Pelagia Research Library

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1 ailabl oli a Plagia Rsa Liba das i pplid i Rsa (5:5-9 IN: ODEN (U: RF HD f oio a ad mass asf flow of isolasi flid mbddd i a poos mdim of aiabl pmabili wi adiaio ff ad a so i slip flow gim aa aga axa * ad.. Db Dpam of pplid amais Vikaada ollg of olog ad aagm liga U.P. Idia R aalsis as b aid o o obai f oi a ad mass asf aaisis of a iompssibl HD isolasi flid flow immsd i a poos mdim of aiabl pmabili bodd b a ifii poos ial pla i slip flow gim i ps of a ass magi fild wi a so ad adiaio ffs. pmabili of poos mdim dass xpoiall wi im abo a osa ma. ppoxima solios a b obaid fo loi mpa oaio ski fiio ad a of a asf. mial sls a displad gapiall o sd ff of sal pi paams s as isolasii pmabili of poos mdim magi fild asof mb modifid asof mb mid mb Padl mb adiaio paam a so/sik paam ad afaio paam o flow a ad mass asf aaisis. mial sls of loi disibio of isolasi flid a ompad wi ospodig flow poblms fo a isos flid. Wods: HD; F oio; Vaiabl pmabili; Visolasi flid; Radiaio UJE LIFIION: 76 76R W5 INRODUION o of o-nwoia flids as bom a fild of ai sa fo las fw dads as is lass of flids ps mamaiall ma idsiall impoa flids s as plasi films ad aifiial fibs i ids. I fa ias img of o-nwoia flids s as mol plasis plps mlsios aqos solios of polalamid ad polisobl. as impoa aw maials ad mial pods i a lag ai of idsial posss as simlad a osidabl aio i as o sd of o- Nwoia flids ad i lad aspo posss. qaios of moio of isolasi Plagia Rsa Liba 5

2 aa aga axa al d. ppl. i. Rs. (5:5-9 flids a o od ig a Nai oks o boda la qaios. al aos a osidd isolasi flids ad a good lis of fs o pblisd wok fo s flids a b fod i [ ]. F oio pomo as b obj of xsi sa. impoa of is pomo is iasig da b da d o ad o i si ad olog abo boa idd moios i amosp bodis i wa ad qasi solid bodis s as a. oio i poos mdia as appliaios i gomal g o oil xaio mal g soag ad flow og filig dis Nild ad ja []. Fom ologial poi of iw HD f oio flows a sigifia appliaios i fild of slla ad plaa magosp aoais mial giig ad lois o ao of i aid impoa s flows a b sdid b sal aos oabl amogs m a liff [] ad am [7]. sd o HD a ad mass asf f oio flow alog a ial sig s i ps of magi fild wi a gaio was aid o b amad ad objjama [8]. ig [] aalzd HD f oio ad mass asf flow wi a so ad mal diffsio. adiai ffs a impoa appliaios i psis ad giig pailal i spa olog ad ig mpa posss. lil is kow abo ffs of adiaio o boda la. mal adiaio ffs ma pla a impoa ol i oollig a asf i polm possig ids w qali of fial pod dpds o a oollig faos o som x. Hig mpa plasmas oolig of la aos liqid mal flids ad pow gaio ssms a som impoa appliaios of adiai a asf fom a ial wall o odi flids. ffs of adiaio o a/mass asf poblms a sdid b kopada [] aja [9] Hossai al. [8] ad Hsiao [9]. sd of flow of a poos mdim is of ga impoa o gopsiiss ad flid damiiss. Yamamoo ad Yosida [] osidd sio ad ijio flow wi oi alaio og a pla poos wall spifiall fo flow osid a ox la. galizaio of abo sd was psd b Yamamoo ad Iwama []. awla ad ig [5] sdid osillao flow pas a poos bd. ffs of aiabl pmabili o ombid f ad fod oio i poos mdia a sdid b adaskaa ad Namboodii [] Vdaaagam al. [] ad ama al. []. ig al. [6] ig ad ma [] aa al. [] a sdid ffs of pmabili aiaio o f oi flow og a poos mdim. Rl ffs of adiaio ad magi fild o f oi flow alog ifii ial pla a sdid b aka al. [8] aasi ad ak []. I gomal gio siaio ma ais w flow boms sad ad slip a boda ak pla as wll. I s siaio of slip flow odia oim appoa fails o ild saisfao sls. a aos a sold poblms akig slip odiios a boda (ig [5]. I ps wok w mak a amp o isiga poblm of f oi a ad mass asf of sad iompssibl HD isolasi flid mbddd i a poos Plagia Rsa Liba 6

