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This paper examines the two-dimensional laminar steady magnetohydrodynamic doublediffusive mixed convection in a curved enclosure filled with different types of nanofluids. The enclosure is differentially heated and concentrated, and the heat and mass source are embedded in a part of the left wall having temperature Th (>Tc) and concentration ch (>cc). The right vertical wall is allowed to move with constant velocity in a vertically upward direction to cause a shear-driven flow. The governing equations along with the boundary conditions are transformed into a nondimensional form and are written in stream function-velocity formulation, which is then solved numerically using the Bi-CGStab method. Based on the numerical results, the effects of the dominant parameters such as Richardson number (1 ≤ Ri ≤ 50), Hartmann number (0 ≤ Ha ≤ 60), solid volume fraction of nanoparticles (0.0 ≤ ϕ ≤ 0.02), location and length of the heat and mass source are examined. Results indicate that the augmentation of Richardson number, heat and mass source length and location cause heat and mass transfer to increase, while it decreases when Hartmann number and volume fraction of the nanoparticles increase. The total entropy generation rises by 1.32 times with the growing Richardson number, decreases by 1.21 times and 1.02 times with the rise in Hartmann number and nanoparticles volume fraction, respectively.

The current study pertains to heat and mass transportation of magnetic fluid flow having dilute diffusion of nanoparticles and motile microorganisms over a permeable stretched sheet to examine the influence of thermal radiation and activation energy. Similarity functions are utilized to convert the highly mixed non-linear partial differential equations into higher-order non-linear ordinary differential equations. Five coupled equations are derived to be resolved numerically by employing a computing function Bvp4c, built-in Matlab. Two sets of thermal boundaries prescribed surface temperature (PSF) and prescribed heat flux (PHF) are considered. Basic physical quantities, temperature distribution, concentration, velocity field, and motile micro-organism profiles are observed as influenced by emerging parameters. The microorganisms distribution undergoes decreasing behavior against growing values of bio-convection Lewis number and Peclet number. These results are highly useful in the application of heat-transmitting devices and microbial fuel cells. It is seen that decreasing trend is observed in velocity profile when parameters Nr and Nc are uplifted. Also, the motility of the nanofluid decreases when the Lb parameter is raised. On the other hand, an increase in Peclet number Pe showed a rising trend in motility profile. Additionally, the implications of Brownian motion, Rayleigh number, Bioconvection Lewis number thermophoresis parameter, Peclet number, and buoyancy ratio parameter are discussed. Moreover, the obtained outcomes are validated as compared to the existing ones as limiting cases. Representative findings for microorganism concentration, skin friction coefficient, temperature gradient, local Sherwood number and density number of motile microorganisms, velocity field, temperature, the volumetric concentration of nanoparticles, are discussed in tabulated and graphical form. [ABSTRACT FROM AUTHOR]

We analyze the stationary configuration of a thin axisymmetric stellar accretion disk, neglecting non-linear terms in the plasma poloidal velocity components. We set up the Grad-Shafranov equation for the system, including the plasma differential rotation (according to the so-called co-rotation theorem). Then, we study the small scale backreaction of the disk to the central body magnetic field and we calculate the resulting radial infalling velocity. We show that the small scale radial oscillation of the perturbed magnetic surface is associated to the emergence of relevant toroidal current densities, able to balance the Ohm law even in the presence of quasi-ideal values of the plasma resistivity. The contribution to the infalling velocity of the averaged backreaction contrasts accretion, but it remains negligible as far as the induced magnetic field is small compared to that of the central body.

On a porous layered inclined plate, magneto-free-convection flow of a rate type fluid is investigated. The problem is modeled as natural convection for oscillating and general movements of an inclined plate moving in a magnetized medium with a slanted external magnetic field that is either stationary or moving in tandem with the plate. The plate is subjected to a symmetric temperature field with double-sided thermal operation. Constant concentration, first order chemical reaction, and thermal conductivity as a general feature of time are used in heat transfer measurement. On the velocity of the fluid, the impact of varying plate angles with the vertical as well as the slanted angle of the magnetic field with the plate are studied. The motion of the plate and temperature distribution in specific situations was discussed. We can retrieve many results by changing the values of the functions and parameters in our general solutions, including the related results for the viscous fluid from the literature as a limiting case. As a result, the matter of identical models is no longer an issue. Furthermore, graphical software is used to do parametric analysis on fluid dynamics.

