Time-dependent Magnetohydrodynamics Research Articles

Unsteady magnetohydrodynamic free convection and heat transfer flow of Al2O3‒Cu/water nanofluid over a non-linear stretching sheet in a porous medium

This article investigates the impact of time-dependent magnetohydrodynamics free convection flow of a nanofluid over a non-linear stretching sheet immersed in a porous medium. The combination of water as a base fluid and two different types of nanoparticles, namely aluminum oxide (Al2O3) and copper (Cu) is taken into account. The impacts of thermal radiation, viscous dissipation and heat source/sink are examined. The governing coupled non-linear partial differential equations are reduced to ordinary differential equations using suitable similarity transformations. The solutions of the prin-cipal equations are computed in closed form by applying the MATLAB bvp4c method. The velocity and temperature pro-files, as well as the skin friction coefficient and Nusselt number, are discussed through graphs and tables for various flow parameters. The current simulations are suitable for the thermal flow processing of magnetic nanomaterials in the chemical engineering and metallurgy industries. From the results, it is noticed that the results of copper nanofluid have a better impact than those of aluminium nanofluid.

Modelling solar coronal magnetic fields with physics-informed neural networks

ABSTRACT We present a novel numerical approach aiming at computing equilibria and dynamics structures of magnetized plasmas in coronal environments. A technique based on the use of neural networks that integrates the partial differential equations of the model, and called physics-informed neural networks (PINNs), is introduced. The functionality of PINNs is explored via calculation of different magnetohydrodynamic (MHD) equilibrium configurations, and also obtention of exact two-dimensional steady-state magnetic reconnection solutions. Advantages and drawbacks of PINNs compared to traditional numerical codes are discussed in order to propose future improvements. Interestingly, PINNs is a meshfree method in which the obtained solution and associated different order derivatives are quasi-instantaneously generated at any point of the spatial domain. We believe that our results can help to pave the way for future developments of time dependent MHD codes based on PINNs.

Thin film flow of the ternary hybrid nanofluid over a rotating disk under the influence of magnetic field due to nonlinear convection

This study focuses on the comprehensive analysis of thermal characterization of the ternary hybrid nanofluid flow within a continuously extending disk. The characteristics of time-dependent magnetohydrodynamics tri-hybrid nanofluids consisting Molybdenum disulfide (MoS2), Silicon dioxide (SiO2), Multi-Walled Carbon Nanotubes (MWCNT), Water (H2O), hybrid (MWCNT + MoS2/H2O) and nanofluid (MWCNT/H2O) movement are analyzed for the thermal applications. With the help of ohmic heating, quadratic convection, and a magnetic field the heat transmission mechanism and fluid dynamics are investigated.The significance of the study describe that tri-hybrid nanofluid has a higher energy transport rate than the traditional fluid at the surface of the disk.The transformed coupled and nonlinear ordinary differential equations are solved analytically using Homotopy Analysis Method (HAM). The impact of some important physical parameters on the fluid flow profile, temperature fields, drag force, and rate of heat transmission is depicted using plots. The outcomes are validated by previous studies and a good degree of consistency is revealed.

Evolution of Viscous Electrically Conducting Fluid Flow on a Rotating Wall in the Presence of a Magnetic Field with Account for the Induction and Diffusion Effects

The evolution of a viscous conducting fluid flow on a rotating plate in the presence of a magnetic field is studied. The analytical solution of the three-dimensional time-dependent magnetohydrodynamics equations is found. In this case, the full magnetic induction equation is used, i.e., both the dissipation effect and the energy dissipation as a result of the electric current flow are taken into account. The fluid, together with the bounding plane, rotates as a whole at a constant angular velocity about a direction not perpendicular to the plane. The velocity field and the induced magnetic field in the flow of viscous electrically conducting fluid that occupies a half-space bounded by a flat wall are determined. The motion of wall is considered in a series of particular cases. Based on the results obtained, the individual structures of the near-wall boundary layers are investigated

Unconditional stability and convergence analysis of fully discrete stabilized finite volume method for the time-dependent incompressible MHD flow

In this paper, we consider the stability and convergence of fully discrete stabilized finite volume method for the unsteady incompressible magnetohydrodynamics (MHD) equations on the quasi-uniform and regular triangulations. The spatial discretization is based on the lowest equal-order mixed finite element pair for the velocity, pressure and the magnetic fields, while the time discretization is based on the backward Euler semi-implicit scheme. In order to overcome the restriction of the discrete inf-sup condition, the local pressure projection stabilized method on the element is employed. This stabilized method has the advantages of parameter-free, no need to calculate the high-order derivatives or the edge-based data structures and it can be implemented at the element level. The unconditional stability of numerical scheme is established by using the Gronwall lemma, mathematical induction and choosing different test functions. Optimal error estimates of numerical approximations in various norms are also presented by constructing the corresponding dual problem. Finally, some numerical results are proposed to verify the established theoretical findings and show the performances of the considered numerical method.

