Magnetic Reynolds Number Research Articles

Thermal analysis of mixed convective peristaltic pumping of nanofluids in the occurrence of an induced magnetic field and variable viscosity

The present study investigates the heat and flow characteristics of mixed convective peristaltic transport of nanofluids containing magnetite γAl2O3 nanomaterials dispersed in conventional liquids, namely, ethylene glycol (C2H6O2) and water (H2O). The research provides a comprehensive analysis, considering various factors such as induced magnetic field, variable viscosity, buoyancy force, viscous dissipation, and porous media effects. The mathematical model is formulated based on a set of governing equations encompassing continuity, temperature, momentum, and induction, which are subsequently transformed into dimensionless form through appropriate scaling. A numerical method is employed to solve the resulting nonlinear differential equations. Results indicate that the velocity profile exhibits substantially higher magnitudes in the case of the γAl2O3-C2H6O2 nanoliquid when compared to the γAl2O3-H2O nanoliquid. Increasing the magnetic Reynolds number leads to a higher magnitude of the axial-induced magnetic field. An observed reduction in system entropy is associated with an increase in the permeability parameter.

Magnetic Filaments: Formation, Stability, and Feedback

As is well known, magnetic fields in space are distributed very inhomogeneously. Sometimes, field distributions have forms of filaments with high magnetic field values. As many observations show, such a filamentation takes place in convective cells in the Sun and other astrophysical objects. This effect is associated with the frozenness of the magnetic field into a medium with high conductivity that leads to the compression of magnetic field lines and formation of magnetic filaments. We analytically show, based on the general analysis, that the magnetic field intensifies in the regions of downward flows in both two-dimensional and three-dimensional convective cells. These regions of the hyperbolic type in magnetic fields play the role of a specific attractor. This analysis was confirmed by numerical simulations of 2D roll-type convective cells. Without dissipation, the magnetic field grows exponentially in time and does not depend on the aspect ratio between the horizontal and vertical scales of the cell. An increase due to compression in the magnetic field of highly conductive plasma is saturated due to the natural limitation associated with dissipative effects when the maximum magnitude of a magnetic field is of the order of the root of the magnetic Reynolds number Rem. For the solar convective zone, the mean kinetic energy density exceeds the mean magnetic energy density for at least two orders of magnitude, which allows one to use the kinematic approximation of the MHD induction equation. In this paper, based on the stability analysis, we explain why downward flows influence magnetic filaments, making them flatter with orientation along the interfaces between convective cells.

Numerical Simulation of the Chemical Reaction on Faraday MHD Accelerator

Magnetohydrodynamic (MHD) is one of the most promising novel propulsion technologies with the advantages of no pollution, high specific impulse, and high acceleration efficiency. As the carrier of this technology, the MHD accelerator has enormous potential for applications in hypersonic wind tunnels, supersonic ramjet engines, and deep space propulsion. In this study, a three-dimensional numerical simulation of an ideal Faraday magnetohydrodynamic (MHD) accelerator is conducted to assess the effect on performance with respect to applied potential and magnetic field intensity. The study is performed by employing a low magnetic Reynolds number MHD model coupled with a 7-component chemical reaction model to simplify the impact of real gas effects. The chemical reaction exhibits an increasing trend with rising applied potential and a decreasing trend with diminishing magnetic field strength. This variation influences the gas conductivity, subsequently affecting the velocity and thrust of the system. Specifically, at a magnetic field intensity of 2.0 T and an applied potential of 600 V, the accelerator exhibits maximum velocity and thrust growth rates of 18.6% and 59.8%, respectively.

The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$ , where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$ . For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

Helical dynamo growth and saturation at modest versus extreme magnetic Reynolds numbers.

Understanding magnetic field growth in astrophysical objects is a persistent challenge. In stars and galaxies, turbulent flows with net kinetic helicity are believed to be responsible for driving large-scale magnetic fields. However, numerical simulations have demonstrated that such helical dynamos in closed volumes saturate at lower magnetic field strengths when increasing the magnetic Reynolds number Rm. This would imply that helical large-scale dynamos cannot be efficient in astrophysical bodies without the help of helicity outflows such as stellar winds. But do these implications actually apply for very large Rm? Here we tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of Rm in a closed volume. We analyze data from numerical simulations with a new method that tracks resistive versus nonresistive drivers of helical field growth. We identify a presaturation regime when the large-scale field grows at a rate independent of Rm, but to an Rm-dependent magnitude. The latter Rm dependence is due to a dominant resistive contribution, but whose fractional contribution to the large-scale magnetic energy decreases with increasing Rm. We argue that the resistive contribution would become negligible at large Rm and an Rm-independent dynamical contribution would dominate if the current helicity spectrum in the inertial range is steeper than k^{0}. As such helicity spectra are plausible, this renews optimism for the relevance of closed dynamos. Our work pinpoints how modest Rm simulations can cause misapprehension of the Rm→∞ behavior.

