One dimensional steady state heat transfer of composite slabs

Transcription

1 BUILDING PHYSICS On dmnsonal sady sa a ransfr of compos slas Par 2 Ass. Prof. Dr. Norr Harmay Budaps Unvrsy of Tcnology and Economcs Dparmn of Buldng Enrgcs and Buldng Srvc Engnrng

2 Inroducon - Buldng Pyscs dfnon Conducon Trmal conducvy conducon coffcn Ha flux On-dmnsonal sady sa conducon roug a plan sla Convcon Sady sa a ransfr of compos slas Ovrall a ransfr coffcn Tmpraur dsruon roug compos slas Ar gaps and nsulaon Maxmzng nnr mpraur dffrnc

3 Ovrall a ransfr coffcn T ovrall a ransfr coffcn, or U-valu, rfrs o ow wll a s conducd ovr a srs of mdums. T ovrall a ransfr coffcn s nfluncd y cnss and rmal conducvy of mdums roug wc a s ransfrrd. T largr coffcn, asr a s ransfrrd from s sourc o produc ng ad.

4 Ovrall a ransfr coffcn W ar rally concrnd w ra of a ransfr wn wo sds of compos sla rar an procss wn surfacs. I s convnn o dfn an ovrall a ransfr coffcn (U-valu), gvn y: ] [ 2 K m W U q ] [ 2 K m W U n j j j Surfac convcon coffcn

5 Ovrall a ransfr coffcn T U-valu masurs ow wll a uldng componn,.g. a wall, roof or a wndow, ps a nsd a uldng. For os lvng n a warm clma U-valu s also rlvan as s an ndcaor of ow long nsd of uldng can p cold. T cncal xplanaon of U-valu pyscally dscrs ow muc rmal nrgy n Was [W] s ranspord roug a uldng componn w sz of squar mr [m²] a a mpraur dffrnc of Klvn [K] (=ºC). Tus un for U-valus s W/(m²K). Szra Csaa, Buldng Pyscs 204

6 Ovrall a ransfr coffcn T ransmsson a flow ra s proporona o U valu, mpraur dffrnc wn ndoor and oudoor ar ( - ) and ara (A) of surfac: Q U A [W] Dffrn naonal sandards s mnmum rqurmns for U- valus.

7 U valus n EU mmr sas Ausra

8 U valus n EU mmr sas Grmany

9 U valus n EU mmr sas Hungary

10 Tmpraur dsruon Calculaon of mpraur dsruon s asd on assumpon a mpraur ln s lnar undr sady sa. Gnrally mpraur dffrnc n-wn wo sds of a layr s: j q j [C][K]

11 Tmpraur dsruon w q q ) ( 2 ) ( q q w ) ( q q ) ( q q w w q q ) ( Szra Csaa, Buldng Pyscs 204

12 Tmpraur gradn In a mullayr wall gr mpraur drops occurs n a maral wc as lowr conducon coffcn rlav o or maral Szra Csaa, Buldng Pyscs 204

13 Modfd conducon of nsulaons In svral cass wn nsulaon s coupld w dffrn uldng marals conducon ra n nsulaon s affcd. For a ffc nul coffcn s appld: ( 0 ) In s quaon 0 s conducon coffcn of nsulaon wc s masurd undr laoraory crcumsancs. κ (-) s nul coffcn wc rprsns modfcaon of conducon. Exampls: Wn nsulaon s fxd on a surfac adsv maral s usd. Ta adsv maral s dffusng o ar clls of nsulaon. Ta ncrass conducon. Szra Csaa, Buldng Pyscs 204

14 Ar gaps In ar gaps comnd a ransfr procss as plac. Tr s a conducv a flow wn oundary surfacs. I would proporona o cnss, f r wouldn' ar movmn n ar gap. If ar gap s n or srafcaon of ar (n orzonal ar gaps) prvns nnsv ar movmn, nsulaon ffc of sagnan ar domnas. ar Szra Csaa, Buldng Pyscs 204

15 Ar gaps Du o dnsy dffrnc naural ar crculaon accompand w convcv a ransfr dvlops n vrcal ar gaps and - dpndng on drcon of a flow - n orzonal ons. T cr ar gap s, mor nnsv convcv ransfr s. From aov wo ffcs an opmum cnss would rsul. Szra Csaa, Buldng Pyscs 204

16 Ar gaps Tr s a radan a xcang wn oppos oundary surfacs. Is nnsy dpnds on mpraurs of surfacs (no only on mpraur dffrnc!) and on manc of surfacs. T nnsy of radan a xcang can dcrasd y slcv surfac coangs. Szra Csaa, Buldng Pyscs 204