Efficient simulation of a quantum system's dynamics is expected to be an important application area for quantum computers as existing classical computers cannot do this. However, quantum systems are not unique in being hard to simulate. For example, classical nonlinear continuum systems and fields are governed by nonlinear partial differential equations whose solution is also hard for classical computers. Solving such equations is essential for many economically important industries/applications such as the aerospace industry, weather‐forecasting, fiber‐optics communication, and plasma magneto‐hydrodynamics. This raises the question: can a quantum computer speed‐up solving these equations? In this Review, a new quantum algorithm is described for solving nonlinear partial differential equations for which the answer is yes. First, a new quantum algorithm is discussed for solving the Navier‐Stokes nonlinear partial differential equations which govern the flow of a viscous fluid. Its construction, verification, and computational cost are described, and it is shown that a significant quantum speed‐up is possible. Its generalization to a quantum algorithm for solving nonlinear partial differential equations is described. The Review closes with a discussion of next steps forward. These new quantum algorithms open up a large new application area for quantum computing with substantial economic impact, including the trillion‐dollar aerospace industry. [ABSTRACT FROM AUTHOR]

Melting phenomena occurs in various industrial applications, such as metal castings of turbine blades, environmental engineering, PCM-based thermal storage devices, etc. During the design of these devices, they are designed for efficient heat transfer rate. To improve the heat transfer rate, understanding of the important flow processes during the melting (and solidification) is necessary. An objective of the present work is to study the effect of natural convection and magnetic field on interface morphology and thereby on melting rate. In this work, therefore, an effect of uniform transverse magnetic field on the melting inside a cavity, filled initially with solid gallium, at various Rayleigh numbers (Ra=3×105, 6×105, and 9×105) is presented. A 2D unsteady numerical simulation, with the enthalpy-porosity formulation, is performed using ANSYS-Fluent. The magnetic field is characterized by the Hartmann number (Ha) and the results are shown for the Ha = 0, 30 and 50. The horizontal walls of the cavity are considered insulated and vertical walls are respectively considered hot and cold. It is observed that the role of natural convection during the melting is significant on the temperature distribution and solid-liquid interface. The increased magnetic field (Ha = 30 and 50) found to have a suppressing effect on the dominance of natural convection at all Rayleigh numbers (Ra=3×105, 6×105, and 9×105).

The effect of source/sink heat location and size on Magneto-hydrodynamic mixed convection in hybrid nanofluid of Al 2 O 3 -Cu/Water within the L-shaped cavity is studied in this paper. Two uniform heat sources are put at the corners of the bottom walls of enclosure and the beginning and the end of L-shape enclosure set to be at the cold temperature. The other parts of enclosure's walls are supposed to be insulated. The finite difference method and Boussinesq approximation is utilized to discrete the governing equations. The fundamental flow physics and thermal behavior are explored in terms of pertinent parameters such as the effects of sink/source heat generation, magnetic field and angle, Hartmann number, cavity length ratio, and hybrid volume fraction on average and surface Nusselt number, streamlines, isotherms, and entropy generation are studied. The results demonstrate that maximum amount of the sink power causes the best heat transfer performance. [ABSTRACT FROM AUTHOR]

