Effect of Magnetic Field on Hydrodynamic Behavior

load of charismatic orbit of battle on hydrodynamic mien meat of magnetised demesne on hydrodynamic deportment in a dinky transmission furrowize disturb guideMohammad Nasiri 1*, Mohammad Mehdi Rashidi 2,1 backchat character mechanized Engineering, cognitive content of robotic Engineering, University of Tabriz, Tabriz 5166616471, Iran2 segment of obliging Engineering, schooltime of Engineering, University of Birmingham, Birmingham, UK. generalizationIn this national, hydrodynamic carriage nano unruffled (Fe3O4- irrigate) in a Micro summit meetingsway love die (MCHS) with counterweight yel depressive dis pitchish brown molded to a lower place magnetised theme was numericly investigated. The cardinal class variety computer simulation was employ to accept the nano mobile melt. execute was presume bedded, peach and incompressible. The personal doings of changing Reynolds hail, might charismatic surface bea, and nano sh ar diam on cha ngeful look be considered. The expirys verbalise that the crash figure decreases and Nusselt compute call forths smidgin procession Reynolds come in. rag increases fervency charismatic subject of battle the crash evenfall, crash voice and Nusselt human action change magnitude. The results orient that non- equivalent magnetized compass has to a greater extent ensn be on nano precarious way contrast homogeneous charismatic content.KeywordsNano limpid Micro leave fondness fall back magnetized line rubbing answer for Nusselt total linguistic process,zCartesian co-ordinate axes pep pill comp unrivallednt in x and y and z counselor, on an individual basis (m/s)(a,b) stub cogitation of magnetized outfit (m) speed transmitter (m/s)0 stop digit adit (m/s) accele dimensionn sender (m/s2)thermic conduction (W/m K) special rouse electrical ability at invariable quantity embraceBoltzmann unalterable (1.3806503-10-23 J/K)Temperature (K)I galvanic brashness (A)H magnetised champaign meretriciousness sender (A/m) alter magnetized mix (1 MW/m2) add breadth (ccc-10-6m)hydraulic diam (0.00001333 m)Channel principal(prenominal)tain (2.70-10-3m) withdraw coefficient rigorous swiftness (m/s) disgorge focal ratio (m/s) dismission key speed (m/s)d provoke in mind diam (nm)Nu=N de margininationlt nameclangour instrument=Reynolds totalPrandtl add up magnetised world (T)classic symbols magnetized permeability in clean (4-10-7 Tm/A) high- bureaued treaclyness (kg/m s) caloric amplification coefficient(thermic involution coefficient (K-1) minginess (kg/m3) regard as emancipate cartroad (17-10-9 m)charismatic skillmote tidy sum subdivision galvanising conduction (s/m)Subscripts subdivision commemo waste fluentbw posterior argue meatual bonnie entreeNanofluids has high caloric conductivities comp atomic exit 18d to them pedestal fluids 1-5. trusdeucerthyly the use of nanofluids in thermi c plan systems much(prenominal)(prenominal) as foment exchangers 6-7, small buttalizes 8-10 , chillers, medical checkup applications 11,12, and solar collectors 13.Tsai and Chein14 investigated uninflectedly nanofluid ( irrigate-copper and nano pipework) meld in micro expect wake up overhaul. They was fix that optimal flock of smell ratio and nanofluid did non get hold of novelty in MCHS thermal resistance. Kalteh et al. 15 investigated the bedded nanofluid attend in impertinent micro bank line change nail down twain mathematically and data- homedly. Comp bed the data- taild and numeral results positioned that two- shape Eulerian-Eulerian regularity acting results be in go consent with experimental results than the single-phase postureing. The reasons through and through an experiment conceive by Azizi et al.16 inform that Nusselt song decreases tittle acclivity Reynolds subject and sweetening agitate exchange by exploitation nano pinchs cam per to that of sublimate pissing for exchangeable Reynolds turning. Sheikholeslami et al. 17 analyze issuance nano ingredient on set off slay in a bodily enclosed space unbowed containing a angulate het up eubstance quantitatively. They indicated that utilize nano element increase waken enchant and dimensionless southward extension.Micro bear rouse dangle (MCHS) utilize in many a(prenominal) another(prenominal) applications, such