EffectofMagneticFieldonOscillatoryFlowPastParallelPlatesinaRotatingSystemwithHeatandMassTransfer

Transcription

1 Global Joual of Scc Fo Rsach: F Mahmacs a Dcso Sccs Volum 4 Issu 4 Vso. Ya 4 yp : Doubl Bl P Rw Iaoal Rsach Joual Publsh: Global Jouals Ic. (SA Ol ISSN: & P ISSN: Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf By Pawa Kuma Shama & Sushl Kuma Sa Amy school of gg. & ch. Ia Absac- hs commucao sgas h ffc of magc fl o oscllaoy flow wh h comb ffcs of flucuag ha a mass asf pas cal paalll poous fla plas. I s assum ha cal chal s oag wh agula locy Ω. h poc suco locy s assum a h pla a oh pla oscllag wh poc f sam locy. h gog quaos a sol by aopg complx aabl oaos. h aalycal xpssos fo locy a mpau fls a oba usg pubao chqu. h ffcs of aous paams o ma pmay ma scoay locy ma mpau ma cocao as locy as mpau as cocao a a of ha a mass asf ms of amplu a phas ffcs ha b scuss a show gaphcally. Kywos: MHD poous mum compssbl flu aual coco ha a mass asf. GJSFR-F lassfcao : MS : A69 EffcofMagcFloOscllaoyFlowPasPaalllPlasaRoagSysmwhHaaMassasf Scly as p h complac a gulaos of : 4. Pawa Kuma Shama & Sushl Kuma Sa. hs s a sach/w pap sbu u h ms of h a ommos Abuo-Nocommcal 3. po Lcs hp://cacommos.og/lcss/by-c/3./ pmg all o commcal us sbuo a pouco ay mum po h ogal wo s poply c.

2 Nos Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Pawa Kuma Shama α & Sushl Kuma Sa σ Absac- hs commucao sgas h ffc of magc fl o oscllaoy flow wh h comb ffcs of flucuag ha a mass asf pas cal paalll poous fla plas. I s assum ha cal chal s oag wh agula locy Ω. h poc suco locy s assum a h pla a oh pla oscllag wh poc f sam locy. h gog quaos a sol by aopg complx aabl oaos. h aalycal xpssos fo locy a mpau fls a oba usg pubao chqu. h ffcs of aous paams o ma pmay ma scoay locy ma mpau ma cocao as locy as mpau as cocao a a of ha a mass asf ms of amplu a phas ffcs ha b scuss a show gaphcally. Kywos: MHD poous mum compssbl flu aual coco ha a mass asf. I. Iouco Magohyoyamcs (MHD (mago flu yamcs o hyomagcs s h suy of h yamcs of lccally coucg flus. Exampls of such flus a clu plasmas lqu mals a sal wa o lcolys. h wo magohyoyamcs (MHD s fom mago- mag magc fl hyo- mag lqu a -yamcs mag mom. h fuamal cocp bh MHD s ha magc fls ca uc cus a mog couc flu whch u cas focs o h flu a also chags h magc fl slf. h s of quaos whch scb MHD a a combao of h Na- Sos quaos of flu yamcs a Maxwll's quaos of lcomagsm. MHD appls qu wll o asophyscs co of h us s ma up of plasma clug sas h plaay mum (spac bw h plas h slla mum (spac bw h sas h galacc mum bula a js. Suspos a caus by h Su's magc fls h sola w s also go by MHD. How magohyoyamc ffcs asf h Su's agula momum o h ou sola sysm slowg s oao. MHD s la o gg poblms such as plasma cofm lqu-mal coolg of ucla acos a lcomagc casg. h wog pcpl ols lcfcao of h poplla (gas o wa whch ca h b c by a magc fl pushg h hcl Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya 4 7 Auho α : Dpam of Appl Mahmacs Amy School of Egg a chology Nw-Dlh Ia. -mal: pawashama@yahoo.com Auho σ : Dpam of Mahmacs Sh Vashwaa sy Gajaula Amoha Pash Ia. -mal: ssahs9@ffmal.com 4 Global Jouals Ic. (S