3 aa aga axa al d. ppl. i. Rs. (5:5-9 mdim of aiabl pmabili bodd b a ifii poos ial pla i slip flow gim wi a so ad adiaio ffs. pmabili of poos mdim dass xpoiall wi im abo a osa ma. ffs of aios goig paams ig io poblm lik isolasii pmabili o poosi paam magi paam asof mb modifid asof mb mid mb a so/sik paam afaio paam ifl of Padl mb ad adiaio paam o loi mpa ski fiio a of a asf a isigad ad aalzd wi lp of i gapial psaios. NOENLURE : magi flx dsi : oaio of flid p : spifi a a osa pss D : offii of mial molla diffsii : asof mb m : modifid asof mb g : alaio d o gai : afaio paam : pmabili of poos mdim k : mal odii : pmabili o poosi paam : magi fild paam N : Nssl mb P : Padl mb q : adiai a flx R : adiaio paam * : so/sik offii : a so/sik paam : mid mb : mpa : ompo of loiis alog x ad diios spil REE YOL : offii of olmi xpasio * : olmi offii of xpasio wi oaio : lial odii : flid dsi : flid dami isosi : flid kimai isosi : dimsiolss mpa : ski fiio : dimsiolss oaio : isolasi offii : isolasi paam w : wall odiio : f sam odiio Fomlaio ad solio W osid wo-dimsioal sad domagi f oio wi adiaio ad a ad mass asf flow of a isos iompssibl ad liall odig isolasi flid ia a poos mdim of aiabl pmabili opig a smi-ifii gio of spa bodd b a ifii ial poos pla wi osa sio ad a so i slip flow gim. magi fild of ifom sg is applid assl o diio of Plagia Rsa Liba 7

4 aa aga axa al d. ppl. i. Rs. (5:5-9 8 Plagia Rsa Liba flow. magi Rolds mb of flow is ak o b small og so a idd magi fild a b gld. W ak x axis alog pla ad axis omal o i ad flow i mdim is il d o boa fo asd b mpa diff bw wall ad flid. isos dissipaio ad Da's dissipaio ms a gld fo small loiis [6]. Ud s assmpios goig boda la qaios of oii momm g ad diffsio old b wi as follows: oii: ( lia momm: g g ρ σ β β ( * ( ( ( g: q p p p k ρ ρ ρ ( * ( diffsio: D ( pmabili of poos mdim is assmd o b of fom ( ε ( (5 w is ma pmabili of mdim al osa im ad ε (< < is a osa qai. adiai a flx q is gi b []: I q ( (6 w k d b k I is absopio offii a wall ad b is Plak fio. boda odiios a: w w L as a (7 w L m m L L big ma f pa ad m axwll's flio offii. oii qaio ( gis (8 w > is osa sio loi a pla. W iod followig dimsiolss qaiis:

5 aa aga axa al d. ppl. i. Rs. (5:5-9 9 Plagia Rsa Liba * * * * w w * ( ( * k P g g p w m w µ β β ρ ρ σ ρ * L D I R p p qaios ( o ( i iw of (5 o (6 i o-dimsioal fom af doppig asisks ( o m d o: m ( ε (9 ( R P ( ( wi ospodig boda odiios as a ( paial diffial qaios (9 o ( a dd o odia o b assmig followig xpssios fo loi mpa ad oaio ( ( ( ε ( ( ( ( ε ( ( ( ( ε (5 bsiig qaios ( o (5 i qaios (9 o ( ad qaig offiis of lik pows of ε followig qaios a obaid: m (6 ( m (7 ( P R P (8

6 aa aga axa al d. ppl. i. Rs. (5:5-9 Plagia Rsa Liba R P P (9 ( ( wi ospodig boda odiios as a ( w pims do diffiaio wi sp o. solios of (6 ( saisfig boda odiios ( a sbsid i qaios ( (5 ( ε ( ( ( ( (5 w ( P R P P [ ] ( ( ( ( ( m ( ( ( ( [ ] ( ( ( ( ( ( Fom qaio ( w alla ski fiio

