Nonhomogeneous Oscillatory Vertically Stratified Flow Between Two Porous Plates
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- Rosalind Stone
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1 Bonrn Inrnonl Jornl o D Mnn Vol. No. Mr 7 Nonomonos Osllor Vrll Srd Flow Bwn Two Poros Pls L. Prsnn Vnks S. Gns nd K.B. Nd Absr In s r w onsdr Nonomonos osllor low o rll srd ld bwn wo rl oros ls ndd b son nd njon oros wlls. Wn rm work o Bossnsq romon or dns oml solon s obnd sn smlr rnsormon nd nrrd. T l nd rnsrs lo rols nd rssr dsrbons r ld nd llsrd n rs. T rsls rsnd r dd on mor lss o solon S.Gns [8] Rjol [] Wn [] o o w rsnl lbl n lrr. T rsl or l lo obnd r rds o rsl or l lo n s o lmnr low bwn rlll ls (.. wn. Kwords Osllor Srd Flow Dns Dsrbon Sron Prmr Brn Vsl Frqn Bossnsq Aromon Smlr Trnsormon T I. INTRODUCTION HE wo dmnsonl sd s lmnr low n nnls w oros wlls s nmros lons n ros brns o Ennrn nd Tnolo s s bondr lr onrol nd rnsron ooln roblms. I ls n morn rol n sd o roblms w nol dson nomn n lown s srm. Brmn [] ws rs rsrr wo sdd roblm o sd low o n nomrssbl sos ld ro oros nnl w rnlr rossson wn Rnolds nmbr s low. H obnd rrbon solon ssmn norml wll los o b ql. Tn Sllrs [6] ndd roblm sdd b Brmn wn Rnolds nmbr s r. Arwrds Yn [] nd Trll [7] sdd roblm or ros ls o son nd njon Rnolds nmbrs. Trll nd Srs [8] nlsd sm roblm ssmn drn norml los wlls. Drk [6] s onsdrd low o n nomrssbl sos ld n lon nnl o rnlr son d o rod rssr rdn. B [5] s sdd nsd L. Prsnn Vnks Asssn Prossor Drmn o Mms Sbm Unrs Cnn Ind Eml: rsnnlsso@ml.om S. Gns Prossor & Hd Drmn o Mms Sbm Unrs Cnn Ind Eml: sns9@oo.om K.B. Nd Prossor Drmn o Mms Sbm Unrs Cnn Ind Eml: kbnd999@ml.om low o sols Mwll ld w rnsn rssr rdn ro rnlr nnl. Ford Osllon n n nsd srd ld bn onsdrd b mn ors Krsn & Srm [9] Hndrso [9] Ro nd Ro [7] Srm nd Nd [] Nd [5] nd Prsnn Vnks []. B r ll work s bn don on osllons n srd sos ld. W onsdr osllor low o srd ld bwn wo rl oros ls ndd b son nd njon oros wlls wn rm work o Bossnsq romon or dns. II. FORMULATION OF THE PROBLEM T low o n nomrssbl sos ld bwn wo rlll oros ls nd lon dron o s s onsdrd. I s ssmd r s rod njon o lo w lowr l nd rod son o lo w r l wr nd r onsns nd s rqn. Hn lo or ( q nd rssr r osn s ollows. q [ ( ˆ ( ˆj ] w nd P( ( w wr ( nd ( r lo omonns o low lon oordn drons o ( rsl. L nd b oordn s rlll nd rndlr o nnl wlls. Eqon o onn ( Eqon o Inomrssbl or srd nomrssbl low d d Eqon o Moon Hr rrsns on o sos nd dns o ld T dns dsrbon n ndsrbd s s kn s ( ( (5 ( ( ( ISSN Bonrn