3 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya 4 8 h oppos co. A mpoa as cac sach s lopg mo pcs mhos fo ly of mc o affc aas. O mho ols h bg of mc o bologcally compabl magc pacls (.g. foflus whch a gu o h ag a caful placm of pma mags o h xal boy. h flow poblms of a lccally coucg flus u h fluc of magc fl ha aac h s of may auhos w of s applcaos o gophyscs asophyscs gg a o h bouay lay cool h fl of aoyamcs. O h oh ha w of h casg chcal applcaos usg magohyoyamcs ffc s sabl o x may of h aalabl scous hyoyamc soluo o clu h ffcs of magc fl fo hos cass wh h scous flu s lccally coucg. Rossow [] Gspa a a [] ha su xsly h hyomagc ffcs o h flow pas a pla wh o whou jco/suco. h hyomagc chal flow a mpau fl was sga by Aa a Koab [3]. Hossa al. [4] ha su h MHD f coco flow wh h sufac p a oscllag sufac ha flux. I w of applcaos of h flow hough poous mum wh h ffc of magc fl aac ao of a umb of scholas. Aloss al [5] Hlmy [6] a Km [7] su h magohyoyamc mx coco fom a cal pla a poous mum. say f coco flow wh h comb ffc of hmal a mass ffuso h psc of magc fl a Hall ffc s sga by aha.al [8]. Ahm al [9] su h hmal ffuso ffc o a h-msoal MHD f coco wh mass asf flow fom a poous cal pla a hamha [] also sgas MHD flow of a ufomly sch cal pmabl sufac h psc of ha gao/absopo a a chmcal aco. h MHD flow bw wo paalll hooal poous pla also sga by hauhay al []. Shama [] su h smulaous hmal a mass ffuso h msoal mx coco flows h psc of poous mum. Sgh.al [3] a La a Kulac [4] h b su h f coc flow pas cal wall. Nl [5] su coco flow hough poous mum wh cl mpau ga. Kllh al. [6] su h ha asf spos of lama f coco bouay lays alog cal ha plas o sufac mpau oscllaos. Shama al [7] su h usay f coco oscllaoy flow hough poous mum wh poc mpau aao. Also h oscllaoy ou flows a oag sysm ha b su by Jaa a Daa [8] Muum [9] a Gaapahy []. Raps a Ps [] also su h oscllaoy flow hough poous mum h psc of coco. hfo h objc of h ps pap s o sga h oscllaoy flow hough oag poous cal chal h psc of magc fl wh flucuag hmal a mass ffuso assumg poc suco locy a h pla a oh pla whch s also flucuag wh poc f sam locy abou a o o cosa ma. h aalycal soluos fo ma pmay ma scoay locy as locy as mpau a cocao a oba usg gula pubao chqu. h ffc of aous paams o flow chaacsc a scuss a show gaphcally. II. Mahmacal Fomulao of h Poblm os a oscllaoy f coc flow of a coucg scous compssbl flu hough hghly poous mum bou bw wo f cal poous plas sac 4 Global Jouals Ic. (S Rf. V. J. Rossow O flow of lccally coucg flus o a fla pla h psc of a ass magc fl N. A.. A. Rp. (

4 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Nos apa. h poc suco locy s appl a h saoay pla a oh pla a whch s oscllag s ow pla wh a locy abou a o o cosa ma locy. h og s assum o b a h pla a h chal s o cally upwa alog h x -axs. h chal oas as a g boy wh ufom agula locy Ω abou -axs whch s ppcula o h cal pla cof wh a scous flu occupyg h poous go. Sc h plas a f x all h physcal quas xcp h pssu p oly o a. Dog h locy compos u w h x y cos spcly mpau by a cocao by. h flow poous mum ols small locs pmg h glc of ha u o scous sspao gog quao. A magc fl of cosa sy s appl ppcula o h chal. h basc quao of magofluyamcs a cooal flu yamcs a ff by oly aoal foc m u o lcomagc fl. h Maxwll's quaos ha o b sasf h fl. I o o h basc quaos fo h poblm u cosao h followg assumpos a ma:. h flow s say a lama a h magc fl s appl ppcula o h pla.. h flu u cosao s scous compssbl a fly coucg wh cosa physcal pops. 3. h magc Ryols umb s a o b small ough so ha h uc magc fl s glc. 4. Hall Effc lccal a polaao ffcs a glc. h quao xpssg h cosao of mass a gy asf oag fam of fc a g by w w (ε cosω ( u u p w Ω g β ( ρ x u u ( J B g β c ( ρ p ( J B w Ω u ρ y ρ wh h fouh m o h gh ha s of quaos (-3 s h Lo foc u o magc fl B a s g by J B σ ( B B (4 sg (4 quaos ( a (3 w ha u u p w Ω g β ( ρ x u u σ B g β c ( u ρ ( (3 (5 Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya Global Jouals Ic. (S