Using data from the Helioseismic Magnetic Imager, we report on the amplitudes and phase relations of oscillations in quiet-Sun, plage, umbra and the polarity inversion line (PIL) of an active region NOAA#11158.We employ Fourier, wavelet and crosscorrelation spectra analysis. Waves with 5 min periods are observed in umbra, PIL and plage with common phase values of φ(v, I)=π/2, φ(v, Blos)=-(π/2). In addition, φ(I, Blos)=π in plage are observed. These phase values are consistent with slow standing or fast standing surface sausage wave modes. The line width variations, and their phase relations with intensity and magnetic oscillations, show different values within the plage and PIL regions, which may offer a way to further differentiate wave mode mechanics. Significant Doppler velocity oscillations are present along the PIL, meaning that plasma motion is perpendicular to the magnetic field lines, a signature of Alvènic waves. A time-distance diagram along a section of the PIL shows Eastward propagating Doppler oscillations converting into magnetic oscillations; the propagation speeds range between 2 and 6kms-1. Lastly, a 3min wave is observed in select regions of the umbra in the magnetogram data. [ABSTRACT FROM AUTHOR]

A key technique for controlling solidification microstructures is magneto-hydrodynamics (MHD), resulting from imposing a magnetic field to solidifying metals and alloys. Applications range from bulk stirring to flow control and turbulence damping via the induced Lorentz force. Over the past two decades the Lorentz force caused by the interaction of thermoelectric currents and a magnetic field, a MHD phenomenon known as Thermoelectric Magnetohydrodynamics (TEMHD), was also shown to drive inter-dendritic flow altering microstructural evolution. In this contribution, high-speed synchrotron X-ray tomography and high-performance computational simulation are coupled to reveal the evolution, dynamics and mechanisms of solidification within a magnetic field, resolving the complex interplay and competing flow effects arising from Lorentz forces of different origins. The study enabled us to reveal the mechanisms disrupting the traditional columnar dendritic solidification microstructure, ranging from an Archimedes screw-like structure, to one with a highly refined dendritic primary array. We also demonstrate that alloy composition can be tailored to increase or decrease the influence of MHD depending on the Seebeck coefficient and relative density of the primary phase and interdendritic liquid. This work paves the way towards novel computational and experimental methods of exploiting and optimising the application of MHD in solidification processes, together with the calculated design of novel alloys that utilise these forces. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Penalization of Dirichlet boundary controlled nonstationary magneto-hydrodynamic equations is considered. Asymptotic behavior of solutions of a penalized control problem with respect to the penalty parameter is investigated. It is proved that solutions of the penalized boundary control problem converge to the solutions of the Dirichlet control problem as penalty parameter goes to zero. The existence of optimal solutions as well as the characterization of such solutions by first order necessary conditions are established. A second order sufficient optimality condition for the optimal control problem is also developed. Numerical results are provided showing the feasibility and effectiveness of the penalty method. [ABSTRACT FROM AUTHOR]

• The effects of a vortex generator (VG) and magneto hydrodynamics (MHD) on the thermal properties of nanofluids in a microchannel is numerically studied. • It was shown that at GR = 1.0, the strength of the vorticity is still high, which can act as a strong turbulator in the wake of the cylinder. • The numerical results demonstrate that when the MHD and VG effects are applied to the model, heat transfer increases by approximately 20%. • It is demonstrated that, for the analyzed models in this work, the effect of the VG mechanism is stronger than the influence of MHD. This paper investigates the effects of a vortex generator (VG) and magneto-hydrodynamics (MHD) on the thermal properties of nanofluids in a microchannel. A variety of test scenarios within the laminar flow regimes are numerically examined: nanofluids in a hot-walled simple channel (SC); nanofluids in a heated-walled channel where a circular cylinder is embedded within the channel and functions as a vortex generator (VG); nanofluids in a heated-walled channel that incorporates both a vortex generator and magneto-hydrodynamics (VG-MHD). The channel has a circular cylinder with a diameter of D that is fixed inside the channel with various gap ratios (GR = G/D) ranging from 0.5 to 4.0. Numerical investigations for laminar flow with Re ≤ 1,000 are carried out. The nanoparticle volume fractions range from 0 % to 7 %, and the magnetic field is set at 0.05 T. The best heat transmission conditions with the lowest skin friction coefficient are evaluated for the optimal GR. It is found that heat transfer is enhanced by approximately 20 % when MHD and VG effects are employed, in contrast to a traditional channel that does not utilize the MHD effect. [ABSTRACT FROM AUTHOR]

