STUDY OF THERMAL PROPERTIES OF POROUS MATERIALS

Transcription

1 SUY OF HRMAL PROPRIS OF POROUS MARIALS Oldři Zeškl, Pvl Šefková Insiue of Pysil nd Alied Ceisry, Fuly of Ceisry, Brno Universiy of enology, Purkyňov 118, CZ-61 Brno, Cze Reubli il: Absr e er exines erl roeries of erils. e rnsien ulse eod ws used for seifi e, erl diffusiviy nd erl onduiviy deerinion. e evluion ws erfored wi e el of eil rus used for sudy of frl sruures roeries. e resuls were obined re e se s e resuls obined by lssil eods. Key words: frl sruure, seifi e, erl diffusiviy, erl onduiviy, rnsien ulse eod 1 Inroduion e rile dels wi e use of new d evluion eod, wi ws desribed in [1]. e eod resuls fro generlized relions were designed for sudy of ysil roeries of frl sruures [], [3]. As i is sown ese relions re in good greeen wi e equions used for e desriion of ie resonses of eerure for e ulse inu of sulied e [4], [5], [6]. erl reers seifi e, erl diffusiviy nd erl onduiviy luled re orresonding for bo eods. eory e deendene of frl sruures rerized by e frl diension in - diension se eerure on e disne fro e soure nd on e ie ws deerined in [1] using e eory of e se-ie frl field [], [3] / /. 1 In is er is e e suly fro e e soure, is e seifi e iy onsn ressure J.kg 1.K 1, is e ss densiy kg. 3 is e iniu vlue of e erl diffusiviy / +.s 1 for frl diension equl o e oologil diension of e se. If e e diffuses by e signifinly sller seed <<, sll disnes or long ies e ers in renesis n be onsidered s signifin in e exnsion of exonenil funion 1 x e nd us we n x wrie / 4 ex, 4

2 were is e ol e rnsferred o e body fro e e soure wi e erl onduiviy λ. e relion is lible for frl diensions, 1, nd oologil diension 3 ublised in [4], [5],[6], see Fig. 1. Fig. 1 He flow geoery for lne-rllel, b ylindril nd seril oordines uliden se. e xiu osiion n be deerined by e derivion of wi e ie 4 log log +. 3 Fro is equion e erl diffusiviy e xil ie n be deerined f, 4 were f is oeffiien rerizes e deforion of e erl field [6]. is oeffiien is equl o one for e idel lne soure 3,. e xiu eerure of e resonse for ir erl ulse is obined by inroduing of e erl diffusiviy 4 in e er / ex. 5 Fro e rio of equions 6 nd nd wi e use of e er 4 1 ex, 1 ex reseively, 6 i is ossible o definie e oeffiien f frl diension reseively for every oin of e exerienl deendene 1 ln ln + f, 1 ln ln + f reseively. 7 e relions on e lef side re used for e eerure inrese; e relions on e rig side re used for e eerure derese. e vlue of e oeffiien f ould be lso ffeed by e geoery of sle [6] or by e finie ulse wid, oo [7]. Fro er 5 i is obined e erl iy / ex1 ex1 f 8 nd erl onduiviy of e sudied frl sruure / ex1 λ, 9 were f nd f re e oeffiiens rerize e deforion of e erl field [6].

3 3 log r -3 3, 3, 1 3, 3, log Fig. ie deendeny of e eerure resonse for e ir erl ulse for e e flow geoery fro Fig. 1 luled by q.. d log r /d log - 3, 3, 1 3, 3, log Fig. 3 ie deendeny of e sloe eerure resonse for e ir erl ulse for e e flow geoery fro Fig. luled by q. 3. e Fig. reresens ie-eerure deendenies ording equion luled for seril, ylindril 1, lnr, nd ubi 3 geoery of e e soure see Fig. 1. I is eviden fro e Fig. nd fro e equion 3 for e funion ees xiu for e ie. All deendenes for e long ie inervls onverge o e syoe, wi is longiudinl wi e ie sle. e inerseion of is syoe wi e veril sle deerines e oeffiien f nd us e frl diension rerizes e seien seu e soure, seien, disribuion of e eerure field, e losses. Wen e vlue f is known i is fesible o deerine e reers of e sudied erl syse wi e id of e 4 9 equions. 3 xerienl e eroysil rnsien eser 1. ws used for esuring of e resonses o e ulse e. I ws develoed e Insiue of Pysis, Slovk Adey of Siene [7]. e order of e exerien is desribed in [1]. erl resonses fro Slovk Adey were used for e d evluion. e esured sle ws round sed wi dieer R,3. Is densiy ws 77,9 kg. 3 for is ikness,75, e erl onduiviy ws λ,54 W..K 1. Fig. 4 Curren flow geoery: lne-rllel, b frl, oin for differen rio of leng on reseively soure.