5 Nos 4 Global Jouals Ic. (S Global Joual of Scc Fo Rsach Volum XIV Issu so I V IV Ya 4 F Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf w ρ c p κ (7. w D ( 8 wh g s h acclao u o gay β s h olumc coffc of hmal xpaso β c s h olumc coffc of xpaso fo cocao s h mpau s h mpau f sam s h mac scosy Ω s h agula locy s h pmably p s h spcfc ha a cosa pssu p s h pssu ρ s h sy s h m a κ s h hmal coucy ω fqucy of flucuaos. h bouay coos of h poblm a. cos ( u : cos ( cos ( u : ω ε ω ε ω ε (9 osg u a lmag h pssu ga fom (5 a (6 w ha ( g ( g w ρ σ β β B c Ω ( u w ρ σ ρ B y p Ω (6 W ouc h followg o-msoal quas as: ( ( u u θ ω ω ( paam (Suco p ffusy hmal w ρ κ α λ ω D Numb Sc ( Schm B Numb Hama M ( ρ σ ( ( umb P (Pal - ( g umb G (Gashof α β

6 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Gc (mof Gashof umb g βc ( - Subsug hs o-msoal quas quaos (7 (8 a ( w g Nos ω ( ε cos λ. Gc λ M III. R G λ θ θ θ θ ω ( ε cos λ ( P ω ( ε cos λ Sc h cospog bouay coos (9 bcom : : ε cos θ ε cos θ Soluo of h Poblm ε cos. I o o sol h poblm w assum h soluos of h followg fom bcaus amplu ε (< < of h aao of mpau s y small ( θ ( θ ( ε θ ( ( ( ε ( ε ( ( Subsug (5 quaos ( ( a (3 a quag h coffc of cal pows of ε a glcg hos of ε ε 3 c. w g // / λ R M G λ θ Gc λ ( (3 (4 (5 (6 / / λ R ω M G λ θ Gc λ λ (7 '// // / θ λ P θ (8 '// / / θ λ P θ ω Pθ -λ Pθ (9 λ Sc // / ( '// / / λ Sc ω Sc -λ Sc ( h cospog bouay coos (4 uc o : : θ θ θ θ. ( Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya 4 4 Global Jouals Ic. (S

7 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Solg quaos (6 o ( u cospog bouay coos ( w g ( λ P 4 λ Sc 5 (3 Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya 4 wh ( 8 3 -λ Sc λ P (4 - λ P - λ P θ ( ( - (5 - λ P (- θ ( λ P (6 ( -Λ (- Sc ( -λ Sc - -λ Sc (7 7 6 λ Sc ( 9 8 (8 [ λ P λ P 4 P ] [ λ P λ P 4 P ] λ P λ ( ω ω 3 P ω 3 ( ( λ P 4 3 ( ( λ P 5 [ λ Sc λ Sc 4ω Sc ] [ λ Sc λ Sc 4ω Sc ] 6 7 λ Sc ( 8 λ Sc ω Nos ( 6 7 ( 9 λ Sc ( 6 7 ( λ Sc 4 Global Jouals Ic. (S