Bu çalışmada, lityum sıvısı dıştan manyetik alan indüksiyonuna maruz bırakılan üç boyutlu dairesel bir kanalda sayısal olarak incelenmiştir. Manyetik alan, kanala akış yönüne dik olarak uygulanmıştır. Re=2250 ve manyetik alan kuvveti sırasıyla 0T, 0.04T, 0.08T ve 0.12T olarak seçilmiştir. Bunun yanında, akışkan sıcaklığı 473.15 K iken cidar sıcaklığı 373.15 K’dir. Hesaplamalar ANSYS-Fluent ticari yazılımı ile gerçekleştirilmiştir. Manyetik alanın akışkan hızı, basınç ve sıcaklık üzerindeki etkileri grafiksel olarak sunulmuştur. Manyetik alan etkisinin akışkan hızını azaltırken, basıncı arttırdığı gözlemlenmiştir. Ayrıca, manyetik alan boru uzunluğu boyunca kanalın farklı bölgelerinde, sıcaklığı farklı şekilde etkilediği gözlemlenmiştir.

We present a radiative magneto-hydrodynamic simulation set-up using the pencil code to study the generation, propagation and dissipation of Alfvén waves in the solar atmosphere which includes a convective layer, photosphere below and chromosphere, transition region and the corona above. We prepare a set-up of steady-state solar convection where the imposed external magnetic field also has reached the final value gradually starting from a very small value. From that state, we start several simulations by varying the magnetic Prandtl number and the forcing strengths. We find the propagation characteristics of waves excited in this simulation run depend strongly on the magnetic Prandtl number and the wave number of the forcing. For magnetic Prandtl number of unity, we obtain localised heating in the corona due to shock dissipation. [ABSTRACT FROM AUTHOR]

The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions of computation hours on current high-performance computing (HPC) hardware. The aim of this work is to describe methods for an efficient parallelisation of boundary conditions and data input/output (IO) strategies that allow for a better scaling towards thousands of processors (CPUs). The Pencil Code is tested before and after optimisation to compare the performance and scalability of a coronal MHD model above an AR. We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. The scalability is improved by more than one order of magnitude through the HPC-friendly boundary conditions and IO strategies. This work describes also the necessary nudging methods to drive the MHD model with observed magnetic fields from the Sun's photosphere. In addition, we present the upper and lower atmospheric boundary conditions (photospheric and towards the outer corona), including swamp layers to diminish perturbations before they reach the boundaries. Altogether, these methods enable more realistic 3D MHD simulations than previous models regarding the coronal heating problem above an AR – simply because of the ability to use a large amount of CPUs efficiently in parallel. [ABSTRACT FROM AUTHOR]

The current numerical study looked into the magneto-hydrodynamics mixed convection of nanofluid in a lid-driven square cavity subjected to heating by a triangular thick wall. The nanofluid heat transfer was modelled by using a two-phase Buongiorno model, whereas obtaining a numerical solution for the governing equations was described using the finite element method. Comparisons made between the proposed method and the experimental and numerical works published prior revealed outcomes of good agreement. An in-depth investigation and discourse on the influences of certain attributes such as Reynolds number, Richardson number, Hartmann number, nanofluid volume fraction, and triangular wall thickness on overall heat transfer and nanoparticle distribution were subsequently put forth. The outcomes revealed the CW rotations for streamlines and nanoparticle migration. Additionally, incremental thermophoresis and Brownian motion resulted in expanding Hartmann number growth, thus yielding increased nanoparticle migration. [ABSTRACT FROM AUTHOR]

