6.6 C, 3.6 C nd 5.9 C in Key We, Peori, Pheonix nd Spokne, repecively. Thee differen rnge of inle ir eperure i due o differen weher nd oil condiion of ech locion. In coprion o he effec of oher preer decribed bove, he ir flow re urned ou o hve lrge effec on he perfornce of he erh ube pipe lengh nd pipe deph. However, when conidering he ir flow re during he deign proce, iply reducing he flow re doe no necerily iprove he erh ube perfornce ince he cooling he rnfer re due o erh ube depend on boh ir flow re nd eperure difference, no on ech fcor lone (q = C T). Thu boh ir flow re nd eperure decree hould be conidered iulneouly. Influence of pipe rdiu Fig. 8 illure he effec of pipe rdiu on he erh ube inle ir eperure. A he pipe rdiu incree, he erh ube inle ir eperure lo incree, regrdle of he locion. Thi i due o he fc h higher pipe rdiu reul in lower convecive he rnfer coefficien on he pipe inner urfce nd lower overll he rnfer coefficien of erh ube ye. Therefore, ller pipe rdiu hould be ued for he beer perfornce of he erh ube. I hould be noed h only ingle pipe i conidered in hi pper nd hu pipe do no hve he e cro ecionl re. Siilrly, he eperure rnge nd he incree in he inle eperure funcion pipe rdiu were differen ong hee locion. A he pipe rdiu incree fro 0.05 o 0.2, he inle ir eperure increed by 0.9 C, 3.5 C,.5 C nd 2.4 C in Key We, Peori, Phoenix nd Spokne, repecively. In er of coprion wih he oher hree effec decribed bove, pipe rdiu did no ffec he reul uch he oher preer. However, iply reducing he pipe rdiu under e ir flow re will incree he ir velociy inide he pipe, reuling in n incree in he erh ube inle ir eperure. Thu pipe rdiu nd ir flow re hould be conidered ogeher nd opiized uing iuled reul. The rend of he reul in er of he influence of deign preer on he perfornce dicued bove were ilir o hoe of oher udie (Mihlkkou e l. 989). Due o he liied pce, he pecific coprion d will no be dicued in hi pper. CONCLUSION In hi pper, he lgorih for he iulion of erh ube i decribed, nd preric udie were crried ou o inveige he effec of ech preer on erh ube. The following concluion were drwn.

8 Alhough he erh ube lone cn no replce convenionl ir-condiioning ye in hee ce udie, i cn ignificnly reduce he cooling lod in he building inveiged. A deeply plced nd longer erh ube wih lower ir velociy nd ller rdiu hould reul in beer perfornce. Thi gree wih coon ene nd i bcked by he odel d, yielding iilr rend o oher referenced udie. However, he renching co nd oher fcor hould lo be conidered when inlling erh ube. In ddiion, pipe lengh, ir velociy inide pipe nd pipe deph urned ou o hve ore influence on erh ube perfornce hn pipe rdiu. However, pipe rdiu nd ir flow re well cooling he rnfer re hould be conidered iulneouly. Furherore, weher nd oil condiion of priculr locion hould be pecificlly conidered when uing n erh ube ince he erh ube will perfor differenly under differen weher nd oil condiion. Thu, he vilbiliy of n erh ube odel in progr uch EnergyPlu i n iporn ep forwrd when eping o deerine wheher or no erh ube hould be ued for priculr building nd o deerine he o opil cobinion wih regrd o deph, lengh, rdiu, nd ir velociy. For exple, een in Fig. 5 ~ 8, n erh ube could probbly no hve uch ipc in Key We or Phoenix, bu dependency on he ye y be beneficil in Peori or Spokne. Bed on hi udy, fuure work h hould be done include he experienl verificion of he newly developed erh ube odel nd he inveigion of he effec of he erh ube during heing eon poenil he ource. ACKNOWLEDGMENT The uhor of hi pper wih o hnk he U.S. Depren of Energy' Lwrence Berkeley Nionl Lborory for funding under Grn 6730 he work which led o hi pper. NOMENCLATURE A : pliude of he oil urfce eperure vriion ( C) C : pecific he of ir (J/kg C) E conv : convecive he rnfer beween he ir nd ground (W/ 2 ) E olrd : olr rdiion borpion by ground urfce (W/ 2 ) E longrd : long-wve rdiion eied fro ground urfce (W/ 2 ) E len : len he lo due o evporion (W/ 2 ) h c : convecive he rnfer coefficien he inner pipe urfce (W/ 2 C) h : convecive he rnfer coefficien he oil urfce (W/ 2 C) k ir : herl conduciviy of he ir (W/ C) k p : pipe herl conduciviy (W/ C) k : oil herl conduciviy (W/ C) L : pipe lengh () : flow re of bien ir hrough pipe (kg/) r : relive huidiy R c : herl reince due o convecion he rnfer beween he ir in he pipe nd he pipe inner urfce ( C/W) R p : herl reince due o conducion he rnfer beween he pipe inner nd ouer urfce ( C/W) R : herl reince due o conducion he rnfer beween he pipe ouer urfce nd undiurbed oil ( C/W) R : ol herl reince beween pipe ir nd oil ( C/W) R : rdiion conn (63W/ 2 ) r : inner pipe rdiu () r 2 : pipe hickne () r 3 : dince beween he pipe ouer urfce nd undiurbed oil () S : ne horizonl olr rdiion (W/ 2 ) S : verge olr rdiion (W/ 2 ) S v : pliude of he olr rdiion (W/ 2 ) : ie elped fro beginning of clendr yer (dy) T : ir eperure bove he ground urfce ( C) T (y) : ir eperure of he pipe he dince y fro he pipe inle ( C) T : bien ir eperure ( C) T : verge oil urfce eperure ( C) T : verge ir eperure ( C) 0 : phe conn of he oil urfce (ec; dy) 0 : phe conn of he ir (ec; dy) T ur : ground urfce eperure ( C) T v : pliude of he ir eperure ( C) T z, : ground eperure ie nd deph z ( C) u : wind velociy bove he ground urfce (/) U : overll he rnfer coefficien of he whole erh ube ye (W/ C) V : verge pipe ir velociy (/) z : deph of he rdil cener of pipe below oil urfce () α : oil herl diffuiviy ( 2 /; 2 /dy) β : oil borpion coefficien (= oil lbedo) ε : heiphericl eince of he ground urfce ϕ : phe ngle beween he inolion nd he ir I eperure (rd) ϕ : phe ngle difference beween he ir nd oil S urfce eperure (rd) w : nnul ngulr frequency (=.992 x 0-7 rd/)

9 REFERENCES Krri, M., Lopez-Alonzo, C., Clridge, D. E. nd Kreider, J. F Anlyicl odel o predic nnul oil urfce eperure vriion. Journl of Solr Energy Engineering 7, pp. 9~99 Lb, K. In: Cook, J., edior 989. Pive cooling. Cbridge Mchue, London, Englnd: MIT Pre Al-Aji, F., Lovedy, D. L. nd Hnby, V. I The Cooling Poenil of Erh-ir He Exchnger for Doeic Building in Deer Clie, Building nd Environen Neci, O. M He Trnfer: A Bic Approch, McGrw-Hill Book Copny Jcovide, C. P. nd Mihlkkou, G An Underground Pipe Sye n Energy Source for Cooling/heing Purpoe. Renewble Energy 6, pp.893~900