8 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Nos ( ( λ λ 4( R M λ λ 4( R M λ P λ Sc [ λ P [ λ Sc G λ λ P ( R M Gc λ λ Sc ( R M λ P G λ λ P ( ( R M ( λ P ( λ λ 4( ω R 8 M λ λ 4( ω R 9 M λ λ λ 7 ( ω R M λ 6 ( ω R M λ Sc λ ] ] λ Sc Gc λ ( R M Sc λ 3 P λ 3 G λ P λ P ( ω R M λ P λ P ( ω R M λ 4 Sc λ 8 Gc λ Sc λ Sc ( ω R M λ Sc λ Sc ( ω R M G λ 4 λ ( ω R M G λ 5 λ ( ω R M 5 Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya Global Jouals Ic. (S

9 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf 6 7 λ 7 Gc λ 9 ( ω R M Gcλ 7 6 λ 6 ( ω R M Nos Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya IV. λ P λ Sc Dscusso a oclusos a Say Flow W a u quao (3 a subsqu compaso of h al a magay pas gs h ma pmay locy u a ma scoay locy. h ma pmay locy s ps Fg. fo fx alus of G Gc a Sc.6 ( fo O a (P.7. h gaph als ha locy cass wh casg suco paam λ a s ffc s obs fo R ( oao paam a ( pmably of poous mum. hs shows ha h poosy a oao of poous mum x ag fluc o h pmay flow. Fg. also shows ma pmay locy fo ff alus of G ( Gashof Numb Gc( Mof Gashof Numb a Sc( Schm Numb. I s obs fom h fgu ha h ma pmay locy cass aply wh casg h G o Gc. h magu of locy s lss cas of Sc.78 ( NH 3 ha ha of Sc.6 ( O. Fuhmo h ma pmay locy cass h cy of h pla. I s sg o o ha f w cas magc fl paam M ( Hama Numb.. mum bcom coucg h h ma pmay locy bcom flucua susoally. h ma scoay locy pofls s show Fg. 3 fo h fx alus of G Gc Sc a P.7(a. I s obs ha cass wh casg R whl s phoma s obs fo λ. I s sg o o ha ma pmay locy cass whl ma scoay locy cass wh R a λ. I s also obs ha u o cas ma scoay locy cass upo ml half of h chal h cass. Fg.4 also show h ma scoay locy fo ff alus of paams. I s obs ha cass wh casg h G Gc a Sc. h magu s low cas of NH 3 ha ha of O. h amou of scoay locy s much low fo Gc ha ha of G. Also u o cas sy of magc fl h ma scoay locy flucuag. h ma mpau a cocao s ps Fg.9. I s obs ha boh cass wh casg λ. h ma mpau a cocao cass xpoally h magu of cocao s lss cas of NH 3 ha ha of O Global Jouals Ic. (S

10 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf b say Flow Rplacg h usay pas Nos ( M M θ ( a ( spcly quaos (4 (6 a (8 w g [ ( θ ( ( ] [ ( θ ( ( ] (9 ε [( M M ( ( ] h pmay scoay locy fls mpau a cocao ms of h flucuag compos a u ( u ε ( M cos M s (3 ( ε ( M cos M s (3 θ ( θ ε ( cos s cos ag ( ε ( s (33 π quaos (3 o (33 w g h xpsso fo as pmay locy as scoay locy as mpau a cocao as π u u ( ε M ( (34 π ( ε M ( (35 π θ θ( ε ( (36 π ( ε ( (37 h as pmay locy compo s show Fg.5 fo fx alus of P G Gc Sc a ω. I s obs ha cass wh casg h R a whl as pmay locy cass wh casg suco paam λ. I s sg o o ha ally h s cas as pmay a ha casg a h oh pla whch s flucuag wh f sam locy. h as pmay locy shf fom pos o ga u o cas sy of magc fl. Fg.6 also shows ha u o cas G a Gc h as pmay locy cass. A cas ω h fqucy of flucuao as locy bha susoally. h as pmay locy cass wh casg Sc a h pla upo <.6 ha cass. I s sg o o ha u o cas M as locy s flucuag susoally. h as scoay locy pofls s g Fg.7 fo ff alus of R a λ. I s obs ha as scoay locy cass wh casg h R a whl casg wh cas λ. h amou of cas locy s much low u o cas pmably of h poous mum. Physcally hs s u bcaus h poous maal offs ssac o h flow so locy cass poous mum. Fg.8 also ps as scoay locy fo ff alus of G Gc Sc a ω. h gaph als ha as scoay locy cass wh h G a Gc. I s sg o o ha alu of (3 Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya Global Jouals Ic. (S