7 aa aga axa al d. ppl. i. Rs. (5:5-9 [ ] τ ε (6 Fom qaio ( w alla a of a asf i ms of Nssl mb P P ( R P N (7 REUL ND DIUION I od o g a la isig of psial poblm mial ompaios a b aid o fo aios als of maial paams s as isolasi paam poosi paam magi paam mid mb adiaio paam R a so/sik paam asof mb modifid asof mb m Padl mb P ad afaio paam wi a of psial ad giig is. mial sls a displad wi lp of gapial illsaios i figs. s figs dpi loi pofils ski fiio pofils mpa pofils ad a of a asf. I figs ad 9 aiaios of loi ad mpa a ompad i ai (P.7 ad wa (P 7. wil i figs 5 6 sls of loi disibio of isolasi flid ( a ompad wi ospodig flow poblms fo a isos flid (. Fom figs ad 9 i is la a bo loi ad mpa ias i ai ompad wi wa. loi pofils fo diff als of magi fild paam a plod agais i Fig.. I ai ad wa i is obsd a loi dass wi iasig als of wi sows a loi dass i ps of magi fild as ompad o is abs. is ags wi xpaios si magi fild xs a adig fo o f oi flow. Fo diff als of poosi paam loi pofils a dmosad i Fig.. I is la a loi iass d o iasig als of poosi paam bo i ai ad wa. I is also obsd a magid of loi disibio aoss boda la iass ad appoaig o zo as iass. Fig. illsas ff of a so ( > o a sik ( < o loi. I ai i is obios a a ias i lads o a is i als of loi. I is also obsd a a som fixd al of loi gap i wa is low a spi loi gap i ai. Fig. xibis loi disibio fo sal als of adiaio paam R. o i ai ad wa loi pofils sow a das wi ias of adiaio paam. aiaios of loi fild fo diff als of asof mb ad modifid asof mb m a plod agais i Figs. 5 ad 6. sls a displad fo isos flid ( as wll as isolasi flid (. Fo bo flids loi iass wi iasig als of ad m. I is also obios a a som fixd al of o m Plagia Rsa Liba

8 aa aga axa al d. ppl. i. Rs. (5:5-9 loi gap fo isos flid is low a spi loi gap fo isolasi flid wi idias a loi iass fo isolasi flid ompad wi isos flid. Psiall > mas aig of flid o oolig of boda sfa < mas oolig of flid o aig of boda sfa ad ospods o abs of f oio. ski fiio pofils a displad agais i Figs. 7 ad 8 fo aios als of maial paams wi a lisd i fig apios. Fom Fig. 7 i is la a ski fiio iass wi ias i m ad dass wi ias i. Fig. 8 sows a ski fiio is mo i isolasi flid as ompad o a i isos flid. I is also la a ski fiio iass i ai ad dass i wa. lso ff of iasig als of ad R sls i a dasig ski fiio. Fmo ski fiio iass i abs of magi fild as ompad o is ps. pial aiaios of dimsiolss mpa pofils i ai ad wa fo diff als of adiaio paam ad a so/sik paam a plod agais i Fig. 9. ff of adiaio paam o mpa is dpid i Fig. 9(a. I is oid fom fig a mpa dass wi iasig als of adiaio paam R. ff of adiaio paam is o d mpa sigifial i flow gio. ias of adiaio paam mas las of a g fom flow gio ad so flid mpa dass as mal boda la ikss boms i. Fig. 9(b displas ff of o mpa. I is la a mpa iass wi ias i. Fom Figs. 9(a ad 9(b i as b obsd a mpa pofils a low i wa as ompad o a i ai. aso is a small als of P a qial o iasig mal odiiis ad fo a is abl o diffs awa fom ad sfa mo apidl a fo ig als of P. Vaiaios of a of a asf i ms of Nssl mb wi R fo diff als of P a psd i Fig.. Fom fig i is oid a a of a asf iass wi iasig als of Padl mb. Fmo ff of iasig als of R sls i iasig a of a asf. ONLUION mai goal of is ail is o sd sad HD a ad mass asf f oio flow of a iompssibl liall odig isolasi flid immsd i a poos mdim of aiabl pmabili bodd b a ifii poos ial pla i slip flow gim wi a so ad adiaio ffs. pmabili of poos mdim dass xpoiall wi im abo a osa ma. fdamal paams fod o aff poblm d osidaio a isolasi paam magi paam pmabili paam asof mb modifid asof mb Padl mb mid mb a so paam adiaio paam ad afaio paam. I is fod a loi ad mpa dass i wa ompad wi ai. I is also obsd a loi as wll as ski fiio iass wi iasig als of m was s d is s wi R ad. ddiioall a of a asf is iasd wi im i P. Plagia Rsa Liba

