HALL CURRENT EFFECTS ON A FLOW IN A VARIABLE MAGNETIC FIELD PAST AN INFINITE VERTICAL, POROUS FLAT PLATE

Transcription

1 IJRRAS 9 () April 4.arpaprss.com/Volums/Vol9Issu/IJRRAS_9 7.pdf ALL CURRENT EFFECTS ON A FLOW IN A VARIABLE MAGNETIC FIELD PAST AN INFINITE VERTICAL, POROUS FLAT PLATE Mark O. Okongo, Gichohi P. Ndritu & Jams M. Mugambi Physical Scincs Dpartmnt, Chuka Univrsity, Knya ABSTRACT In this study, natural convction flo of an incomprssibl fluid past an infinit vrtical flat plat in a variabl magntic fild has bn invstigatd. Th rsarch is don to find th ffcts of all currnt on primary and scondary vlocitis of a fluid. In this cas th flo is considrd as stady and rstrictd to laminar domain. Th quations govrning th flo ar solvd numrically using finit diffrnc mthod. Th diffrnc quations ar thn solvd itrativly for various valus of all currnt paramtr ranging from. to.. This study shos that an incras in th all currnt affcts th vlocity of th fluid. Kyords: Elctron prssur gradint, all currnts, Magntohydrodynamics, Magntic induction vctor, Magntic fild intnsity.. INTRODUCTION ydro magntic is th scinc of th motion or flo of lctrically conducting fluid in th prsnc of a magntic fild. Th situation is on of mutual intraction btn th fluid vlocity fild and th lctromagntic fild. Whn an lctrically conducting matrial (hthr solid or dnsr fluid) movs in a magntic fild, it xprincs a forc that tnds to mov it prpndicularly to th lctric fild. In th cas of a fluid, this happns du to th magntic fild acting on both lctrons and ionizd atoms. Th motion of th lctrically conducting fluid past a magntic fild inducs currnt, a phnomnon knon as all Effct. This inducd currnt in turn producs inducd magntic fild. Lt B b th magntic fild and E b th lctric fild. If th magntic fild B is prpndicular to E, thr ill b an lctromagntic forc. Th rsulting currnt and magntic fild combin to produc a forc that rsists th fluid motion. Th inducd currnt also gnrats its on magntic fild, hich distorts th original magntic fild. If th lctromagntic forc gnratd is of th sam ordr of magnitud as th hydro dynamical and inrtia forcs, th lctromagntic forcs hav to b takn into account in th flo fild. Th first rsarch in magnto hydrodynamics (MD) flos as don by Faraday [] in 839. prformd an xprimnt ith mrcury floing in a glass tub btn th pols of a magnt and proposd th us of tidal currnts in th trrstrial magntic fild for por gnration. Prasada t al [] solvd th problm of MD flo ith avy porous boundary, th influnc of th hat sourc, paramtrs, suction vlocity and avinss of th boundary on th flo fild as numrically analyzd. Kumar t al [3] prsntd thir study on comprssibl magnto hydrodynamic boundary layr in th stagnation rgion of a sphr. Th ffcts of th inducd magntic fild, mass transfr and viscous dissipation r takn into account. Rao t al [4] studid th hat transfr in a porous mdium in th prsnc of transvrs magntic fild. Th ffcts of th hat sourc paramtr and Nusslt numbr r analyzd. Thy discovrd that th ffct of incrasing porous paramtr is to incras th Nusslt numbr. Ram [5] usd th finit diffrnc mthod to analyz th MD stoks problm for a vrtical plat and ion-slip currnts. Dash and Asha [6] prsntd magnto hydrodynamic unstady fr convction ffct on th flo past an xponntially acclratd vrtical plat. Thy obsrvd that xponntial acclration of th plat has no significant contribution ovr th impulsiv motion. Dash and Das [7] considrd hat transfr in viscous flo a long a plan all ith priodic suction and hat sourc. Th ffcts of various paramtrs on th hat transfr in a thr-dimnsional laminar boundary layr past a flat plat in th prsnc of a hat sourc hn a sinusoidal transvrs suction vlocity is applid to th alls r studid. Ram t al [8] analyzd th ffcts of all currnt and all tmpratur oscillation on convctiv flo in a rotation fluid through porous mdium boundd by an infinit vrtical limiting surfac. Th ffct of various paramtrs on th vlocity and shar strss r dtrmind. ong-sn and uang [9] invstigatd som transformations for natural convction on a vrtical flat plat mbddd in porous mdia ith prscribd all tmpratur. Thy analyzd transformation for boundary layr quation for to dimnsional stady natural convction a long a vrtical flat plat, mbddd in a porous mdia ith prscribd all tmpratur. 96

