Development of a Heat Transfer Model for the Integrated Façade Heating

Transcription

1 Dvlopmnt of Ht rnsfr Modl for th Intgrtd Fçd Htng Dvd E. Clrdg Phd P.E Xngyng Gong Dvd H. Archr PhD Profssor Grdut tudnt Profssor Enrgy ystms bortory Cntr for Buldng Prformnc nd Dgnostcs Dprtmnt of Mchncl Engnrng chool of Archtctur xs A&M nvrsty Crng Mllon nvrsty ABRAC Fçd htng s spcl pplcton of rdnt htng nd coolng tchnology nd s usd to nhnc th ndoor comfort lvl of offcs, hotls nd musums. Mullon rdtors r th typclly usd to mplmnt fçd htng. hs ppr nlyzs th ht trnsfr procss of fçd htng (mullon rdtors n plot rsrch projct n Pttsburgh, PA. h ht trnsfr modl for fçd htng s dvlopd nd vrfd by msurd dt. h comprson shows tht th ht trnsfr modl prdcts th msurd tmprturs wth root mn squr rror (RME of th hot wtr rturn tmprtur, th mullon surfc tmprtur, nd th wndow surfc tmprtur of 0.90 F, 0.98 F nd.5 F, rspctvly. h fctors whch ffct th htng cpcty of mullon rdtors hv bn nlyzd. h nlyss shows tht th supply wtr tmprtur s th prmry fctor whch ffcts th htng or coolng cpcty of wndow mullons nd th mullon surfc tmprtur. Rturn wtr tmprtur nd mullon surfc tmprtur r qus-lnr functons of th wtr supply tmprtur. Mullon surfc tmprtur, ndoor r tmprtur nd th outdoor r tmprtur ll ffct wndow surfc tmprtur dstrbuton. h tmprtur grdnt on th glzng surfc wthn on foot from mullons s much hghr thn n th cntrl prt of th wndow. h tmprturs n th cntrl ft of 4-foot wndow show lmost no nflunc by th mullon surfc tmprtur. Also, th conductv thrml rsstnc of th mullon doubl tubs wth fllngs btwn two tubs plys dcsv rol n controllng th mullon nd wndow frm tmprturs. INRODCION Intgrtd fçd htng nd coolng s n mrgng buldng htng nd coolng tchnology whch strtd n Europ nd ms to nhnc buldng comfort lvl. h fçd htng or coolng dvc s normlly formd by hot wtr crcut whch xtnds through cvts of th vrtcl or horzontl mtl scton of n xtror wll or wndow. Mullon htng nd coolng s on commonly usd form of fçd htng nd coolng s shown n Fgur. h mullon rdtors r nstlld vrtclly long th wndow frms nd r n ntgrtd prt of th buldng fçd. h mullon systm s usd to offst th htng nd coolng lod from th wndows, nd to ncrs comfort lvls nr th wndow r. gnfcnt rsrch hs bn don rgrdng th ht trnsfr modls of wndows (Munr t l. [], Omor t l. [], rsson t l. [3], Collns t l. [4], Collns [5], but no ltrtur bout modlng nd prformnc vluton of mullon htng nd coolng hs bn found. Bcus th mullons r ctully rdtors nd r so clos to th wndow glzng, th ht trnsfr procsss btwn th mullons nd th wndow glzng, wndow frms, room surfcs nd nsd r r complctd. ndrstndng ths prncpls s mportnt for ccurt dsgn of th HVAC systms n ths typ of buldng. hs ppr studs th ht trnsfr procss of wndow mullon rdtors. Msurd dt s comprd wth th mthmtcl modls.. h smultd rsults mtch th msurd dt vry wll. Fgur. Rdnt Mullon Wndow mullon rdtors RCRE OF MION RADIAOR AND IMAION AMPION h fçd htng nstllton studd s smll unvrsty offc r whch ncluds spc for fculty, grdut studnt nd stff offcs, nd mtng room loctd n Pttsburgh, PA. hs offc s usd s tst st for dvncd HVAC systms nd qupmnt. h offc spc hs n r of 580m (68 ft nd uss rdnt htng nd coolng systm combnd wth sold dsccnt vntlton

