Unsteady Magnetohydrodynamic Stokes Flow of Viscous Fluid with Radiative Heat Transfer

Transcription

1 IOSR Jornal o ahmacs IOSR-J -ISS: ISS: X. Volm Iss Vr. VI ar - Ar. 5 PP 6- Unsad agnohdrodnamc Soks Flow o Vscos Fld wh Rada Ha ransr.sharmlaa *.Gaahr * Darmn o ahmacs P.S.G.R rshnammal ollg or Womn ombaor amlnad Inda Rsarch Scholar P.S.G.R rshnammal ollg or Womn ombaor amlnad Inda Absrac: h nsad magnohdrodnamc low o an lcrcall condcng scos ncomrssbl ld bwn wo aralll oros las o a channl n h rsnc o a ransrs magnc ld whn h ld s bng whdrawn hrogh boh h walls o h channl a h sam ra s dscssd. An ac solon s oband or all als o R Scon Rnolds nmbr and Harmann nmbr. Erssons or h loc comonns and h rssr ar oband. h grahs o aal and radal loc rols ha bn drawn or drn als o. words: Unsad low aralll oros las ransrs magnc ld scon Rnolds nmbr Harmann nmbr rssr dro. I. Inrodcon h nsad magnohdrodnamc low n a channl s a classcal roblm whos solon has man alcaons n magnohdrodnamc owr gnraors coolng ssm arodnamcs hang olmr chnolog rolm ndsr cnrgal saraon o mar rom ld rcaon o crd ol and ld drols sras. Hassann and ansor 99 dscssd h Unsad magnc low hrogh a oros mdm bwn wo nn aralll las. agch 996 sdd h roblm o Unsad low o scolasc awll ld wh ransn rssr gradn hrogh a rcanglar channl.aa and ob 996 sdd h Sad ll dlod HD low and ha ransr bwn wo aralll las wh mrar dndn scos. Aa 999 ndd h roblm o h ransn sa. Ezza al. 999 sdd h roblm o mcroolar agnohdrodnamc bondar lar low. Abol-Hassan and Aa dscssd h Flow o a condcng scolasc ld bwn wo horzonal oros las n h rsnc o a ransrs magnc ld. abl al. 3 sdd h HD low o non-nwonan sco-lasc ld hrogh a oros mdm nar an acclrad la. Aa 4 has consdrd h Unsad Harmann low wh ha ransr o a sco-lasc ld consdrng h Hall c. Haa al. 4 sdd h Hall cs on h nsad hdromagnc oscllaor low o a scond grad ld. rshnambal and Gansh 4 dscssd h Unsad soks low o scos ld bwn wo aralll oros las. Aa 5 sdd h Unsad lamnar low o an ncomrssbl scos ld and ha ransr bwn wo aralll las n h rsnc o a norm scon and njcon consdrng arabl rors. Aa 5 sdd h Unsad low o a ds condcng ld bwn aralll oros las wh mrar dndn scos. rshnambal and Gansh 7 dscssd h Unsad magnohdrodnamc soks low o scos ld bwn wo aralll oros las. Sharma and sngh9 s nsgad h c o arabl hrmal condc and ha sorc/snk on low o a scos ncomrssbl lcrcall condcng ld n h rsnc o norm ransrs magnc ld and arabl r sram nar a sagnaon on on a non condcng srchng sh. alash and Umaah 997 sdd wo-has HD low and ha ransr n an nclnd channl n h rsnc o boanc cs or h saon whr onl on o h hass s lcrcall condcng. alash al. analzd h roblm o ll dlod wo ld magnohdrodnamc lows wh and who ald lcrc ld n an nclnd channl. Fl Ilsanm Alao Samson aband Folarn3 nsgad h smlar solon o h nlnc o h hrmal radaon and ha ransr on sad comrssbl bondar lar low. h objc o hs sd s o anals h Unsad agnohdrodnamc Soks low o scos ld bwn wo aralll oros las whn h ld s bng whdrawn hrogh boh h walls o h channl a h sam ra. h roblm s rdcd o a hrd ordr nonlnar drnal qaon whch dnds on a Scon. Rnolds nmbr R and a Harmann nmbr or whch an ac solon s oband. II. ahmacal Formlaon h nsad lamnar low o an ncomrssbl scos ld n a channl s consdrd n h rsnc o a ransrs magnc ld H ald rndclar o h walls. Also h c o ha ransr s consdrd. h orgn s akn a h cnr o h channl. L and b h coordna as aralll and rndclar o h channl walls. L and b h loc comonns n and drcons rscl. DOI:.979/ Pag

2 Unsad agnohdrodnamc Soks Flow o Vscos Fld wh Rada Ha ransr DOI:.979/ Pag h qaon o conn s h qaons o momnm ar 3 q 4 h bondar condons ar : w : w cos 5 hod o solon L 6 h rada ha l s gn b q o 4 h qaons -4 bcoms 7 8 o 4 9 L b h sram ncon sch ha h qaon o conn can b sasd b a sram ncon o h orm h loc comonns can b wrn as Eqaons 7 and 8 ar rdcd as o lmna drna and wh rsc o and rscl