17 Ar gaps Also a ra of a ransfr roug an ar gap dpnds on drcon of a flow n orzonal cass. T comnd ffc of aov pnomna s caracrzd y quvaln rmal rssanc of ar-gaps, gvn n funcon of aov mnond paramrs. Szra Csaa, Buldng Pyscs 204

18 Maxmzng nnr mpraur dffrnc Maxmum mpraur dffrnc s gvn for an nnr surfac and amn mpraur of a compos wall consrucon. Ts s du o surfac condnsaon and mould grow prolm. If xra nsulaon s addd o xsng compos sla apar from rducng a ransfr roug nvlop, undr smlar crcumsancs, mpraur dffrnc wn nrnal surfac and amn mpraur s dcrasng. Szra Csaa, Buldng Pyscs 204

19 Maxmzng nnr mpraur dffrnc,max w rc rc ns. ns. q Basd on qualy of a a flux wo quaons can wrn: q,max wr,max s maxmum rqurd nrnal mpraur dffrn ( - w ), s nnr surfac rssanc (/ ), s ovrall mpraur dffrnc ( - ), s ncssary ovrall rssanc of nsulad wall ( + rc + ns + ). Szra Csaa, Buldng Pyscs 204

20 Maxmzng nnr mpraur dffrnc Afr rordrng o, aov quaon coms: T only unnown n quaon s ns, wc s nsulaon rssanc: ns rc,max max, ) ( ) ( max,,max rc rc rc ns Szra Csaa, Buldng Pyscs 204

21 Maxmzng nnr mpraur dffrnc us ns ns ns ns ns,0 ns,max rc ( ) ns,0 rc No a: If orgnal wall as no only on layr, rc coms orgnal, wc s ovrall rssanc of orgnal compos sla. Szra Csaa, Buldng Pyscs 204

22 Fulfllng nw U-valu rqurmn for xsng wall Old uldng walls av g ovrall a ransfr coffcn. Tos coffcns ar always gr an nw rgulaon xpcs so r s a nd for addonal nsulaon. If xra nsulaon s addd o xsng compos sla, apar from rducng mpraur dffrnc wn nrnal surfac and amn mpraur, a ransfr roug nvlop s dcrasng. Szra Csaa, Buldng Pyscs 204

23 Fulfllng nw U-valu rqurmn for xsng wall qr U r r Addonal rmal rssanc can smad w a followng quaon: r o q0 U o o Wr r s rqurd rssanc (/U r ), o s rssanc of orgnal consrucon (/U o ). ns. ns Szra Csaa, Buldng Pyscs 204.

24 Fulfllng nw U-valu rqurmn for xsng wall Szra Csaa, Buldng Pyscs 204 q0 qr ns. ns. U o o U r r ns Wr ns s ncssary rssanc of nsulaon. Tus from s pon xampl s smlar o prvous xampl: ns ns ns ns ordrng quaon for only unnown ncssary ra of rmal nsulaon can calculad: ns ns,0 ns ns,0

25 Exrcs Calcula ovrall a ransfr coffcn of a compos sla (A)! Calcula a loss of on squar mr (B), and mpraur dsruon (C)! T layr ordr from nrnal o xrnal s plasr (cm), rc (38cm), plasr (2,5cm). Conducon coffcns ar: plasr 0,8W/(mK), rc.3 W/(mK). Inrnal mpraur s 20 C, xrnal mpraur s -2 C. Inrnal surfac convcon coffcn s 8W/(m 2 K), xrnal surfac convcon coffcn s 24W/(m 2 K).

26 Exrcs U-valu ] K m W [ 2 n j j j U U sul U = 2.0 W/m²K

27 Exrcs a loss q W [ 2 m ] p rc p plasr plasr rc rc plasr plasr sul q = 44,0 W/m²

28 Exrcs mpraur dsruon ( w) q q ( w 2) q q ( ) q 2 q 2 2 5,5 C 0,5 C 2,7 C C 4,0 C 4,5 C 3 ( 23 w) q 3 q 3 3,35 C,3 C -0,5 C ( ) q q w,8 C -2,3 C

29 Homwor Wall nsulaon 8 cm 2 cm 2 3 Masonry cavy wall nsulaon. Calcula U-valu, Ha Loss and Tmpraur Dsruon of dncal masonry wall w 8 cm and 2 cm Expandd Polysyrn nsulaon (EPS). Conducon coffcn of EPS nsulaon: λ () = 0,035 W/(m K)