2 unt. h rdnt mullons r usd n ths offc to mt prt of th snsbl htng nd coolng lod. h dtld structur of mullon rdtor s shown n Fgur. h mullons hv doubl tub structur whch s ttchd to th vrtcl porton of th wndow frm by n lumnum fn. h outr tub s lumnum, th nnr tub s stl nd th spc btwn ths two tubs s flld wth poxy rsn. h dtld wndow frm structur s shown on th lft sd of Fgur. o dfn th modl usd to vlut th prformnc of th mullons, th spc round th mullon s smplfd s n nclosur rprsntd by dottd lns n Fgur 3. h dottd lns stnd for n mgnry wll wth unform surfc tmprtur 3. h mgnry wll s ssumd to b nfntly long whn clcultng th vw fctors btwn th mgnry wll nd othr surfcs n th nclosur. 3 s ssumd to b qul to th mn rdnt tmprtur (MR of th spc (AHRAE 005. MR s rltd to th ndoor r tmprtur, th rto of wndow r to xtror wll r, nd th sz of th spc. AHRAE rcommnds tht th MR should b qul to th room r tmprtur n rdntly htd spc. Gong nd Clrdg [6], studd th mn rdnt tmprtur dstrbuton n mxd rdnt nd r htd offc. hr rsults showd tht th mn rdnt tmprtur would b 0 - o F hghr thn th room r tmprtur n htng sson, dpndng upon th locton of th rdtors n 00% rdntly htd spc. In th currnt smulton, th MR s ssumd to b 0.5 o F hghr thn room r tmprtur n th htng modl. h dtl of th wndow frm s complctd. h wndow frm s n lumnum structur wth on-nch thrml gp. h vlu of th frm s pproxmtly 0.49 Btu/(ft -hr- F. On th lft sd of Fgur, on of th common frm structurs s shown. In ths smulton, th wndow frm nd mullon r smplfd s shown on th rght sd of Fgur. h wndow frm s ssumd to hv n unform thrml rsstnc of R.04 (ft -hr- F /Btu. h wndows n th studd offc r doubl pn wth n r spc of ½ nch nd low -cotng. h typcl vlu of ths nd of wndow n th htng sson s Btu/( ft -hr- F (AHRAE 005. h msurd dt suggst tht 0.43 Btu/( ft -hr- F s clos to th rl vlu n wntr condtons. h corrspondng R-vlu of th wndow s.95 (ft -hr- F/Btu. o vlut th mpct of th mullon rdtors on ht trnsfr t th wndow surfc, th thrml rsstnc of th wndow glss hs bn dcomposd nto thr prts: nsd surfc rsstnc (round 0.68 ( ft -hr- F /Btu, conductv thrml rsstnc (.365 ( ft -hr- F /Btu, nd outsd surfc rsstnc (round 0.5 ( ft -hr- F /Btu. h surfc rsstnc vrs wth th surfc tmprtur nd rdnt ht xchngs wth othr surfcs. hrfor, th nsd nd outsd surfc rsstncs r vlutd bsd on th oprton nd wthr condtons nstd of usng constnt vlus. h mullons hv doubl tub structur. h nnr tub s stl nd th outr tub s lumnum. Epoxy rsn flls th gp btwn th nnr tub nd th outr tub. h totl thrml rsstnc of th doubl tub s stmtd to b (ft -hr- F/Btu ( vlu of.5-33 Btu/(ft -hr- F. A clbrtd smulton hs shown tht th thrml rsstnc of th wlls of th doubl tubs s clos to (ft -hr- F/Btu. h hot wtr flowng nsd th mullons s ssumd to b fully dvlopd flow nd th ntrnc ffcts r gnord. h hot wtr s ssumd to b vnly dstrbutd n ll th mullons n th studd offc Dtld Wndow Frm nd Mullon mplfd Wndow Frm nd Mullon Fgur Cross cton of Mullon Rdtor nd Wndow Frm 3

3 3 5 4 Fgur 3 Wndow Mullon, Frm, nd Glss (Not to scl HEA RANFER MODE OF FAÇADE HEAING As shown n Fgur 3, fv surfc tmprturs r ssumd to b n th nclosur: tub surfc, wndow glss surfc, mgnry wll surfc 3, wndow frm surfc 4 nd tub fn 5. h mgnry wll surfc 3 s ssumd to b constnt. At stdy stt, ch surfc xchngs rdnt ht wth th othr surfcs nd convctvly xchngs ht wth room r. h wndow glss nd frm lso los ht to th outsd nvronmnt by conducton. h ht s suppld to th nclosur by hot wtr flowng nsd th mullon tub. wo bsc ht trnsfr modls xst n th bov control nclosur. h frst modl s th surfc tmprtur modl whch s usd to solv