2 Bonrn Inrnonl Jornl o D Mnn Vol. No. Mr 8 ISSN Bonrn Wr ( ( (6 s onsn dns ( s lnrl dsrbd ( s rrbon dns sron rmr ( onsn so Brn Vsl rqn N boms N nd Rnold s nmbr s n b υ UL LU L L U R (wr υ Ts s lld soks low wn R s smll R<< low s lld soks low or smll Rnolds s nmbr low or rn low. For Soks low ( nd ( boms (7 (8 (9 W s Bosnsq s romon n nrl rms w mns ( ( Drnn ( nd ( w rs o ( ( Usn (9 n ( ( ( T bondr ondons o roblm r ( ( ( ( Drnn ( Prll w rs o (5 No: Drnn ( Prll w rs o (6 Sbrn (6 rom (5 w (7 W dn Srm Fnon s nd (8 Eqon (7 boms N (9 P ( ( Ψ ( ( ( nd Eqon (9 boms Ψ Ψ N ( T non ( s nrodd s ollows ( b Sllrs [6]: Ψ ( ( Wr nd o s r nrn lo. From Eqon ( ( Ψ Ψ Sbsn bo n qon ( ( D D ( wr D d d. Eqon ( s drnl qon o ordr w onsn on or w solon s n b Alr Eqon m m Soln w m ±
3 Bonrn Inrnonl Jornl o D Mnn Vol. No. Mr 9 m ± m ± α ( wr ± ( α wr ( ( nd Tror Gnrl Solon o qon ( s n b α ( α ( T Bondr Condons r rnsormd n rms o r s ollows ( ( ( nd ( ( ( T rsl obnd b ln bondr ondons on ( r ( (5 ( α α (6 ( α α (7 nd ( α α α α (8 Soln bo qons ls o onsns r s ollows. α α α α( α ( α ( α ( α ( α ( α α α ( α α α α α ( α ( α (9 ( ( ( ( α α ( α ( α Now o sr bo onsns no rl nd mnr rs l s onsdr α α ( α ( α A B (s α nd wr ( ( α α A B ( α ( α ( ( ( ( ( ( ( ( ( os sn ( ( ( ( ( os sn ( ( Sbsn l o ( α α (( os sn n ( srm non s lld. Usn rsson or nd qon (8 lo omonns (( os sn r drmnd. ( os ( sn ( os ( ( sn Tror A B (( os sn (( os sn ( os ( sn ( os ( sn Sbsn bo Vls n Consns w ( ( ( A B A( os os B sn sn A B ( B( os os A sn sn A B R I ( α α α ( A B [( A B os sn ( A B sn os ] A B (( A B sn os ( A B os sn A B R I α ( A B ( Aos Bsn A B A B R I α A ( ( Asn B os B ( R I os sn ( R sn I os R I ( R I ( R I ( R I ( os sn ( R I ( os sn R R R os I sn R os I sn I I R sn I os I os R sn ISSN Bonrn
4 Bonrn Inrnonl Jornl o D Mnn Vol. No. Mr ( ( os ( sn ( ( ( sn ( os ( ( os ( sn ( ( sn ( os ( T rsl obnd rom qons ( ( nd ( r ( ( (5 ( ( (6 B dnon o ol drnon d ( ( III. d d d ( ( d Inrn bo qon rsl obnd s 5 PRESSURE DISTRIBUTION ( d ( ( ( ( ( ( d ( d ( (7 wn r nrn lo s.5. From bo rs s sn mnd o l lo drss s nrss rom o or drn ls o. T Fr rrsns l lo rols o.5 wn nl lo s nrsd o rom.5. I s lrl sn mnds o l lo r mor wn l o nl lo s nrsd o. or. or drn ls o w. I s lso sn n Fr 5 rdl lo π nss or w nd rdl lo rols r nonr or ll lnr or or ls o w. T bo s drn ls o. T Fr 6 rrsns l lo rols drn ls o nml wn r nrn lo s.5. W s rols r rbol or drn ls o. T Fr 7 rrsns rdl lo rol or drn ls o wn w. T Fr 8 rrsns l lo rols or drn ls o wn w nd. Hr lso w s rols r rbol or drn ls o. Fr : Al Vlo Prols or nd o.5 or Drn Vls o 5 ( ( T rbrr onsn 5 s obnd s (8 5 k ( w n sn ( (9 T rssr dro s n b ( ( ( ( d ( IV. RESULTSS AND DISCUSSION T nmrl ls o (dron nd (dron lo rols bn lld or drn ls o nd. I s ssmd nd. Frs nd r l lo rols drn ross sons o nnl nml nd.5 Fr : Al lo Prols or nd o.5 or Drn Vls o ISSN Bonrn