2 IJRRAS 9 () April 4 Kinyanjui t al [] prsntd thir ork on MD fr convction hat and mass transfr of a hat gnrating fluid past an impulsivly statd infinit vrtical porous plat ith all currnt and radiation absorption. An analysis of th ffcts of th paramtrs on skin friction, rats of mass and hat transfr as rportd. Kanza t al [] prsntd thir ork on MD stroks fr convction flo past an infinit vrtical porous plat subjctd to a constant hat flux ith ion-slip and radiation absorption. Th concntration, vlocity and tmpratur distributions r discussd and rsult r prsntd in tabls and graphs. Adl t al [] invstigatd hat and mass transfr along a smi-infinit vrtical flat plat undr th combind buoyancy forc ffcts of thrmal and spcis diffusion in th prsnc of a strong non-uniform magntic fild. Th similarity quations r solvd numrically by using a forth-ordr Rung-Kutta schm ith th shooting mthod. Emad t al [3] studid all currnt ffct on magnto hydrodynamics fr-convction flo past a smi-infinit vrtical plat ith mass transfr. Thy discussd th ffcts of magntic paramtr, all paramtr and th rlativ buoyancy forc ffct btn spcis and thrmal diffusion on th vlocity, tmpratur and concntration. Youn J. [4] invstigatd th unstady to-dimnsional laminar flo of a viscous incomprssibl lctrically conducting fluid in th vicinity of smi-infinit vrtical porous moving plat in th prsnc of a transvrs magntic fild. Th plat movs ith constant vlocity in th dirction of fluid flo, and th fr stram vlocity follos th xponntially incrasing small prmutation la, th ffct of incrasing valus of th suction vlocity paramtr rsults into a slight incras in surfac skin friction for lor valus of plat moving vlocity. It as also obsrvd that for svral valus of Prandtl numbr, th surfac hat transfr dcrass by incrasing th magnitud of suction vlocity. Emad t al [5] studid th ffcts of viscous dissipation and Joul hating on MD fr convction flo past a smi-infinit vrtical flat plat in th prsnc of th combind ffct of all and ion-slip currnt for th cas of th por-la variation of th all tmpratur. Thy found th magntic fild acts as a rtarding forc on th tangntial flo but hav a proplling ffct on th inducd latral flo. Th skin-friction factor for th latral flo incrass as th magntic fild incrass. Th skin- friction factor for th tangntial and latral flos ar incrasd hil th Nusslt numbr is dcrasd if th ffct of viscous dissipation, Joul hating and hat gnration ar considrd all and ion-slip trms r ignord in applying Ohm s la as it has no markd ffct for small and modrat valus of th magntic fild. ayat T t al [6] invstigatd th unstady flo of an incomprssibl fluid in a circular duct mbddd in a porous mdium. Th fluid as mad to conduct in th prsnc of magntic fild and th influnc of all currnt as invstigatd. Laplac transform tchniqu as usd to dtrmin th xact solution for; constantly acclrating flo, suddn startd flo, flo rat of trapzoidal variation ith tim and oscillatory flo. Aftr xamining th govrning quation for an unstady incomprssibl, lctrically conducting fluid in circular duct, thy discovrd that th flo, all Effct and porosity dpnd on th matrial paramtrs. Angail [7], studid th magnto hydrodynamic modl of boundary layr quations for conducting viscous fluids to find th ffct of fr convction currnts ith to rlaxation tims on th flo of a viscous conducting fluid. adoptd th solution of on-dimnsional transint problm to a hol spac ith a plan distribution of hat sourcs. obsrvd that as th Alfvn vlocity th vlocity of th fluid incrasd. This as mainly du to th fact that th ffct of magntic fild tnds to dclrat in fluid particls. also notd that th vlocity incrasd as th Grashof numbr (Gr) incrasd hil it dcrass hn th Prandtl numbr (Pr) incrass. Eldab N.T. t al [8] discussd numrical solutions for problms hich involvd both th hat and mass transfr in hydro magntic flo of a micro polar fluid past a strtching surfac ith Ohmic hating and viscous dissipation using Chbychv finit diffrnc mthod. Various magntic fild paramtrs r usd and thy concludd that dcras in magntic fild paramtrs rsultd to incras in tmpratur and concntration and dcras in vlocity profils. Jordon [9] analyzd th ffcts of thrmal radiation and viscous dissipation on MD fr-convction flo ovr a smi-infinit vrtical porous plat. Th ntork simulation mthod as usd to solv th boundary-layr quations basd on th finit diffrnc mthod. It as found that an incras in viscous dissipation lads to an incras of both vlocity and tmpratur profils, an incras in th magntic paramtr lads to an incras in th tmpratur profils and a dcras in th vlocity profils. Finally an incras in th suction paramtr lads to an incras in th local skin-friction and Nusslt numbr.. PROBLEM FORMULATION: APPROXIMATIONS AND ASSUMPTIONS In simplifying th quations govrning th fluid flo in this study, th folloing assumptions ill b mad;. Liquid mtals and ionizd gass hav prmability, so that rit B ˆ ˆ.. All vlocitis considrd ar much smallr compard to vlocity of light 3. Th fluid flo is rstrictd to a laminar domain. q / c <<. 97