for th tub surfc tmprtur nd for th wndow glss surfc tmprtur. h scond modl s th mullon shpd fn modl, whch consdrs th mullon fn nd wndow frm to b on ntgrtd prt. hs modl s usd to solv for fn surfc tmprtur, wndow frm tmprtur, nd conducton ht loss from th mullon surfc to th fn nd wndow frm. hs two modls r coupld togthr. urfc mprtur Modl h objctv of th frst modl s to dtrmn th convcton nd rdton ht trnsfr coffcnts n ordr to solv for th surfc tmprtur. h convcton ht trnsfr coffcnt s dtrmnd by th tmprtur dffrnc btwn th wll surfc nd th room r. h rdton ht trnsfr coffcnt s dtrmnd by th vrg tmprtur of th two corrspondng surfcs, s shown n th followng qutons. h unts of tmprtur nd ht trnsfr coffcnts r R nd Btu/ (ft -hr- F. Pls rfr to th nomncltur scton for symbol dfntons. h 0.3 c 0.6( s ( h r m ( 3 4εσm s (3 In th qutons bov, h c s th convcton ht trnsfr coffcnt nd h r s th rdnt ht trnsfr coffcnt. s s th surfc tmprtur. m s th vrg tmprtur of surfc s nd surfc. If ll surfc tmprturs r ssumd to b unform, th nrgy blnc quton for th wndow glss cn b wrttn s: o 4 4 h ( ( cwn Fwn εσ 0 (4 R wn F wn- s th vw fctor from th wndow glss to th nclosur surfc. s th wndow glss nnr surfc tmprtur. h nrgy blnc quton for th tub surfc cn b wrttn s: q & s hc m ( F hr ( q& (5 fn whr q & '' fn s th conducton ht flux t th fn bs. q& s s th ht supply from hot wtr, whch cn b dtrmnd from Equton (6. q& h ( (6 s n ns b 3

4 ns s th nsd surfc tmprtur of th nnr tub, b s th bul tmprtur of th hot wtr, nd h n s th convcton ht trnsfr coffcnt t th nnr surfc of th tub. For on dffrntl lngth, d, n Fgur 4, q & s lso quls th nthlpy chng of th flud n th dffrntl lngth d s shown n Equton (7. db hn ( ns b m& C p (7 d h n cn b clcultd by Equton (8. h Nusslt numbr cn b dtrmnd usng Equtons (9 nd (0 [3] for turbulnt flow nd lmnr flow, rspctvly. N Dn hn (8 K f (RD 000 Pr (turbulnt flow (9 N 8 D f.7 3 Pr 8 N (lmnr flow (0 VD R ( υ Doubl ub of Mullon d s b Mullon Fn fn 4 Wndow Frm Fgur 4 Wndow Mullon Assumng th conductv thrml rsstnc from th nsd surfc of th nnr tub to th outsd surfc of th outr tub s R t, th ht flux from th flud to th nsd surfc of th nnr tub wll qul th ht flux from th nsd surfc to th outsd surfc of th mullon tub, whch cn b xprssd by th quton: ns q& s hn ( ns b ( R t h nnr surfc tmprtur ns cn b solvd s: ns Rt hn R h t n b (3 Whl q & s cn b xprssd s: hn ( b q & s (4 Rt hn If th dffrntl lngth d s suffcntly smll, th bul flud tmprtur, b, cn b sn s qul to th dffrntl nlt tmprtur of th flud. In dffrntl clculton, ths b cn b ssumd to b nown. By substtutng Equton (4 nto Equton (5, th followng quton cn b obtnd: hn ( b (5 R h t n h cm ( F hr ( q& In th nclosur of Fgur, 3 s nown. 4 nd 5 r consdrd to b surfc tmprturs of th - shpd fn, nd cn b dtrmnd usng th -shpd fn modl. q & fn cn lso b obtnd from th - shpd fn modl. sng ntl stmts of th ht trnsfr coffcnts, th unnowns n th nclosurs r th mullon tub surfc tmprtur nd th wndow glss tmprtur. By combnng Equton (4 nd Equton (5 s two-quton mtrx, solutons for nd r found usng smll dffrntl lngth. Onc th surfc tmprtur s nown, th ht trnsfr coffcnts r thn rclcultd nd nsrtd n th frst nd scond modls to gn solv for surfc tmprtur. h procss s trtd untl th ht trnsfr coffcnts convrg; thn th ht flux, q, s clcultd for th dffrntl lngth. Onc q of th dffrntl lngth s obtnd, th flud outlt tmprtur cn lso b found. h