FINITE ELEMENT ANALYSIS OF UNSTEADY MHD FREE CONVECTION FLOW PAST AN INFINITE VERTICAL PLATE WITH SORET, DUFOUR, THERMAL RADIATION AND HEAT SOURCE

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1 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om FIIE ELEME AALYSIS OF SEAY MH FREE OVEIO FLOW AS A IFIIE VERIAL LAE WIH SORE FOR HERMAL RAIAIO A HEA SORE J. Anand Rao. Ramsh ab and R. Snvasa Ra 3 pamn of Mahmas nvs ollg of Sn Osmana nvs Hdabad langana Sa Inda pamn of Mahmas S Koam las Rdd Mmoal ollg of Engnng Konda Vllag Ial Mandal Mahaboob aga langana Sa Inda 3 pamn of Mahmas GIAM nvs Hdabad amps Rdaam langana Sa Inda E-Mal: amsh.paa@ahoo.n ASRA A sd has bn ad o o analz h ombnd ffs of So hmal-dffson and fo dffsonhmo on an nsad magnohdo dnam f onvon flo pas an nfn val pla n a poos mdm n psn of hmal adaon and ha so. A nfom magn fld as ppndla o h poos sfa. Eng qaon as no aon of vsos dsspaon hmal adaon and fo ffs. h govnng dffnal qaons a ansfomd no a s of non-lna opld paal dffnal qaons and solvd sng smla analss h nmal hnq sng appopa bonda ondons fo vaos phsal paams. h dmnsonlss govnng qaons a solvd nmall sng Galn fn lmn mhod. Favoabl ompasons h pvosl pblshd o on vaos spal ass of h poblm a oband. h ffs of vaos phsal paams on h dmnsonlss vlo mpa and onnaon pofls a psnd gaphall. In addon h loal vals of h Sn-fon offn ssl nmb and Shood nmb a also shon n abla fom. Kods: so and dfo hmal adaon ha so MH galn fn lmn mhod.. IROIO onvon flos n poos mda hav gand sgnfan anon n h n as bas of h mpoan n ngnng applaons sh as gohmal ssms sold max ha xhangs hmal nslaons ol xaon and so of nla as maals. hs an also b appld o ndgond oal gasfaon gond a hdolog all oold aal aos ng ffn dng posss and naal onvon n ah s s. h nsad MH ansn f onvon flo of an nompssbl vsos lall ondng fld bn o nfn val paalll poos plas h vaabl mpa and mass dffson has bn sdd b Rap and Sah nd h assmpon ha h ndd magn fld s nglgbl. Appld magn fld s fxd lav o h fld and plas. h Lapla ansfom mhod has bn sd o fnd h solons fo h vlo mpa and onnaon pofls. Anand Rao and Snvasa Ra nvsgad appld magn fld on ansn f onvv flo of an nompssbl vsos dsspav fld n a val hannl. El-Amn onsdd h MH f onvon and mass ansf flo n a mopola fld ov a saona val pla h onsan son. hadha and Shama 6 onsdd ombnd ha and mass ansf b lamna mxd onvon flo fom a val sfa h ndd magn fld. Hdomagn nsad mxd onvon and mass ansf flo pas a val poos pla mmsd n a poos mdm as nvsgad b Shama and hadha 8. Kandasam al. 5 dsssd ha and mass ansf ff along a dg h ha so and onnaon n h psn of son/non ang no aon h hmal aon of fs od. Whn hnologal posss a pla a hgh mpas hmal adaon ha ansf has bom v mpoan and s ffs anno b ngld. h ff of adaon on MH flo ha and mass ansf bom mo mpoan ndsall. Man posss n ngnng aas o a hgh mpa and noldg of adaon ha ansf boms a v mpoan fo h dsgn of h pnn qpmn. h qal of h fnal pod dpnds o a ga xn on h ha onollng faos and h noldg of adav ha ansf n h ssm an lad o a dsd pod h sogh qals. h ffs of vaabl vsos and hmal aon ffs on flo ha and mass ansf haass n a vsos fld ov a poos dg n h psn of ha adaon sdd b Kandasam al. 7. h all of h dg s mbddd n a nfom aan poos mdm n od o allo fo possbl fld all son o non. h govnng bonda la qaons a n no a dmnsonlss fom b smla ansfomaons. h ansfomd opld nonlna odna dffnal qaons a solvd nmall b sng h R. K. Gll and shoong mhods. h ffs of hmal adaon on nsad f 5338