The fluid flow and convective heat transfer occurring in a lid-driven cavity which is filled with electricity conductive fluid and subjected to external magnetic field, is analyzed comprehensively. The variations in inclination angle of magnetic field and its strength are addressed during the investigation. The cavity is heated by a linearly varying heat source applied on the left wall. Different regimes of heat transfer are considered by varying pertinent flow-parameters namely Reynolds number (Re), Richardson number (Ri) and Hartmann number (Ha). The effects of magnetic field and the wall motion are studied extensively. The study is carried out using a well-validated in-house CFD code based on finite volume method and SIMPLE algorithm. The obtained results reveal strong influence of Ri and Ha on the heat transfer characterization. [ABSTRACT FROM AUTHOR]

In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum equations due to the "Brinkman-Forcheimer-extended-Darcy" law of flow in porous media. [ABSTRACT FROM AUTHOR]

A numerical study of mixed convection in a square enclosure from a heating element to a cold moving wall is performed under the isothermal heating conditions. The heater is placed at the bottom boundary and the cold upper wall moves horizontally towards right side with constant velocity. The lateral walls are insulated. The study includes the thermal performance of nanofluid for various shaped obstacles kept at center of the enclosure. The application of hydro-magnetism with uniform and constant magnetic intensity throughout the bottom wall is considered. The heat convection is studied at two Richardson number (0.01 and 10), four percentage volume of silver nanoparticles (0%, 2%, 5%, and 8%) and four Hartmann number (0, 10, 20, and 50). Grashof number, Prandtl number, and Reynolds number have a constant value of 104, 6.2 and 100 respectively. The obtained results indicate the suppression of heat fluxes with increasing intensity of magnetic field whereas it increases with increasing Richardson number and percentage volume of the nano-material in the base fluid. [ABSTRACT FROM AUTHOR]

In this paper, we consider numerical approximations for solving the nonlinear magnetohydrodynamical system, that couples the Navier–Stokes equations and Maxwell equations together. By combining the projection method and some subtle implicit–explicit treatments for nonlinear coupling terms, we develop a fully decoupled, linear and unconditionally energy stable scheme for solving this system, where a new auxiliary velocity field is specifically introduced in order to decouple the computations of the magnetic field from the velocity field. We further prove that the fully discrete scheme with finite element approximations is unconditional energy stable. By deriving the L ∞ bound of the numerical solution and the relation between the new auxiliary velocity field and the velocity field, and using negative norm technique, we obtain the optimal error estimates rigorously. Various numerical experiments are implemented to demonstrate the stability and the accuracy in simulating some benchmark problems, including the Kelvin–Helmholtz shear instability and the magnetic-frozen phenomenon in the lid-driven cavity. [ABSTRACT FROM AUTHOR]

In ongoing investigation the unsteady magnetohydrodynamics flow and heat transfer with viscous dissipation of a third grade fluid passed between two long parallel flat porous plates is discussed. With the physical assumptions a coupled system of non-linear partial differential equation is procured as governing MHD flow and heat transfer problem, which is then transformed to a system of non-linear algebraic equations by descretising using fully implicit finite difference scheme and solved numerically by damped-Newton method. Finally the problem is coded using MATLAB programming. The numerical results which characterize the imposing physical parameters are described through various graphs. The foremost finding of the present study is that out two elastic parameters the visco-elastic parameterα has a dominant role over the non-Newtonian parameter γ and has a control over reducing thevelocity flow of third grade fluid. Again more viscous dissipation energy is generated when the parameter values of E increases, as a result temperature profile increases. [ABSTRACT FROM AUTHOR]