flud outlt tmprtur of on dffrntl lngth wll b usd s th nlt tmprtur of th nxt dffrntl lngth. By dvdng th mullon doubl tubs long th flow drcton nto crtn numbr of dffrntl lngths, th tmprturs of th mullon tub surfc nd th wndow glss surfc cn b solvd numrclly. h ht nput of on mullon cn b found by summng q& s da of ll th dffrntl sgmnts long th flow drcton. fn & s & s -hpd Fn Modl In th frst modl, th blty to dtrmn th mullon surfc tmprtur nd wndow glss tmprtur dpnds upon th blty to dtrmn fn surfc tmprtur 5, frm tmprtur 4 nd th ht flux t th fn bs, q& fn. hs tmprturs cn b found usng th fn modl. Bcus th fn nd wndow frm r sngl prt, thy r trtd s -shpd fn. h two shouldrs of th wndow frm 4

5 cn b sn s th xtnson of th horzontl br of th -shpd fn. In ordr to smplfy th clculton, th thcnsss of prts nd r ssumd to b th sm. h tp condton of prt s ssumd to b dbtc. h boundry condtons for Equtons (6 nd (7 r: h -shpd fn cn b smultd s two prts. h bs of th hs lngth s shown n Fgur 5. h cross-mmbr of th s th wndow frm surfc (th horzontl prt n Fgur 5. Assumng tht th ovrll ht trnsfr coffcnt on th surfc of prt s n nd pplyng nrgy blnc on dffrntl lngth, dy, of th prt, th followng dffrntl quton cn b obtnd: 0 Y, (8 Y, 0 X Y (9 X Y Y (0 dy d n ( (6 0 Y Y ( sng dffrntl quton to xprss th ht trnsfr modl of th rl wndow frm, s shown n Fgur, s lmost mpossbl. Howvr, f th ovrll ht trnsfr coffcnt from th nsd surfc of th wndow frm to th outsd r s ssumd to b out, th wndow frm surfc cn b smplfd s fn wth n nsd ovrll ht trnsfr coffcnt of n nd n outsd ovrll ht trnsfr coffcnt of out. By pplyng nrgy blnc to dffrntl lngth of th wndow frm, th dffrntl quton cn b obtnd s: h gnrl soluton of govrnng Equton (6 s: y y C C ( (3 0.5 n (4 h gnrl soluton of govrnng Equton (7 s: dx d o out n out n (7 x s x s C C 4 3 (5 (6 5 4 out n dy dx d dy n x y o (7 0.5 out n (8 0.5 o out n (9 Applyng boundry condtons (8 nd (9 to Equtons ( nd (5, th constnts C, C, C 3, C 4 cn b solvd s shown n Equtons (30 - (33. h tmprtur dstrbuton long th -shpd fn cn b clcultd wth Equtons ( nd (5 ftr solvng for C, C, C 3, nd C 4 s: Fgur 5 mplfd Clculton Dgrm for Wndow Mullon ( ( ( ( C (30 ( ( ( ( C (3 5

6 C3 ( C4 ( ( ( (3 ( (33 ( In th qutons bov,. s th mullon tub surfc tmprtur. Onc th tmprtur dstrbuton long th fn s nown, th conducton ht flux t th fn bs, q& fn, cn b dtrmnd usng Equton (34. Corrspondngly, th vrg tmprtur of th fn (5 nd th wndow frm ( 4 cn b found by usng ntgrton mthods. By substtutng q& fn, 4, nd 5 nto th surfc tmprtur modl, th frst modl cn b solvd. q& fn ( d (34 Y Y 0 In th fn modl, th ovrll ht trnsfr coffcnts n nd n r th summton of th convcton ht trnsfr coffcnt nd th wghtd rdton ht trnsfr coffcnt. Ech ovrll ht trnsfr coffcnt n nd n cn b found by th quton: hc f hr (35 whr h c s th convcton ht trnsfr coffcnt t th studd surfc, f s th vw fctor from th studd surfc to nothr surfc,, n th nclosur, nd hr s th rdton ht trnsfr coffcnt from th studd surfc to nothr surfc,, n th nclosur. hc nd hr r dcdd by th surfc tmprtur dffrncs, s shown n Equtons ( nd (. h rdnt tmprtur s ssumd to b th sm s th r tmprtur n ordr to smplfy th fn modl clculton. MODE VERIFICAION FOR AMPE PERIOD h ht trnsfr modls ntroducd n th prvous scton combnd numrcl nlyss wth thortcl nlyss mthods. A progrm hs bn wrttn bsd on ths modls. h progrm uss hot wtr supply tmprtur, flow