3 IJRRAS 9 () April 4 4. Th fluid is incomprssibl (dnsity is assumd to b constant). 5. Thr is no xtrnal applid lctric fild. 6. Th plat is lctrically non-conducting. 7. Th fluid is considrd to b lctrically conducting ith no surplus lctric charg distribution. 8. Viscosity is assumd to b constant. 9. Thrmal conductivity k is assumd to b constant.. Thr ar no chmical ractions taking plac in th fluid.. Body forcs action on th fluid causd by gravity and magntic filds ar assumd vital in th analysis.. Th forc Ê du to lctric fild is ngligibl compard to th forc J ˆ B ˆ du to th magntic fild. 3. GENERAL GOVERNING EQUATIONS Th quations govrning th flo of an incomprssibl, lctrically conducting fluid in th prsnc of a strong, non-uniform magntic fild ar highlightd in this chaptr. Th quations ar quation of continuity, quation of momntum, nrgy quation, concntration quation, Maxll s quation and Ohm s la. 3.. Equation of Continuity This quation is basd on to propositions: That th mass of th fluid is consrvd. That is mass can nithr b cratd nor dstroyd. That th flo is continuous that is mpty spacs do not occur btn particls hich r in contact. In this cas considr an incomprssibl fluid (i.. dnsity is a constant), thrfor th quation of continuity in tnsor form u t x u x u x If this motion is thr dimnsions, quation 3. in x, y, z componnt bcoms u v x y z Equation of continuity in vctor form u t x Sinc dnsity is constant thn. t Th quation rducs to q hr i j k x y z (3.3) hnc in thr dimnsion i j k ui vj k x y z u v x y z If th flo is along x axis, and th plat is infinit it xtnds and lis along x and z axis thus th physical condition dpnds only on y, thn th quation 3.4 rducs to v y (3.) (3.) (3.3) (3.4) (3.4.a) 98