2 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om onvon flo pas an xponnall alad nfn sohmal val pla h mass ansf n h psn of magn fld b Rash and Vaa Kma Vama 9. h fld onsdd h s a ga absobng/mng adaon b a non-sang mdm. h govnng qaons a solvd n losd fom b h Lapla ansfom hnq. h adaon ff on nsad ha and mass ansf flo of a hmall ang fld pas a sm-nfn val pla h vsos dsspaon sdd b Snvasa Rao and Anand ab. nsad MH flo adaon and mass ansf of a vsos nompssbl ondng fld pas on mplsvl sad nfn val poos pla h vaabl mpa n h psn of homognos hmal aon s sdd b Anand Rao al.. h govnng qaons a solvd b sng h fn lmn mhod. Radaon ffs on MH flo hogh poos mda pas an mplsvl sad val osllang pla h vaabl mass dffson s sdd b Rap and Snda Kma. h fld onsdd s ga absobng-mng adaon b a non-sang mdm. h govnng qaons nvolvd n h psn analss a solvd b h Lapla ansfom hnq. Va Kma al. 3 nvsgad h ffs of h ha so hmal aon and adaon absopon on nsad MH flo h ha and mass ansf of an nompssbl vsos lall ondng fld pas an nfn val movng pla h onsan mpa n h psn of ansvs appld magn fld. An xa solon fo h flo poblm has bn oband b solvng h govnng qaons sng Lapla ansfom hnq. Infln of vsos dsspaon and adaon on nsad MH f onvon flo pas an nfn had val pla n a poos mdm h mdpndn son sdd b Isal-oo al. 3. n h abov mnond sds fo and So ms hav bn ngld fom h ng and onnaon qaons spvl. I has bn fond ha ng flx an b gnad no onl b mpa gadn b also b onnaon gadn as ll. h ng flx asd b onnaon gadn s alld fo ff and h sam b mpa gadn s alld h So ff. hs ffs a v sgnfan hn h mpa and onnaon gadn a v hgh. Mohammad Al and Mohammad Shah Alam dsssd h ff of So and Hall n d o ha gnaon on opld ha and mass ansf b magnohdodnam f onvon ov a pmabl val shng sh. h govnng bonda la qaons a fomlad and ansfomd no a s of smla qaons sng dmnsonlss smla vaabls. h govnng fndamnal s of a ssm of non-lna loall smla odna dffnal qaons a solvd nmall b Rng-Ka foh-ffh od ngaon shm along h shoong hnq. h ffs of Hall ns So and fo on an nsad magnohdodnam flo and ha ansf along a poos fla pla h mass ansf sdd b Anand Rao and Snvasa Ra. osln sdd smlanos ha and mass ansf b naal onvon fom a val pla mbddd n lall ondng fld saad poos mdm sng a-ossnsq s modl nldng So and fo ffs. Aff 9 ad o an analss o sd f onvv ha and mass ansf of an nompssbl lall ondng fld ov a shng sh n h psn of son and non h hmal-dffson and dffson-hmo ffs. Alam al. 6 sdd nmall h fo and So ffs on ombnd f-fod onvon and mass ansf flo pas a sm-nfn val pla nd h nfln of ansvsl appld magn fld. Manso al. 8 nvsgad h ffs of hmal aon hmal safaon So and fo nmbs on MH f onvv ha and mass ansf of a vsos nompssbl and lall ondng fld ov a val shng sfa mbddd n a saad poos mdm. Osals al. 8 nvsgad hmo dffson and dffson-hmo ffs on ombnd ha and mass ansf of a sad hdomagn onvv and slp flo d o a oang ds n h psn of vsos dsspaon and Ohm hang. h ffs of hmal adaon and Ha so on an nsad MH f onvon flo pas an nfn val pla h hmal-dffson and dffson-hmo dsssd b Snvasa Ra al. 3. In sp of all hs sds h fo and So ffs on nsad MH f onvv ha and mass ansf pas an nfn val pla mbddd n a poos mdm n h psn of hmal adaon and ha so has vd ll anon. Hn h ppos of hs pap s o xnd Isal-oo al. 3 o sd h mo gnal poblm hh nlds hmal adaon Ha so So and fo on nsad MH f onvv flo pas an nfn val pla. h momnm hmal and solal bonda la govnng qaons a ansfomd no a s of paal dffnal qaons and hn solvd sng Galn fn lmn mhod. h ffs of vaos govnng paams on h vlo mpa and onnaon pofls as ll as h loal sn-fon offn loal ssl nmb and loal Shood nmb a psnd gaphall and n abla fom. h s of h pap s sd as follos. In Son fomla h poblm n Son 3 gv h mhod of solon. O sls a psnd and dsssd n Son and n Son 5 psn som bf onlsons. 5339