4 In Fig. 4 ree ossible onfigurions of exerien rrngeens re sown. In Fig. 4 e dieer of seien is equl o e dieer of e soure, in Fig. 4 dieer of e soure is fr sller n seien s dieer. Fig. 4b sows e rel siuion, wen e e is delivered irregulrly eier fro e soure of finie size iy or fro soure wi seifi oosiion of e soures e.g. o-dis. 4 Resuls e Fig. 5 reresens e yil ie resonses of eerure for e se wise of inu ower. e oeffiien f frl diension reseively of e frl e soure for every oin of e exerienl deendene esured eerure deended on ie ws luled using e q. 7. e frl e soure rerizes e disribuion of e eerure in e seien in seifi ie. Fro e Fig. 6 i is eviden for very sor ie ere is e vlue of e frl diension nd erefore, e lne e soure is fored. e vlue of e frl diension dereses wi inresing ie vlue sine e e diserses ino e se. Fro e ie τ 1 16 s e inerseion of ngens of e urves e frl diension is geing seled o e vlue,15. e sil disribuion of e eerure in e sle does no nge ye in is re. I is ossible o deerine e 7 1 oeffiien of e e soure f 1 nd e diffusiviy of e seien s fro e exroled vlue of e frl diension o e ie s. is vlue is idenil o vlue deerined by e Insiue of Pysi, Slovk Adey of Sienes, Brislv. e deviions beween e exerienl e blk urve nd e odel e red urve resonse obvious in e desending r of e rerisis re used by e e dissiion fro e eril vi e ylinder surfe of e seien. is uses fser derese of e eerure n e eory redied. e ourse of e eerure deviion beween e odel nd exerienl rerisi is illusred s e blue urve in e Fig. 5. Negive vlues of funionl deendene sow e e dissiions fro e seien. is deviion s lso is own exree iniu, wi ens for e vlue of ie < 5s e losses re rising nd for longer ie inervls e loses re sller. 9 7 fi ex loss eerure r C ie s Fig. 5 erl resonse of e sle esured by e ulse rnsien eod blk exerienl d, red odel d, blue differene beween exerienl nd odel d.

5 Fro e desending rerisi we n gin deerine, by using 7 for e oin of exerienl deendene of esured eerure on ie, oeffiien f, frl diension of e frl soure of old resened by seien surfe. Fro Fig. 6b i is eviden ere re no ny old sos over e surfe of seien for ie inervls lose o e xiu e frl diension of e sos is equl o e oologil diension 3. Wi rising ie e vlue of frl diension of deresing eerure is sller gin unil e vlue. is is frl diension of e seien surfe. e ie onsn of is desen is τ 86 s. Fro e roorion of ie onsns exeing diffusiviy of e eril does no nge we n resue e disne beween e soure of e dissiion nd e erooule x τ τ1.17. is vlue roxiely resonds o e seiens rdius., 3, 1,5,8 frl diension 1,,5 frl diension,6,4,, ie s, ie s Fig. 6 Frl diension of e e disribuion in e seien fro inresed nd fro b deresed r of rerisis. 5 Conlusion In is rile, e resuls of erl resonses o e ulse of sulied e evluions re disussed. o inerre e ouoes, e silified e onduiviy odel is used [1]. e odel is bsed on exeions ublised in [4]. Resuls sow e ige of e disribuion in e seien, in vrious ie inervls fer e e suly fro e soure. ese evluions ould be used for ore ure deerinion of e erl reers of sudied ers. Referenes [1] Zeškl O., Buníček M., Nežádl M., Šefková P., Coušek R.: erl Proeries of Frl Sruure Merils. In eroysis 3. Kočove 3. [] Zeškl O., Nežádl M., Buníček M.: Frl Cnorin Geoery, Husdorff iension nd e Fundenl Lws of Pysis. Cos, Solions & Frls 3; 17: [3] Zeškl O., Nežádl M., Buníček M.: Field nd Poenil of frl Cnorin sruures nd l Nsie's infinie eory. Cos, Solions & Frls 4; 19: 113 1

6 [4] Crslw H.S., Jeger J. C.: Conduion of He in Solids. Clrendon Press London 1959, 496. [5] Kreský J.: Mesureen of eroysil uniies. VA Brislv 1969, 87. [6] Kubičár L.: Pulse Meod of Mesuring Bsi eroysil Preers. VA Brislv nd lsevier Nederlnd 199, 344. [7] V. Boáč, Ľ. Kubičár, V. Vreenár: Meodology of reer esiion of ulse rnsien eod nd e use of PMMA s sndrd referene eril. In MPMKO 4, 9 Inernionl Syosiu on eerure nd erl Mesureens in Indusry nd Siene, 5 June 4 Cv - ubrovnik Croi. [8] eroysil rnsien eser Model R 1.. Insiue of Pysi, Slovk Adey of Sienes