4 IJRRAS 9 () April 4 Sinc th vlocity gradint is along y axis. On intgrating 3.4a gt V = constant = V (3.4.b) 3. Equation of momntum Th quation of motion is basd on th Nton scond la of motion. Th nt rat of chang of momntum must qual th nt sum of forcs acting on th fluid. Ths quations ar also knon as Navir-Stoks Equation. In vctor notation, th quation of motion considring th body forc du to gravity and lctromagntic forc only is rittn as q q. q p q F t q t q. q hr is th tmporal acclration.. (3.5) is th convctiv acclration and allos for acclration vn hn th flo is stady. p is prssur gradint. q is forc du to viscosity. F is th body forc Considring th body forcs du to gravity and th lctromagntic forc only, thn ths to forcs rplac th body forc. nc q q. q p q F Fg (3.6) t F E J B (3.7) Th lctromagntic forc hr J = currnt dnsity B = Magntic fild E = lctric fild = spac charg Which is approximatd to nc th Navir Stok quation bcoms q t F J B. (3.8) q. q p q g J B. (3.9) E in many flo problms is ngligibly small in comparison ith th lctromagntic Th lctrostatic forc forc J B. Th intraction btn th magntic fild and th flo fild is important in th dynamics of a conducting fluid. Whn th lctromagntic forc F is in th dirction prpndicular to both th magntic fild and th currnt dnsity J thr ill b a significant influnc on th flo fild. Thus th dirction of th magntic fild ill hav a significant influnc on th flo fild. 3.. Equation of nrgy This quation is drivd from th first la of thrmodynamics Th amount of hat addd to a systm dq quals to th chang in intrnal nrgy de plus th ork don dw dq de dw (3.) If hat producd by xtrnal forcs is ignord thn in tnsor form is rittn as p h U jh U jp q j t x t x x j j j (3.) 99

5 IJRRAS 9 () April 4 Whr is th viscous dissipation in thr dimnsion and it is givn by u v u v v v x y z dy y z y x z Whn apply thrmodynamic dfinition of h. dq de dw bcoms p h E. (3.) hr E is th spcific intrnal nrgy. In diffrntial form quation (3.) bcoms dp dh de pd. (3.3) 3.4. Concntration quation This is basd on th principl of mass consrvation for ach spcis in a fluid mixtur. In tnsor form th diffusion quation is Cj J j. (3.4) t x 3.5. Ohm s la j Th la charactrizs th ability of a matrial to transport lctric charg undr th influnc of an applid lctric fild. For an lctrically conducting matrial at rst th currnt dnsity is Jˆ E ˆ (3.5) In moving lctrically conducting fluids th magntic fild inducs a voltag in th conductor of th magnitud ˆq ˆ B Th gnralizd Ohm s la is Jˆ Eˆ qˆ B ˆ. (3.6) Maxll s quation Ths quations provid links btn th lctric and magntic filds indpndnt of th proprtis of th mattr. In this considr th folloing st of quations ˆ Jˆ. Bˆ ˆ ˆ B E. t (3.7) 4. SPECIFIC EQUATIONS GOVERNING FLUID FLOW In this sction th spcific quations govrning incomprssibl fr convction fluid flo in th prsnc of a variabl magntic fild ar drivd. Th magntohydrodynamic flo is considrd past an infinit vrtical porous plat. Th x axis is takn along th plat in vrtical upard dirction, hich is th dirction of th flo

6 IJRRAS 9 () April 4 X-axis Variabl magntic fild Dirction of fluid flo Z-axis Y-axis 4.. Magntic transport quation Combining Maxll s quation and Ohm s la ˆ J ˆ E ˆ V ˆ B ˆ (4.) hr E Vˆ Bˆ ˆ = Magntic fild intnsity Ĥ = Elctrical conductivity = Magntic induction vctor ˆB Ê = Elctric fild 4.. Momntum quation Sinc th fluid is in motion it possss momntum, hnc considr th quation of momntum. qˆ P qˆ qˆ qˆ g Jˆ Bˆ t x. (4.) Th momntum quation is valuatd at th dg of th boundary layr hr bcaus at th boundary layr th vlocity of th fluid is at its minimum. Th prssur gradint in th y dirction rsults from th chang of lvation Thus P g x hr is th dnsity nar th plat. Combining th prssur trm and th body forc trm, givs g g g g g Th vlocity profil at various Y positions is v v qˆ qˆ u v x y v qˆ x andv. This is