rt, ndoor zon tmprtur nd outsd r tmprtur s nputs to clcult mullon systm hot wtr rturn tmprtur, mullon surfc tmprtur dstrbuton, wndow frm tmprtur dstrbuton, wndow surfc tmprtur dstrbuton, nd ht nput by th mullon systm. h progrm clcults th vrg mullon nd wndow surfc tmprturs (,, 4 nd 5 n Fgur. h mullon systm oprtng dt r rcordd by th oprtng ngnr of th studd offc. h vlbl msurd dt wr collctd from Fbrury 4, 006, to Mrch 4, 006. h dt wr trndd vry 30 mnuts. Durng th 0 dy msurmnt prod, th systm ws shut down thr by th control systm or mnully for crtn prods of tm. Whn th systm s down, smll mount of hot wtr runs through th systm du to mullon vlv lg. h msurd dt, durng th systm shut downs, show lrg vrton n mullon nd wndow surfc tmprturs for dffrnt wndow ornttons. h rson pprs to b tht hot wtr s unvnly dstrbutd mong th prlll mullons whn th flow rt s vry smll. hs prt of th msurd dt s not usd n th nlyss bcus th dt do not rflct th norml oprtng condtons. h msurd mullon tmprturs t th north wndow r usd for comprson wth th smultd dt bcus snsors n ths wndow rcv fwr dsturbncs du to occupnt ctvts nd rdton thn th othr wndows. h msurd dt r comprd wth smultd rsults. h smultd hot wtr rturn tmprtur, mullon surfc tmprtur, rt wn nd wndow surfc tmprtur, hv bn found to b snstv to th nput prmtrs for hot wtr supply tmprtur hws, conductv thrml rsstnc of doubl tub Rt, wndow frm ht trnsfr coffcnt out, nd wndow glss conductv thrml rsstnc R wn. Hot Wtr Rturn mprtur Fgur 6 shows th comprson of th smultd rsults wth th msurd rsults s functons of supply wtr tmprtur. h smultd rsults r qut consstnt wth th msurd rsults. Fgur 6 ndcts tht th rturn wtr tmprtur s clos to lnr functon of th supply wtr tmprtur. hs mpls tht th mullon rturn wtr tmprtur cn b ccurtly stmtd bsd on th supply wtr tmprtur whn th ndoor r tmprtur rmns rltvly constnt t 7 F. mu 6

7 Fgur 6 sm.-ms. O F Fgur 7 sm.-ms. O F Msurd nd multd HW Rturn mprturs s Functons of HW upply mprturs HW Rturn mprtur Rsdus y 0.07x HW upply mprtur o F Err_rturn nr (Err_rturn Rsduls of Hot Wtr Rturn mprtur s Functon of Hot Wtr upply mprtur HW Rturn mprtur Rsdu y x Err_rturn nr (Err_rturn wtr tmprtur. h non-zro slop my ndct tht fctor or prmtr othr thn th supply wtr tmprtur lso ffcts th smulton rrors. Fgur 8 shows tht th rsdul trnd ln slop ( s clos to zro whn thy r plottd s functon of th dffrnc btwn supply tmprtur nd zon tmprtur. h flt slop ndcts tht th rturn wtr tmprtur s mor ccurtly modld s functon of th dffrnc btwn supply tmprtur nd zon tmprtur. Fgur 8 consdrs th ffcts of th zon tmprtur (vrg tmprtur of th south zon nd th north zon on th smulton rsults. Mullon urfc mprtur h modl smults th tmprtur dstrbuton long th mullon tub, fn, nd wndow frm. h output surfc tmprturs r th vrg vlus of th tmprturs of ths surfcs. All th mullon tmprtur snsors n th studd offc r nstlld on th fn surfc t hght of 38cm (5 nchs bov th floor. hrfor, th fn surfc tmprturs t th snsor ponts r usd s th mullon surfc tmprturs n ordr to compr thos vlus wth th msurd mullon tmprtur t th sm pont. h msurd nd smultd mullon surfc tmprturs r plottd n Fgur 9 s functon of th hot wtr supply tmprtur. h smultd tmprturs mtch th msurd tmprtur vry wll xcpt for smll numbr of outlr ponts. Fgur 9 shows tht mullon surfc tmprtur s clos to lnr functon of th hot wtr supply tmprtur. Fgur 8. s-zon O F Rsduls of Hot Wtr Rturn mprtur s Functon of th Dffrnc Btwn upply mprtur nd Zon mprtur Fgurs 7 nd 8 show th rsduls of th hot wtr rturn tmprtur. h rsduls r dfnd s th smultd rsults mnus th msurd rsults. h root mn squr rror (smpl dvton of th smulton rsduls s 0.9 F. Fgur 8 shows tht th rsdul trnd ln hs non-zro slop (0.07 whn th rsduls r plottd s functon of th supply Fgur 9. Msurd vs. multd Mullon urfc mprtur s Functon of Hot Wtr upply mprtur 7