3 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om 53 Fg-. h phsal modl and oodna ssm of h poblm. FORMLAIO OF HE ROLEM W onsd h nsad flo of an nompssbl vsos adang hdomagn fld pas an nfn poos had val pla h mdpndn son n an opall hn nvonmn. h phsal modl and h oodna ssm a shon n Fg-. h x axs s an along h val nfn poos pla n h pad don and h axs nomal o h pla. A m h pla s manand a a mpa hh s hgh nogh o na adav ha ansf. A onsan magn fld o H s manand n h don and h pla movs nfoml along h posv x don h vlo. nd ossnsqs appoxmaon h flo s govnd b h follong qaons: Eqaon of onn Momnm Eqaon g g H * Eng qaon Q q S m o z 3 Eqaon of adav ha flx q q z z Sps dffson qaon m m 5 h ospondng bonda ondons a as a all fo : : 6 Sn h mdm s opall hn h lavl lo dns and h adav ha flx gvn b qaon n h sp of ogl al. 968 boms q z 7 Wh 8 H s a fqn. Fh fom qaon s la ha s a onsan o a fnon of m onl and so assm A 9 Sh ha A and h ngav sgn ndas ha h son vlo s oads h pla. In v of qaons 8 and 9 qaons 3 and 5 bom

4 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om 53 Momnm qaon G G M A Eng qaon S R A Sps dffson qaon S S A S S Wh hav sd h follong dmnsonlss vaabls: S S H M Q S R g G g G o S m m o m p o p * 3 Eqaons and a no sb o h bonda ondons as on all fo : : h mahmaal samn of h poblm s no ompl and mbods h solon of qaons and sb o bonda ondons. h Sn-fon ssl nmb and Shood nmb a mpoan phsal paams fo hs p of bonda la flo. h Sn-fon a h pla hh n h nondmnsonal fom s gvn b o v 5 h a of ha ansf offn hh n h non-dmnsonal fom n ms of h ssl nmb s gvn b x R x 6 h a of mass ansf offn hh n h non-dmnsonal fom n ms of h Shood nmb s gvn b x Sh R x Sh 7 Wh x o R s h loal Rnolds nmb.

5 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om MERIAL SOLIO Y FIIE ELEME MEHO applng Galn fn lmn mhod fo qaon ov h lmn s: d 8 Wh G G M A ; Ingang h fs m n qaon 8 b pas on obans d 9 glng h fs m n qaon 9 on gs: d L b h lna ps appoxmaon solon ov h lmn h and a h bass fnons. On obans: d d d d d Smplfng g 6 6 l l Wh pm and do a dnos dffnaon h sp o and m spvl. Assmblng h lmn qaons fo o onsv lmns and follong s oband:

6 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om l 6 6 l o p o ospondng o h nod o zo fom qaon h dffn shms h l h s: h 6 h 6 Applng h apzodal l follong ssm of qaons n an-holson mhod a oband: n n n n n n * A A A3 A A5 A6 o fom qaons and follong qaons a oband: 3 n n n n n n * Q n n n n n n * R Wh A h A 8 8 A h A 3 h A 8 8 A h 6 5 h R S 8 8 6R 6 S 3 h R S h R S R 6 S 6 h R S S h 8 S 8 S S h 3 S S h 8 S S S h * G * Q Q 8 ** * R R 8 S S ; H = and h a msh szs along - h don and m-don spvl. Indx fs o spa and fs o h m. In h qaons 3 and ang n and sng bonda ondons hn h follong ssm of qaons a oband: A X fo n 5 h A s a mas of od n and X s a olmn mas havng n -omponns. h solons of abov ssm of qaons a oband b sng homas algohm fo vlo mpa and onnaon. Also nmal solons fo hs qaons a oband b MALA-pogamm. In od o pov h onvgn and sabl of Galn fn lmn mhod h sam MALA-pogamm as n h small vals of h and no sgnfan hang as obsvd n h vals of and. Hn h Galn fn lmn mhod s sabl and onvgn. 533

7 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om RESLS A ISSSIOS In h pvos sons hav fomlad and solvd h poblm of an nsad MH f onvon flo pas an nfn had val pla n a poos mdm h hmal-dffson dffson-hmo adaon and ha so. nvong h opall hn dffnal appoxmaon fo h adav ha flx n h ng qaon. In h nmal ompaon h andl nmb. 7 hh osponds o a and vaos vals of h maal paams a sd. In addon h bonda ondon s appoxmad b max hh s sffnl lag fo h vlo o appoah h lvan sam vlo. h mpa and h sps onnaon a opld o h vlo va Gashof nmb G and Modfd Gashof nmb G as sn n qaon. Fo vaos vals of Gashof nmb and Modfd Gashof nmb h vlo pofls a plod n Fg- and Fg-3. h Gashof nmb G sgnfs h lav ff of h hmal boan fo o h vsos hdodnam fo n h bonda la. As xpd s obsvd ha h s a s n h vlo d o h nhanmn of hmal boan fo. Also as G nass h pa vals of h vlo nass apdl na h poos pla and hn das smoohl o h f sam vlo. h Modfd Gashof nmb G dfns h ao of h sps boan fo o h vsos hdodnam fo. As xpd h fld vlo nass and h pa val s mo dsnv d o nas n h sps boan fo. h vlo dsbon aans a dsnv maxmm val n h vn of h pla and hn dass popl o appoah h f sam val. I s nod ha h vlo nass h nasng vals of Modfd Gashof nmb G. Fg- llsas h vlo pofls fo dffn vals of andl nmb. h nmal sls sho ha h ff of nasng vals of andl nmb sl n dasng vlo. h na of vlo pofls n psn of fogn sps sh as Hdogn S =. Hlm S =. Oxgn S =.6 and Wa vapo S =.66 a shon n Fg-5..5 G = 3 3 Fg-. Vlo pofls fo dffn vals of G. G = 3 3 Fg-3. Vlo pofls fo dffn vals of G. h flo fld sffs a das n pma vlo a all pons n psn of hav dffsng sps. h ff of h magn fld paam M s shon n Fg-6 n as of oolng of h pla. I s obsvd ha h vlo of h fld dass h h nas of h magn fld paam vals. h das n h vlo as h Hamann nmb M nass s bas h psn of a magn fld n an lall ondng fld nods a fo alld h Lonz fo hh as agans h flo f h magn fld s appld n h nomal don as n h psn sd. hs ssv fo slos don h fld vlo omponn as shon n Fg-6. h vaaons of vlo dsbon h fo dffn vals of h fo nmb and So nmb S a shon n Fg-7 and Fg-. I an b lal sn ha h vlo dsbon n h bonda la nass h h fo and So nmbs. 53

