Low Magnetic Reynolds Number Research Articles

Investigation of viscous dissipation in the nanofluid flow with a Forchheimer porous medium: Modern transportation of heat and mass

In this article, the motion of a viscous nanofluid over a shrinking/stretching sheet is analyzed. This study also focuses on the non-Darcian transport in the stagnation-point flow of a nanofluid. The nanofluid consists of Brownian motion and thermophoresis effects. A magnetic field is applied in the vertical direction under the assumption of low magnetic Reynolds number. The Cattaneo-Christov phenomenon is incorporated to investigate the characteristics of heat and mass transfer. The characteristics of heat transfer are evaluated for the first time by utilizing the viscous dissipation with the Cattaneo-Christov theory. The equations (PDEs) governing the flow, heat and mass transport are first derived and then transformed into the corresponding ordinary differential equations via using similarity solutions. A homotopic proceduce is addressed to obtain the solutions for the accomplished ordinary differential equations. The variation of the divergent involved parameters on the fluid temperature, velocity and concentration distributions is disclosed through graphs and analyzed in detail. The features of the skin friction coefficient is graphed in order to understand the flow processes. It is noted that an increase in the Darcy number results in the decrease in the velocity field. Further impacts of Brownian diffusion and Eckert number on the temperature are quite similar.

Perturbation of eddy-currents by one inclusion in liquid metal

In this article, we present an analytical model to calculate the perturbation of the magnetic vector potential due to a non-conducting inclusion in a liquid metal translated at constant velocity. The model is valid for a low magnetic Reynolds number, Rem, and a low shielding parameter, Sω. We establish that the first order perturbation of the vector potential can be directly obtained from the value of the unperturbed eddy-current calculated at the location of the inclusion. An ECFM (Eddy-Current FlowMeter) device has been designed to validate the model and to study the frequency effects of the eddy-current and the volume of one inclusion and its location. We observe a good agreement between the model predictions and experimental data within the limit of the validity of the model. Based on scaling analysis, we show that a unique relation exists between the perturbation of the emf (electromotive force) measured with the ECFM and the volume of the inclusion and its location, which reflects the self-similarity of the model solution.

MHD tangent hyperbolic nanofluid with chemical reaction, viscous dissipation and Joule heating effects

In this article, the motion of a non-Newtonian tangent hyperbolic nanofluid past a stretching sheet is analyzed. Nanofluid is comprised of thermophoresis and Brownian motion effects. Magnetic field is implemented in vertical direction under the assumption of low magnetic Reynolds number. The phenomenon of heat transfer has been examined subject to the viscous dissipation and Joule heating whereas the mass transfer has been analyzed under the effect of chemical reaction. The partial differential equations (PDEs) governing the flow, heat and mass transport are re-framed in the form ordinary differential equations (ODEs) by means of the similarity solutions. A numerical procedure known as the Keller-box method has been implemented to obtain the solutions for the accomplished ODEs. The effects of the variations of different involved parameters on fluid temperature, velocity and concentration distributions are disclosed through graphs and analyzed in detail. The features of skin friction, heat and mass transfer coefficient are tabulated and graphed in order to perceive the flow, heat and mass transport processes. It is noticed that an increment in the Weissenberg number results in a reduction in the velocity field.

Numerical analysis of influence of thermochemical model on hypersonic magnetohydrodynamic control

<sec> In hypersonic flow, extremely high temperature due to shock aerodynamic heating leads plasma flow to form. By adding energy and momentum to the plas-ma flow field through the magnetic field on aircraft, the control of plasma flow field around aircraft can be realized. This has a broad prospect of applications in hypersonic aerodynamic control, aerothermal protection, and plasma distribution adjustment. Very recently, chemical reaction model and thermodynamic model were suggested to study the hypersonic magnetohydrodynamic control. However, the influence of different models and surface catalytic efficiency on hypersonic magnetohydrodynamic control are rarely analyzed in depth. </sec><sec> In this study, a comparison of different chemical reaction models and the influence of surface catalytic efficiency are discussed. Three-dimensional (3D) nu-merical simulation method and program of extra magnetic field coupled with reentry plasma flow under the assumption of low magnetic Reynolds number are developed by solving 3D chemical non-equilibrium Navier-Stokes equations and Maxwell electromagnetic field governing equations. Based on this method, the influence of different gas component models, chemical reaction models, and surface catalytic efficiency on hypersonic magnetohydrodynamic control are analyzed. The results show that the conductivity of plasma, calculated by different gas component models and chemical reaction models, can be quite different from each other, thus can influence the accurate study on the structure of hypersonic magneto flow field as well as the aerothermal and aerodynamic characteristics. Based on the calculation conditions in this paper, the Park chemical model has advantages in the consistency and accuracy in numerical simulation. The magnetic thermal protection is greatly influenced by the surface catalytic efficiency and the correlation between the magnetic thermal protection and the surface catalytic efficiency is nonlinear and can be quite different in different region. As the surface catalytic efficiency increases, the influence of magnetic field on heat flux at stagnation point drops drastically, then increases slowly, which is a joint result of thermal conduction and chemical component diffusion. The influence of magnetic field on magnetohydrodynamic drag character is less affected by the surface catalytic efficiency. As the catalytic efficiency increases, the influence of magnetic field on magnetohydrodynamic drag character drops slowly. </sec>