Directional solidification (DS) of alloys under static magnetic field has attracted extensive attention due to the development of thermoelectric magnetohydrodynamics (TEMHD). Assessing the influence of static magnetic field on solidification microstructures in single crystal (SX) superalloys is of great significance for both the development of SX superalloys and the understanding of external field-assisted solidification. In this contribution, under different transverse static magnetic fields, the evolution of dendritic structure in a SX nickel-based superalloy directionally solidified over a range of solidification velocities is systematically investigated. The results show that applying a transverse static magnetic field (TSMF) during DS does not disrupt the crystal orientation of SX superalloys. The distribution of dendrites or local primary dendrite arm spacings within the cross section of SX superalloys shows a gradient variation in the direction perpendicular to the TSMF. Additionally, the formation of gradient-distributed dendritic structure is closely related to the applied TSMF intensity and solidification velocity. It is easier to form a gradient-distributed dendritic microstructure at low solidification velocities and high magnetic fields. Based on the experiments and simulations, the formation of gradient-distributed dendritic microstructure is supposed to attribute to the variation of interdendritic constitutional undercooling created by the change of solute concentration in interdendritic region, which is induced by the TEMHD. The SX superalloy with a gradient distribution of dendrites may have potential applications due to its gradient properties. Meanwhile, these findings also provide a new method for preparing alloys with gradient microstructures. [Display omitted] • A SX superalloy DD3 is directionally solidified over a range of solidification rates under different transverse static magnetic fields (TSMFs). • Applying a TSMF during directional solidification does not disrupt the crystal orientation of SX superalloys. • The distribution of dendrites or local primary dendrite arm spacings within the cross section of SX superalloys shows a gradient variation in the direction perpendicular to the magnetic field. • The formation of gradient-distributed dendritic microstructure is closely related to the applied magnetic field intensity and solidification rate. • The formation of gradient-distributed dendritic microstructure should be attributed to the change of interdendritic constitutional undercooling caused by the TEMHD. [ABSTRACT FROM AUTHOR]

Liquid alloy systems have a high degree of thermal conductivity, far superior to ordinary nonmetallic liquids and inherent high densities and electrical conductivities. This results in the use of these materials for specific heat conducting and dissipation applications for the nuclear and space sectors. Uniquely, they can be used to conduct heat and electricity between nonmetallic and metallic surfaces. The motion of liquid metals in strong magnetic fields generally induces electric currents, which, while interacting with the magnetic field, produce electromagnetic forces. Electromagnetic pumps exploit the fact that liquid metals are conducting fluids capable of carrying currents, which is a source of electromagnetic fields useful for pumping and diagnostics. The coupling between the electromagnetics and thermo-fluid mechanical phenomena and the determination of its geometry and electrical configuration, gives rise to complex engineering magnetohydrodynamics problems. The development of tools to model, characterize, design, and build liquid metal thermo-magnetic systems for space, nuclear, and industrial applications are of primordial importance and represent a cross-cutting technology that can provide unique design and development capabilities as well as a better understanding of the physics behind the magneto-hydrodynamics of liquid metals. First studies for the development of computational tools for the design of liquid metal electromagnetic pumps are discussed.

A steady laminar two-dimensional magneto-hydrodynamics (MHD) natural convection flow in a square enclosure filled with an electrically conducting fluid is numerically investigated using Lattice Boltzmann Method (LBM). The left and right vertical sidewalls of the square enclosure are maintained at hot and cold temperatures respectively. The horizontal top and bottom walls are considered thermally insulated. An adiabatic square shaped body is located in the center of a square enclosure and an external magnetic field is applied parallel to the horizontal x-axis. In the present work, the following parametric ranges of the non-dimensional groups are utilized: Hartmann number is varied as 0 ⩽ Ha ⩽ 50, Rayleigh number is varied as 103 ⩽ Ra ⩽ 105, Prandtl number is varied 0.05 ⩽ Pr ⩽ 5. It is found that the Hartmann number, Rayleigh number, and Prandtl number have an important role on the flow and thermal characteristics. It is found that when the Hartmann number increases the average Nusselt number decreases. The results also explain that the effect of magnetic field on flow field increases by increasing Prandtl number. However, the Prandtl number effect on the average Nusselt number with a magnetic field is less than the case without a magnetic field. Comparisons with previously published numerical works are performed and good agreements between the results are observed.

