Ferrofluid Flow Research Articles

Numerical study of time-dependent ferrofluid flow past a cylinder in the presence of stationary magnetic field

This work investigates time-dependent ferrofluid flow past in a cylinder in the presence of a 10 kilo-ampere per meter magnetic field. The Reynolds number is about a hundred to keep the laminar flow and it is high enough to form a von Karman vortex street. This study presents the results for the velocity distributions, pressure distributions, lift coefficient, and drag coefficient under the influence of the stationary magnetic field. These results are compared with the flow in the absence of the magnetic field. The presence of the magnetic field diminishes the velocity distributions in the flow due to magnetization force and magnetic field dependent viscosity. This reduction in the velocity reduces the average velocity in the flow and therefore the magnetic field intensity enhances the coefficients of drag and lift. In the presence of the applied magnetic field, the velocity drops from 2.19 to 1.97 m/s at t = 7 s. However, the lift coefficients enhance from 3 m2s2/kg to 3.4 m2s2/kg and the drag coefficient enhances from 0.9 to 3 m2s2/kg. The numerical simulation of the problem is obtained using the finite element method in COMSOL Multiphysics.

MAGNETIC FLUID-BASED SQUEEZE FILM BETWEEN CURVED POROUS ANNULAR PLATES CONSIDERING THE ROTATION OF MAGNETIC PARTICLES AND SLIP VELOCITY

The ferrofluid flow model of the Shliomis and continuity equation for the film and porous interface with the theory of Darcy, the modified Reynolds equation for ferrofluid squeeze film between curved annular plates is discussed with the impact of the rotation of Ferro-particles and slip velocity at the boundary. Beavers and Joseph’s slip conditions are adopted to study the impact of slip velocity. The generalized non-dimensional pressure equation is derived and expression for dimensionless load-carrying capacity is obtained for the same. The graphical representation suggests that the bearing's performance enhances due to ferrofluid, considering the appropriate values of parameters for slip velocity and porosity.

Analysis of entropy generation of ferrofluid flow in the microchannel with twisted porous ribs: The two-phase investigation with various porous layers

Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels, due to their increased surface and better thermal performance than that of normal heat sinks were used in electronic cooling devices. In this numerical investigation, the first and second laws of the thermodynamic impact of twisted porous ribs on the microchannel were studied. The effects of the Reynolds number and volume fraction of nanoparticles were investigated. The range of Reynolds number was 250 to 1000. All types of the microchannel in this study consisted of a clear microchannel, a twisted porous ribbed microchannel with two and three layers of twisted porous ribs. The results show that by inserting porous ribs, the local cross-section decreases, and the local Reynolds number increases. Also, twisted porous ribs are the cause of nanofluid flow circulation and make the heat transfer coefficient greater. Increasing the porous layer from one layer to three layers has an increasing effect on the heat transfer coefficient, and the friction factor and increasing the φ is the reason for increasing the friction factor. Finally, the microchannel with triple layers of twisted porous ribs has better performance in total entropy generation, and by inserting twisted porous ribs, the entropy generation decreases.

Finite element analysis of water-based Ferrofluid flow in a partially heated triangular cavity

PurposeThis study aims to deal with the numerical investigation of ferrofluid flow and heat transfer inside a right-angle triangular cavity in the presence of a magnetic field. The vertical wall is partially heated, whereas other walls are kept cold. The effects of thermal radiation are included in the analysis. The governing equations including continuity, momentum and energy equations are converted to nondimensional form using viable variables.Design/methodology/approachFinite element method (FEM)-based simulations are performed using finite element approach to investigate the effects of the volume fraction of ferroparticles (Fe3O4), the length of the heating element and the dimensionless numbers including Rayleigh and Hartmann numbers on the streamlines, isotherms and Nusselt number.FindingsIt is demonstrated that both horizontal and vertical velocity components increase with the length of the heating element, whereas the dimensionless temperature decreases the heating domain. It is observed that an increase of 10% in the volume fraction of ferroparticles increases Nusselt number more than 12%, and 20% increase in the volume fraction of ferroparticles increases more than 30%, depending upon the length of the heating element.Originality/valueThis is a new study showing the significance of the magnetic nanoparticles for the enhancement of heat transfer rate in a triangular cavity.

Impacts of variable magnetic field on a ferrofluid flow inside a cavity including a helix using ISPH method

Purpose The purpose of this paper is to study the unsteady ferrofluid flow with a hot source helix inside a cavity under the impacts of a variable magnetic field by using the incompressible smoothed particle hydrodynamics method. Design/methodology/approach The governing equations are formulated by considering the basics of the magnetohydrodynamic and ferrohydrodynamics. Different locations of a variable magnetic source outside the geometry are investigated. The helical coils are extensively applied in the cooling and heating of air conditioners and heat pumps. Computations were carried out for different lengths of the heated helix (0.2 ≤ Lh ≤ 0.8), different locations of the magnetic source, (a = 0.5, b = −0.01), (a = 0.5, b = 1.01), (a = 1.01, b = 0.5), (a = −0.01, b = 0.5), different numbers of the inner helix (one helix, two helixes and three helixes) and different values of the nanoparticles volume fraction (0% ≤ ϕ ≤ 10%). Findings The outcomes of the investigations revealed that an increase in the lengths of a helix by 0.4 results in a reduction of the stream function by 25.60%. In addition, when the magnetic wire is located near the center of the right wall, the maximum values of the average Nusselt number are obtained while the smallest values of the average Nusselt number are given when the magnetic source is located near center of the top wall. Originality/value The novelty of this paper is investigating the natural convection flow from two different models of an inner hot helix inside a cavity with considering different locations of variable magnetic sources.

Polarization force and geothermal viscosity driven unsteady Bödewadt transport phenomenon over a ferrofluid saturated disk

This work aims to investigate mass transport phenomena on time dependent Bödewadt flow of magnetic Nanoliquid embedded in the porous medium with vertical polarization force and geothermal viscosity variations. The resultant nonlinear coupled system of partial differential equations is solved numerically. For thorough understanding of flow and transport phenomenon, a wider range of Prandtl number is taken to analyze the effects of various physical entities including polarization force, geothermal viscosity, permeability and rotation. Eventually, some new marvels are found. The diffusion rate enhances significantly for higher values of Prandtl, Schmidt numbers and the boundary layer thickness decimates with all parameters except depth dependent viscosity. Besides, frictions on the surface of the plate have also been computed and found them very high for all above mentioned entities. In nutshell, to have the realistic view, this investigation reveals that the polarization force and viscosity variation due to the temperature and depth have imperative role on the unsteady transport phenomenon in ferrofluid flow.

Effect of magnetic field on the mixed convection $$\hbox {Fe}_{3}\hbox {O}_{{{4}}}/\hbox {water}$$ ferrofluid flow in a horizontal porous channel

The effect of an external magnetic field on the mixed convection $$\hbox {Fe}_{{3}}\hbox {O}_{{4}}/$$ water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman–Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles $$0\le \varphi \le 0.05$$ , magnetic numbers $$0\le \hbox {Mn} \le 100$$ , Reynolds numbers $$100\le \hbox {Re}\le 500$$ , Darcy numbers $$\hbox {10}^{{-3}}\le \hbox {Da}\le 10^{{-1}}$$ and porosity parameters $$0.7\le \varepsilon \le 0.9$$ while fixing the Grashof number at $$10^{{4}}$$ . Results show the formation of recirculation zone in the vicinity of the magnetic source under the influence of Kelvin force. It grows as the magnetic number increases. The friction factor increases by increasing the magnetic number and diminishes with the increase in Darcy number. The flow accelerates as the magnetic field intensifies. The heat transfer rate increases by increasing the volume fraction of the nanoparticles and the magnetic number. The effect of magnetic field on the hydrodynamic and thermal behaviours of the ferrofluid flow considerably intensifies by increasing Reynolds number and Darcy number. The combined effect of ferromagnetic nanoparticles and magnetic field on the enhancement rate of heat transfer becomes more pronounced at high values of Reynolds number, permeability and/or porosity parameter.

Impact of induced magnetic field on thermal enhancement in gravity driven Fe3O4 ferrofluid flow through vertical non-isothermal surface

The ferrofluid are useful nanofluid and can be prepared by mixing magnetic types of nanoparticles in base fluid. The mathematical modelling of ferrofluid under induced magnetic field through a vertical stretching surface is formulated in the current theoretical study. The study is performed for ferrofluid by considering magnetite Fe3O4 magnetic nanoparticles in base fluid. In ferrofluid, the appropriate mixture of magnetic nanoparticles can lead to desire heat transfer phenomena. This theoretical study indicates that both Nusselt number and skin friction coefficient for Fe3O4-water ferrofluid increase by improving the effects of magnetic parameterβ. Velocity and magnetic boundary layer thicknesses increase/decrease for assisting/opposing flow by strengthening magnetic effects and in the presence of magnetic type Fe3O4 nanoparticle boundary layer thickness further enhances for pure water as compared to Fe3O4 type of ferrofluid. Temperature profile and thermal boundary layer thickness increase for both assisting/opposing flow with enhancing the concentration of Fe3O4 magnetic nanoparticle, however, thermal distribution reduces/upsurges in case of assisting/opposing flow with the increase of magnetic strength and thermal boundary layer thickness is greater for Fe3O4- water based ferrofluid as compared to regular fluid. The bvp4c built-in code in MATLAB software is employed for solution purposes. Results are displayed for the selection of effective parameters in data and graphical forms for both assisting and opposing flows.

Nonuniform Kelvin Force Effect on Laminar Flow of Nanomaterials

Abstract In the current study, Kelvin force as an external source has been used to affect the ferrofluid flow style. The presence of wire below the pipe creates a variable magnetic force that generates rotating eddies near the wire inside the pipe. To augment the cooling rate, the type of operating fluid changes from pure water to Fe3O4-water ferrofluid. Laminar flow was studied with involving homogeneous model for the ferrofluid. A new term was added to momentum equations as Kelvin force due to the gradient of the magnetic field. Impacts of magnetic number (Mn), the fraction of ferrofluid (φ), and Reynolds number (Re) on the configuration of hydrothermal behavior as well as Nusselt number (Nu) and Darcy factor (f) have been investigated. Utilizing ferrofluid can enhance Nu, while the pressure drop augmentation is negligible. So, selecting such kind of ferrofluid is a promising way to gain better performance. Given Re = 50, Nu enhances by about 1.3% with an increase of the concentration of ferrofluid from 0.01 to 0.04. The rise of Re needs greater pumping power as a higher pressure drop will appear in this case. Besides, a thinner boundary layer has been formed with the growth of Re, which offers a higher Nu. When Mn* = 1.57, the growth of Re provides an augmentation of Nu by 39%. With augmenting Kelvin force, the velocity of ferrofluid enhances, which results in a higher pressure drop.

Heat exchange enhancement of ferrofluid flow into rectangular channel in the presence of a magnetic field

Heat exchange and Fe3O4/water nanofluid flow behaviors into horizontal channel subjected to the effect of a magnetic field was studied numerically. The basic equations were solved using the finite volume method with the time-splitting algorithm. The results were represented by temperature field, streamlines, velocity field, averaged and normalized Nusselt numbers, for various nanoparticles volume fractions, Reynolds numbers and magnetic numbers. Results show that the isotherms, the streamlines and the heat exchange rate are strongly changed by applying a magnetic field. A recirculation region is created near the magnetic source where the thermal boundary layer is removed enhancing so the local heat exchange. The overall heat exchange is enhanced by suspending nanoparticles and/or by increasing magnetic field strength. In the absence of a magnetic field, suspending nanoparticles can enhance heat exchange rate up to 20%. Under the only action of magnetic field a maximum 60% heat exchange enhancement is obtained. It can reach up to 86% as the combined effects of both nanoparticles and magnetic field are considered.

Unified simplified multiphase lattice Boltzmann method for ferrofluid flows and its application

A unified simplified multiphase lattice Boltzmann method (USMLBM) is constructed in this work for simulating complex multiphase ferrofluid flows with large density and viscosity ratios. In USMLBM, the Navier–Stokes equations, the Poisson equation of the magnetic potential, and the phase-field equation are utilized as the ferrohydrodynamics behavior modeling and interface tracking algorithm. Solutions of the macroscopic governing equations are reconstructed with the lattice Boltzmann framework and resolved in a predictor–corrector scheme. Various benchmark tests demonstrate the efficiency and accuracy of USMLBM in simulating multiphase ferrofluid flows. We further adopt USMLBM to analyze in detail the mechanisms of bubble merging inside a ferrofluid under a uniform external magnetic field. The numerical results indicate that the bubbles tend to move toward each other and further merge together, even for a large initial separation between the bubbles. Due to complex interaction between the bubbles and the ferrofluid during the magnetophoretic acceleration process, the nonlinear effect on bubble merging is observed when the initial separation increases. Moreover, at a larger initial separation, the shape of bubbles seems to be not sensitive to the initial separation.

Water-based ferrofluid flow and heat transfer over a stretchable rotating disk under the influence of an alternating magnetic field

Flow and heat transfer of water-based nanofluid over a stretchable rotating disk under the influence of an alternating magnetic field is investigated. The external magnetic field creates a hindrance in the flow and depends on the frequency of the alternating magnetic field. The frequency of an alternating magnetic field can increase or decrease the viscosity of the magnetic fluid in the flow. A set of nonlinear differential equations in the present theoretical model is solved numerically using the finite element method. Volume concentration, frequency of the alternating magnetic field, magnetic polarization force, and Prandtl number play an important role in the velocity and temperature distributions of iron/water nanofluid. A comparative study for velocity and heat transfer is presented for iron/water, nickel/water, and cobalt/water ferromagnetic nanofluid. The rotational viscosity enhances the heat transfer in nanofluid provided the magnetic field should be stationary.

Effect of nanoparticle shape on unsteady liquid film flow of MHD Oldroyd-B ferrofluid

A computational framework is carried out to investigate the drive, and thermal transport of the thin-film flow of unstable magnetohydrodynamic (MHD) Oldroyd-B ferrofluid suspend with cobalt ferrite (CoFe2O4) nanoparticles in water. The governing PDEs of the flow are transmuted as ODEs by applicable similarity conversions and resolved using R-K and Newton’s approaches. We examined the variations in the drive and energy field designations along with the local Nusselt number influenced by the relevant non-dimensional parameters. The results are explored for different nanoparticle shapes (spherical, cylindrical, and laminar) and originate that the energy transport efficiency is advanced in spherical shaped ferrous particles when compared to tube and laminar shaped particles. The Deborah number and unsteadiness parameter has the power to regulate the Nusselt number.

Framing the Impacts of Highly Oscillating Magnetic Field on the Ferrofluid Flow Over a Spinning Disk Considering Nanoparticle Diameter and Solid–Liquid Interfacial Layer

Abstract This article communicates on the ferrofluid flow over a spinning disk in the presence of highly oscillating magnetic field. The flow is presumed to be unsteady. Ferrous nanoparticles are suspended within base medium water. This investigation reveals how presence and absence of oscillating magnetic field influence the hydrothermal basis of the flow. Also, the effects of particles diameter and solid–liquid interfacial layer have been precisely incorporated to reveal the thermal integrity of the system. Shliomis theory is introduced to frame the leading equations of the system. Resulting equations have been solved using innovative spectral quasi-linearization method (SQLM). Residual error analysis is included to explore the advantage of such computational scheme. The influence of dynamic parameters on the velocities and temperature is deliberated through graphs and tables. Several 3D pictures and contour plots are depicted to extract the key points of the flow. The results exhibit that heat transfer is reduced for nanoparticle diameter but amplifies for base liquid nanolayer conductivity ratio and elevated field frequency enhances the temperature. Relative magnetization reduces for high field frequency, but increases for angular displacement. SQLM exhibits an accurate computational scheme with fast convergence.

Numerical Simulation of Water Based Ferrofluid Flows along Moving Surfaces

The steady two-dimensional boundary layer flow past a stretching flat sheet in a water-based ferrofluid is investigated. The spatially varying magnetic field is created by two line currents. The similarity method is applied to transform the governing equations into a system of coupled ordinary differential equations. Numerical investigations are performed for ferrofluids, the suspensions of water, and three types of ferroparticles (magnetite, cobalt ferrite, and Mn-Zn ferrite). The impact of the solid volume fraction, the surface stretching parameter, and the ferromagnetic coefficient on the dimensionless velocity and temperature profiles, the skin friction coefficient, and the local Nusselt number are analysed for the three types of ferrofluid.

FERROFLUID FLOW IN MAGNETIC FIELD ABOVE STRETCHING SHEET WITH SUCTION AND INJECTION

The aim of this paper is to investigate the boundary layer of ferrofluid flow induced by a permeable stretching sheet. Fluid is electrically non-conducting in the presence of non-uniform magnetic field. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations by applying a similarity transformation. Numerical solutions are obtained by using Maple. The effects of the magnetic field, the Reynolds number and the porosity on the velocity and thermal fields are investigated. The impact of the parameters on the skin friction and the local Nusselt number is numerically examined. The skin friction and heat transfer coefficients are decreasing with enhancing the stretching, the values of porosity and the ferromagnetic parameter.

Magnetization diffusion in duct flow: The magnetic entrance length and the interplay between hydrodynamic and magnetic timescales

In this work, computational fluid dynamics simulations of a ferrofluid plane Poiseuille flow in the presence of a constant applied magnetic field are performed. The orientation of the field is perpendicular to the direction of the flow. An original numerical methodology for calculating magnetic and hydrodynamic fields is proposed, including an important discussion about an identified magnetization entrance region. Three different magnetization models are considered to calculate the magnetization field. These models are implemented and validated according to analytic and asymptotic theories, including the one developed in this manuscript. Discrepancies between the models are discussed and interpreted physically. An intricate balance between different physical mechanisms is shown to be responsible for a diffusive-like behavior of the magnetization field. This balance is governed by a competition between the flow’s vorticity and the mechanisms of magnetic relaxation. The physical parameters responsible for this non-equilibrium magnetization dynamics are identified and interpreted using the problem’s timescales. It seems that the combination of three different timescales governs the dynamics of non-equilibrium magnetization: the Brownian diffuse timescale, a hydrodynamic (convective) timescale, and a controllable magnetic timescale associated with the intensity of the applied magnetic field. The results indicate toward the possibility of controlling the development of the flow’s magnetization field through the applied magnetic field, particle size distribution, fluid concentration, and flow rate. In addition, several results are presented regarding the fully developed flow, including magnetization profiles and angles between the applied field H and the magnetization field M.

Study of magnetoviscous effects on ferrofluid flow

Present results show the effect of magnetic field-dependent viscosity on the flow of magnetic fluid due to a non-conducting rotating disk. Shliomis model has been used in the problem formulation. A similarity transformation has been used to reduce a set of partial differential equations into nonlinear coupled differential equations. The nonlinear coupled differential equations involved in the problem are solved numerically through mathematical modeling in COMSOL Multiphysics. The radial, tangential, and axial velocity distribution is presented for different values of the magnetic field-dependent viscosity parameter. Some theoretical results used in the model have verified mathematically. These theoretical results are useful to validate the Shliomis model for rotational motion. The results indicate that the Shiliomis model is more appropriate to study the ferrofluid flow due to an infinite rotating disk in comparison to the Rosensweig model.

Study of ferrofluid flow in a rotating system through mathematical modeling

This work investigates the ferrohydrodynamic flow between a rotating disk and a rod in order to optimize the use of ferrofluids for liquid seals in a rotating system. Rotational viscosity effects in the flow, due to the difference of rotation between the magnetic particles and fluid in the presence of a magnetic field, are considered in the present mathematical model. The magnetic field on the disk has been directed in the radial and tangential directions and its impact on the momentum and energy equations has been considered. Similarity transformation has been used to transform the equations of the developed mathematical model into a dimensionless form. The transformed system of equations has been solved numerically with the help of the COMSOL Multiphysics software in the framework of a finite element method. The results for radial, tangential, and axial velocity distributions along with heat transfer analysis have been presented in the presence of physical parameters involved in the problem. The radius of the rod and magnetization force plays a crucial role in the velocity distribution and heat transfer enhancement.

Non-Newtonian ferrofluid flow over an unsteady contracting cylinder under the influence of aligned magnetic field

In this paper the basic design of the study is comparison between the magnetohydrodynamic (MHD) flow and heat transfer of non-Newtonian (Sodium Alginate) base fluid with three ferroparticles, that is Cobalt ferrite (CoFe2O4), Manganese–Zinc ferrite (Mn−ZnFe2O4) and Nickel–Zinc ferrite (Ni−ZnFe2O4) over an unsteady contracting cylinder. In this inspection the aligned magnetic field effects are taken into consideration. The process of bringing the governing PDE's to the form of ODE's is achieved with the similarity transformations. At this point the changed over conditions are numerically understood by Runge-Kutta method of fourth order with shooting technique. The non-Newtonian behavior is discussed employing Casson model. By means of visual image we explain and interpret the behaviours of several emerging parameters on the velocity and temperature profiles. Calculation for the local skin friction coefficient and local Nusselt number are evaluated and examined for the deserving parameters. Also, it is seen that the alignment of magnetic field helps in advancing the velocity profile. Comparing the nanoparticles it is observed that CoFe2O4 nanoparticle is dominant over the other for the local skin friction values whereas Ni−ZnFe2O4 nanoparticle has higher rate of heat transfer.