Magnetofluid Dynamics Research Articles

Magneto-eklinostrophic Flow, Electromagnetic Columns, and von Kármán Vortices in Magneto-Fluid Dynamics

An analogy between magneto-fluid dynamics (MFD/MHD) and geostrophic flow in a rotating frame of reference, including the existence of electromagnetic columns identical to Taylor–Proudman columns, is identified and demonstrated theoretically here. The latter occurs within the limit of large values of a dimensionless group representing the magnetic field number. Such conditions are shown to be easily satisfied in reality. Consequently, the electromagnetic fluid flow subject to these conditions is two dimensional and the streamlines are shown to be identical to the pressure lines, in complete analogy to rotating geostrophic flows. These results suggest that von Kármán vortices are anticipated in the wake of virtual electromagnetic columns. An experimental setup is suggested to confirm the theoretical results experimentally.

Externally applied magnetic force effect on the Couette flow of a viscous incompressible fluid with heat source/sink

PurposeThis study aims to investigate the effect of externally applied magnetic force and heat transfer with a heat source/sink on the Couette flow with viscous dissipation in a horizontal rotating channel. The magnetic force is added to the governing equations. The effects of fluid flow parameters are observed under the applied magnetic force. In this system, the magnetic force is applied perpendicular to the plane of the fluid flow. In recent years, the magnetic field has renewed interest in aerospace technology. The physical and theoretical approach in the multidisciplinary field of magneto fluid dynamics (MFD) is applied in the field of aerospace vehicle design.Design/methodology/approachAuthors use the perturbation method to solve and find the approximate solutions of differential equations. First, convert the partial differential equation to ordinary differential equation and calculate the approximate solutions in two cases. The first solution got by assuming heat generating in the fluid and the second one got when heat absorbing. After applying the external magnetic force, the effects of various fluid parameters velocity, temperature, skin friction coefficient and Nusselt number are found and discussed using tables and graphs.FindingsIt is found that the velocity of the fluid has decreased tendency when the rotation of the fluid and magnetic force on the fluid increases. The temperature of the fluid, Prandtl value and Eckert number increased when the heat source generated heat. When heat absorbs the heat, sink parameter increases and the temperature of the fluid decreases. Also, while heat absorbs, the temperature increases when the Prandtl value and Eckert number increase.Originality/valueThe skin friction coefficient on the surface increases, when the rotation parameter and the magnetic force parameter of the fluid increase. In the case of heat generating, the Nusselt number increased, while the Eckert number and Prandtl numbers increased. Also, the Nusselt number has larger values when the heat source parameter has near the constant temperature, and it has smaller values when the temperature varies. In the case of heat-absorbing, the Nusselt number decreased when the Eckert and Prandtl numbers increased. Also, the Nusselt number varies up and down while the heat absorbing parameter increases.

Relaxed magnetohydrodynamics with ideal Ohm's law constraint

The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity ‘ideal’ Ohm's law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. The augmentation combines a pointwise vector Lagrange multiplier method and global penalty function method and can be used either for iterative enforcement of the IOL to arbitrary accuracy, or for constructing a continuous sequence of magnetofluid dynamics models running between RxMHD (no IOL) and weak IMHD (IOL almost everywhere). This is illustrated by deriving dispersion relations for linear waves on an MHD equilibrium.

Duel Solutions in Hiemenz Flow of an Electro-Conductive Viscous Nanofluid Containing Elliptic Single-/Multi-Wall Carbon Nanotubes With Magnetic Induction Effects

Abstract Modern magnetic nanomaterials are increasingly embracing new technologies including smart coatings, intelligent lubricants, and functional working fluids in energy systems. Motivated by studying the manufacturing magnetofluid dynamics of electroconductive viscous nanofluids, in this work, we analyzed the magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid containing carbon nanotubes (CNTs) past a stretching sheet. Magnetic induction effects are included. Similarity solutions are derived where possible in addition to dual branch solutions. Both single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are considered taking water and kerosene oil as base fluids. The governing continuity, momentum, magnetic induction, and heat conservation partial differential equations are converted to coupled, nonlinear systems of ordinary differential equations via similarity transformations. The emerging control parameters are shown to be Prandtl number (Pr), nanoparticle volume fraction parameter (φ), inverse magnetic Prandtl number (λ), magnetic body force parameter (β) and stretching rate parameter (A), and the type of carbon nanotube. Numerical solutions to the ordinary differential boundary value problem are conducted with the efficient bvp4c solver in matlab. Validation with earlier studies is included. Computations of reduced skin friction and reduced wall heat transfer rate (Nusselt number) are also comprised in order to identify the critical parameter values for the existence of dual solutions (upper and lower branch) for velocity, temperature, and induced magnetic field functions. Dual solutions are shown to exist for some cases studied. The simulations indicate that when the stretching rate ratio parameter is less than 1, SWCNT nanofluids exhibit higher velocity than MWCNT nanofluids with increasing magnetic parameters for water- and kerosene-oil-based CNT nanofluids. Generally, SWCNT nanofluids achieve enhanced heat transfer performance compared to MWCNT nanofluids. Water-based CNT nanofluids also attain greater flow acceleration compared with kerosene-oil-based CNT nanofluids.