This paper deals with the perturbation analysis of mixed convection heat and mass transfer of an oscillatory viscous electrically conducting micropolar fluid over an infinite moving permeable plate embedded in a saturated porous medium in the presence of transverse magnetic field. Analytical solutions are obtained for the governing basic equations. The effects of permeability, chemical reaction, viscous dissipation, magnetic field parameter and thermal radiation on the velocity distribution, micro-rotation, skin friction and wall couple stress coefficients are analyzed in detail. The results indicate that the effect of increasing the chemical reaction has a tendency to decrease the skin friction coefficient at the wall, while opposite trend is seen by increasing the permeability parameter of the porous medium. Also micro-rotational velocity distribution increases with an increase in the magnetic field parameter.

Abstract We establish backward compactness of a pullback random attractor (PRA) from a backward limit-set compact cocycle. We prove that backward compactness of a PRA is a necessary and sufficient condition such that its time-fibers are upper semi-continuous at negative infinity, and obtain the minimal compact limit-set. Also, we obtain the maximal limit-set in the lower semi-continuity sense. These results greatly reinforce the upper semi-continuity result at the finite time, given by Cui et al. (2018). In the application part, we show existence, backward compactness and longtime robustness of a PRA for the non-autonomous stochastic magneto-hydrodynamics equations perturbed by a backward tempered force. Moreover, we prove that the PRA does not change on different attracted universes, this fact allows us to establish the finite-time robustness of the PRA if the force is tempered only. Highlights • A longtime robust attractor for the stochastic MHD equation is obtained. • Longtime robustness and backward compactness of the attractor are equivalent. • Both attractors on different universes are identical. • The tempered condition can ensure the finite-time robustness of the attractor. [ABSTRACT FROM AUTHOR]

The resistive Magneto-hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. For problems involving the plasma with an open boundary to very low pressure/vacuum regions, the continuum assumption is no longer valid in the entire domain of interest. For example, this is seen in a plasma accelerator where a dense plasma expands into a vacuum background. A common practice to deal with this issue is to assign small values of density and pressure to the vacuum regions and proceed to solve the continuum based MHD equations throughout the domain. We show that this approach fails to produce solutions consistent with the physics of the problem and can give rise to unacceptable artifacts such as spurious shocks. We develop a plasma–vacuum interface tracking approach to mitigate this problem. The plasma–vacuum interface is tracked in a physically consistent manner and the MHD equations are solved only in the regions that contain the plasma. The interface tracking is achieved using a face-flux formulation derived from the theoretical solution to a 1D free expansion problem. Coupled with a threshold based approach, the interface tracking is implemented for both explicit and implicit time stepping frameworks on generalized unstructured grids. Simulations of magnetized thermal plasma jets expanding into a vacuum background indicate plume profiles devoid of the unphysical shock obtained using the small background density approach. In the context of resistive MHD simulations, the interface tracking approach overcomes the numerical stiffness induced by specifying a large background resistivity in the vacuum regions, resulting in significant wall-clock time gains. [ABSTRACT FROM AUTHOR]

This paper examines the unsteady free convective viscous incompressible MHD flow past a vertical porous flat plate with convective surface boundary condition in slip flow regime under the influence of uniform magnetic field acting perpendicular to the porous surface. Assuming time dependent variable suction velocity at the porous plate, analytical expressions for the flow characteristics are obtained by using perturbation technique which converts the non-linear partial differential equations into ordinary differential equations. The effect of various parameters such as Prandtl number, Grashoff number, the Magnetic field parameter, Suction parameter and Convective heat change parameter on the transient velocity, transient temperature, skin friction coefficient and the rate of heat transfer are discussed with the help of graphs. [ABSTRACT FROM AUTHOR]

In this study, the lithium fluid was numerically analyzed in a threedimensional circular channel exposed to external magnetic field induction. The magnetic field is applied perpendicular to the flow direction of the channel. Re=2250 and the magnetic field strength was selected as 0T, 0.04T, 0.08T and 0.12T, respectively. Besides, while the fluid temperature is 473.15 K, the wall temperature is 373.15 K. Calculations were performed with ANSYS-Fluent commercial software. The effect of the magnetic field on the fluid velocity, pressure and temperature has presented graphically. While the magnetic field seriously has reduced the fluid velocity, the pressure has observed to increase. Also, it has been observed that the magnetic field affects the temperature differently in different regions of the channel along the pipe length. [ABSTRACT FROM AUTHOR]