5 Bonrn Inrnonl Jornl o D Mnn Vol. No. Mr V Fr : Al Vlo Prols or nd o.5 or Drn Vls o Fr 7: Trnsrs Vlo Prols or.5 nd nd or Drn Vls o Fr : Al Vlo Prols or nd o. or Drn Vls o Fr 8: Al Vlo Prols or nd wn Fr 5: Trnsrs Vlo Prols or.5 nd or Drn Vls o Fr 6: Al Vlo Prols or.5 nd nd or Drn Vls o V. CONCLUSION In bo nlss lss o solons o Nonomonos Osllor rll srd soks low o sos ld bwn wo rlll oros ls s rsnd wn r ss rbl son or njon wlls. T rsls rsnd r dd on mor lss o solon S. Gns [8] Rjol [] Wn [] o o w rsnl lbl n lrr. T rsl or l lo obnd r rds o rsl or l lo n s o lmnr low bwn rlll ls (.. wn. T o sron s ond n rssr dsrbon. REFERENCES [] E. Abo El D Hrmnn low w norm son nd njon bondn ls MS Tss Hlwn Unrs E 99. [] H.A. A Unsd Hrmnn low w rnsr o sols ld onsdrn Hll E Cndnn J. Ps. R. Cn. Ps. Vol. 8 No. P. 79. [] H.A. A T o son nd njon on nsd low bwn wo rlll ls w rbl rors Tmkn Jornl o Sn nd En. Vol. 8 P ISSN Bonrn
6 Bonrn Inrnonl Jornl o D Mnn Vol. No. Mr [] A.S. Brmn.A.S Lmnr low n nnls w oros wlls J. Al. Ps. Vol. P [5] I.C.B Unsd low o sols Mwll ld w rnsn rssr rdn ro rnlr nnl Ind. J. M. M [6] D. G.Drk On low n nnl d o rod rssr rdn Qr.J. M. Al. M. Vol. 8 P [7] M.C. Hndrso Imlsl srd osllons n ron srd ld J. Fld M. Vol. 8 P [8] S.Krsnmbl nd S. Gns Unsd soks low o sos ld bwn wo rlll oros ls Nonl onrn on Mml Modln nd Anlss (NCMMA BITS Pln C. P.. [9] D.V. Krsn nd L.V.K.V. Srm "Moon o n smmr bod n ron srd ld onnd bwn wo rlll lns J. Fld M. Vol. 8 P [] K.B.Nd Srd ld lows P.D. Tss 97. [] K.B.Nd Srd Vsos Flow bwn wo Oslln Clndrs Indn Jornl o Pr nd Ald Mms Indn Nonl Sn Adm Vol.5 No. P [] R.L. Pnon Inomrssbl low Sond don J. Wl Nwork 996. [] V.S. Ro nd G.V.P. Ro On ws nrd n ron srd lqds b rlln orn s J. Fld M. Vol.6 P [] K.R. Rjol A.Z. Szr C.Y. L Asmmr low bwn rlll ron dsks Jornl o Fld Mns Vol. 6 P. 5. [5] L.V.K.V. Srm nd K.B. Nd Sor n ron srd ld A M. Vol. P [6] J.R.Sllrs Lmnr low n nnls w oros wlls son Rnolds nmbr J.Al.Ps Vol [7] Trrll R.M Lmnr low n norml oros nnl. T Aronl Qrrl 5 P [8] R.M. Trll nd G.M. Srs Lmnr low ro rlll nd norml oros wlls o drn rmbl Zm Vol. 6 P [9] I. Tn Sd moon o lrll ondn nd sos lds n nnls J. Aros s Vol. 9 P [] S.W.Yn Frr nsons o lmnr low n nnls w oros wlls J. l. Ps Vol. 7 P [] M.B.Zrsk P.G. Drzn W.H.H. Bnks On low o sos ld drn lon nnl b son oros wlls Fld Dn. Rs. Vol. P [] C.Y. Wn "E solons o sds Nr Soks qons" Annl Rw o Fld Mns Vol. P [] F.M. W Vsos ld low Sond d. MrwHll omn Nw York 99. L. Prsnn Vnks born Trjrm (Kmbkonm dsr TmlNd INDIA on Jl 979. H dd s ndr rdon B.S (999. nd os rdons M.S (. nd M.Pl (. n Mms n A.M. Jn Coll Mnmbkkm Cnn INDIA. H s rrnl don P.D. n ld o ld dnms Sbm Unrs Cnn INDIA. H s rrnl workn s Ass Prossor D o Mms Sbm Unrs nd s n rn o rs n bo UG nd PG orss. Hs rsn rsr s n r o srd lows. ISSN Bonrn
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