Influence of parametric modulation on the onset of thermomagnetic convection

Magnetic fluids – so called ferrofluids – are suspensions of nano-scaled particles in an appropriate carrier liquid. The flow properties of these fluids can be influenced by applying an external magnetic field. It is possible to introduce a magnetic force in a horizontal ferrofluid layer which is able to drive a convective flow. The magnetic force arises in the presence of an external magnetic field if a temperature gradient exists in the fluid gap. The behaviour of the onset of convection depends on the strength of the external magnetic field and on the temperature gradient. In this paper the onset of convection under the influence of time-modulated magnetic field has been investigated. The experimental results presented here show a shift in the onset of convection depending on the frequency of the external magnetic field. This behaviour confirms in principle the theoretical predictions which are also presented here. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermomagnetic convection induced by a time-modulated driving force in magnetic fluids

It is well-known that the flow properties of magnetic fluids – so called ferrofluids – can be modified by applying an external magnetic field. Under certain conditions, the magnetic force induced by this external field causes a convective flow. What has yet to be investigated is what happens when this driving force is modulated in time. For this purpose, a horizontal ferrofluid layer has been exposed to an intermittent magnetic field, which causes a time-modulated force. This force depends on the strength of the external magnetic field and the fluid temperature, and therefore the flow phenomenon generated is called thermomagnetic convection. In addition, if the fluid layer is heated from below, the classical thermal convection contributes to the flow system. In our studies, both effects – thermomagnetic and thermal – contribute together to the convection. The experimental results presented here confirm previous theoretical investigations about the influence of the frequency of the driving force on the strength of the convective flow, which reach minimum values at certain frequencies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Double diffusive convection in porous media under the action of a magnetic field

The onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed. The critical Rayleigh thermal numbers at which steady and Hopf convection can occur, are determined. Sufficient conditions guaranteeing the effective onset of convection via steady or oscillatory state are provided.

     

Inhibition or enhancement of chaotic convection via inclined magnetic field

In this paper, we investigate the onset of convection in a horizontal layer of fluid which is heated from the underside. An inclined magnetic field is applied to the layer. The Galerkin truncated approximations were used to obtain a Lorenz-like model. The nonlinear system was solved by the fourth-order Runge–Kutta method. The results show that the Hartmann number and the angle of inclination of the magnetic field could inhibit or enhance the onset of chaotic convection.     

The effect of a high-frequency progressive vibration on the convective instability of a two-layer fluid

The influence of a high-frequency progressive vibration on the onset of thermal convection in a two-layer system of viscous immiscible fluids is investigated. The interface is deformable, the outer walls are rigid, and heat-transfer conditions of a general form are assigned on them. The starting equations are taken in the generalized Oberbeck–Boussinesq approximation. An averaging method is employed. It is shown that the averaged problem contains a vibrogenic external force and vibrogenic stresses that are proportional to the square of the amplitude of the vibration rate. A quasi-equilibrium solution that satisfies the closure condition is found, and its stability is investigated. It is established that, unlike the case of a single-layer fluid, the horizontal component of the vibration influences the onset of convection and have a destabilizing effect. The vertical component stabilizes the two-layer system by increasing the surface tension. The long-wavelength asymptotic is investigated. Calculations are performed for the silicone oil–Fluorinert and acetonitrile–n-hexane systems.     

Nonlinear dynamics and stability of two streaming magnetic fluids

This paper concerns the linear and nonlinear instability of Kelvin–Helmholtz flows in magnetic fluids under external driving. The fluids are subjected to an oblique magnetic field. With the use of the method of multiple scaling, a generalized derivation of the amplitude equation is obtained in marginally unstable regions of parameter space. A Melnikov function is formulated for such an instability and it is shown that there exist transverse homoclinic orbits leading to chaos.     

Effect of magnetic field dependent viscosity on ferroconvection in the presence of dust particles

This paper deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis and a normal mode analysis method. For the case of stationary convection, dust particles always have a destabilizing effect, whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, non-buoyancy magnetization may have a destabilizing or a stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M ₁. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.     

Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite-difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of particles movement in cellular flows under the influence of magnetic forces

A numerical model of particle motion in fluid flow under the influence of hydrodynamic and magnetic forces is presented. As computational tool, a flow solver based on the Boundary Element Method is used. The Euler-Lagrange formulation of multiphase flow is considered. In the case of a particle with a magnetic moment in a nonuniform external magnetic field, the Kelvin body force acts on a single particle. The derived Lagrangian particle tracking algorithm is used for simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient, added mass and magnetophoretic force. As a benchmark test case the magnetite particle motion in cellular flow field of water is computed with and without the action of the magnetic force. The effect of the Kelvin force on particle motion and separation from the main flow is studied for a predefined magnetic field and different values of magnetic flux density. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A numerical study of flows driven by a rotating magnetic field in a square container

The influence of the geometry on the magnetically driven flow is studied by means of numerical simulations. Low–frequency, low–induction and low–interaction conditions are assumed. The rotating magnetic field (RMF) gives rise to a time–independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time–dependent part that is neglected due to the low interaction parameter. Flow results of the cylindrical and square container are compared with respect to the magnetic body force, time–averaged velocity fields, first flow instabilities and Reynolds stress tensors. The dependency of the maximal velocity magnitude and the intensity of the magnetic induction is identical in axisymmetric and non–axisymmetric containers and in good agreement with Davidson's theory. However, significant differences are recognized, for instance, in the distribution of the Reynolds stress tensors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Distortion of liquid metal flow in a square duct due to the influence of a magnetic point dipole

We consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three-dimensional direct numerical simulations with a finite-difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow

Many practical applications, which have an inherent interest of physical and mathematical nature, involve the hydrodynamic flow in the presence of a magnetic field. Magnetic fluids comprise a novel class of engineering materials, where the coexistence of liquid and magnetic properties provides us with the opportunity to solve problems with high mathematical and technical complexity. Here, our purpose is to examine the micropolar magnetohydrodynamic flow of magnetic fluids by considering a colloidal suspension of ferromagnetic material (usually non‐conductive) in a carrier magnetic liquid, which is in general electrically conductive. In this case, the ferromagnetic particles behave as rigid magnetic dipoles. Thus, the application of an external magnetic field, apart from the creation of an induced magnetic field of minor significance, will prevent the rotation of each particle, increasing the effective viscosity of the fluid and will cause the appearance of an additional magnetic pressure. Despite the fact that the general consideration consists of rigid particles of arbitrary shape, the assumption of spherical geometry is a very good approximation as a consequence of their small size. Our goal is to develop a general three‐dimensional theoretical model that conforms to physical reality and at the same time permits the analytical investigation of the partial differential equations, which govern the micropolar hydrodynamic flow in such magnetic liquids. Furthermore, in the aim of establishing the consistency of our proposed model with the principles of both ferrohydrodynamics and magnetohydrodynamics, we take into account both magnetization and electrical conductivity of the fluid, respectively. Under this consideration, we perform an analytical treatment of these equations in order to obtain the three‐dimensional effective viscosity and total pressure in terms of the velocity field, the total (applied and induced) magnetic field and the hydrodynamic and magnetic properties of the fluid, independently of the geometry of the flow. Moreover, we demonstrate the usefulness of our analytical approach by assuming a degenerate case of the aforementioned method, which is based on the reduction of the partial differential equations to a simpler shape that is similar to Stokes flow for the creeping motion of magnetic fluids. In view of this aim, we use the potential representation theory to construct a new complete and unique differential representation of magnetic Stokes flow, valid for non‐axisymmetric geometries, which provides the velocity and total pressure fields in terms of easy‐to‐find potentials, via an analytical fashion. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of the magnetic field on direct contact melting transport processes during rotation

Contact melting heat transfer occurs via relative motion between the heating source and a phase change material (PCM) during melting in various applications. In this study, we investigated the physics of the close contact melting process generated by rotation and when subjected to an applied magnetic field. We transformed the physical model comprising the three-dimensional mass, momentum, and energy equations of the liquid melt layer in the cylindrical coordinate system, including the effects of the Lorentz forces and coupled with an interfacial energy jump condition, into a set of nonlinear similarity equations. Various characteristic dimensionless variables were identified, including an external force parameter σ, which defines the relationship between the external load on the PCM and the centrifugal force due to rotation, and a magnetic field parameter M. Numerical results were obtained and we systematically studied and interpreted the effects of various dimensionless variables on the contact melting and heat transfer processes during rotation, including the structures of the flow and thermal fields, melt layer thickness, and the melting and heat transfer rates. In particular, our results demonstrate that the melting and heat transfer rates increase while the liquid melt film becomes thinner as the external force parameter σ increases. By contrast, an increase in the magnetic field parameter M decreases the melting and heat transfer rates, while yielding relatively thicker melt layers.     