The objective of the present study is the active flow control of blood in the aorta with atherosclerosis using an External Magnetic Field (EMF) in order to facilitate the blood flow. For that purpose, a numerical investigation has been developed with a Magneto-hydrodynamics flow modelisation. The blood is considered homogeneous, incompressible and Newtonian and the fluid flow is assumed to be unsteady, two-dimensional and laminar. The aorta tissue is electrically conductive. Fluent software has been used to solve the governing equations. The results relating to velocity, pressure and the wall shear stress indicate that the presence of the EMF considerably influences the blood flow. The flow control deals with the effects of the EMF direction of application and its intensity. The results show that by applying an EMF, the blood velocity and pressure in the aorta are entirely affected. The direction and the intensity of the EMF allow minimization of the flow instabilities due to the geometrical singularities. Therefore, applying an EMF can be considered an appropriate method for flow control in order to obtain a uniform blood circulation around the atherosclerosis. [ABSTRACT FROM AUTHOR]

Parametric studies are conducted on different aspects of a planar MHD propulsion system called propulsive MHD blanket. Effects of nine different parameters on the electro-magnetic thrust, efficiency, and heat transfer of the blanket are investigated. To efficiently conduct the parametric analysis, the Taguchi test design method is used and 16 cases are defined. The Ansys-CFX commercial code is utilized as numerical solver and the obtained results are validated using the Hartman problem which indicated a negligible error of 0.16%. Electromagnetism, energy, mass, and momentum equations are considered for the fluid domain and heat transfer and electromagnetism equations are solved for the solid domain. On one hand, magnet shapes and type are found to be the highest effective parameters, followed by the electrodes voltage, length, and width. On the other hand, a prediction of the best combination of parameters for obtaining the highest electro-magnetic thrust are statistically accomplished which has produced an electro-magnetic thrust of 18.02 N per square meter for the MHD blanket which is twice the maximum electro-magnetic thrust obtained in the 16 initial test cases. It is demonstrated in the present paper that the unique applications of propulsive MHD blanket can compensate the very low efficiencies of MHD systems. It has also been shown that efficiency can be improved by enhancing the water conductivity, which is intended as a future study. [ABSTRACT FROM AUTHOR]

The paper is concerned with the free boundary problem for two-dimensional current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of the discontinuity near the onset of the instability, Hunter and Thoo [On the weakly nonlinear Kelvin-Helmholtz instability of tangential discontinuities in MHD, J. Hyperbolic Differ. Equations 8(4) (2011) 691-726] have introduced an asymptotic quadratically nonlinear integro-differential equation for the amplitude of small perturbations of the planar discontinuity. The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation was shown in [Approximate current-vortex sheets near the onset of instability, J. Math. Pures Appl. 105(4) (2016) 490-536; Existence of approximate current-vortex sheets near the onset of instability, J. Hyperbolic Differ. Equations]. In the present paper, we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard. [ABSTRACT FROM AUTHOR]

The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of the discontinuity near the onset of the instability, Hunter and Thoo (J Hyperbolic Differ Equ 8(4):691–726, 2011) have introduced an asymptotic quadratically nonlinear integro-differential equation for the amplitude of small perturbations of the planar discontinuity. The local-in-time existence of smooth solutions to the Cauchy problem for such amplitude equation was already proven in Morando et al. (J Math Pures Appl 105(4):490–536, 2016; J Hyperbolic Differ Equ 14(2):193–248, 2017), under a suitable stability condition. The aim of the present note is to provide a new proof of the existence result of the solution, with optimal regularity with respect to the initial data. The existence of the solution follows from a fixed point argument, where the main ingredient is the a priori estimate of Q φ proven in Morando et al. (J Hyperbolic Differ Equ 14(2):193–248, 2017). [ABSTRACT FROM AUTHOR]