SIGNIFICANCE OF MAGNETOHYDRODYNAMICS AND MODIFIED DARCY'S LAW ON THE ELECTROOSMOTIC PROPULSION OF VISCOELASTIC RADIATIVE NANOFLUID IN A MICROCHANNEL

Magnetofluiddynamics (MFD) is an emerging and interesting scientific area with various industrial and medical applications such as monitoring the blood flow, power generator, wire and fiber coating, geothermal reservoirs, magnetic drug targeting and cell separation. In view of significance of the magnetic field in the industrial and medical sciences, the current study focusses the effect of magnetohydrodynamics and modified Darcy's law on the viscoelastic nanofluid flow under various effects such as electroosmosis, thermal radiation, Hall currents and slip boundary conditions. We have considered the equations governing the flow problem in Cartesian coordinate system. The governing equations for the nanofluid flow have been simplified by using appropriate assumptions and nondimensional quantities, and provided the closed form solutions for the velocity, temperature and nanoparticle volume fraction profiles. Later, the numerical simulations are presented for diverse parameters on the various flow quantities. The current results reveal that, the velocity deduces with enhancing the strength of the magnetic field and it enhances with respect to solute Grashof number, and the temperature decreases with increase of radiation effects. The current analysis is relevant to electrokinetic hemodynamics and microfluidics.

Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics

We investigate the causality and the stability of the relativistic viscous non-resistive magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfvén and the magneto-sonic modes. In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfvén modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.

In situ Weak Magnetic-Assisted Thermal Stress Field Reduction Effect in Laser Welding

For decades, post-welding magnetic treatment has been used to reduce residual stress of welds by improving the crystal structure of solid-state welds. In this paper, we propose a new magnetic treatment method, which can reduce the time-dependent thermal stress field in situ and reduce the final residual stress of welds by simply exerting an assisted weak magnetic field perpendicular to the welding direction and workpiece during laser welding. A new finite-element model is developed to understand the thermal–mechanical physical process of the magnetic-assisted laser welding. For the widely used 304 austenite stainless steel, we theoretically observed that this method can reduce around 10 pct of the time-dependent thermal stress field, and finally reduce approximately 20 MPa of residual stress near the heat-affected zone with a 415-mT magnetic field for typical welding process parameters. A new mechanism based on magneto-fluid dynamics is proposed to explain the theoretical predications by combining high-speed imaging experiments of the transient laser welding process. The developed method is very simple but surprisingly effective, which opens new avenues for thermal stress reduction in laser welding of metals, particularly heat-sensitive metallic materials.

Novel mechanism for vorticity generation in black-hole accretion disks

Vorticity generation in accretion disks around Schwarzschild and Kerr black holes is investigated in the context of magnetofluid dynamics derived for both General Relativity (GR), and modified gravity formulations. In both cases, the Kerr geometry leads to a "stronger" generation of vorticity than its Schwarzschild counterpart. Of the two principal sources, the relativistic drive peaks near the innermost stable circular orbit (isco), whereas the baroclinic drive dominates at larger distances. Consequences of this new relativistic vorticity source are discussed in several astrophysical settings.

Magnetofluid dynamics in curved spacetime

A grand unified field $\mathcal{M}^{\mu\nu}$ is constructed from Maxwell's Field tensor and appropriately modified flow field, both non-minimally coupled to gravity, to analyze the dynamics of hot charged fluids in curved background space-time. With a suitable $3+1$ decomposition, this new formalism of the hot fluid is then applied to investigate the vortical dynamics of the system. Finally, the equilibrium state for plasma with non-linear coupling through Ricci scalar $R$ to gravity is investigated to derive a double Beltrami equation in curved space-time.

Stochastic modeling of MHD turbulence in magnetized plasma

This paper concerns the magneto-fluid dynamics modeled by the stochastic flow where the turbulent term is driven by the random forcing. Magnetohydrodynamic (MHD) turbulence can be interpreted in terms of a standard map (SM), modeling perturbed Hamiltonian systems, to explain some of the features of the problem. The dynamics generated by SM, although being chaotic, are influenced by periodic islands embedded in the chaotic sea due to stickiness effect and also to the behavior of the diffusion coefficient. Anomalous diffusion exists only up to some crossover time, beyond which the diffusion is Gaussian consistent with quasi-linear predictions. The results can be applicable to systems where there exist intensive interaction between a stochastic turbulent system and waves.

