Effect of Magnetic Field on Hydrodynamic Behavior

Effect of magnetized Field on Hydrodynamic BehaviorEffect of Magnetic Field on hydrodynamic behavior in a Micro delight take fire SinkMohammad Nasiri 1*, Mohammad Mehdi Rashidi 2,1 Department Mechanical Engineering, Faculty of Mechanical Engineering, University of Tabriz, Tabriz 5166616471, Iran2 Department of obliging Engineering, School of Engineering, University of Birmingham, Birmingham, UK.ABSTRACTIn this study, hydrodynamic behavior nanofluid (Fe3O4- water supply) in a MicroChannel Heat Sink (MCHS) with Offset Fan Shaped under magnetised world was numerically investigated. The two phase mixture model was substance abused to simulate the nanofluid flow. Flow was assumed laminar, steady and incompressible. The effects of changing Reynolds bit, power magnetic cranial orbit, and nano pinch diam on fluid behavior be considered. The results show that the friction federal agent decreases and Nusselt number enhances shred upgrade Reynolds number. Whit increases potency magnetic orbital cavity the compel drop, friction part and Nusselt number increasing. The results indicate that non-uniform magnetic work has more effect on nanofluid behavior compare uniform magnetic field.KeywordsNanofluid Microchannel oestrus drip Magnetic field Friction cipher Nusselt numberNomenclature,zCartesian coordinate axesVelocity component in x and y and z direction, on an individual basis (m/s)(a,b)Center of magnetic wire (m)Velocity vector (m/s)0Velocity inlet (m/s)Acceleration vector (m/s2)Thermal conductivity (W/m K)Specific kindle capacity at constant pressureBoltzmann constant (1.3806503-10-23 J/K)Temperature (K)IElectric intensity (A)HMagnetic field intensity vector (A/m)Heat flux (1 MW/m2)Channel width (300-10-6m)Hydraulic diam (0.00001333 m)Channel length (2.70-10-3m)Drag coefficientMean velocity (m/s)Drift velocity (m/s)Slip velocity (m/s)dMean diameter (nm)Nu=Nuselt numberfriction factor=Reynolds numberPrandtlnumberMagnetic field (T)Greek symbolsmagn etic permeability in vacuum (4-10-7 Tm/A) self-propelling viscosity (kg/m s)Thermal expansion coefficient(thermal expansion coefficient (K-1)Density (kg/m3)Mean free path (17-10-9 m)Magnetic susceptibility fragment volume fraction galvanizing conductivity (s/m)SubscriptsParticleBase fluidbwBottom wallEffectiveAverageIntroductionNanofluids has higher thermal conductivities compared to them base fluids 1-5. Currently the use of nanofluids in thermal engineering systems such as heat exchangers 6-7, microchannels 8-10 , chillers, medical applications 11,12, and solar collectors 13.Tsai and Chein14 investigated analyticly nanofluid (water-copper and nanotube) flow in microchannel heat sink. They was found that optimum value 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 numerically and experimentally. Compared the experimental and numerical results prese nted 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 dispatch by employ nanoparticles camper to that of pure water for similar Reynolds number. Sheikholeslami et al. 17 heapvass effect nanoparticle on heat transfer in a cavity square containing a rectangular heated body numerically. They indicated that using nanoparticle increasing heat transfer and dimensionless entropy generation.Micro channel heat sink (MCHS) using in many a(prenominal) applications, such as microelectronics and high expertness laser. MCHS cooling is very important because heat flux in this channel higher than regular channel. Many studies analyzed the convective heat transfer characteristics of nanofluids in micro channel heat sink in recently many years ago18-24.Sakanova et al. 25 inves tigated 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 efficient technique for enhance heat transfer. Tabrizi and Seyf 27 investigated laminar Al2O3-water nanofluid flow in a microchannel heat sink. They showed that increasing volume 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 reasonable friction factor 1.1-8.28 propagation bigger than the regular microchannel, while used the offset fan-shaped ribs was 1.22-6.27 times increases. Also the microchannel with large ribs height and small rib s spacing, the frictional entropy generation rate increases and thermal entropy generation rate decreases comparing than the smooth microchannel.Magnetic fluid (ferrofluid) is a stable colloidal suspension consisting of a base liquid and magnetic nanoparticles that are coated with a surfactant layer and it can be controlled by external magnetic fields 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 condition. Aminfar et al. 34-36 studied effect different magnetic field on ferrofluid for different channels. They showed that using the uniform and non-uniform transverse magnetic increasing heat transfer coefficient and friction factor. Also shown that non-uniform transverse 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 mixture model. The effects of uniform and non-uniform transverse power magnetic fields, Reynolds number and nanoparticle diameter variation are studied in details.Governing equalitysResearchers 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- forcible properties. The effects of body forces 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 term refers 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 share at the (a, b).Also, M is the magnetization in comparability (2) and determined as 36(6)where is magnetic susceptibility of ferrofluid at 4% volume fraction for different pie-eyed diameter is present in Table 1.Table 1. magnetic susceptibility of ferrofluid for different meanspirited 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 velocity vector, also is the bring on 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 mean velocity and the drift velocity, respectively, that be defined as(11)(12)where is the volume fraction of nanoparticles.The drift velo city depends on the mooring 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 physiologic 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.Properties irrigateFe3O4Density (kg/m3)997.15200Specific heat capacity (J/kgK)4180670Thermal conductivity (W/mK)0.6136 galvanising conductivity (s/m)5.325,000Dynamic viscosity (kg/ms)0.0009963The physical mixture properties are calculated by means of the following equations Density 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 in the midst of a pair cavity is 300 m.The channel length is 2.70 mm with a thickness of 350 m and the pitch distance of two longitudinal microchannels is cl m.The channel cross section heat sink has a constant width of 100 m and constant depth of 200 m and spoke of the fan-sh aped 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 order upwind scheme and the solid phase equations became discretization by first order scheme.In this study for evaluate of effect the pursue points on the precision of the results, several grid sizes have been tested for the constant heat flux at Re = 300 are given in Table 3. The 1188000 grids is adequately suitable.Table 3. Grid independent test (Re = 200,T0 = 300, 4% vol.).V/V0T/T0Grid1.0381.0276729141.0291.0198894401.0231.01311880001.021.0111591128In order to validate this, the amount of mean temperature at the bottom of the microchannel compared by num erical 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. date 2. comparability 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 boundary 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 enforce at micro heat sink bottom wall (y = 0).Results and discussionThe variations of pressure drop and Reynolds number for various transverse magnetic fields are s hown 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 secondary flow near wall became larger and powerful. Also descale up particle diameter of 10nm to 30nm decreasing pressure drop (Fig. 3c).a)b)c)Fig. 3. cause 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 veer stream. By increases intensity magnetic field the nanofluid flow shift to near wall and thereupon the vortex 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 overcome 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) therefore, the friction factor increases at maximum 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 veloci ty 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 too 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 beef up 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 no n-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