Entropy generation on biomagnetic gold-copper/blood hybrid nanofluid flow driven by electrokinetic force in a horizontal irregular channel with bioconvection phenomenon

Present research deals with the study of time-dependent pulsatile MHD (Magnetohydrodynamics) hybrid nanofluid with entropy optimization and electrokinetic force in a channel. The current mathematical model is formulated as the [Formula: see text] blood (Casson fluid) hybrid nanofluids flow between the bottom and wavy top walls. The pulsatile flow is subjected to an inverse magnetic field of uniform force to study the effect of the resulting Lorenz force. Exact solutions for velocity, temperature, heat transfer rate, and streamlines are constructed by employing the perturbation approach to evaluate coupled nonlinear partial differential equations (PDEs). The velocity [Formula: see text] of the blood-based [Formula: see text] hybrid nanofluid increases with increasing values of the electro-osmotic parameter. The higher values of copper-gold nanoparticle volume fraction increase the entropy generation [Formula: see text]. This theoretical investigation helps estimate entropy in systems biology, which is used to treat cancer and improve the function of medical devices.

Thermal radiation effect on unsteady three-dimensional MHD flow of micropolar fluid over a horizontal surface of a parabola of revolution

This paper explores the time-dependent magnetohydrodynamics (MHD) micropolar fluid flow over a three-dimensional variable stretching surface in the occurrence of radiation effect. The model time-dependent partial differential equations (PDE's) in three independent variables are transformed into ordinary differential equations (ODE's) by the suitable self-similarity variables. Homotopy perturbation method (HPM) and Runge-Kutta (RK) 4th order method along with shooting technique are used in the present model. And also, HPM results are compared with Runge-Kutta (RK) 4th order method along with the shooting technique. The velocity, micro rotation in x and y directions, temperature, skin friction factor and heat transfer rates are examined for the emerging parameters. The velocity profiles and momentum boundary layer thickness intensification with increasing values of the vortex viscosity parameter. The higher value of a magnetic parameter declines the skin friction coefficient. This type of investigation may be profitable to the polymer fluids, exotic lubricants, electronic chips, artificial fibers, drawing of copper wires, etc.

Time varying control of magnetohydrodynamic duct flow

Optimal control of the unsteady, laminar, fully developed flow of a viscous, incompressible and electrically conducting fluid is considered under the effect of a time varying magnetic field B0(t) applied in the direction making an angle with the y–axis. Thus, the coefficients of convection terms in the Magnetohydrodynamics (MHD) equations are also time-dependent. The coupled time-dependent MHD equations are solved by using the mixed finite element method (FEM) in space and the implicit Euler scheme in time. FEM solutions are obtained for various values of the Hartmann number, Reynolds number, magnetic Reynolds number and for several types of time dependence of applied magnetic field at transient level and steady-state.In this study, we aim to control the unsteady MHD flow by using the time varying coefficient function f(t) in the applied magnetic field B0(t)=B0f(t) as a control function. In addition, control problem is designed to involve the determination of the optimal parameters of the system (Reynolds number, magnetic Reynolds number and the angle θ) regarded as control variables.In the optimization, a discretize-then-optimize approach with a gradient based algorithm is followed. Cost function is designed to regain the prescribed velocity and induced magnetic field profiles as well as the smooth control function with respect to time. Controls are investigated for the regularization parameters included in the cost function. Optimal solutions are achieved for several states of the flow considering Hartmann number and at the time level where the flow stabilizes.

Transverse oscillations of a double-structured solar filament

Aims.We study the transverse oscillations of a double-structured solar filament.Methods.We modelled the filament numerically via a 2D magnetohydrodynamic (MHD) model, in which we solved a full set of time-dependent MHD equations by means of the FLASH code, using the adaptive mesh refinement method. We used the wavelet analysis method as a diagnostic tool for analysing periods in simulated oscillations.Results.We present a model of a solar filament combined with semi-empirical C7 model of the quiet solar atmosphere. This model is an alternative model of a filament based on the magnetostatic solution of MHD equations. We find that this double-structured filament oscillates with two different eigen frequencies. The ratio is approximately 1.75 (∼7.4 min/∼4.2 min), which is characteristic for this type of filament model. To show the details of these oscillations we present a time evolution of the plasma density, temperature, plasma beta parameter, and the ratio of gravity to magnetic pressure taken along the vertical axis of the filament atx = 0. The periods found by numerical simulations are then discussed in comparison with those observed.