Gravitoturbulent dynamos in astrophysical discs

The origin of large-scale and coherent magnetic fields in astrophysical discs is an important and long standing problem. Researchers commonly appeal to a turbulent dynamo, sustained by the magneto-rotational instability (MRI), to supply the large-scale field. But research over the last decade in particular has demonstrated that various non-ideal MHD effects can impede or extinguish the MRI, especially in protoplanetary disks. In this paper we propose a new scenario, by which the magnetic field is generated and sustained via the gravitational instability (GI). We use 3D stratified shearing box simulations to characterise the dynamo and find that it works at low magnetic Reynolds number (from unity to ~100) for a wide range of cooling times and boundary conditions. The process is kinematic, with a relatively fast growth rate ($< 0.1 \Omega$), and it shares some properties of mean field dynamos. The magnetic field is generated via the combination of differential rotation and spiral density waves, the latter providing compressible horizontal motions and large-scale vertical rolls. At greater magnetic Reynolds numbers the build up of large-scale field is diminished and instead small-scale structures emerge from the breakdown of twisted flux ropes. We propose that GI may be key to the dynamo engine not only in young protoplanetary discs but also in some AGN and galaxies.

MHD stratified nanofluid flow by slandering surface

Current attempts focus on doubling the stratified effects of the magnetohydrodynamic flow of second grade nanoliquid over an impermeable surface stretching in a non-linear manner. The mathematical formulation is made using the boundary layer concept and assumptions of low magnetic Reynolds number. The non-linear stretching surface with variable thickness generates the flow. Incompressible non-Newtonian liquid is electrically conducted subject to a varying magnetic field. Heat transfer characteristics with heat generation/absorption, Joule heating and variable thermal conductivity effects are addressed. Novel features regarding Brownian motion and thermophoresis are also included. Mathematical representation of the considered aspects results in non-linear ODEs. The non-linear system is then computed and the derived solutions are adequate for convergence. The physical interpretation of quantities of interest are shown by graphical illustrations. The skin friction coefficient is also computed and inspected. Our computed results report that the influence of velocity ratio and Hartmann number result in similar velocity field characteristics. Furthermore, these aspects of nanoparticles, variable thermal conductivity and Hartmann number enhance the temperature distribution.

Magneto-fluid-structure interaction issues for vibrating rigid bodies in conducting fluids: The numerical and the analytical approaches

To study the magneto-fluid-structure interaction (MFSI) problems for rigid bodies and conducting fluids, a numerical method and an analytical approach have been carried out. The numerical scheme is based on a partitioned arbitrary Lagrangian-Eulerian framework, and is suitable for viscous, incompressible magneto-fluid-structure interaction simulation. A displacement prediction-pressure stabilization scheme has been established to enhance the stability and efficiency. Meanwhile, a consistent and conservative scheme for deforming configurations has been developed. This method can numerically ensure the divergence-free condition of the current density, and can conserve the momentum from the Lorentz forces after grids update. The analytical approach has considered a vibrating cylinder surrounded by confined fluids in a magnetic field. By assuming a small amplitude and a low magnetic Reynolds number, the analytical solution can describe the temporal and spatial distribution of the fluid fields, the electromagnetic fields, and the solid motion. These solutions are also suitable for general fluid-structure interaction (FSI) problems. Comparative results suggest good agreement between the two methods developed in this paper. Nonlinear effects of the magnetic fields were presented and discussed based on the numerical results. These cases are based on careful validations, and can hopefully be used for future verification and validation work.

Magnetic field advection in a rotating magnetic field driven flow induced by a non-ideal inductor

The limits of the axisymmetric ideal inductor approach and the low magnetic Reynolds number (Rem) approach are demonstrated for the case study of a flow driven by a rotating magnetic field induced by an explicit-pole non-ideal inductor. These effects are studied for an intermediate range of the magnetic Reynolds number 0.1 ≤ Rem ≤ 1. It is shown that phenomena that do not exist under the ideal inductor approach change the distribution of the electromagnetic body force (EMBF) from axial symmetry to rotational symmetry. However, it is found that the magnetic field advection (MFA), which is neglected under the low Rem approach, induces body force that changes the distribution of the EMBF so that it effectively becomes closer to being axisymmetric. Therefore, it is suggested that the ideal inductor approach should not be applied in low Rem applications; this approach can be applied in high Rem applications. It is also found that the effect of MFA on the averaged velocity field is negligible for higher values of Rem than traditionally assumed, but MFA has a significant effect in reducing the turbulent kinetic energy. The reduction is found to be a result of the MFA-induced EMBF reducing the turbulence production.