7 IJRRAS 9 () April 4 Equation 4. bcoms v v v v u v g Jˆ Bˆ t x y x Th volumtric cofficint of thrmal xpansion T hr T is tmpratur T T T T T T Th currnt dnsity J v B J v. nc th forc trm v. Thus quation 4.3 rducs to, But B J B v v v v v u v g T T v t x y x Dividing both sids by to gt v v v v u v g T T v t x y x In th Z axis dirction, th forc trm J B bcoms Whr is th vlocity of th fluid in th Z dirction nc th quation of momntum in th Z axis ill b u v t x y x. (4.3). (4.4). (4.5) 4.3. Non Dimnsionalization Th non dimnsionalization procss is important bcaus th rsults obtaind for a surfac xprincing on st of conditions can b applid to a gomtrically similar surfac undr diffrnt conditions. Ths conditions may b natur of th fluid, th fluid vlocity or siz of th surfac. In MD flo problms th som non-dimnsional paramtrs ar important and ar dfind as follos Rynolds numbr, R It is th ratio of inrtia forc to th viscous forc if for any flo this numbr is lss than on th inrtia forc is ngligibl and if it is larg, on can ignor viscous forc. R UL UL.

8 IJRRAS 9 () April Grashof numbr, Gr It is th ratio of buoyancy forcs to viscous forcs. If it is larg thn thr is strong convctiv currnt. Gr g T T U Prandtl numbr, Pr It is th ratio of viscous forc to thrmal forc. Th Prandtl numbr is larg hn thrmal conductivity is lss than on and viscosity is larg and it is small hn viscosity is lss than on and thrmal conductivity is larg. Pr C p. k Magntic paramtr/artmann Numbr, M It is th ratio of magntic forc to th viscous forc. M U Eckrt numbr, Ec. It is th ratio of th kintic nrgy to thrmal nrgy. U Ec. CpT T If lt all th variabls ith th suprscript () star to rprsnt dimnsional variabls thn th nondimnsionalization can b basd on th folloing scaling variabls. t v tu v U,, x xu, U, y yu and u u U T T T T Equations 4.4 and 4.5 can b rittn using dimnsional variabls as. v v v v u v gt T t x y x u v t x y x v (4.6) (4.7) Ths ar non-dimnsionalizd as follos x U x x x x x x U x x x U U U x x 3

9 IJRRAS 9 () April 4 v vu y v U U y y y y = v y y U v v vu t v U U 3 v U t t t t t 3 v vu x v U uu v u Uu uu x x x x x 3 v vu y v U vu v v vu vu y y y y y v vu x v U U v x U x x x x x x x x 3 U U v U v x x T T T T, Substituting th abov, quation (4.7) bcoms Uv U v uu v vu v U v g T T t x y x Multiplying by 3 U v v v v g v u v 3 T T t x y x U U But Thus Gr g T T U 3 and M U v v v v u v Gr M v t x y x U t U U 3 U t t t t t 3 U x U uu u uu uu x x x x x 3 U y U vu v vu vu y y y y y U x U 3 x U U U x x x x x x x x x x, U. (4.8) 4

10 IJRRAS 9 () April 4 Substituting ths, quation 4.7 bcoms U U uu vu U t x y x 3 U U u v 3 t x y x U Multiplying both sids by u v t x y x U Thus But U t x y x M u v M. (4.9) 5. Finit diffrnc approximations To giv a rlationship btn th partial drivativ in th diffrntial quation and th function valus at th adjacnt nodal points, us a uniform msh. In this cas th x-y plan is dividd into a ntork of uniform rctangular clls of idth y and hight x. X (i +, k) (i, k ) (i, k) (i, k+) x (i, k) y Y Whr i rfrs to X k rfrs to Y If x rprsnt incrmnt in X thn X=i x. If y rprsnt incrmnt in Y thn Y=k y. Using Taylor s sris xpansion of dpndnt variabls about a grid point (i,k) hav ( i, k ) ( i, k) / // /// 3 ( i, k) y ( i, k)( y) ( i, k)( y ) 6... (5.) ( i, k ) ( i, k) / // /// 3 ( i, k) y ( i, k)( y) ( i, k)( y ) 6... (5.) 5