MPI-AMRVAC FOR SOLAR AND ASTROPHYSICS

In this paper we present an update on the open source MPI-AMRVAC simulation toolkit where we focus on solar- and non-relativistic astrophysical magneto-fluid dynamics. We highlight recent developments in terms of physics modules such as hydrodynamics with dust coupling and the conservative implementation of Hall magnetohydrodynamics. A simple conservative high-order finite difference scheme that works in combination with all available physics modules is introduced and demonstrated at the example of monotonicity preserving fifth order reconstruction. Strong stability preserving high order Runge-Kutta time steppers are used to obtain stable evolutions in multidimensional applications realizing up to fourth order accuracy in space and time. With the new distinction between active and passive grid cells, MPI-AMRVAC is ideally suited to simulate evolutions where parts of the solution are controlled analytically, or have a tendency to progress into or out of a stationary state. Typical test problems and representative applications are discussed, with an outlook to follow-up research. Finally, we discuss the parallel scaling of the code and demonstrate excellent weak scaling up to 30 000 processors allowing to exploit modern petascale infrastructure.

Numerical analysis for magnetohydrodynamic chemically reacting and radiating fluid past a non-isothermal uniformly moving vertical surface adjacent to a porous regime

A mathematical model is conducted for the unsteady magnetohydrodynamic viscous, incompressible free convective flow of an electrically conducting Newtonian fluid over an impulsively-started semi-infinite vertical plate adjacent to saturated porous medium in the presence of appreciable thermal radiation heat transfer and chemical reaction of first order taking transverse magnetic field into account. The fluid is assumed optically thin gray gas, absorbing-emitting radiation, but a non-scattering medium. The governing non-linear partial differential equations are non-dimensionalized and are solved by an implicit finite difference scheme of Crank–Nicholson type. It is found that, increasing magnetic parameter serves to decelerate the flow, but increased temperatures and concentration values. An increase in the porosity parameter (K) is found to escalate the local skin friction (τx), Nusselt number (Nux) and the Sherwood number (Shx). Applications of the model include fundamental magneto-fluid dynamics, MHD energy systems and magneto-metallurgical processing for aircraft materials.

MATHEMATICAL MODELING FOR POROUS MEDIA TRANSPORT IN NEWTONIAN RADIATING/CHEMICALLY REACTING FLUID OVER AN IMPULSIVELY-STARTED VERTICAL PLATE: A FINITE DIFFERENCE APPROACH

Theoretical investigation is presented here for the model of unsteady MHD thermal convection flow of a viscous incompressible absorbingemitting optically thin gray gas along an impulsivelystarted semi-infinite vertical plate adjacent to the Darcian porous regime in the presence of a first order chemical reaction and significant thermal radiation effects. The conservation equations are nondimensionalized and are solved by an accurate and unconditionally stable implicit finite difference scheme of Crank-Nicholson type. The flow is found to be accelerated with increasing porosity parameter (K), whereas the temperature and concentration distributions are reduced in the Darcian regime. Flow velocity and Temperature are found to be depressed with progression of thermal radiation (Ra) contribution, but enhanced the concentration distribution. Applications of the model arise in solar energy collector analysis, magneto-fluid dynamics and industrial materials processing.

Experimental modal analysis of resistive wall toroidal pinch plasma dynamics

The linearized magnetofluid dynamics of a magnetically confined reversed-field pinch plasma is extracted from a set of perturbative randomized nondestructive experiments. The spectrum of the generically estimated linear time-invariant system is compared to solutions of the corresponding eigenvalue problems formed by the ideal magnetohydrodynamic model. Stable and unstable nonresonant resistive wall modes are accurately identified.

A two-dimensional nodal model with turbulent effects for the synthesis of Si nano-particles by inductively coupled thermal plasmas

Nano-particle synthesis by means of inductively coupled plasma torches is a material process of large technological interest. Numerous parameters are involved in the optimization of this process; hence the development of numerical models for the prediction of thermal and magneto-fluid dynamics fields, precursor powder trajectories and thermal history, as well as nano-particle formation and growth, is necessary for the up-scaling of these devices from laboratory batch production to an industrial continuous process. In this work, a two-dimensional (2D) discrete-type model (nodal model) for the analysis of nano-powder nucleation and growth is presented, taking into account convection, diffusion and turbulent effects on particle formation. Discrete-type models feature high precision and reveal a great deal of information useful for clarifying the nano-particle formation process. Using Si as the precursor material, 2D simulations of a nano-particle synthesis RF plasma apparatus with a reaction chamber are carried out. Good agreement is found when comparing results obtained with this model with those coming from a well-established nucleation-coupled moment method. Moreover, the extended amount of obtainable information that characterizes the nodal model is underlined.