Simultaneous effects of melting heat and internal heat generation in stagnation point flow of Jeffrey fluid towards a nonlinear stretching surface with variable thickness

This paper investigates the magnetohydrodynamic (MHD) stagnation point flow of Jeffrey material towards a nonlinear stretching surface with variable surface thickness. Heat transfer characteristics are examined through the melting process, viscous dissipation and internal heat generation. A nonuniform applied magnetic field is considered. Boundary-layer and low magnetic Reynolds number approximations are employed in the problem formulation. Both the momentum and energy equations are converted into the non-linear ordinary differential system using appropriate transformations. Convergent solutions for resulting problems are computed. Behaviors of various pertinent parameters on velocity and temperature distributions are studied in detail. Further the heat transfer rate is also computed and analyzed.

Inverse and Direct Energy Cascades in Three-Dimensional Magnetohydrodynamic Turbulence at Low Magnetic Reynolds Number

This experimental study analyzes the relationship between the dimensionality of turbulence and the upscale or downscale nature of its energy transfers. We do so by forcing low-Rm magnetohydrodynamic turbulence in a confined channel, while precisely controlling its dimensionality by means of an externally applied magnetic field. We first identify a specific length scale l[over ^]_{⊥}^{c} that separates smaller 3D structures from larger quasi-2D ones. We then show that an inverse energy cascade of horizontal kinetic energy along horizontal scales is always observable at large scales, and that it extends well into the region of 3D structures. At the same time, a direct energy cascade confined to the smallest and strongly 3D scales is observed. These dynamics therefore appear not to be simply determined by the dimensionality of individual scales, nor by the forcing scale, unlike in other studies. In fact, our findings suggest that the relationship between kinematics and dynamics is not universal and may strongly depend on the forcing and dissipating mechanisms at play.

Plasma Characteristics and Performance of Nonequilibrium Disk Magnetohydrodynamic Generator with Swirl Vanes

Two-dimensional () numerical simulations of a nonequilibrium disk-shaped magnetohydrodynamic generator with swirl vanes were conducted to clarify the influences of electrical conductivity of swirl vanes and wakes induced by the swirl vanes on plasma flow and generator performance. The working gas was assumed to be helium seeded with cesium vapor. The thermal input to the magnetohydrodynamic generator and the strength of the applied magnetic field were set to 11 MW and 3 T, respectively. The swirl vanes were assumed to be made of either electrically conductive or insulated material. Low magnetic Reynolds number magnetohydrodynamic equations coupled with a conventional two-temperature plasma model were used for the simulations. The numerical results showed that the electron temperature and electrical conductivity of the plasma in the region between vanes for the conductive vanes were higher than those for the insulated ones. The differences between the two cases, however, rapidly disappeared right after the plasma passed through the region between vanes. Consequently, the swirl vane’s electrical conductivity hardly influenced the generator performance. The numerical results also demonstrated for the first time that the inside and the vicinity of the wakes had either low-power-output densities or negative ones corresponding to power consumption.

An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty faced in the process is the excessive computational cost. In this paper, we present an efficient, partitioned ensemble algorithm to determine multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which models MHD flows at low magnetic Reynolds number. The algorithm decouples the fully coupled problem into two smaller subphysics problems, which reduces the size of the linear systems that to be solved and allows the use of optimized codes for each subphysics problem. Moreover, the resulting coefficient matrices are the same for all realizations at each time step, which allows faster computation of all realizations and significant savings in computational cost. We prove this algorithm is first order accurate and long time stable under a time step condition. Numerical examples are provided to verify the theoretical results and demonstrate the efficiency of the algorithm.

Edge-Based Finite Element Formulation of Hypersonic Flows Under an Imposed Magnetic Field

The paper presents an edge-based finite element method for the simulation of three-dimensional hypersonic flows subject to an imposed magnetic field. Under the magnetogasdynamics assumptions and at low magnetic Reynolds numbers, a current continuity equation is employed instead of the system of Maxwell equations to obtain the induced electric field. The flow can be modeled by the Reynolds-averaged Navier–Stokes equations, and the electromagnetic body force and joule heating resulting from the imposed magnetic field introduced through source terms. Both inviscid and viscous flows over a sphere, as well as an Apollo-like reentry capsule geometry, are used to validate the approach. For both geometries, inviscid and viscous results show that the shock standoff distance increases with the magnetic-field intensity, whereas the heat flux at the stagnation point decreases. Moreover, it is observed that the induced electric field has a substantial impact on the effectiveness of magnetohydrodynamic heat shield and cannot be neglected in the calculations. An anisotropic mesh adaptive mesh methodology is used to refine the results and to demonstrate grid independence.