8 Fgur 0 Msurd vs. multd Wndow urfc mprtur s Functon of th Outsd Ar mprtur An rror nlyss shows tht rrors of mullon surfc tmprtur r normlly dstrbutd. h root mn squr rror of th mullon surfc tmprtur (smpl dvton s 0.98 F. Wndow urfc mprtur h smultd nd msurd wndow surfc tmprturs r plottd n Fgur 0 s functons of th outsd r tmprtur. Both msurd nd smultd dt r scttrd, whch mns tht othr fctors lso hv n mpct on th wndow glss tmprtur. h root mn squr rror of th wndow tmprtur smulton s.5 F. h wndow glss tmprtur snsor on th north wndow s loctd 8 nchs from th bottom dg of th wndow nd 3 nchs from th dg of th wndow frm. h surfc snsor s -typ thrmocoupl mbddd n coppr bloc. h rror of th thrmocoupl snsor tslf s lss thn.8 F (ºC[7]. h structur of th snsor lmnts th prtl nflunc of rdton, nd th rdng s clos to th vrg wndow surfc tmprtur. h wndow surfc tmprtur n th smulton output s th vrg tmprtur of th wndow. h smulton rrors r normlly dstrbutd. h rndom rrors of th thrmocoupl snsors or th stmton of th thrml conductvty of th wndow glss my cus th rrors. DICION ypcl wntr nd summr condtons ssumd for th dscusson n ths scton r zon tmprtur of 7 F wth wntr outsd r tmprtur of 38 F nd summr vlu of 68.6 F x hws 0 F hws 90 F Fgur. Wndow mprtur Profls for wo Dffrnt Hot Wtr Condtons 8

9 bl Mullon prformnc t dffrnt wndow wdths Wndow Wdth (Mullon pc 3.5ft 4.0ft 4.5ft 5.0ft Hot Wtr upply mprtur º F Htng Input Pr Mullon (Btu/(hrmullon ub urfc mprtur º F Fn urfc mprtur º F Wndow Frm mprtur º F Avrg Wndow Glss Insd urfc mprtur º F Wndow Insd urfc mprtur o F Fgur mprtur Dstrbuton t th Cntrln of th Glss (hlf of wndow hght hws0 F 64.0 hws0 F hws00 F 63.5 hws90 F Wndow Horzontl ngth(ft Innr Glzng mprtur Dstrbuton t th Mdpont of th Wndow Hght Wndow urfc mprtur As dscussd n th modl scton, th wndow surfc tmprtur s ssumd to b unform ovr on dffrntl lngth whn th rdton ht trnsfr btwn th mullon surfc nd th wndow surfc s clcultd. Howvr, th wndow surfc tmprtur chngs from th wndow frm to th cntr of th wndow glss. Durng htng, th closr to th wndow frm, th hghr th glss tmprtur. Dffrnttng th vw fctor from th wndow glss to th mullon t ch numrcl lngth, s dscussd n th modlng scton, llows th tmprtur dstrbuton long th horzontl drcton to b found by n nrgy blnc nlyss. Fgur shows th tmprtur profls of th wndow glss t two dffrnt hot wtr supply tmprturs. As shown n Fgur, th hghr th hot wtr supply tmprtur, th hghr th wndow dg tmprtur. h tmprtur vrton from frm to cntr s hghr whn th mullon rdton tmprtur s hgh. h vrton s bout 3 F whn th hot wtr tmprtur s 0 F. h vrton dcrss to F whn th hot wtr tmprtur s 90 F. Howvr, th tmprtur t th cntr of th glss only ncrss by pproxmtly 0. F, whn th supply wtr tmprtur ncrss from 90 F to 0 F. Fgur shows th tmprtur dstrbutons of nnr glzng t mdpont of th wndow hght t four dffrnt mullon hot wtr supply tmprturs. h grdnt of th nnr glzng surfc tmprtur shown n Fgur vrs from XX F/ft wthn foot from th wndow mullon to low of YY F/ft t th cntr of th glss. h Effct of pc btwn Mullons h spc btwn two mullons hs n nsgnfcnt mpct on th htng cpcty of ch mullon, s sn n bl. Incrsng mullon spcng from 3.5 ft to 5 ft ncrss ht output by lss thn 0.