On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos

Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma ${\beta \sim 1}$ . Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at $\beta \gg 1$ . This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of $\beta \gg 1$ . We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as ${\mathcal {R}}_{m}^{2/3}$ . We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of ${\mathcal {R}}_{m} \sim 10^{10}$ . We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.

Исследование электровихревого течения между плоскостями с помощью различных вычислительных подходов

Electrovortex flows arise when an electric current of varying density passes through a well-conducting fluid (e.g., acid or metal melt). In such a case, the electric current generates a magnetic field, which leads to the Lorentz force causing swirling currents of the medium. There are different methods of theoretical study of such currents. As a rule, to avoid the necessity to find the pressure dependence on coordinates, the variables "vector potential of velocity - swirl" ("scalar current function – swirl" in the case of axisymmetric flows) are used. In such a case, it is quite effective to use automodel variables, which allow to reduce the dimensionality of the problem. In this case, the solution for the introduced function can be sought in the form of an expansion by the electro-vortex flow parameter proportional to the square of the magnetic Reynolds number. Also, this solution can be obtained numerically, for example, using finite-difference methods. Nowadays, more and more often the solutions are investigated by means of direct numerical modeling methods, when no automodel approximations are made, which reduce the accuracy of the solution. Nevertheless, in such a case the number of computations can be quite large and requires the use of supercomputer resources. A separate difficulty is presented by the boundary conditions: for example, for the velocity vector potential we obtain a fourth-order equation, which imposes significant restrictions on the time steps in the evolution equation. The problem can be avoided by using approximate boundary conditions, but this again reduces the accuracy of the solution. In this paper, using the example of electro-vortex flow between planes, the solutions that can be obtained using the various computational approaches mentioned above are examined. The results obtained are compared, and they are also compared with analytical approximations.

Growth of Massive Molecular Cloud Filament by Accretion Flows. I. Slow-shock Instability versus Ambipolar Diffusion

The Herschel Gould Belt Survey showed that stars form in dense filaments in nearby molecular clouds. Recent studies suggest that massive filaments are bound by the slow shocks caused by accretion flows onto the filaments. The slow shocks are known to be unstable to corrugation deformation of the shock front. Corrugation instability could convert the accretion flow's ram pressure into turbulent pressure that influences the width of the filament, which, according to theory, determines the self-gravitational fragmentation scale and core mass. In spite of its importance, the effect of slow-shock instability on star-forming filaments has not been investigated. In addition, the linear dispersion relation obtained from ideal magnetohydrodynamics (MHD) analysis shows that the most unstable wavelength of shock corrugation is infinitesimally small. In the scale of dense filaments, the effect of ambipolar diffusion can suppress the instability at small scales. This study investigates the influence of ambipolar diffusion on the instability of the slow shock. We perform two-dimensional MHD simulations to examine the linear growth of the slow-shock instability, considering the effect of ambipolar diffusion. The results demonstrate that the most unstable scale of slow-shock instability is approximately 5 times the length scale of ambipolar diffusion ℓ AD calculated using post-shock variables, where ℓ AD corresponds to the scale where the magnetic Reynolds number for ambipolar diffusivity is unity.

Mixed convection phenomenon for hybrid nanofluid flow exterior to a vertical spinning cylinder with binary chemical reaction and activation energy

The study of hybrid nanofluids over spinning cylindrical configurations is widely used in numerous engineering and technological applications. Compared to conventional coolants, nanofluids explore superior thermal conductivities and thereby promote outstanding heat transport capabilities. In this study, hybrid nanofluid flow and thermal transmission across a vertical spinning cylinder are examined in the presence of an externally applied transverse magnetic field. The working fluids used are Ag/water nanofluid and Al2O3-Ag/water hybrid nanofluid. The analysis of heat transmission is carried out in the presence of slip and convective conditions, nonlinear thermal radiation, activation energy, and viscous dissipation. Partial differential equations (PDEs) are used to model the physical situation and are subsequently transformed into ordinary differential equations (ODEs). Through the use of MATLAB's bvp4c technique for ODEs, graphical and computational results are produced and validated with previously reported studies. The important findings are that the flow field diminishes as the magnetic field parameter and Reynolds number increase. Further, for larger levels of nano particle's fraction and thermal Biot number, the thermal features increase. Moreover, it is noted that the mass diffusion rate is lowered by the system's activation energy.