Numerical Analysis of an Artificial Compression Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers

Magnetohydrodynamics (MHD) is the study of the interaction of electrically conducting fluids in the presence of magnetic fields. MHD applications require substantially more efficient numerical methods than currently exist. In this paper, we construct two decoupled methods based on the artificial compression method (uncoupling the pressure and velocity) and partitioned method (uncoupling the velocity and electric potential) for magnetohydrodynamics flows at low magnetic Reynolds numbers. The methods we study allow us at each time step to solve linear problems, uncoupled by physical processes, per time step, which can greatly improve the computational efficiency. This paper gives the stability and error analysis, presents a brief analysis of the non-physical acoustic waves generated, and provides computational tests to support the theory.

Publisher’s Note: “Numerical simulation of turbulent Taylor-Couette flow between conducting cylinders in an axial magnetic field at low magnetic Reynolds number” [Phys. Fluids 30, 015107 (2018)

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Numerical study for heat generation/absorption in flow of nanofluid by a rotating disk

Abstract Here MHD three-dimensional flow of viscous nanoliquid by a rotating disk with heat generation/absorption and slip effects is addressed. Thermophoresis and random motion features are also incorporated. Velocity, temperature and concentration slip conditions are imposed at boundary. Applied magnetic field is utilized. Low magnetic Reynolds number and boundary layer approximations have been employed in the problem formulation. Suitable transformations lead to strong nonlinear ordinary differential system. The obtained nonlinear system is solved numerically through NDSolve technique. Graphs have been sketched in order to analyze that how the velocity, temperature and concentration fields are affected by various pertinent variables. Moreover the numerical values for rates of heat and mass transfer have been tabulated and discussed.

Flow of nanofluid by nonlinear stretching velocity

Abstract Main objective in this article is to model and analyze the nanofluid flow induced by curved surface with nonlinear stretching velocity. Nanofluid comprises water and silver. Governing problem is solved by using homotopy analysis method (HAM). Induced magnetic field for low magnetic Reynolds number is not entertained. Development of convergent series solutions for velocity and skin friction coefficient is successfully made. Pressure in the boundary layer flow by curved stretching surface cannot be ignored. It is found that magnitude of power-law index parameter increases for pressure distibutions. Magnitude of radius of curvature reduces for pressure field while opposite trend can be observed for velocity.

Multi-Physics Mathematical Model of Weakly-Ionized Plasma Flows

This work presents a multidisciplinary mathematical model, as a set of coupled governing equations and auxiliary relations describing the fluid-flow, thermal, and electric fields of partially-ionized plasma with low magnetic Reynolds numbers. The model is generic enough to handle three-dimensionality, Hall effect, compressibility, and variability of fluid, thermal, and electric properties of the plasma. The model can be of interest to computational modelers aiming to build a solver that quantitatively assesses direct extraction of electric energy from a plasma flow. Three different approaches are proposed to solve numerically for the electric fields with different levels of tolerance toward possible numerical instability encountered at a large Hall parameter, where the effective conductivity tensor loses diagonal dominance and becomes close to singular. A submodel for calculating the local electric properties of the plasma is presented in detail and is applied to demonstrate the effect of different factors on the electric conductivity, including the fuel’s carbon/hydrogen ratio and the alkaline seed element that acts as the ionizing species. An analytical expression for the collision cross-section for argon is developed, such that this noble gas can be included as one of the gaseous species comprising the plasma.

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor–Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

Numerical simulation of turbulent Taylor-Couette flow between conducting cylinders in an axial magnetic field at low magnetic Reynolds number

The effect of an axial homogeneous magnetic field on the turbulence in the Taylor-Couette flow confined between two infinitely long conducting cylinders is studied by the direct numerical simulation using a periodic boundary condition in the axial direction. The inner cylinder is rotating, and the outer one is fixed. We consider the case when the magnetic Reynolds number Rem ≪ 1, i.e., the influence of the induced magnetic field on the flow is negligible that is typical for industry and laboratory study of liquid metals. Relevance of the present study is based on the similarity of flow characteristics at moderate and high magnetic field for the cases with periodic and end-wall conditions at the large flow aspect ratio, as proven in the earlier studies. Two sets of Reynolds numbers 4000 and 8000 with several Hartmann numbers varying from 0 to 120 are employed. The results show that the mean radial induced electrical current, resulting from the interaction of axial magnetic field with the mean flow, leads to the transformation of the mean flow and the modification of the turbulent structure. The effect of turbulence suppression is dominating at a strong magnetic field, but before reaching the complete laminarization, we capture the appearance of the hairpin-like structures in the flow.