8 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om.8 = = Fg-. Vlo pofls fo dffn vals of..6 Fg-7. Vlo pofls fo dffn vals of..8 S = R = Fg-5. Vlo pofls fo dffn vals of S..6 Fg-8. Vlo pofls fo dffn vals of R..6 M = 3 S = Fg-6. Vlo pofls fo dffn vals of M. Fg-9. Vlo pofls fo dffn vals of S. h ff of h hmal adaon paam R on h pma vlo and mpa pofls n h bonda la a llsad n Fg-8 and Fg-5 spvl. Inasng h hmal adaon paam R pods sgnfan nas n h hmal ondon 535

9 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om of h fld and s hmal bonda la. hs nas n h fld mpa nds mo flo n h bonda la asng h vlo of h fld h o nas. Fg-9 and Fg- has bn plod o dp h vaaon of vlo and mpa pofls agans fo dffn vals of ha so paam S b fxng oh phsal paams. Fom hs Gaph obsv ha vlo and mpa das h nas n h ha so paam S bas hn ha s absobd h boan fo dass h mpa pofls. Fg- shos h ffs of a nmb on h vlo pofls fo oolng as ll as hang of h pla. Fo a oolng pla fld vlo nass has fo a hang pla dass h nas of. a nmb s h masmn of h poos of h mdm. As h poos of h mdm nass h val of nass. Fo lag poos of h mdm fld gs mo spa o flo as a onsqn s vlo nass. Fg- llsas h mpa pofls fo dffn vals of andl nmb. I s obsvd ha h mpa das as an nasng h andl nmb. h ason s ha small vals of a qvaln o nas n h hmal ondv of h fld and hfo ha s abl o dffs aa fom h had sfa mo apdl fo hgh vals of. Hn n h as of small andl nmb h hmal bonda la s h and h a of ha ansf s dd. h fo nmb dos no n dl no h momnm and mass qaons. hs h ff of fo nmb on vlo and mass pofls s no appan...8 S = 3. 3 Fg-. Vlo pofls fo dffn vals of S. = θ.5 3 Fg-. mpa pofls fo dffn vals of..5 χ = 3 θ.5 = 3 3 Fg-. Vlo pofls fo dffn vals of. 3 Fg-3. mpa pofls fo dffn vals of. 536

10 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om θ.5 R = 3 3 Fg-5. mpa pofls fo dffn vals of R. Fg-. mpa pofls fo dffn vals of S. Fg-3 shos h vaaon of mpa pofls fo dffn vals of. h paam has mad ffs on h mpa pofls. I s obsvd ha h mpa pofls nas h h nasng vals of. I s also obsvd fom hs fg ha hn =. ha s hn h ao bn mpa and onnaon gadn s v small h mpa pofl shos s sal nd of gadal da. As fo nmb boms lag h pofls ovshoo h nfom mpa los o h bonda. h ffs of Shmd nmb S and So nmb S on h onnaon fld a psnd n Fg-6 and Fg-7. abl-. Vaaon of nmal vals of Sn-fon fo dffn vals of G G S M S S and R. G G S M S S R

11 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om abl-. Vaaon of ssl nmb fo dffn vals of S and R. S R abl-3. Vaaon of Shood nmb Sh fo dffn vals of S and S. S S Sh * abl-. ompason of psn Sn-fon sls h h Sn-fon sls oband b Isal-oo al. 3 fo dffn vals of G M and R. G M R * Fg-6 shos h onnaon fld d o vaaon n Shmd nmb S fo h gasss Hdogn Hlm Wa-vapo Oxgn and Ammona. I s obsvd ha onnaon fld s sadl fo Hdogn and falls apdl fo Oxgn and Ammona n ompason o a-vapo. hs Hdogn an b sd fo mananng ffv onnaon fld and Wavapo an b sd fo mananng nomal onnaon fld. In Fg-7 s obsvd ha an nas n h So nmb S lads o nas n h onnaon fld. abl- shos h vaaon of dffn vals G G S M S S and R on Snfon. Fom hs abl s onldd ha h Snfon nass as h vals of G G S and nas and hs bhavo s fond s vs h h nas of S M S and R. abl- shos h vaaon of ssl nmb dffn vals of S and R. Fom hs abl s onldd ha h ssl nmb nass as h val of nass and hs bhavo s fond s vs h h nas of S and R. abl-3 shos h vaaon of Shood nmb Sh dffn vals of S and S. Fom hs abl s onldd ha Shood nmb Sh nas as h val of S nass and hs bhavo s fond s vs h h nas of S. In od o asan h aa of h nmal sls h psn sn-fon sls a * ompad h h pvos sn-fon sls of Isal-oo al. 3 n abl-. h a fond o b n an xlln agmn. OLSIOS In onlson hfo h flo of an nsad MH f onvon pas an nfn had val pla 538