3 Unsad agnohdrodnamc Soks Flow o Vscos Fld wh Rada Ha ransr DOI:.979/ Pag d d 3 From and 3 d d 4 Ingrang 4 wh rsc o cons cons 5 ow nrodcng dmnsonlss arabls and aramrs a Ua P W 4 Eqaon 5 bcoms 6 Solng6 A 7 8 Wh bondar condons Solng7 and8 w g A Eqaons 7 and 8 bcoms 9 Usng dmnsonlss arabl θ W W Eqaon 9 s rdcd as P wh bondar condons cos : : o sol 9 l

4 Unsad agnohdrodnamc Soks Flow o Vscos Fld wh Rada Ha ransr DOI:.979/ Pag Eqaon 9 bcoms P Eqang & P whr 3 P whr 4 wh bondar condons / : : Solng and w g sn sn sn sn Fnall h mrar dsrbon s sn sn sn sn 5 From qaon 6 9 and h loc comonns can b oband 6 7 From and 5 d d d d d d Ingrang d Hnc h rssr dro s gn b d 8 III. Rsl And Dscsson h c o Pcl nmbr on mrar dsrbon s shown n grs -3 rscl. I s obsrd ha h mrar ncras wh ncrasng Pcl nmbr or =. s obsrd ha h mrar dcras and sard ncrasng a a cran on wh ncrasng Pcl nmbr or =. And s obsrd ha h mrar ncras and sard dcrasng a a cran on wh ncrasng Pcl nmbr or =3. h c o ssl nmbr on mrar dsrbon s shown n grs 4-6 rscl. I s obsrd ha h mrar ncras wh ncrasng ssl nmbr or P= and P=3 and dcrass or P=.

5 Unsad agnohdrodnamc Soks Flow o Vscos Fld wh Rada Ha ransr IV. onclson In h abo analss a class o solons o h c o rada ha ransr on nsad magnohdrodnamc soks low whn h ld s bng whdrawn hrogh boh h walls o h channl. Aroma solons ha bn oband or loc rols mrar and rssr dsrbon. h conclson o h sd s as ollows. I s obsrd ha h mrar ncras wh ncrasng Pcl nmbr or =. s obsrd ha h mrar dcras and sard ncrasng a a cran on wh ncrasng Pcl nmbr or =. And s obsrd ha h mrar ncras and sard dcrasng a a cran on wh ncrasng Pcl nmbr or =3. I s obsrd ha h mrar ncras wh ncrasng ssl nmbr or P= and P=. Rrncs []. Abol-Hassan A.L and H.A. Aa "Unsad hdromagnc low o a scolasc ld wh mrar dndn scos" an. J. Ph. R. an. Phs. 8: 5-4. []. H.A. Aa and.a. ob 996 " HD low bwn wo aralll las wh ha ransr" Aca chanca 7: 5. [3]. H.A. Aa 999 " HD low and ha ransr bwn wo aralll las wh mrar dndn scos" ch. Rs. omm.6: 5. DOI:.979/ Pag

6 Unsad agnohdrodnamc Soks Flow o Vscos Fld wh Rada Ha ransr [4]. H.A. Aa 4 "Unsad Harmann low wh ha ransr o a scolasc ld consdrng h Hall c" an. J. Phs. an. Phs. 8: [5]. H.A.Aa 5a "h c o scon and njcon on h nsad low bwn wo aralll las wh arabl rors" amkang J. Sc. Engg. 8:7-. [6]. H.A. Aa 5b "h nsad low o a ds condcng ld bwn aralll oros las wh mrar dndn scos" rk J. Phs. 9: [7]. agch. I. 996 "Unsad low o scolasc awll ld wh ransn rssr gradn hrogh rcanglar channl" Ind. J. ch. ah. 4:. [8]. Ezza..Ohman and.hlm 999 "A roblm o a mcroolar HD bondar lar low" an. J. Phs. 77:83. [9]. Hassann. I.A and.a. ansor 99 "Unsad magnc low hrogh a oros mdm bwn wo nn aralll las" Asrohscs sac scnc srngr hrlands 63:4-46. []. Haa.. Y.Wang and.hr 4 "Hall cs on h nsad hdromagnc oscllaor low o a scond grad ld" In. J. onlnar chancs 39: []. rshnambal. S and S. Gansh 4 "Unsad soks low o scos ld bwn wo aralll oros las" aonal conrnc on ahmacal odlng and Analss A 4 IS Plan. h-3: 5-3. []. abl... Eldab and Galal. oamd and H.S. Al 3 "HD low o on-nwonan scolasc ld hrogh a oros mdm nar an acclrad la" an. J. Phs. R. an. Phs. 8: [3]. rshnambal. S and S. Gansh 7 "Unsad magnohdrodnamc soks low o scos ld bwn wo aralll oros las" Jornal o ald scncs Asan nwork or scnc normaon. 73: [4]. Wbsh Ibrahm andar Shankr "Unsad ondar Lar Flow and Ha ransr D o a Srchng Sh b Qaslnarzaon chnq" World Jornal o chancs [5]. Fl Ilsanm Alao Samson aband Folarn 3 "Smlar Solon o h Inlnc o h hrmal Radaon and Ha ransr on Sad omrssbl ondar Lar Flow" On Jornal o Fld Dnamcs DOI:.979/ Pag