Critical magnetic Reynolds number of the turbulent dynamo in collisionless plasmas

ABSTRACT The intracluster medium of galaxy clusters is an extremely hot and diffuse, nearly collisionless plasma, which hosts dynamically important magnetic fields of ∼μG strength. Seed magnetic fields of much weaker strength of astrophysical or primordial origin can be present in the intracluster medium. In collisional plasmas, which can be approximated in the magnetohydrodynamical (MHD) limit, the turbulent dynamo mechanism can amplify weak seed fields to strong dynamical levels efficiently by converting turbulent kinetic energy into magnetic energy. However, the viability of this mechanism in weakly collisional or completely collisionless plasma is much less understood. In this study, we explore the properties of the collisionless turbulent dynamo using three-dimensional hybrid-kinetic particle-in-cell simulations. We explore the properties of the collisionless turbulent dynamo in the kinematic regime for different values of the magnetic Reynolds number, Rm, initial magnetic-to-kinetic energy ratio, (Emag/Ekin)i, and initial Larmor ratio, (rLarmor/Lbox)i, i.e. the ratio of the Larmor radius to the size of the turbulent system. We find that in the ‘un-magnetized’ regime, (rLarmor/Lbox)i > 1, the critical magnetic Reynolds number for the dynamo action Rmcrit ≈ 107 ± 3. In the ‘magnetized’ regime, (rLarmor/Lbox)i ≲ 1, we find a marginally higher Rmcrit = 124 ± 8. We find that the growth rate of the magnetic energy does not depend on the strength of the seed magnetic field when the initial magnetization is fixed. We also study the distribution and evolution of the pressure anisotropy in the collisionless plasma and compare our results with the MHD turbulent dynamo.

Effect of Magnetic Interaction Parameter and the Electrical Conductivity of the Fluid on the Stability of Hydromagnetic Channel Flow

The influence of magnetic interaction parameter and conductivity of the fluid on the stability against small perturbations on the streamlined base flow between two infinitely long parallel fixed plates is studied numerically. By normal mode analysis, the disturbance equations are reduced to Orr-Sommerfeld-type. Using the energy method, sufficient conditions for stability are derived by using the nature of the growth rate and sufficiently small values of the Reynold numbers. The disturbance equations are then solved using the Galerkin method corresponding to the base functions as Legendre-polynomials. Critical values for the Reynolds number, wave number, and speed of the wave are computed for various ranges of the magnetic interaction parameter and the magnetic Reynolds number. The curves of neutral stability are presented for different values of the nondimensional parameters that appeared in this study. The stability analysis is also discussed with the help of the plots of the rate of growth of disturbances for several values of the electrical conductivity and the magnetic interaction parameter. It is observed that both the fluid conductivity and the magnetic interaction parameter have direct control over fluctuations in the system. The results of this study are accurate and are comparable with the existing literature in the absence of a parallel magnetic field.

Comparative study of MHD boundary layer flow of hybrid nanofluid in a channel

AbstractThe interest of this study is to comprehensively explore the boundary layer flow of hybrid nanofluid within two infinite horizontal plates under the impact of magnetohydrodynamics (MHD), viscous and magnetic dissipation. The fluid is colloidal mixture of water and a very dilute suspension of Copper Oxide and Silver The flow is generated as a result of uniformly stretching of lower plate in direction. Nonlinear governing equations are modified into ordinary differential equations by nondimensional transformation. MATLAB based bvp4c and Mathematica based NDSolve are employed to compute the solutions of the reduced equations. A numerical and graphical comparison is done between bvp4c and NDSolve to verify the findings. The influence of significant parameters like magnetic field, Reynolds number, Prandtl number, Eckert number and heat absorption/generation are computed graphically. Additionally, numerical information about the heat mass flux is also tabulated to achieve complete picture of heat related data and evaluate its impact on flow dynamics. The outcomes of the present analysis can be used in various engineering processes where nanoparticles enhance thermal conductivity and conservation of energy.