12 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om n a poos mdm nd h smlanos ffs of hmal-dffson dffson-hmo adaon and ha so s affd b h maal paams. h govnng qaons a appoxmad o a ssm of lna paal dffnal qaons b sng Galn fn lmn mhod. h sls a psnd gaphall and an onld ha h flo fld and h qans of phsal ns a sgnfanl nflnd b hs paams. a h vlo nass as Gashof nmb G Modfd Gashof nmb G fo nmb and So nmb S nass. Hov h vlo as fond o dass as h Hamann nmb M andl nmb Shmd nmb S hmal adaon paam R Ha so paam S and a paam a nass. b h fld mpa as fond o dass as h hmal adaon paam R Ha so paam S and andl nmb a nass and fond o nas as fo nmb nass. h fld onnaon as fond o dass as h Shmd nmb S and nass as h So nmb S nass. d Fom abl- s onldd ha h Snfon nass h h nasng vals of G G S and and hs bhavo s fond s vs h h nasng of S M S and R. Fom abl- s onldd ha h ssl nmb nass h h nasng vals of and hs bhavo s fond s vs h h nasng of S and R. f Fom abl-3 s onldd ha h Shood nmb Sh nass h h nasng vals of S and hs bhavo s fond s vs h h nasng of S. g On ompang h Sn-fon sls * h h Sn-fon sls of Isal-oo al. 3 n abl-. I an b sn ha h ag v ll. omnla A Small posv paam Wall mpa Rfn mpa mnsonal f sam vlo g v x mnsonal m Alaon d o gav mnsonal son vlo mnsonal vlo omponns mnsonal asan oodnas H onsan ansvs magn fld mnsonal poos paam Spf ha apa p s M G G S S m R onnaon sspbl on-dmnsonal Hamann nmb andl nmb Gashof nmb Modfd Gashof nmb Shmd nmb So nmb fo nmb hmal dffsv Molla dffsv Man absopon offn onnaon mnsonlss onnaon onnaon na h pla onnaon n h fld fa aa fom h pla Radaon paam Man vlo of qz S Radav ha flx lan s fnon Ha so G smbols Small posv paam offn of Volm xpanson 539