11 IJRRAS 9 () April 4 Subtracting quation 5. from quation 5. hav / ( i, k) ( i, k ) ( i, k ) / ( i, k) ( i, k ) ( i, k ) y Adding quation 5. to quation 5. rsults to // // ot ( i, k)( y) ( i, k) ot ( i, k ) ( i, k ) ( i, k ) ( i, k) ( i, k ) ( i, k) ot ( y) Th cntral diffrnc formula for th first and scond drivativ ith rspct to x ar / ( i, k) ( i, k) ot x // ( i, k) ( i, k) ( i, k) ( x) ot (5.3) (5.4) (5.5). (5.6) n Lt th msh point variabl at tim t n b dnotd by ( ik, ). Thn th forard diffrnc for th first ordr drivativ ith rspct to tim t ill b / n ( ik, ) n n ( i, k ) ( i, k ) t ot. (5.7) Using forard finit diffrnc for th first ordr tim drivativ and cntral finit diffrnc for th first and scond ordr partial drivativs, thn th govrning quations 4.8 and 4.9 can b rittn in th finit diffrnc form as follos v v v v u v Gr M v t x y x bcoms v v v v v v v v v n n n n n n n n n ( i, k ) ( i, k ) ( i, k ) ( i, k ) n ( i, k ) ( i, k ) ( i, k) ( i, k) ( i, k) u v( ik, ) t x y ( x) Gr M v n n n ( i, k ) ( i, k ) ( i, k ) n Making v th subjct gt ( ik, ) n n n n v( i, k ) v( i, k ) v( i, k ) v n ( i, k ) u v( ik, ) x y n n v( i, k ) v( i, k ) t v v v n n n ( i, k ) ( i, k ) ( i, k ) n n n Gr ( i, k ) M ( i, k ) v( i, k ) ( x) u v M t x y x bcoms. (5.8) n n n n n n n n n ( i, k ) ( i, k ) ( i, k ) ( i, k) n ( i, k ) ( i, k ) ( i, k) ( i, k) ( i, k) u v( ik, ) M t x y ( x) n n ( i, k ) ( i, k ) n Making th subjct hav ( ik, ) 6

12 IJRRAS 9 () April 4 n n n n ( i, k ) ( i, k ) ( i, k ) n ( i, k ) u v( ik, ) x y n n ( i, k ) ( i, k ) t n n n ( i, k ) ( i, k ) ( i, k ) n n M ( i, k ) ( i, k ) ( x). (5.9) In this cas assum that th inducd magntic fild is ngligibl so that th fluid is prmatd by a strong variabl magntic fild of magnitud Th gnralizd Ohm s la including th ffcts of all currnt paramtr is m J J E q P o o o o (5.) hr m is all Currnt paramtr. For short circuit problm, th applid lctric fild E= and for partially ionizd gass th lctron prssur gradint may b nglctd. nc quation (5.) bcoms m J J o q o o In componnt form i j k i j k m J y J y J z v o J This givs z o o y z o. (5.) J m J (5.) and J z m J y v o (5.3) Solving quations (5.) and (5.3) simultanously gt o m v o m v J y and J z m m But nc J J q, y J z z Substituting z v y y m v m v. o o m v m m v m. y and o m v o m this yild z in quations 5.8 and 5.9 gt th final quations as 7