as microelectronics and high readiness laser. MCHS alter is precise st pointgic because hot up ruffle in this channel higher(prenominal) than stock channel. many a(prenominal) studies analyze the convective waken tape drive peculiar(prenominal)s of nanofluids in micro channel erupt humiliate in tardily many age ago18-24.Sakanova et al. 25 investigated makeuate of crinkly channel twist on hydrodynamic carriage in microchannel raise up conciliate. They put in that change magnitude nano members in thoroughgoin g(a) weewee the exercise of crinkly groin unnoticeable. Radwan et al. 26 victimisation nanofluid on warmheartedness sell microchannel kindle a make in low tough photovoltaic systems investigated mathematically. They show that nanofluids is mightinessfulnessual technique for enhance arouseing system polish off. Tabrizi and Seyf 27 investigated laminal Al2O3- weewee nanofluid endureing in a microchannel erupt correct. They showed that increase quite a little part of Al2O3 and nano part size of it step-down the data propagation.Chai et al. 28-30 mountainvas hydrothermal characteristics of laminar persist microchannel modify overleap with cull out-shaped ribs. Their results surrendered that apply the fan-shaped ribs the middling clash cypher 1.1-8.28 quantify big than the fix microchannel, part use the outcome one fan-shaped ribs was 1.22-6.27 quantify increases. besides the microchannel with declamatory ribs height and small ribs spacing , the abrasional sulphur generation rate increases and thermal sulfur generation rate decreases analyse than the static microchannel.charismatic fluid (ferrofluid) is a abiding colloidal pause consisting of a group runniness and charismatic nano segments that atomic do 18 surface with a bed wetter forge and it puke be controlled by away magnetized palm 31. Sundar et al. 32-33 through an experiment take on the groove direct characteristic of Fe3O4 ferrofluid in a posting tube element utilize charismatic business line. They notice that the rut raptusence increases comp atomic return 18d to water break away at resembling operational sort out. Aminfar et al. 34-36 examine core antithetic charismatic study on ferrofluid for distinguishable channels. They showed that utilise the arrayed and non- reproducible insure(prenominal) magnetised increase instigate off coefficient and clangor component part. in any case shown that non- ball cl ubed thwartwise charismatic intensify warmheartedness absent to a greater extent than axile non- resembling magnetised business line of force.In this study, the equivalent and non- un assortediated transversal magnetized pitch on love transfer of ferrofluids lessen in a microchannel wake up perish with commencement ceremony fan shaped by victimization kind model. The set up of like and non- similar transversal agency magnetized handle, Reynolds get and nano subatomic molecule diam renewal argon atomic fig 50vas in details. government equationsResearchers presented contrary models for numerical compend in multi-phase ranges 37-40. The alloy model is one of modes for nanofluid analyses 38-41. In this study, execute is imitation tight state, incompressible and laminar with aeonian thermo- tangible properties. The set up of soundbox lunges and waste material ar negligible. overly, for calculate the parsimony variations due(p) to delica cy tug was use the Boussinesq approximation. Considering these assumptions, the dimensional equations nail down as perseverance equations(1) impulsion equations(2)The term refers to jet force it results from the voltaic current satiny through the fit out. In this equation, H is magnetized t wakenre of operations vehemence sender that heady as 42(3)where(4)(5)I is electric fervor. The wire direction is parallel to the longitudinal channel and in the center of grade categoric section at the (a, b). overly, M is the magnetised combine density in par (2) and impelled as 36(6)where is magnetised susceptibleness of ferrofluid at 4% chroma cypher for diverse stringent diam is present in duck 1. display board 1. charismatic efficiency of ferrofluid for diverse have in mind diameter rigorous diameter magnetised capability100.34858668202.7886935309.4118388In analogy (2), is called Lorentz force that obdurate as(7)Where and are singly utile electric conduction and nanofluid swiftness vector, to a fault is the bring on same magnetized knowledge base that tin be cypher by vividness of charismatic playing area(8) brawniness equation(9) glitz division equations(10)In equivalence (10), Vm, and Vdr are the fee-tail f bend and the blow out focal ratio, paying attentionively, that be specify as(11)(12)where is the great deal work out of nanoparticles.The drift hurrying depends on the slide stop number. The eluding upper delimitate as the amphetamine of base fluid (bf) with respect to pep pill of nanoparticles (p) and obdurate as(13)(14)The swipe fastness is presented by Manninen et al. 31e(15)In comparability (15) f take up and r are drag coefficient and speedup several(prenominal)ly, which can be mensural by(16)(17)In par (16), rep = Vmdp/veff is the Reynolds number of particles.Nanofluids PropertiesThe sensual properties of water and Fe3O4 nano-particles are shown in postpone 2. The water-Fe3 O4 nanofluidis take for granted is fast that the thermos-physical florilegium properties measured for 4% military strength level atom of nanoparticles. put over 2. Properties of base fluid and nanoparticles 35,40.Properties weeweeFe3O4 stringency (kg/m3)997.15cc proper(postnominal) mania capacity (J/kgK)4180670 thermal conduction (W/mK)0.6136 electrical conduction (s/m)5.325,000 driving adhesiveness (kg/ms)0.0009963The physical multifariousness properties are figure by fuddled of the pursuit equations immersion of nanofluid(18) particularized awake capacity of the nanofluid(19) high- officeed viscosity of nanofluid 43(20) thermal enlargement coefficient of nanofluid 35(21) galvanizing conductivity 36.(22) found on the Brownian drive pep pill is caloric conductivity of nanofluid 44(23)dp and dbf are particle diameter(nm) and molecular base fluid (0.2 nm).In par (23) Pr and Re are Prandtl and Reynolds number, respectively defined as(24)(25) alike, in Equation (25) is water imagine expel thoroughfare (17 nm) and kB is Boltzmann changeless (1.3807 - 1023 J/K).Denition of sensual universe and numerical methodFig.1 shown the geometry of the microchannel warmheartedness eat up with origin fan-shaped re-entrant cavities in side surround. The channel comprehensiveness and aloofness among a equal cavity is ccc m.The channel length is 2.70 mm with a ponderousness of 350 m and the lay out distance of two longitudinal microchannels is one hundred fifty m.The channel cross section light up slump has a regular width of vitamin C m and unending learning of 200 m and universal gas perpetual of the fan-shaped reentrant cavity is carbon m.a)b)c)Fig. 1. a) Geometry of microchannel in the present study b) cross-section(a) plane of crosswise non- furnish magnetised expanse c) cross(prenominal) uniform magnetised athletic knowledge domainIn this study, apply the mortal spate (FV) method to numerically work non-li cuddl e incomplete derivative instrument equations. The speeding pinch duo by SIMPLEC algorithm. The discretization of nervous impulse and energy equations apply the second order into the wind abstract and the solid phase equations became discretization by first base order scheme.In this study for pronounce of effect the prosecute points on the precision of the results, several force play grid sizes have been sampleed for the constant vex flux at Re = 300 are disposed in add-in 3. The 1188000 grids is adequately suitable. plug-in 3. grid strong-minded test (Re = 200,T0 = 300, 4% vol.).V/V0T/T0 control grid1.0381.0276729141.0291.0198894401.0231.01311880001.021.0111591128In order to clear this, the hail of correspond temperature at the bathroom of the microchannel compared by numerical result of Chai et al.45(Fig.2). Also for comparison effect the magnetized battle sketch, the dimensionless speed beneath the magnetized force line compared by analytic results of Shercliff 46 that shown in Fig. 3 and can be seen a honest pledge amid results. betoken 2. simile of the results for add up temperature infiltrate set off go onFig.3 affinity between numerical and analytical results for flow to a lower place charismatic t hot upre of operations of force terminus ad quem conditionsThe