Magnetogasdynamic natural convection in a long vertical microchannel

Since the transport behavior of ionized gases at the microscale could be influenced by an applied magnetic field with ease, microscale magnetogasdynamics (MGD) promises to be particularly advantageous for magnetically controllable microfluidic devices. The purpose of this study is to investigate how magnetic force affects the MGD natural convection within a long asymmetrically heated vertical planar microchannel. The fully developed solutions of the thermal-flow fields and their characteristics are analytically derived on the basis of the first-order slip and jump boundary conditions and then presented for the thermophysical properties of ionized air at the standard reference state flowing through the microchannel with complete accommodation. The calculated results reveal that magnetic force plays a damping role in flow and results in decreases in flow rate, average flow drag, and average heat transfer rate. In addition, it is interesting that because the flow near the core is suppressed and the shear stress on the wall surface is reduced by the magnetic effects, a flatter velocity profile could be achieved by a greater magnetic force. These magnetic effects could be further magnified by increasing gas rarefaction or increasing cooler wall temperature.     

Thermomagnetic convection under alternating magnetic fields

Thermomagnetic convection within a square cavity filled with a magnetic fluid was studied under alternating magnetic field. The aim was to explore the response of the magnetic fluid towards alternating magnetic fields. A set of frequencies for the sinusoidal variation of the magnetic field intensity was used to study the heat transfer characteristics across the problem geometry. The effect on heat transfer was quantified by an averaged Nusselt number. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite difference method of solution of unsteady magnetic hydrodynamic boundary layer equations in a natural convection

The paper presents an investigation of the effect of a transverse magnetic field on an unsteady natural convection along a heated vertical plate. Finite difference method is employed to solve the non-linear equations governing the motion. The difference scheme satisfies consistency and stability conditions. The stability condition depends on time step which has to be satisfied in every time step. Proper care has been taken for the non-linear terms. The solutions have been deduced for different values of the magnetic field intensity. The results are satisfactory. In long run our results coincides with the steady state solutions already existing in the literature.     

Strong solutions to the equations of electrically conductive magnetic fluids

We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier–Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution.     

Influence of induced magnetic field on peristaltic flow in an annulus

This paper looks at the influence of the induced magnetic field on peristaltic transport through a uniform infinite annulus filled with an incompressible viscous and Newtonian fluid. The present theoretical model may be considered as mathematical representation to the movement of conductive physiological fluids in the presence of the endoscope tube (or catheter tube). The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow analysis has been developed for low Reynolds number and long wave length approximation. Exact solutions have been established for the axial velocity, stream function, axial induced magnetic field, current distribution and the magnetic force function. The effects of pertinent parameters on the pressure rise and frictional forces on the inner and outer tubes are investigated by means of numerical integrations, also we study the effect of these parameters on the pressure gradient, axial induced magnetic field and current distribution. The phenomena of trapping is further discussed.     

On the controllability of the Vlasov–Poisson system in the presence of external force fields

In this work, we are interested in the controllability of Vlasov–Poisson systems in the presence of an external force field (namely a bounded force field or a magnetic field), by means of a local interior control. We are able to extend the results of Glass (2003) [8], where the only present force was the self-consistent electric field.     

Numerical modeling of crystal growth under strong magnetic fields: An application to the travelling heater method

The article presents a 3-D numerical simulation study for the growth of single crystal semiconductors under strong magnetic fields. In such high fields, the magnetic body force components, which also depend on the flow velocity components present numerical challenges particularly in terms of convergence of iterations. To remedy such difficulties, a novel numerical approach was introduced in an in-house 3-D finite volume-based computer code. As an application, the Travelling Heater Method (THM) was selected for the growth of CdTe crystals under a static vertical magnetic field.