13 IJRRAS 9 () April 4 v v n n ( i, k ) ( i, k ) u v v v v n n n n ( i, k ) ( i, k ) n ( i, k ) ( i, k ) v( ik, ) x n n n n n (, ) (, ) (, ) o m v( i, k ) i k i k i k n ( i, k ) n Gr ( i, k ) M v n ( i, k ) ( x) m v( ik, ) v v v y t. (5.4) u n n n n ( i, k ) ( i, k ) n ( i, k ) ( i, k ) v( ik, ) x n n ( i, k ) ( i, k ) n n n n n ( i, k ) ( i, k ) (, ) o m ( i, k ) v i k ( i, k ) n M n ( ik, ) ( x) m ( ik, ) y t. (5.5) Sinc X-axis is along th infinit vrtical porous plat thn x varis from to infinity. If st i= to corrspond to x and x y. thn hav x i x.. Th initial condition (hr t=) At x= v,, u 5 At x> (, k ) v, ( ik, ) (, k ), u 5 ( ik, ) For i> and all k, th boundary conditions (hr t>) taks th form At x= v (, k), (, k ), u 5 At x () v (, k), (, k ), u 5, For all n. Th computations ar don hn t is small. St t =.5. Th Prandtl numbr is takn as.7 hich corrspond to air. Magntic paramtr M = hich signifis a strong variabl magntic fild. Grashof numbr, Gr > (.4) corrsponding to convctiv cooling of th plat. Rynolds numbr, R < (.6) so that th inrtia forc is ngligibl. Th all currnt paramtr m is varying from,.5,.5,.75,.. 6. RESULTS AND DISCUSSION W analyzd th rsults accruing from th itrations to gt th ffcts of all currnt on th primary vlocity and scondary vlocity. Th rsults ar prsntd in tabls and graphs. 8

14 IJRRAS 9 () April 4 TABLE 5.: TABLE FOR PRIMARY VELOCITY X V V V3 V4 V

15 IJRRAS 9 () April 4 Figur 5.: Graph of primary vlocity Incras in all currnt paramtr rsults dcras in th primary vlocity and th vlocity incrass as mov aay from th plat. This is bcaus incras in all currnt rsults to incras in cyclotron frquncy hich rducs th vlocity of th fluid.

16 IJRRAS 9 () April 4 TABLE 5.:TABLE FOR SECONDARY VELOCITY X W W W3 W4 W

17 IJRRAS 9 () April 4 Figur 5.: Graph of scondary vlocity For small valus of th all currnt, th scondary vlocity fluctuats as mov aay from th plat. But as th all currnt is incrasd th scondary vlocity tnd to b constant (zro). Th fluid particls nxt to th plat hav a vlocity of zro, hovr sinc th flo is laminar, vlocity incrass and dcrass aay from th plat du to th prsnc of th variabl magntic fild. 6.. CONCLUSION An analysis of th ffcts of all currnt on th primary and scondary vlocitis of fluid floing across a variabl magntic fild has bn carrid out. Th spcific govrning quations hav bn solvd by numrically and th rsults hav bn analysd. In this study, it has notd that incras in th all currnt affcts th vlocity of th fluid. ovr du to lack of quipmnts, no xprimntal rsults hav bn obtaind hnc thr is no comparison btn ths numrical valus and xprimntal valus RECOMMENDATIONS MD fluid flos involvs id ara of study among hich hav not bn considrd in this projct. It is rcommndd that futur rsarchrs xtnd this ork considring th folloing;. Th xprimntal rsults of our rsarch to hlp in th comparison to ths numrical rsults.. Fluid flo btn to moving plats across a variabl magntic fild. 3. Flo of fluids ith variabl thrmal conductivity. 4. Flo of fluids ith variabl viscosity. 5. all currnt ffcts on flos in turbulnt boundary layr. 6. Flo of fluids hn th variabl magntic fild is at an angl to th plat.