11 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya 4 6 as scoay locy s ga cas of NH 3 ha ha of O. Fuhmo locy cass aply h cy of h pla wh ω ha cass a h oh h pla whch s flucuag wh f sam locy. h as scoay locy Fg.7-8 bcom flucuag wh casg M. as mpau a as cocao a g Fg.. I s obs ha as mpau a cocao boh a casg wh suco paam. h mpau a cocao a casg xpoally wh sac apa cal chal. Ha asf: I h yamcs of scous flu o s o much s o ow all h als of h locy a mpau fls bu woul caly l o ow quay of ha xchag bw h boy a h flu. Sc a h bouay h ha xchag bw h flu a h boy s oly u o couco accog o Fou s law w ha qw κ ( (38 wh s h co of h omal o h sufac of h boy. W ca calcula h msolss coffc of ha asf ms of Nussl Numb as follows Nu q θ θ θ w ( ( ε ( κ ( I ms of h amplu a phas h a of ha asf ca b w as: wh H H H Nu θ ( H cos ( ε φ H H H coffc of ε aφ H quao (4 Mass asf: Accog o Fc s Law h msolss coffc of mass asf a h pla ms of Shawoo Numb s g as follows Sh ( ( ε ( (4 I ms of h amplu a phas h a of mass asf ca b w as: wh S S S H. (39 (4 Sh ( S cos ( ε ϕ (4 S S S coffc of ε aϕ S S quao (4 h amplus of a of ha a mass asf ps Fg.. h gaph als ha boh a cass wh casg ω h fqucy of flucuaos upo λ <.8 ha hy cass fo hgh alus of suco paam. I s also obs ha amplu of mass asf s hgh cas of NH 3 ha ha of O.. Nos 4 Global Jouals Ic. (S

12 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Fg. shows h phass of a of ha a mass asf. I s obs fom h fgu ha phass of ha a mass asf cass wh casg ω. h phas of mass asf cass wh cas Sc. h magu s hgh fo NH 3 ha ha of O. I s also obs fom h fgu ha phass of ha a mass asf cass fo λ<.5 ha hy cass a bcom ga fo small alus of ω. Nos Rfcs Réfécs Rfcas. V. J. Rossow O flow of lccally coucg flus o a fla pla h psc of a ass magc fl N. A.. A. Rp. ( H. P. Gspa a G. F. a h MHD flow pas a fla pla J. Flu Mch. 6 ( H. A. Aa N. A. Koab MHD flow bw wo paalll plas wh ha asf Aca Mch. 7 ( M. A. Hossa S. K. Das I. Pop Ha asf spos of MHD f coco flow alog a cal pla o sufac mpau oscllao I. J. No-la Mch ( Aloss. K. Al-Nm M. A. Jaah M. A. a Al-Sha' B. J. :Magohyoyamc mx coco fom a cal pla mb a poous mum Numcal Ha asf Pa A ol. 8 o. 5( Hlmy K. A.: MHD usay f coco flow pas a cal poous pla ZAMM ol. 78 o. 4 ( Km Y. J. say MHD coc ha asf pas a sm-f cal poous mog pla wh aabl suco Iaoal Joual of Egg Scc ol. 38 o. 8 ( aha H. S. Roy S. a Nah G. say f coco flow o a f cal poous pla u o h comb ffcs of hmal a mass ffuso magc fl a Hall cus Ha a Mass asf ol. 39 o. ( Ahm N. Samah H. K. a Kala D.: hmal ffuso ffc o a h-msoal MHD f coco wh mass asf flow fom a poous cal pla La Amca Appl Rsach ol. 4 ( hamha A. J. : MHD flow of a ufomly sch cal pmabl sufac h psc of ha gao/absopo a a chmcal aco Iaoal ommucaos Ha a Mass asf ol. 3 o. 3 ( hauhay R.. Shama Pawa Kuma Mahu A.K. : h msoal MHD flow bw wo hooal plas wh aspao coolg J. of MHD Plasma a Spac Rsach (7-9.. Shama Pawa Kuma Smulaous hmal a mass ffuso h msoal mx coco flow hough poous mum J. Poous Ma 8(4 ( SghP. MsaJ.K. a NaayaK.A.: F coco alog a cal wall a poous mum wh poc pmably aao. I. J. Num. Aal. Mhos Gomh. 3 ( LaF..a KulacF.A.: h ffc of aabl scosy o coc ha asf alog a cal sufac a saua poous ma. I. J. Ha Mass asf. 33 ( Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya Global Jouals Ic. (S