Magnetohydrodynamical Torsional Oscillations from Thermoresistive Instability in Hot Jupiters

Hot Jupiter atmospheres may be subject to a thermoresistive instability where an increase in the electrical conductivity due to ohmic heating results in runaway of the atmospheric temperature. We introduce a simplified one-dimensional model of the equatorial substellar region of a hot Jupiter that includes the temperature dependence and time dependence of the electrical conductivity, as well as the dynamical back-reaction of the magnetic field on the flow. This model extends our previous one-zone model to include the radial structure of the atmosphere. Spatial gradients of electrical conductivity strongly modify the radial profile of Alfvénic oscillations, leading to steepening and downward transport of magnetic field, enhancing dissipation at depth. We find unstable solutions that lead to self-sustained oscillations for equilibrium temperatures in the range T eq ≈ 1000–1200 K and radial magnetic field strength in the range ≈10–100 G. For a given set of parameters, self-sustained oscillations occur in a narrow range of equilibrium temperatures that allow the magnetic Reynolds number to alternate between large and small values during an oscillation cycle. With our simplified geometry, outside of this temperature window the system reaches a steady state in which the effect of the magnetic field can be approximated as a magnetic drag term. Our results show that thermoresistive instability is a possible source of variability in magnetized hot Jupiters at colder temperatures and emphasize the importance of including the temperature dependence of electrical conductivity in models of atmospheric dynamics.

Darcy resistant of Soret and Dufour impact of radiative induced magnetic field sutterby fluid flow over stretching cylinder

The incompressible two-dimensional steady flow of Sutterby fluid over a stretching cylinder is taken into account. The magnetic Reynolds number is not deliberated low in the present analysis. Radiation and variable thermal conductivity are considered to debate the impact on the cylindrical surface. The Dufour and Soret impacts are considered on the cylinder. The mathematical model is settled by employing boundary layer approximations in the form of differential equations. The system of differential equations becomes dimensionless using suitable transformations. The dimensionless nonlinear differential equations are solved through a numerical scheme(bvp4c technique). The flow parameters of physical effects on the velocity, temperature, heat transfer rate, and friction between surface and liquid are presented in tabular as well as graphical form. The velocity function declined by improving the values of the Sponginess parameter. The fluid temperature is reduced by increment in curvature parameter.

Melting heat transfer of Maxwell–Sutterby fluid over a stretching sheet with stagnation region and induced magnetic field

Steady flow of incompressible Maxwell–Sutterby fluid at stretching sheet is discussed in the presence of stagnation point region. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied to the fluid flow. Temperature-dependent properties with radiation influence are considered in this analysis. The heat source or sink and melting impact are also debated in this analysis. A differential model of mathematics is developed by employing a governing constitutive equation. The differential equations’ model is condensed and becomes ordinary differential equations by implementing the appropriate transformations. Furthermore, these equations are elucidated by the numerical scheme. The physical influence of physical parameters is exhibited in the graphs and tabular form. The escalating values of M cause a shear thinning attitude in the fluid; as a result, devaluation in the velocity is detected in the case of [Formula: see text], while it depicted the counter behavior for [Formula: see text]. The skin friction is heightened with improving values of [Formula: see text] because [Formula: see text] boosted which improved the viscosity of liquid as well as heightened the friction at sheet. The enhancing values of [Formula: see text] cause a decrement in skin friction. The melting parameter is enriched which reduces the viscosity of fluid due to temperature boosting as well as friction reduction. The diminution in skin friction is found for enhancing the values of [Formula: see text].

Simultaneous Measurement of Flow Velocity and Electrical Conductivity of a Liquid Metal Using an Eddy Current Flow Meter in Combination with a Look-Up-Table Method.

The Eddy Current Flow Meter (ECFM) is a commonly employed inductive sensor for assessing the local flow rate or flow velocity of liquid metals with temperatures up to 700 ∘C. One limitation of the ECFM lies in its dependency on the magnetic Reynolds number for measured voltage signals. These signals are influenced not only by the flow velocity but also by the electrical conductivity of the liquid metal. In scenarios where temperature fluctuations are significant, leading to corresponding variations in electrical conductivity, it becomes imperative to calibrate the ECFM while concurrently monitoring temperature to discern the respective impacts of flow velocity and electrical conductivity on the acquired signals. This paper introduces a novel approach that enables the concurrent measurement of electrical conductivity and flow velocity, even in the absence of precise knowledge of the liquid metal's conductivity or temperature. This method employs a Look-Up-Table methodology. The feasibility of this measurement technique is substantiated through numerical simulations and further validated through experiments conducted on the liquid metal alloy GaInSn at room temperature.