18 IJRRAS 9 () April 4 REFERENCES []. Faraday, M.: Exprimntal rsarchs in lctricity, Richard and John Edard Taylor (839). []. Prasada, R. and Sivaprasad, R.; MD flo in a channl ith avy porous boundary, Proc. Indian National. Acad.Vol.5A,no.,p.39-46,(985) [3]. Kumar, B. and Sigh, R.P: Rol of porosity and magntic fild on fr convntion flo past an xponntially acclratd vrtical porous plat, modl. Simul. Control B, vol. 3, no. 3, p (99). [4]. Rao, P. S. and Maurthy,M.V.R.:Transint MD flo through a rctangular channl, Proc.Indian Natl.Sci.Acad.Part A,vol 53,p (987). [5]. Ram, P. C.: Finit diffrnc analysis of th MD stoks problm of a vrtical plat ith all and Ion-slip currnts, Astrophys spac scinc 76;p63-7(99) [6]. Dash, G. C. and Das, D.P.: at transfr in viscous flo along a plan all ith priodic suction and hat sourc, Modl.Simulation. control B,vol.7,no.,p.47-55(99) [7]. Dash, G. C. and Das, D.P.: at transfr in viscous flo along a plan all ith priodic suction and hat sourc, Modl.Simulation. control B,vol.7,no.,p.47-55(99) [8]. Ram, P. C.: Finit diffrnc analysis of th MD stoks problm of a vrtical plat ith all and Ion-slip currnts, Astrophys spac scinc 76;p63-7(99) [9]. ong-sn kou and uang, Dr-kun.: Som transformations for natural convction on a vrtical flat plat mbddd in porous mdia ith prscribd all tmpratur, Int. commun. at mass Transfr. vol. 3,no., p (996) []. Kinyanjui, M., Kanza, J. K. and Uppal, S.M: MD fr convction hat and mass transfr of a hat gnrating fluid past an impulsivly startd infinit vrtical porous plat ith all currnt and radiation absorption, Enrgy Convrsion. Mgmt Vol. 4 p (). []. Kanza, J. K. Kinyanjui, M. and Uppal, S.M: MD stoks forc convction flo past an infinit vrtical porous plat subjctd to constant hat flux ith ion-slip currnt and radiation absorption, Far East Journal. Applid Mathmatics. () P. 5-3 (3). []. Adl A. Mgahd, Soliman R. Komy, Ahmd A. Afify. Similarity analysis in magnto hydrodynamics: all ffcts on fr convction flo and mass transfr past a smi-infinit vrtical flat plat. Intrnational journal of Non-linar Mchanics 38, p (3) [3]. Emad M. Aboldahab, Elsayd M.E Elbarbary: all currnt ffct on magnto hydrodynamic fr-convntion flo past a smi-infinit vrtical plat ith mass transfr. Intrnational Journal of Enginring Scinc vol39, p.64-65(). [4]. Youn J. Kim: Unstady MD convctiv hat transfr past a smi-infinit vrtical porous moving plat ith variabl suction. Intrnational Journal of Enginring Scinc 38, 8-845(). [5]. Emad M. Aboldahab, Elsayd M.E Elbarbary: all currnt ffct on magnto hydrodynamic fr-convntion flo past a smi-infinit vrtical plat ith mass transfr. Intrnational Journal of Enginring Scinc vol39, p.64-65(). [6]. ayat, T., Naz, R. and Asghar, S.: all ffcts on unstady duct flo of non-ntonian fluid in a porous mdium. Applid Mathmatics and Computation vol.57 Issu, p.3 4 (4). [7]. Angail, A. S.: Stat spac formulation for magnto hydrodynamic fr convction flo ith to rlaxation tims. Applid Mathmatics and Computation vol.5, Issu, p.99 3 (4). [8]. Eldab, N. T. and Mahmoud, E. M.: Chbyshv finit diffrnc mthod for hat and mass transfr in a MD flo of micropolar fluid past a strtching surfac ith Ohmic hating and viscous dissipation. Applid Mathmatics and Computation vol.77 Issu, p (6). [9]. Jordon J. Z: Ntork simulation mthod applid to radiation and viscous dissipation ffcts on MD unstady fr convction ovr vrtical porous plat. Applid Mathmatical Modling vol3 p.9-33, (7) []. Osalusi E. Sid J. arris R.: Th ffcts of Ohmic hating and viscous dissipation on unstady MD and slip flo ovr a porous rotating disk ith variabl proprtis in th prsnc of all and Ion-slip currnts. Int. Commun. at Mass Transfr. (7), doi;.6/j.ichatmasstransfr []. Alam M.N: Effctivnss of viscous dissipation and Joul hating on stady MD ovr an inclind radiating isothrmal surfac: Communication of Non-linar Scinc and Numrical Simulation.Vol4 Issu5, p3-43(8) 3