13 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya NlD.A.: oco a poous mum wh cl mpau ga: a aoal suls. I. J. Ha Mass asf. 37 ( Kllh M. D. a Yag K.. ; Ha asf spos of lama f coco bouay lays alog cal ha pla o sufac mpau oscllaos ZAMP ( Shama Pawa Kuma Shama Bhupa Kuma a hauhay R.. : say f coco oscllaoy ou flow hough a poous mum wh poc wall mpau amag Joual of Mahmacs 38 ( Jaa R.N. Daa N.: Hall ffc o MHD ou flow a oag sysm ch. J. Phys. B 3 ( MuumB.S.: A xac soluo of oscllaoy ou flow a oag sysm. J. Appl. Mch. 58 ( GaapahyR.:. A o o Oscllaoy ou flow a oag sysm. J. Appl. Mch. 6 ( Raps A. a Ps.P.:Oscllaoy flow hough a poous mum by h psc of f coc flow I. J. Egg. Sc. 3 ( u Fg.. Ma pmay locy fo P.7 G Gc a Sc R λ Μ 5 5 Nos 4 Global Jouals Ic. (S

14 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Fg.. Ma pmay locy pofls fo P.7 R a λ 3.5 Nos.5 u G Gc Sc.6 M G 5 Gc Sc.6 M G Gc 5 Sc.6 M G Gc Sc.78 M G Gc Sc.78 M Fg.3. Ma scoay locy pofls fo P.7 G Gc a Sc.6 R λ Μ Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya Global Jouals Ic. (S

15 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf 3 Fg.4. Ma scoay locy pofls fo P.7 R a λ G Gc Sc.6 M G 5 Gc Sc.6 M G Gc 5 Sc.6 M G Gc Sc.78 M G Gc Sc.78 M Nos Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya 4 3 u Fg.5. as pmay locy pofls fp P.7 G Gc ε. Sc.6 ω a π / R λ Μ Global Jouals Ic. (S

16 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Fg.6. as pmay locy pofls fo P.7 R ε. λ a π / Nos u G Gc Sc ω Μ Fg.7. as scoay locy pofls fp P.7 G Gc ε. Sc.6 ω a π / R λ Μ Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya Global Jouals Ic. (S

17 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf 4 Fg.8. as scoay locy pofls fo P.7 R ε. λ a π / Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya 4 3 θ Fg.9. Ma mpau ( P.7 a cocao pofls Sc λ G Gc Sc ω Μ Nos Global Jouals Ic. (S

18 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Fg. as mpau (P.7 a as cocao (Sc.6 pofls fo ε. ω.5 a π / Nos θ l H l l S l λ.5 λ. λ.5 λ. Fg. Amplus of a of ha asf ( P.7 l H l a a of mass asf l S l ω Sc Global Joual of Scc Fo Rsach F Volum XIV Iss u IV V so I Ya λ 4 Global Jouals Ic. (S

19 Effc of Magc Fl o Oscllaoy Flow Pas Paalll Plas a Roag Sysm wh Ha a Mass asf Fg. Phass of a of ha asf ( aφ fo P.7 a a of mass asf (aϕ..6 Nos Global Joual of Scc Fo Rsach F Volum XIV Issu IV V so I Ya 4 34 aφ aϕ λ Sc ω Global Jouals Ic. (S