%. h htng cpcty of ch mullon dpnds on th supply wtr tmprtur, th conductv rsstnc of ch mullon, nd th totl surfc r of th mullon rdtor (th tub surfc plus th fn nd s lmost ndpndnt of th spc btwn th two mullons. Howvr, th spc btwn th two mullons ffcts th nsd tmprtur dstrbuton of th wndow glss. Fgurs nd show tht th nsd glss tmprturs wthn on foot from th mullons r ffctd by mullon tmprtur. Whn mullon spcng s smll, grtr prcntg of wndow glss surfc wll b ffctd by th mullon tmprtur. h vrg nsd surfc tmprtur of th wndow glss wll b slghtly ncrsd. bl shows th htng cpcty nd surfc tmprturs for four dffrnt mullon spcngs. It cn b sn tht th surfc tmprturs r lmost th sm t four mullon spcngs or wndow wdths. h vrg wndow tmprtur vrs by 0.4 F. 9

10 hrml Conductvty of Mullon Doubl ubs h thrml conductvty of th mullon doubl tubs s prmry fctor ffctng th htng cpcty nd surfc tmprtur of th mullons. h doubl tubs nd gp-fllng mtrl r usd to control th surfc tmprtur of th mullon. h totl mullon tub conductv thrml rsstnc cn b vrd by usng dffrnt gp-fllng mtrls. h fllng lowrs th mullon htng cpcty. Howvr, whn th mullon s usd for coolng, th doubl tub structur nd gp-fllng mtrl ncrs th mullon surfc tmprtur nd rduc th rs of mostur condnston on th mullon surfc. Fgur 3 Htng Cpcty of Mullons t Four Dffrnt Vlus of ub Wll hrml Rsstnc (nt of R: ( ft -hr- F /Btu Fgur 3 shows th mullon htng nput to th spc t four dffrnt vlus of tub wll thrml rsstnc. From ths fgur, t cn b sn tht th htng cpcty of on mullon cn ncrs bout % f th conductv rsstnc of th tub s rducd from 0.04 (ft -hr- F /Btu to 0.0 (ft -hr- F /Btu. h mullon htng cpcty wll dcrs bout 9% f th conductv rsstnc of th tub ncrss from 0.04 (ft -hr- F /Btu to 0.06 (ft -hr- F /Btu. CONCION hs ppr studs th ht trnsfr prncpls of wndow mullon htng. wo ht trnsfr modls r dvlopd usng dffrntl nlyss. h smulton rsults r comprd wth 0 dy s msurd dt. h comprson shows tht th ht trnsfr modls prdct th msurd tmprturs wth root mn squr rrors (RME of th hot wtr rturn tmprtur, th mullon surfc tmprtur, nd th wndow surfc tmprtur of 0.90 F, 0.98 F nd.5 F, rspctvly. h smulton study lds to th followng conclusons: Hot wtr supply tmprtur nd chlld wtr supply tmprtur r th prmry fctors tht ffct th htng or coolng cpcty of wndow mullons nd th mullon surfc tmprtur. Hot nd chlld wtr rturn tmprtur nd mullon surfc tmprtur r ll qus-lnr functons of th hot wtr supply tmprtur. Wndow surfc tmprtur dstrbuton s ffctd by th mullon surfc tmprtur nd th outsd r tmprtur. h wndow surfc tmprtur clos to th mullon s 3 F hghr thn tht t th cntr of th wndow glss whn hot wtr supply tmprtur s 0ºF. h tmprtur n th cntr of th wndow glss only vrs bout 0.4 F, whn hot wtr tmprtur chngs from 90ºF to 0 F. h snstvty study n th dscusson scton shows tht th conductv thrml rsstnc of th mullon doubl tubs plys dcsv rol n controllng th mullon nd wndow frm tmprturs. h doubl tubs nd gp fllngs ncrs th thrml rsstnc of th mullon tubs, whch rsults n lowr surfc tmprtur for htng nd hghr surfc tmprtur for coolng. If th thrml rsstnc s rducd to hlf of ts currnt vlu, th htng cpcty of th mullon would ncrs %; whl