Effect of Magnetic Field on Hydrodynamic Behavior

Effect of magnetized Field on hydrodynamic BehaviorEffect of Magnetic Field on hydrodynamic mien in a micro line of business hop up SinkMohammad Nasiri 1*, Mohammad Mehdi Rashidi 2,1 incision Mechanical Engineering, Faculty of Mechanical Engineering, University of Tabriz, Tabriz 5166616471, Iran2 Department of Civil Engineering, trail of Engineering, University of Birmingham, Birmingham, UK.ABSTRACTIn this study, hydrodynamic behavior nanofluid (Fe3O4-water) in a MicroChannel Heat Sink (MCHS) with Off restrain Fan Shaped beneath magnetised champaign was numerally investigated. The two word form mixed bag model was used to replicate the nanofluid period. Flow was assumed stratified, steady and incompressible. The readys of changing Reynolds egress, power magnetized depicted object, and nanoparticle diam on fluid behavior atomic human activity 18 considered. The results show that the clash component part decreases and Nusselt number rises whit rising Reynolds number. Whit increases fervor charismatic demesne the pressure cast off, detrition ingredient and Nusselt number change magnitude. The results indicate that non- similar magnetized land has more(prenominal) launch on nanofluid behavior comp argon uniform magnetised champaign.KeywordsNanofluid Micro job screw up square off Magnetic field Friction factor Nusselt numberNomenclature,zCartesian coordinate axesVelocity component in x and y and z direction, respectively (m/s)(a,b)Center of magnetic outfit (m)Velocity transmitter (m/s)0Velocity inlet (m/s)Acceleration vector (m/s2)Thermal conduction (W/m K) precise light capacity at constant pressureBoltzmann constant (1.3806503-10-23 J/K)Temperature (K)IElectric extravagance (A)HMagnetic field intensity vector (A/m)Heat unify (1 MW/m2)Channel width (ccc-10-6m)Hydraulic diam (0.00001333 m)Channel length (2.70-10-3m) induce coefficientMean speed (m/s)Drift amphetamine (m/s)Slip upper (m/s)dMean diameter (nm)Nu=Nuselt n umber clank factor=Reynolds numberPrandtlnumberMagnetic field (T)Greek symbolsmagnetic permeability in vacuum (4-10-7 Tm/A)Dynamic viscosity (kg/m s)Thermal expansion coefficient( thermal expansion coefficient (K-1) niggardness (kg/m3)Mean free path (17-10-9 m)Magnetic susceptibilityParticle strength cypher electrical conductivity (s/m)SubscriptsParticleBase fluidbwBottom skirtEffectiveAverageIntroductionNanofluids has higher thermal conductivities compared to them nucleotide fluids 1-5. Currently the use of nanofluids in thermal engineering systems much(prenominal) as waken exchangers 6-7, micro packs 8-10 , chillers, medical applications 11,12, and solar collectors 13.Tsai and Chein14 investigated analytically nanofluid (water-copper and na nonube) flow in microchannel heat ensconce. They was gear up that optimum values of aspect ratio and nanofluid did not make conversion in MCHS thermal resistance. Kalteh et al. 15 investigated the laminar nanofluid flow in rectangular microchannel heat sink both mathematically and experimentally. Compared the experimental and numeral results innovateed that two-phase Eulerian-Eulerian method results are in better accordance with experimental results than the single-phase modeling. The reasons experimentally study by Azizi et al.16 reported that Nusselt numbers decreases whit rising Reynolds number and enhancement heat switch by use nanoparticles camper to that of nice water for similar Reynolds number. Sheikholeslami et al. 17 stick outvass effect nanoparticle on heat transferral in a cavum square containing a rectangular het corpse numerally. They indicated that apply nanoparticle increasing heat transfer and dimensionless entropy propagation.Micro channel heat sink (MCHS) using in many applications, such(prenominal) as microelectronics and high susceptibility laser. MCHS cooling is very important because heat flux in this channel higher than regular channel. Many studies canvas the convective heat transfer characteristics of nanofluids in micro channel heat sink in recently many years ago18-24.Sakanova et al. 25 investigated effects of wavy channel structure on hydrodynamic behavior in microchannel heat sink. They found that increasing nanoparticles in pure water the effect of wavy wall unnoticeable. Radwan et al. 26 using nanofluid on heat transfer microchannel heat sink in low concentrated photovoltaic systems investigated numerically. They show that nanofluids is effective technique for enhance heat transfer. Tabrizi and Seyf 27 investigated laminar Al2O3-water nanofluid flow in a microchannel heat sink. They showed that increasing mountain fraction of Al2O3 and nanoparticle size reducing the entropy generation.Chai et al. 28-30 studied hydrothermal characteristics of laminar flow microchannel heat sink with fan-shaped ribs. Their results presented that used the fan-shaped ribs the average friction factor 1.1-8.28 times larger than the regular microchannel, while u sed the offset fan-shaped ribs was 1.22-6.27 times increases. Also the microchannel with large ribs height and small ribs spacing, the frictional