Bioconvection analysis of EMHD and dissipative Williamson nanofluid over a three dimensional Riga plate with Joule heating effect

ABSTRACT The current study investigates the weakly hydromagnetic and bioconvection nanofluid flow of Williamson fluid, which conveys gyrotactic microorganisms, over a three-dimensional Riga surface. The primary objective is to stabilize biological, mechanical, and thermal systems through the introduction of exponentially decaying rheology in both the momentum and energy equations, known as the electro-magneto-hydrodynamic actuator (EMHD). As such, the working fluid is assumed to be dissipative, with significant consideration given to the magnetic Reynolds number and a higher-order reaction rate. To simplify the phenomenon of suspended nanoparticles’ bioconvection, an appropriate similarity transformation is applied, converting the system of partial differential equations (PDEs) into systems of ordinary differential equations (ODEs). To analyze the governing flow parameters, the numerical approach, Galerkin Weighted Residual Method (GWRM), is employed. The results are presented through tables and graphs, providing valuable insights. The findings of the study highlight that Hartmann number improves the weak movement of the Williamson fluid, thermophoresis number positively affects all flow distributions. Moreover, the temperature field is influenced by Brownian motion, leading to inflation, while the concentration field experiences a decrease due to a lower number of fluid particles available for reaction. Furthermore, higher buoyancy forces indicate significant fluid movement, resulting in a reduction in the Williamson fluid chemical reaction rate.

Suppression of small-scale dynamo in time-irreversible turbulence

ABSTRACT The conventional theory of small-scale magnetic field generation in a turbulent flow considers time-reversible random flows. However, real turbulent flows are known to be time irreversible: the presence of energy cascade is an intrinsic property of turbulence. We generalize the ‘standard’ model to account for the irreversibility. We show that even small time asymmetry leads to significant suppression of the dynamo effect at low magnetic Prandtl numbers, increases the generation threshold, and may even make generation impossible for any magnetic Reynolds number. We calculate the magnetic energy growth rate as a function of the parameters of the flow.

Numerical Computation of Williamson Hybrid Nanofluid Flow Over the Curved Surfaces With Effects of Thermal Radiation

Abstract The current investigation is based on Williamson's features of a hybrid nanofluid flow over a curved surface made mixture of silver (Ag) and titanium dioxide (TiO2) with engine oil. Under the presumption of a low magnetic Reynolds number, a constant homogenous magnetic field is applied. Consideration is given to the ramping temperature and the time-varying surface concentration. Thermal absorption and first-order consistent chemical reaction are also taken into account. To create a hybrid nanofluid, silver (Ag), and titanium nanoparticles are dispersed in a base fluid made of water and engine oil. Quasi-linearization technique and Finite difference scheme are employed on the nondimensional partial differential equations. All physical parameters of practical importance, such as velocity, temperature, and concentration profile are analyzed and provided in tables and graphs along with the impact of physical parameters. As the Williamson parameter (W) increases, the surface velocity of the steep plate decreases. Also, as the parameter temperature ratio of Nt and Rd increases, the forces opposing the flow field reduce the friction force, and the thermal field increases with temperature effects.

The magnetic non-hydrostatic shallow-water model

We consider the dynamics of a set of reduced equations describing the evolution of a magnetised, rotating stably stratified fluid layer, atop a stagnant dense, perfectly conducting layer. We consider two closely related models. In the first, the layer has, above it, relatively light fluid where the magnetic pressure is much larger than the gas pressure, and the magnetic field is largely force-free. In the second model, the magnetic field is constrained to lie within the dynamical layer by the implementation of a model diffusion operator for the magnetic field. The model derivation proceeds by assuming that the horizontal velocity and the horizontal magnetic field are independent of the vertical coordinate, whilst the vertical components in the layer have a linear dependence on height. The full system comprises evolution equations for the magnetic field, horizontal velocity and height field together with a linear elliptic equation for the vertically integrated non-hydrostatic pressure. In the magneto-hydrostatic limit, these equations simplify to equations of shallow-water type. Numerical solutions for both models are provided for the fiducial case of a Gaussian vortex interacting with a magnetic field. The solutions are shown to differ negligibly. We investigate how the interaction of the vortex changes in response to the magnetic Reynolds number ${Rm}$ , the Rossby deformation radius $L_D$ , and a Coriolis buoyancy frequency ratio $f/N$ measuring the significance of non-hydrostatic effects. The magneto-hydrostatic limit corresponds to $f/N\to 0$ .