th htng cpcty wll dcrs 9% f th thrml rsstnc s ncrs 50% of ts currnt vlu. h hghr surfc tmprtur for coolng my b ntndd to lowr th rs of mostur condnston on th surfc of th mullon n th coolng condton. Howvr, th nhncd thrml rsstnc dcrss th htng nd coolng cpcty of th mullons. If th mullons r only usd for htng, sngl tub structur s rcommndd. From dsgn prspctv, th wndow wdth or spcng btwn th mullons hs lttl mpct on th htng cpcty or mullon surfc tmprtur. Whn th wdth of wndows ncrss from 3.5 ft to 5.0 ft, th htng cpcty of sngl mullon only vrs bout Btu/hr s shown n bl. Howvr, th spc btwn th mullons wll somwht ffct th wndow s nnr surfc tmprtur dstrbuton nd th wndow s vrg tmprtur. Whn th wndow wdth dcrss from 5 ft to 3.5 ft, th vrg wndow surfc tmprtur ncrss from 6.3 F to 6.73 F t n mbnt tmprtur of 38 F. NOMENCARE f IA nsd r tmprtur wghtng fctor f OA outsd r tmprtur wghtng fctor Fwn vw fctor btwn wndow nd surfc 0

11 F vw fctor btwn mullon tub nd surfc h c thrml conductvty, Btu/(hr-ft- F convctv ht trnsfr coffcnt, Btu/(hr-ft - F hc wn convctv ht trnsfr coffcnt t wndow ndoor surfc, Btu/(hr-ft - F ns b rt room r tmprtur, F quvlnt r tmprtur, F mullon tub nsd surfc tmprtur, F hot wtr bul tmprtur, F hot or chlld wtr rturn tmprtur, F hc m convctv ht trnsfr coffcnt t h n h r m& m& totl N P r q& s q& fn Q & totl R wn R t o mullon tub, Btu/(hr-ft - F convctv ht trnsfr coffcnt btwn wtr nd mullon tub nsd surfc, Btu/(hr-ft - F mu fr hws rdton ht trnsfr coffcnt btwn surfc I nd surfc s, Btu/(hr-ft - F fn lngth, ft 3 hlf of wndow frm wdth, ft hot or chlld wtr mss flow rt pssng through sngl mullon, gpm 5 hot or chlld wtr mss flow rt pssng through mullon systm, gpm nusslt numbr prndtl numbr ht trnsfr loss from mullon tub surfc, Btu/(hr-ft conducton ht trnsfr rt t fn root, Btu/(hr-ft mullon systm htng or coolng cpcty, Btu/hr wndow conductv rsstnc, (hr-ft-ºf/btu conductv thrml rsstnc of mullon doubl tubs, (hr-ft-ºf/btu outsd r tmprtur, F 4 n n out mullon surfc tmprtur, F wndow frm surfc tmprtur, F hot wtr supply tmprtur, F mullon tub surfc tmprtur, F wndow glss nsd surfc tmprtur, F mn rdnt tmprtur of ndoor spc, F wndow frm tmprtur, F wndow fn surfc tmprtur, F thcnss of mullon fn, ft ovrll ht trnsfr coffcnt t mullon fn surfc, Btu/(hr-ft -ºF ovrll ht trnsfr coffcnt t wndow frm surfc, Btu/(hr-ft -ºF ovrll ht trnsfr coffcnt of wndow frm, Btu/(hr-ft -ºF REFERENCE [] Munr,., N. Abodhb, A. Glchrst Combnd Conducton, Convcton, nd Rdnton Ht rnsfr Modl for Doubl-Glzd Wndows, Buldng rvc Engnrng Rsrch & chnology, v8, n4, pp [] Omor,.;. Murm,. Kto Numrcl multon of olr Ht Absorpton Wthn Indoor pc by Mns of Compost Grd Mthod, AHRAE rnsctons, v03, n, pp

12 [3] rsson,.; B. Moshfgh, M. ndbrg hrml Anlyss of upr Insultd Wndows (Numrcl nd Exprmntl Invstgtons, Enrgy nd Buldngs, v9, n, pp. -8. [4] Collns, M.; P.H. Oosthuzn,.J. Hrrson, D. Nylor Numrcl Modlng of Rdtv nd Conductv Ht rnsfr from An Irrdtd Complx Wndow Assmbly, Amrcn octy of Mchncl Engnrs, Ht rnsfr Dvson, (Publcton HD, v366, pp [5] Collns, M Convctv Ht rnsfr Coffcnts from Intrnl Wndow urfc nd Adjcnt unlt Vntn Blnd, Enrgy nd Buldngs, v36, n3, pp [6] Gong, X. nd D. Clrdg, 007. Impct of th Poston of th Rdtors on Enrgy Consumpton nd hrml Comfort n Mxd Rdnt nd Convctv Htng ystm, AHRAE rnsctons, v3(: pp [7] hrml coupl rfrnc tbls, Omg wbst, Accssd n Jnury 006