9 aa aga axa al d. ppl. i. Rs. (5: ε....6 R m Օ P P Fig.. Vaiaio of loi wi fo sal als of ε....6 R m. Օ.5. P P Fig.. Vaiaio of loi wi fo sal als of. Plagia Rsa Liba

10 aa aga axa al d. ppl. i. Rs. (5: ε....6 R m. Օ..5. P P Fig.. Vaiaio of loi wi fo sal als of ε m R. Օ R 5. R P P Fig.. Vaiaio of loi wi fo sal als of R. Plagia Rsa Liba

11 aa aga axa al d. ppl. i. Rs. (5: ε P.7 m R. 5. Օ Fig.5. Vaiaio of loi wi fo sal als of.. ε P.7 5 R..8 m. Օ m.5 m Fig.6. Vaiaio of loi wi fo sal als of m. Plagia Rsa Liba 5

12 aa aga axa al d. ppl. i. Rs. (5: ε....6 P.7 R. m Օ τ Fig.7. ki fiio τ plod agais fo diff als of m ad...9 ε m.7 τ.5.. P R.7.6. Օ Fig.8. ki fiio τ plod agais fo diff als of P ad R. Plagia Rsa Liba 6

13 aa aga axa al d. ppl. i. Rs. (5: R. Օ R. R. P P Fig.9 (a. R..8.5 Օ P P Fig.9 (b Fig.9. Effs of P ad R o mpa. Plagia Rsa Liba 7

14 aa aga axa al d. ppl. i. Rs. (5: N P.7 Օ R Fig.. Vaiaio of a of a asf N wi R fo sal als of P. REFERENE [] aa. Das.. ad ig L.P. Idia J. P ppl. a. (. [] labi al. azid oamd.. ad d amod. El pplid amais ( [] dsso H.I. a aia Vol. 95 ( [] adaskaa.. ad Namboodii P... I. J. Ha ass asf 8 ( [5] awla.. ad ig. a. ( [6] ogl.. Vii W.. ad ills.e. I J. 6 ( [7] am.p. ad Pai.L. ago flid damis fo gis ad applid psis - aw Hill ook ompa Nw Yok (97. [8] Hossai.. lim.. ad Rs D.. I. J. of Ha ass asf ( [9] Hsiao.L. Joal of ais Vol. No. J (8. [] Hilgol R.R. ad Pa-i N. Flid mais of isolasii Elsi Nw Yok (997. [] aasi. ad ak.. aia ads ( 77. [] kopada. ad Lak.. I. J. of Ha ad mass asf 5 ( [] Nild D.. ad ja. oio i poos mdia d Ediio pig-vlag li (998. [] Raa.. ad ago.. das i ppl.. Rsa Plagia Rsa Liba ( ( [5] Rapis.. I. omm. Ha mass asf 6 ( [6] Rdaia N. adaskaa.. Vabadaaia R. ad Nagaaj.. P is sia Pis aglo (979. [7] addk.. ompaioal maials si 8 ( Plagia Rsa Liba 8

15 aa aga axa al d. ppl. i. Rs. (5:5-9 [8] amad.. ad objjama. Rs. J. of ppl.. Egg. ad olog ( ( [9] aaaa R. ka. ad. ad Rdd R. Hmadi das i ppl.. Rsa ( ( -9. [] apakaa. IHE Joal Vol. 7 (96-8. [] ama P.R. awla ma ad ama.. Jo. of Idia ad. a. Vol. 9 No. (7 -. [] liff J.. x book of magododamis Pgamo pss Lodo (965. [] ig.. J. Eg a mass asf ( [] ig.d. ad ma. J. a. Ps. i. 7 (99. [5] ig P. P.D. sis Rajasa Uisi (99. [6] ig P. isa J.. ad Naaa.. I. J. Nmial ad alial ods omais (989. [7] ka. aaaa R. Vkaaamaa. ad Rdd R. Hmadi das i ppl.. Rsa ( ( 6-6. [8] aka H.. ola R..R. ad odalgka V.. I. J. Nm. ods fo Ha ad Flid flow 6 ( ( [9] aja Raj ad Jai N.. Jaaba / ( 69. [] Vdaaagam. Jai P. ad Faiwa. I. omm. Ha ass asf ( [] Yamamoo. ad Iwama N. J. Egg. a. (976. [] Yamamoo. ad Yosida Z. J. Ps. o. Japa 7 ( Plagia Rsa Liba 9