13 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om * Volm offn of Expanson h onnaon v Knma vsos Elal ondv mabl Fld dns mnsonal f sam fqn of osllaon hmal ondv Absopon offn a nmb REFEREES Radaon absopon offn Rap S and Sah K.. ansn f onvon MH flo bn o long val paalll poos plas h vaabl mpa and mass dffson. AR Jonal of Engnng and Appld Sns. 68: Anand Rao J and Snvasa Ra R.. Appld magn fld on ansn f onvv flo of an nompssbl vsos dsspav fld n a val hannl. Jonal of Eng Ha and Mass ansf. 3: El-Amn MF.. Magnohdodnam f onvon and mass ansf flo n mopola fld h onsan son. Jonal of Magnsm and Magn Maals. 33: hadha R and Shama K. 6. ombnd ha and mass ansf b lamna mxd onvon flo fom a val sfa h ndd magn fld. Jonal of Appld hss. 993: Shama K and hadha R. 8. Hdomagn nsad mxd onvon and mass ansf flo pas a val poos pla mmsd n a poos mdm h hall ff. Engnng ansaons. 56: 3-3 Kandasam R asam K and ash Svagnana KK. 5. Effs of hmal aon ha and mass ansf along dg h ha so and onnaon n h psn of son o non. Innaonal Jonal of Ha and Mass ansf. 87: Kandasam R Hashm I Mhamn and Rhala. 7. Effs of vaabl vsos. Ha and mass ansf on nonlna mxd onvon flo ov a poos dg h ha adaon n h psn of homognos hmal aon. AR Jonal of Engnng and Appld Sns. 5: -53 Rash V and Vaa Kma Vama S. 9. Radaon and mass ansf ffs on MH f onvon flo pas an xponnall alad val pla h vaabl mpa. AR Jonal of Engnng and Appld Sns. 6: -6 Snvasa Rao V and Anand ab L.. Fn lmn analss of adaon and mass ansf flo pas smnfn movng val pla h vsos dsspaon. AR Jonal of Engnng and Appld Sns. 5: -6. Anand Rao J Svaah S and sln S.. Radaon ffs on an nsad MH val poos pla n h psn of homognos hmal aon. AR Jonal of Engnng and Appld Sns. 77: Rap S and Snda Kma.. Radaon ffs on MH flo hogh poos mda pas an mplsvl sad val osllang pla h vaabl mass dffson. AR Jonal of Engnng and Appld Sns. 7: 8-3. Vaa Kma AG Ravnda ab K Rddappa and Vama SVK. 3. Effs of hmal aon and adaon absopon on h nsad MH f onvv flo pas an nfn val movng pla h onsan ha so. AR Jonal of Engnng and Appld Sns. 85: Isal-oo Ogl A and Ombo-ppl V. 3. Infln of vsos dsspaon and adaon on nsad MH f onvon flo pas an nfn had val pla n a poos mdm h m-dpndn son. Innaonal Jonal of Ha and Mass ansf. 6: Mohammad Al and Mohammad Shah Alam.. So and Hall Eff on MH flo. Ha and mass ansf ov a val shng sh n a poos mdm d o ha gnaon. AR Jonal of Engnng and Appld Sns. 93: Anand Rao J and Snvasa Ra R.. h ffs of Hall ns. So and fo on MH flo and ha ansf along a poos fla pla h mass ansf. Jonal of Eng Ha and Mass ansf. 33:

14 VOL. O. JLY 5 ISS AR Jonal of Engnng and Appld Sns 6-5 Asan Rsah blshng o AR. All ghs svd..apnonals.om osln A. Infln of a magn fld on ha and mass ansf b naal onvon fom val sfas n poos mda onsdng So and fo ffs. Innaonal Jonal of Ha and Mass ansf. 76-7: Aff AA. 9. Smla solon n MH ffs of hmal-dffson and dffson-hmo on f onvv ha and mass ansf ov a shng sfa onsdng son and non. ommnaons onlna Sn and mal Smlaon. : -. Alam S Rahman MM Malq A and Fdos M. 6. fo and So ffs on sad MH ombnd f fod onvv and mass ansf flo pas a sm nfn val pla. hammasa Innaonal Jonal Sn and hnolog.. Manso MA El-Anssa F and Al AM. 8. Effs of hmal aon and hmal safaon on MH f onvv ha and mass ansf ov a val shng sfa mbddd n a poos mda onsdng So and fo nmbs. hmal Engnng Jonal. 5: Osals Sd E and Has R. 8. hmal-dffson and dffson-hmo ffs on ombnd ha and mass ansf of sad MH onvv and slp flo d o a oang ds h vsos dsspaon and Ohm hang. Innaonal ommnaons n Ha and Mass ansf. 35: Snvasa Ra R Sdhaa K and Rangamma M. 3. h ffs of hmal adaon and Ha so on an nsad MH f onvon flo pas an nfn val pla h hmal-dffson and dffsonhmo Jonal of Inson of Engns Inda: Ss. 9: ogl A Vnn WG and Glls SE ffnal appoxmaon fo adav ansf n a on-g gas na qlbm. Aman Ins of Aonas and Asonas. 6: