MAGNETO-HYDRODYNAMIC EFFECTS ON SHOCK WAVES PROPAGATION IN ARTERIAL BLOOD FLOW

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1 ian Jnal Sin Rah6(5):4-8 ISSN: ailabl Onlin: h://aj.blih./ GNEO-HYDRODYNI EFFES ON SHOK WVES PROPGION IN RERIL BLOOD FLOW Rid:Jan6 W.I.. Okyad Dan ahai/saii Uniiy P HaP Ha Nigia. Eail: wiakyad@gail. d: Fb6 ba h agni ild n hk wa ain again in h aial bld lw in h n id banh a aind. h qain niniy n ngy gning h nady lw a ld analyially by h hd wa n anin. h id banh a and by h indin a diibd lw nin in h qain niniy. h nding l in n ngy d h lw a al iid. Elii in h hk in h a liy h i dian a whih hk bgin a baind. h l a did qaniaily. I i ablihd ha agni ild nd dlay hk ain whn hy a d nghn h. Kywd: i Bld Flw agni Fild Olw Shk Wa. INRODUION h ai a lagd by a nb dia. ng h diad-iain i h aial in h inn ling h aial al hgh whih bld la h ha. h inn ling h al ni an bal a wdg h lw. F hi a lag an bld jd h nil ding yl lw bak h ha. ainain h ihal ilain ina h l bld jd h nil h ha nlag il in n h alid h l nlag h ding ab i hydali in h lw aiabl []. gd nb wk in lia i n hk wa again in h aial bld lw. F al [] aind hk wa ain in h aa ing h analyi hd haaii baind h dian a whih hk dininii igh ; [] [4] [5] inigad h ndiin nd whih hk wa a d nd ha in ad b hy a d ali na h nan han nid b; ha iiy ha a dlaying n hk ain. Fh [6] [7] [8] [9] inigad h banhing lw n h hk ain bd ha i d h diibin h lw. [] ha a ha agni ild d bld lw; [] inigad h agni ild n h abnal lw ndiin ad by h n n in h ai ing analyial aah h ady laina lw bd ha h all agni ild i ina ian h lw wall ha d h abnalii h lw d igla bndai; [] nidd nially h inln agni ild n h lid lw haaii bld in li-n ai d ha i ina h kin iin a; [4] ad ha lagni ild al nwbn ha a [5] did h lail HD lw in an inlind ahizd ni ay d ha h wall ha ina wih inaing agni ild. hi n a ain h agni ild whih i d ing a ain ing aial in h inn ling h aial al agni Rnan Iaging (RI) h a anning X-aying n aial hk ain again. hi a i ganizd in h llwing a: in i h hyi bl gning qain; in i h hd lin; in 4 hld h l; in 5 i h diin in 6 i h nlin. PHYSIS OF PROBLE ND GOVERNING EQUIONS hi dl i dld n h bai h llwing ain: ai a dinibl ad ha id banh a naind lngidinal in ha nly h ai-yi blging in h b a nidd; h adi h ay i h all han h yial walngh h l ha adial alain a ngld nly h lngidinal gadin aial lid liy a nidd; h lw l aga wih h lal liy nd; bld i ibl Nwnian; h iiy bld ay wih a; h nin bld a in a hgn h alin nn h bld lid ak i agnially ibl I a h lii nn in h aial dina diin hn h qain a balan n ngy gning h lw a: () B J K k () () h din bwn qain () h al ngy qain i h inlin h. ding [5] i ili ha h ngy d in h lai wall h ai i aanid by hal. i a dinibl h h -inal aa ay wih dian h ha h ha (4) (5)

2 ian Jnal Sin Rah 6(5):4-8 5 i dind a h ininiial wa again liy in h lw. By qain (4) (5) qain () b (6) Siilaly qain () an b win a wh J (7) B J J Eqain (6) (7) a wa qain hy ni a hybli qai-lina i d aial dinial qain iila h h n-dininal nady ga dynai. Hn h i h ibiliy ha dininii in h hk wa dl in h lin. Fh w ak h llwing lan: k / [9]) J 8 ( []) ( [4] [5] [6] [7] [8] J.. ( [9]) ding [4] h h ady a l h Hagn- Piill lw an nady lw bl i bjinabl. Hw i i blid ha h n bl i lad a anabl i h iin n h hk wa ain. By h lan qain (6) (7) () b (8) (9) / () Nw qain (8) (9) () a h dl qain. lina binain qain (8) (9) gi hi haaii () hi haaii al hw ha dininii ay dl in h lin. EHOD OF SOLUION h dl qain (8) (9) () a wa qain. Elnay lin lik h h il wa qain ay n b ibl h. Hn w hall k h wa n bain anin hd in whih w a h i a j in h i diai h lin whih aga alng h wa n haaii hgh h igin in h gin n whih ay b inini a in. h + haaii a gin by d d. nd aa h ndibd gin in h -lan h dibd n. L diid h qa lan ( ) in an ndibd gin a dibd gin. h gin a aad by h wa n haaii n whih. In h gin h w a h llwing wa anin: ()... Fh w nid h llwing nain anin anain: k... () : (4) Uing qain () (4) in qain (8) -() ily qaing h iin h w z w ha (5) (6)

3 W.I.. Okyad.al 6 (7) nd :... (8) ) ( - (9) () Uing qain (6) in qain (5) w ha h ha qain (8) (9) b () () Fh qain (6) gi () Sbiing qain () in qain () () adding hi l a liinad w ha: O + (4) hi qain i an dinay dinial qain h Riai y. I aiy h ndiin () wh i h nila d d i h i a hang h nila whn ai al l. l by qain (7) w ha (5) n wking qain ha dd qain () - (5). Vi Flw in Ennially ad b: H ( [8]). > nd h b whih b naw a h aial dian ina < nd b whih b wid a h aial dian ina. Uing 8 whih 8 (6) (7) d d (8) wh 4 h lin qain (8) i (9) Eqain (9) hw ha b inini whn ln () () Hn a hk i d idd I i nwhy ha a = h bl d h a wh lw i ad b inigniian. RESULS h ain i aid ing al ahaial wa. Uing h llwing alii nan al add [6] [6]:.4 i g/. 5 dyn/ 5 /

4 ian Jnal Sin Rah 6(5): /dyn. dyn/()( ).98 al/(g)( O ) ain aling dwn h l w ha h llwing: abl() P diibin wih aiain in ( ) =. =.5 =. = E-.85E-.858 E-.47 E-.4.6E-.68E-.64E-.5478E E-.4E-.44 E-.79E-.8. E-4.E-4.56E-4.974E E-5.568E5.87E5.9 E-5 abl ()a diibin wih aiain in ( ) =. =.5 =. = E.97E-.4 E-.7E.4.85E.87E-.94E-.684E.6.8E.86E-.96E-.57E.8.89E4.9 E-4.5E E4..E5.7 E -5.E-5.67E5 abl() Vliy diibin wih aiain in ( ) =. =.5 =. = E-.7E-.75E.548E E E-.99E.595E E-.9E-.977E.74E-.8.78E4.888 E-4.848E-4.648E E-5.77E-5.784E E-5 abl(4) Shk i wih aiain in ( ) abl(5) P diibin wih aiain in =. =.5 = E-.568E-5.9E-.4.6E-.956E-.46E-.6.45E-.69E-5.778E-.8.E-4.8E-.68E-4..49E-5.494E-5.664E-5 abl(6) a diibin wih aiain in X =. =.5 = E-.6E-5.58E-.4.85E-.4585E-.55E-.6.8 E-.798 E-5.87E-.8.89E-4.87E-.4E-4..4E-5.4E-5.5E-5 abl(7) Vliy diibin wih aiain in =. =.5 = E-.7E-5.75E E-.9876E-.99E E-.9E-5.977E E-4.888E-.848E E-5.77E E-5 abl(8) Shk i wih aiain in E E E E- DISUSSION hi a ain h agni ild diibd lw nin n h hk again in aial bld lw. hi abl - abl 8 hw h agni ild lw aa n h hk ain again. h dndn lw aiabl h a h hk. abl abl 4 hw ha agni ild ina h hk h i hy a likly. h ina in bqnly ina h liy whih in n ina h kini ngy whih i a nin liy. h an wha i n in abl abl. On h h h abl 5 abl 8 hw ha h hk h i hy a likly da wih inaing lw nin. h l h a in agn wih [6] [7] [8] [9]. h n h diibd lw in h hannl d h h ha h liy bqnly d. l h din in h liy d h kini ngy h lw. nd h an h bain nid in abl 5 abl 7. h bl nd nidain ha halh iliain n h ain. h ab i in h a hwi alld hynin hyhia ily ni halh hallng. h ing h ain a agni ild inln ibly a lng i wld aggaa h iain. nly hk a dd in h n h diibd lw. h h lw nin b naal iin nlling hk in aial bld lw. ONLUSIONS h agn-hyddynai n h hk ain again i inigad. h analy hi dl india ha agni ild dlay hk ain whn hy a d nghn h. Shk whih ni halh hallng a nghnd by h n a agni ild. h i i adiabl n h a ain a agni ild inln h a RI a lng i. I i al n ha h lw banh d hk. hy b naal iin nlling hk in aial bld lw.

5 8 knwldgn h ah i hankl P (Ei) E.. kinl Obai wlw Uniiy Il -I Nigia hi gid. Rn [].J. Pdly (h lid hani lag bld l abidg Uniiy P abidg (98).. [] Gg Rding. Shk wa in ahaial dl h aa SE Jnal lid hani l (97). [] H.W. Hgan.H. Si. ahaial hy hk wa ain in aial bld lw a hani (978). [4] E.. kinl R.O. yni. Shk wa in aial bld lw Jnal Nigian ahaial Siy l (98). [5] R.O. yni E.. kinl. On a a h iiy n bld a in h ai Jnal hial Bilgy l (984).. [6]. nilik R.L. Rkwll E. Ogdn. Nnlina analyi l hk wa in ai II Z. ngnw ah.phy l (97). [7].J. Van d W. Signiian aa in aial liy dln J. Bihani l (974).. [8] Kiiy llin. Nnlina wa again in ilai b: aliain ai Jnal Bihani l (974). [9].H. Si. On dling diibd lw in n-dininal dl aial bld lw Jnal lid ahai Phyi (ZP) (98). [].N. Sndk.. Pnika K.V. Za Ian. Ha an Si Rah l.. 96 (978). [].F. Banhy. Bilgial agni ild Pln P Nw Yk (969). [] B.. hakhaa N. Rdaiah. HD lw hgh a hannl aying ga Indian Jnal P lid ah l (98). [] B. ahih. agablh. agni ild n ha an lid lw haaii n bld lw in ni ai Ha a an l. 44() (8). [4]SinDaily. Inba lagni ild al nwbn ha a ihigan Sa Uniiy U.S. (8 ay 8) [5].K. Shaa S. Singh S. Baal. Plail HD lw in an inlind ahizd nd ay wih li n h wall Jnal Bihanial Sin Engining l. 44().97-7 (4). [6] G. aih D. aida G. Pkin Sl. ahaial Biin l. 5 9 (98). Li Sybl -inal aa h ay ii ha aaiy h lid a nan l iinal iin a ady lw in ila b a lw Rynld nb J n l ni lngh h b k hal ndiiy h lid Haann nb a nn-ngai nin whih dl h aying lakag alng h b innal din a h wall h b a j in h aiabl a nan akn a h aillay a h lid a n a a j in h a aiabl liy lw alng h aial diin a j in h liy aiabl aial dina a ii nan an nnial a h aing h b dniy h lid ha an iin a nan iiy a nin a h an b aid any nan. l lw ni lngh hgh h wall lal Day nb. lial ndiiy h lid B agni lid l kinai iiy h lid agni abiliy h bld lid abiliy iin h wall h b n h wall h b ngy l ni lngh hgh h wall. W.I.. Okyad.al

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