entropy generation rate increases and thermal entropy generation rate decreases comparing than the undisturbed microchannel.Magnetic fluid (ferrofluid) is a stable colloidal suspension consisting of a base liquid and magnetic nanoparticles that are coated with a surface-active agent layer and it can be controlled by external magnetic field 31. Sundar et al. 32-33 experimentally studied the heat transfer characteristic of Fe3O4 ferrofluid in a circular tube whit applied magnetic field. They detected that the heat transfer increases compared to water flow at same operating causality. Aminfar et al. 34-36 studied effect different magnetic field on ferrofluid for different channels. They showed that using the uniform and non-uniform thwartwise magnetic increasing heat transfer coefficient and friction factor. Also shown that non-uniform t ransversal magnetic enhanced heat transfer more than axial non-uniform magnetic field.In this study, the uniform and non-uniform transverse magnetic effect on heat transfer of ferrofluids flow in a microchannel heat sink with offset fan shaped by using mixed bag model. The effects of uniform and non-uniform transverse power magnetic fields, Reynolds number and nanoparticle diameter variation are studied in details.Governing EquationsResearchers presented different models for numerical analysis in multi-phase flows 37-40. The mixture model is one of methods for nanofluid analyses 38-41. In this study, flow is assumed steady state, incompressible and laminar with constant thermo-physical properties. The effects of body makes and dissipation are negligible. Also, for calculate the density variations due to buoyancy force was used the Boussinesq approximation. Considering these assumptions, the dimensional equations define asContinuity equations(1)Momentum equations(2)The bourn ref ers to Kelvin force it results from the electric current flowing through the wire. In this equation, H is Magnetic field intensity vector that determined as 42(3)where(4)(5)I is electric intensity. The wire direction is parallel to the longitudinal channel and in the center of cross region at the (a, b).Also, M is the magnetic intensity in Equation (2) and determined as 36(6)where is magnetic susceptibility of ferrofluid at 4% volume fraction for different destine diameter is present in Table 1.Table 1. magnetic susceptibility of ferrofluid for different mean diametermean diametermagnetic susceptibility100.34858668202.7886935309.4118388In Equation (2), is called Lorentz force that determined as(7)Where and are respectively effective electrical conductivity and nanofluid swiftness vector, also is the generate uniform magnetic field that can be calculated by intensity of magnetic field(8)Energy equation(9)Volume fraction equations(10)In Equation (10), Vm, and Vdr are the mea n velocity and the drift velocity, respectively, that be defined as(11)(12)where is the volume fraction of nanoparticles.The drift velocity depends on the slip velocity. The slip velocity defined as the velocity of base fluid (bf) with respect to velocity of nanoparticles (p) and determined as(13)(14)The slip velocity is presented by Manninen et al. 31e(15)In Equation (15) f drag and r are drag coefficient and acceleration respectively, which can be calculated by(16)(17)In Equation (16), Rep = Vmdp/veff is the Reynolds number of particles.Nanofluids PropertiesThe physical properties of water and Fe3O4 nano-particles are shown in Table 2. The water-Fe3O4 nanofluidis assumed is homogenous that the thermos-physical mixture properties calculated for 4% volume fraction of nanoparticles.Table 2. Properties of base fluid and nanoparticles 35,40.PropertiesWaterFe3O4Density (kg/m3)997.15200 special(prenominal) heat capacity (J/kgK)4180670Thermal conductivity (W/mK)0.6136Electrical conductiv ity (s/m)5.325,000Dynamic viscosity (kg/ms)0.0009963The physical mixture properties are calculated by means of the following equationsDensity of nanofluid(18)Specific heat capacity of the nanofluid(19)Dynamic viscosity of nanofluid 43(20)Thermal expansion coefficient of nanofluid 35(21)Electrical conductivity 36.(22)Based on the Brownian motion velocity is Thermal conductivity of nanofluid 44(23)dp and dbf are particle diameter(nm) and molecular base fluid (0.2 nm).In Equation (23) Pr and Re are Prandtl and Reynolds number, respectively defined as(24)(25)Also, in Equation (25) is water mean free path (17 nm) and kB is Boltzmann constant (1.3807 - 1023 J/K).Denition of Physical Domain and numerical methodFig.1 shown the geometry of the microchannel heat sink with offset fan-shaped reentrant cavities in sidewall. The channel width and space between a pair cavity is 300 m.The channel length is 2.70 mm with a thickness of 350 m and the tend distance of two longitudinal microchannels i s 150 m.The channel cross section heat sink has a constant width of 100 m and constant depth of 200 m and radius of the fan-shaped reentrant cavity is 100 m.a)b)c)Fig. 1. a) Geometry of microchannel in the present study b) Cross-sectional plane of transverse non-uniform magnetic field