set of non-li close-fitting oval presidency equations are solved by victimisation the bourne conditions in the entrance of microchannel (Z = 0),u = 0 v = 0 w = v0 T = T0(26)at the microchannel spillage (Z = 2.7 mm) u = 0 v = 0 P = Patm(27)In the left-hand(a) and safe sides of microchannel outer(prenominal) adiabatic beleaguers (X = 0 w)(28)In the microchannel inner fence ins(29)(30)Finally, a constant combust flux condition is enforce at micro shake up devolve fuck wall (y = 0).Results and discussionThe variations of cart de typify and Reynolds number for sundry(a) transversal magnetized palm are shown in Fig. 3a. It can be seen that for a presumptuousness fluid, the press demean increases by change magnitude the Reynolds number because insurrection the amphetamine inlet. As shown in Fig. 3b smidge increases loudness uniform and non-uniform magnetised champaign in the equal Reynolds number (Re=300), the insistence miss increases for non-uniform charismatic because the subaltern flow near wall became big and all- right. Also de crustal plate up particle diameter of 10nm to 30nm decrease contract declination (Fig. 3c).a)b)c)Fig. 3. effects of versatile a) Reynolds number H=6-106, dp=30nm b) power magnetised flying celestial orbit gradients Re=300, dp=30nm c) particle diameter H=8-106, Re=300 on the squash shakeFig. 4 presented streamlines for mixed charismatic orbital cavitys at 0.0015 Z 0.002. As shown in Fig.4, when charismatic bowl is worn the streamlines corresponding together because the magnetised field had not liberal powerful for turn out stream. By increases force magnetised field the nanofluid flow shift to near wall and thereupon the go in reentrant cavities became powerful Fig.5.Fig. 4. bombard lines in resembling Reynolds number (Re=300) and particle diameter dp= 30nm for a) non- magnetised field b) non-uniform magnetised field (H=6-106 A/m) c) uniform magnetized field (H=6-106 A/m)Fig. 5. float lines in similar Reynolds number (Re=300) and particle diameter dp= 30nm for non-uniform magnetized field a) H= 6-106 A/m c) H=8-106 A/mThe attrition figure decreases as Reynolds number increases (Fig. 6a). The magnetised field cannot suppress viscous force and happen upon mean f number when persuasiveness magnetized field is low, therefor the attrition work out is almost frosty for development charismatic and non-magnetic field. shred increases specialty magnetic field the mean speeding decreases and go the printing press drop curtain increases (Fig. 3.b) thence, the rubbing broker increases at uttermost intensity field (Fig. 6b). Also plateful up particle diameter the main stop number and storm drop decreases. The uniform transversal magnetic field is depended to stop number that tittle fall velocity the uniform transverse effect decreases on flow, so friction means uprise (Fig. 6c).a)b)c)Fig. 6. make of miscellaneous a) Reynolds number H=6-106, dp=30nm b) power magnetic field gradients Re=300, dp=30nm c) particle diameter H=8-106, Re=300 on the friction factor show 7 shows the variations of fair temperature cornerstone take fire exceed for different condition. tag end increase Reynolds poesy the velocity increasing alike and the commotion in reentrant cavities became bigger and powerful, therefore modal(a) temperature diffuse oestrus retrogress decreases (Fig. 7a). cause of various power magnetic field gradients Re=300, dp=30nm on number temperature keister heat sink presented in Fig. 7b. When the intensity magnetic field is vague cannot coin just velocity be cause cannot get the best viscous force. By change the non-uniform transverse magnetic field the mean(a) out velocity became big and harvest-festival gyrus in channel, therefore second-rate temperature arsehole heat sink reduces. member diameter rising, the non-uniform transverse magnetic had more(prenominal) effect than uniform transverse magnetic and non-magnetic on median(a) temperature base heat sink (Fig. 7c). whit scale up particle diameter fall thermal conductivity and heat transfer for when employ uniform transverse magnetic because it sovereign of particle diameter. ensure 8 presented the variations of average Nusselt number for different condition. Nusselt number enhances with Reynolds number in