Models for coronal mass ejections

Coronal mass ejections (CMEs) play a key role in space weather. The mathematical modelling of these violent solar phenomena can contribute to a better understanding of their origin and evolution and as such improve space weather predictions. We review the state-of-the-art in CME simulations, including a brief overview of current models for the background solar wind as it has been shown that the background solar wind affects the onset and initial evolution of CMEs quite substantially. We mainly focus on the attempt to retrieve the initiation and propagation of CMEs in the framework of computational magnetofluid dynamics (CMFD). Advanced numerical techniques and large computer resources are indispensable when attempting to reconstruct an event from Sun to Earth. Especially the simulations developed in dedicated event studies yield very realistic results, comparable with the observations. However, there are still a lot of free parameters in these models and ad hoc source terms are often added to the equations, mimicking the physics that is not really understood yet in detail.

Implicit methods for fluid dynamics

This paper represents the contributions to the development of implicit procedures for solving the equations of fluid dynamics made by Briley and McDonald (1975) [1], Beam and Warming (1976, 1978) [2,3] and Lombard et al. (1983) [4]. The contributions of Briley and McDonald and Beam and Warming are well known, but Lombard has not been fully recognized for his innovative contributions to flux vector splitting and use of the DDADI (Diagonally Dominate Alternating Direction Implicit) algorithm. Their contributions are presented herein. Fully implicit algorithms are applied to two complex flow problems of current interest, (1) hypersonic non-equilibrium flow about a blunt nosed body and (2) flow within an MFD (magneto-fluid dynamics) accelerator. These two applications would be exceeding costly without the use of fully implicit methods.

Magnetofluid dynamics of magnetized cosmic plasma: firehose and gyrothermal instabilities

Both global dynamics and turbulence in magnetized weakly collisional cosmic plasmas are described by general magnetofluid equations that contain pressure anisotropies and heat fluxes that must be calculated from microscopic plasma kinetic theory. It is shown that even without a detailed calculation of the pressure anisotropy or the heat fluxes, one finds the macroscale dynamics to be generically unstable to microscale Alfvenically polarized fluctuations. Two instabilities are considered in detail: the parallel firehose instability (including the finite-Larmor-radius effects that determine the fastest growing mode) and the gyrothermal instability (GTI). The latter is a new result - it is shown that a parallel ion heat flux destabilizes Alfvenically polarized fluctuations even in the absence of the negative pressure anisotropy required for the firehose. The main conclusion is that both pressure anisotropies and heat fluxes trigger plasma microinstabilities and, therefore, their values will likely be set by the nonlinear evolution of these instabilities. Ideas for understanding this nonlinear evolution are discussed. It is argued that cosmic plasmas will generically be "three-scale systems," comprising global dynamics, mesoscale turbulence and microscale plasma fluctuations. The astrophysical example of cool cores of galaxy clusters is considered and it is noted that observations point to turbulence in clusters being in a marginal state with respect to plasma microinstabilities and so it is the plasma microphysics that is likely to set the heating and conduction properties of the intracluster medium. In particular, a lower bound on the scale of temperature fluctuations implied by the GTI is derived.

Numerical Investigation of Decomposed Magnetofluid Dynamics Equations

In addition to the two commonly used formulations for magnetofluid dynamics, a third formulation based on the decomposition of the magnetic field for solving full magnetofluid dynamics equations is explored. The governing equations are transformed to a generalized computational domain and discretized using a finite difference technique. A time-explicit multistage Runge―Kutta scheme augmented with total variation diminishing limiters for time integration is implemented. The developed codes have been validated with the existing closed-form solution of the magnetic Rayleigh problem. Results obtained from the decomposed magnetofluid dynamics equations compare well with results obtained by solving the classical full magnetofluid dynamics equations for a wide range of magnetic Reynolds numbers. It is shown that the decomposed magnetofluid dynamics technique requires substantially less computation time compared with classical full magnetofluid dynamics equations for the solution involving flowfields with high imposed magnetic fields.

Numerical Solutions of Two Heat Transfer Limits of MFM Square Duct Flow Using MatLab Program

The heat transfer of a magneto-fluid-dynamics (MFM) laminar flow in an electricallyinsulated square duct subjected to two boundary condition limits of constant heat flux and constant wall temperature is examined numerically. The working fluid is electrically conducting fluid (i.e. liquid metal). The central finite difference scheme is used to discretize the governing equations and the resulting equations are solved by MatLab using the iterative Gauss-Seidel method. The solutions for these heat transfer limits, the constant temperature boundary condition (with non-linear energy equation) and the constant heat flux boundary condition (with linear energy equation) are compared with previous work done for ducts of circular cross section subjected to constant heat flux boundary condition. The results show that the circular duct with constant heat flux exhibits the highest heat transfer rate whereas the square duct with constant temperature has the lowest heat transfer rate.