c) Transverse uniform magnetic fieldIn this study, used the finite volume (FV) method to numerically solved non-linear partial differential equations. The velocity pressure coupling by SIMPLEC algorithm. The discretization of momentum and energy equations used the second place upwind scheme and the solid phase equations became discretization by first order scheme.In this study for evaluate of effect the mesh points on the precision of the results, several grid sizes have been tried for the constant heat flux at Re = 300 are granted in Table 3. The 1188000 grids is adequately suitable.Table 3. Grid freelancer test (Re = 200,T0 = 300, 4% vol.).V/V0T/T0Grid1.0381.0276729141.0291.0198894401.0231.01311 880001.021.0111591128In order to validate this, the amount of mean temperature at the empennage of the microchannel compared by numerical result of Chai et al.45(Fig.2). Also for comparison effect the magnetic field, the dimensionless velocity under the magnetic field compared by analytical results of Shercliff 46 that shown in Fig. 3 and can be seen a good agreement between results. determine 2. similitude of the results for average temperature bottom heat sinkFig.3 Comparison between numerical and analytical results for flow under magnetic fieldBoundary conditionsThe set of non-linear elliptical governing equations are solved by using the bound conditions in the entrance of microchannel (Z = 0),u = 0 v = 0 w = v0 T = T0(26)at the microchannel outlet (Z = 2.7 mm) u = 0 v = 0 P = Patm(27)In the left and right sides of microchannel outer adiabatic walls (X = 0 w)(28)In the microchannel inner walls(29)(30)Finally, a constant heat flux condition is imposed at micro heat sink bottom wall (y = 0).Results and discussionThe variations of pressure drop and Reynolds number for motley transverse magnetic fields are shown in Fig. 3a. It can be seen that for a given fluid, the pressure drop increases by increasing the Reynolds number because rising the velocity inlet. As shown in Fig. 3b whit increases intensity uniform and non-uniform magnetic field in the same Reynolds number (Re=300), the pressure drop increases for non-uniform magnetic because the inessential flow near wall became larger and powerful. Also scale up particle diameter of 10nm to 30nm decreasing pressure drop (Fig. 3c).a)b)c)Fig. 3. effect of various 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 pressure dropFig. 4 presented streamlines for various magnetic fields at 0.0015 Z 0.002. As shown in Fig.4, when magnetic field is weak the streamlines same together because the magnetic field had not enough powerful for ve er stream. By increases intensity magnetic field the nanofluid flow shift to near wall and thereupon the offer in reentrant cavities became powerful Fig.5.Fig. 4. Stream lines in same Reynolds number (Re=300) and particle diameter dp= 30nm for a) non-magnetic field b) non-uniform magnetic field (H=6-106 A/m) c) uniform magnetic field (H=6-106 A/m)Fig. 5. Stream lines in same Reynolds number (Re=300) and particle diameter dp= 30nm for non-uniform magnetic field a) H= 6-106 A/m c) H=8-106 A/mThe friction factor decreases as Reynolds number increases (Fig. 6a). The magnetic field cannot surpass viscous force and affect mean velocity when intensity magnetic field is low, therefor the friction factor is almost fixed for using magnetic and non-magnetic field. Whit increases intensity magnetic field the mean velocity decreases and while the pressure drop increases (Fig. 3.b) thence, the friction factor increases at maximal intensity field (Fig. 6b). Also scale up particle diameter the main velocity and pressure drop decreases. The uniform transverse magnetic field is depended to velocity that whit decreasing velocity the uniform transverse effect decreases on flow, so friction factor rising (Fig. 6c).a)b)c)Fig. 6. Effects of various 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 factorFigure 7 shows the variations of average temperature bottom heat sink for different condition. Whit increasing Reynolds numbers the velocity increasing withal and the vortex in reentrant cavities became bigger and powerful, thus average temperature bottom heat sink decreases (Fig. 7a). Effects of various power magnetic field gradients Re=300, dp=30nm on average temperature bottom heat sink presented in Fig. 7b. When the intensity magnetic field is weak cannot affect average velocity because cannot overcome viscous force. By strengthening the non-uniform transverse magnetic field the average velocity became larger and growth vortex in channel, therefore average temperature bottom heat sink reduces. Particle diameter rising, the non-uniform transverse magnetic had more effect than uniform transverse magnetic and non-magnetic on average temperature bottom heat sink (Fig. 7c). Whit scale up particle diameter decreasing thermal conductivity and heat transfer for when applied uniform transverse magnetic because it independent of particle diameter.Figure 8 presented the variations of average Nusselt number for different condition. Nusselt number enhances with Reynolds number in