Time-Dependent MHD Flow of Non-Newtonian Generalized Burgers' Fluid (GBF) Over a Suddenly Moved Plate With Generalized Darcy's Law

Time dependent magnetohydrodynamic (MHD) motion of a generalized Burger's fluid (GBF) is investigated in this article. GBF is a highly complicated non-Newtonian fluid and is of highest degree in the class of rate type fluids. GBF is taken electrically conducting by using the restriction of small magnetic Reynolds' number. The Darcy’s law has been used here in its generalized form using the GBF constitutive relation, hence the medium is made porous. The impulsive motion in the fluid is induced due to sudden jerk of the plate. Exact expressions for velocity and as well as for shear stress fields are obtained using the Laplace transform method. The solutions for hydrodynamic fluid (absence of MHD) in a non-porous medium, as well as those for a Newtonian fluid (NF) executing a similar motion are also recovered. Results are sketched in terms of several plots and discussed for embedded parameters. It is found that the Hartmann number and porosity of the medium have strong influence on the velocity and shear stress fields.

Pulse-beam heating of deep atmospheric layers, their oscillations and shocks modulating the flare reconnection

Aims.We study the processes occurring after a sudden heating of deep atmospheric layers at the flare arcade footpoints, which is assumed to be caused by particle beams.Methods.For the numerical simulations we adopt a 2D magnetohydrodynamic (MHD) model, in which we solve a full set of the time-dependent MHD equations by means of the FLASH code, using the adaptive mesh refinement (AMR) method.Results.In the initial state we consider a model of the solar atmosphere with densities according to the VAL-C model and the magnetic field arcade having the X-point structure above, where the magnetic reconnection is assumed. We found that the sudden pulse-beam heating of deep atmospheric layers at the flare arcade footpoints generates two magnetohydrodynamic shocks, one propagating upwards and the second propagating downwards in the solar atmosphere. The downward-moving shock is reflected at deep and dense atmospheric layers and triggers oscillations of these layers. The period of these oscillations in our case is about 174 s. These oscillations generate the upward-moving magnetohydrodynamic waves that can influence the flare magnetic reconnection in a quasi-periodic way. These processes require a sudden heating in very localized regions in dense atmospheric layers; therefore, they can be also associated with seismic waves.

A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part II: A Robust Solver

In [L. Li, M. Ni, and W. Zheng, SIAM J. Sci. Comput., 41 (2019), pp. B796--B815] a charge-conservative finite element method is proposed for solving inductionless and incompressible magnetohydrodynamic (MHD) equations. The purpose of this paper is to propose a robust solver for the discrete problem. Using the framework of field-of-values-equivalence, we first study the preconditioned Krylov space method for the continuous problem in the setting of Hilbert spaces. The algebraic preconditioner for the discrete problem is then obtained by representing the preconditioner for the continuous problem in finite element spaces. By three numerical examples, the optimality of the solver to the number of unknowns is demonstrated for both stationary and time-dependent MHD problems.

Three-Dimensional Flow Studies in Cylindrical Magnetohydrodynamic Experiments Using Ultrasound Array Velocimetry.

Crystal growth processes can profit from an electromagnetically driven melt flow since controlling them allows optimizing the mass and heat transfers in the melt and, thereby, improves the structural and electrical properties of the grown crystals. This process optimization requires a precise understanding of magnetohydrodynamics (MHD) phenomena in crystal growth. Studying time-dependent MHD demands for a high temporal resolution combined with a long measurement duration to analyze the transitional flow behavior. Furthermore, a spatially resolved measurement of the global flow structure is desired to capture the complex 3-D flow structures. We present an ultrasound array Doppler velocimeter (UADV) for time-resolved flow imaging in MHD model experiments with low-melting metals. Flow imaging at frame rates of several Hertz is achieved by using a combined spatial and temporal multiplexing scheme. Long-running measurements are enabled by a field-programmable gate array (FPGA)-based signal processing that reduces the measurement data rate by a factor of 5. A reconstruction of the 3-D flow structure in cylindrical containers with a rotation-symmetric flow is proposed. The UADV is demonstrated at an MHD experiment with a melt flow in a cylindrical container driven by a traveling magnetic field. The transition from a laminar to a time-dependent flow is studied, revealing an oscillating flow. The demonstration of the 3-D reconstruction gives comprehensive insight into the global flow structure. Hence, the UADV method is shown to be a valuable tool for measuring complex, time-dependent melt flows, which can contribute to a better understanding of the flow phenomena during crystal growth.

Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere

A numerical analysis is provided to scrutinize time-dependent magnetohydrodynamics (MHD) free and forced convection of an electrically conducting non-Newtonian Casson nanofluid flow in the forward stagnation point region of an impulsively rotating sphere with variable wall temperature. A single-phase flow of nanofluid model is reflected with a number of experimental formulae for both effective viscosity and thermal conductivity of nanofluid. Exceedingly nonlinear governing partial differential equations (PDEs) subject to their compatible boundary conditions are mutated into a system of nonlinear ordinary differential equations (ODEs). The derived nonlinear system is solved numerically with implementation of an implicit finite difference procedure merging with a technique of quasi-linearization. The controlled parameter impacts are clarified by a parametric study of the entire flow regime. It is depicted that from all the exhibited nanoparticles, Cu possesses the best convection. The surface heat transfer and surface shear stresses in the x - and z -directions are boosted with maximizing the values of nanoparticle solid volume fraction φ and rotation λ . Besides, as both the surface temperature exponent n and the Casson parameter γ upgrade, an enhancement of the Nusselt number is given.

An MHD Simulation of Solar Active Region 11158 Driven with a Time-dependent Electric Field Determined from HMI Vector Magnetic Field Measurement Data

Abstract For realistic magnetohydrodynamics (MHD) simulation of the solar active region (AR), two types of capabilities are required. The first is the capability to calculate the bottom-boundary electric field vector, with which the observed magnetic field can be reconstructed through the induction equation. The second is a proper boundary treatment to limit the size of the sub-Alfvénic simulation region. We developed (1) a practical inversion method to yield the solar-surface electric field vector from the temporal evolution of the three components of magnetic field data maps, and (2) a characteristic-based free boundary treatment for the top and side sub-Alfvénic boundary surfaces. We simulate the temporal evolution of AR 11158 over 16 hr for testing, using Solar Dynamics Observatory/Helioseismic Magnetic Imager vector magnetic field observation data and our time-dependent three-dimensional MHD simulation with these two features. Despite several assumptions in calculating the electric field and compromises for mitigating computational difficulties at the very low beta regime, several features of the AR were reasonably retrieved, such as twisting field structures, energy accumulation comparable to an X-class flare, and sudden changes at the time of the X-flare. The present MHD model can be a first step toward more realistic modeling of AR in the future.

EUHFORIA: European heliospheric forecasting information asset

The implementation and first results of the new space weather forecasting-targeted inner heliosphere model “European heliospheric forecasting information asset” (EUHFORIA) are presented. EUHFORIA consists of two major components: a coronal model and a heliosphere model including coronal mass ejections. The coronal model provides data-driven solar wind plasma parameters at 0.1 AU by constructing a magnetic field model of the coronal large-scale magnetic field and employing empirical relations to determine the plasma state such as the solar wind speed and mass density. These are then used as boundary conditions to drive a three-dimensional time-dependent magnetohydrodynamics model of the inner heliosphere up to 2 AU. CMEs are injected into the ambient solar wind modeled using the cone model, with their parameters obtained from fits to imaging observations. In addition to detailing the modeling methodology, an initial validation run is presented. The results feature a highly dynamic heliosphere that the model is able to capture in good agreement with in situ observations. Finally, future horizons for the model are outlined.

On an efficient second order backward difference Newton scheme for MHD system

For the 2D/3D time-dependent magnetohydrodynamics (MHD) system, we propose a new second order backward difference formula Newton scheme (SBDFN) which is a combination of second order backward difference approximation of the time derivative terms and Newton treatment of the nonlinear terms. Meanwhile, the finite element method is applied as spatial discretization. Firstly, the optimal convergence of spatially semi-discrete form is deduced. Secondly, the stability and well-posedness of SBDFN scheme are provided under τ<C, where C is independent of h. Based on these results, optimal error estimates of the scheme in time are proved by negative norm technique. Finally, numerical experiments are carried out to validate the theoretical analysis.

A partitioned finite element scheme based on Gauge-Uzawa method for time-dependent MHD equations

In this paper, we mainly introduce a partitioned scheme based on Gauge-Uzawa finite element method for the 2D time-dependent incompressible magnetohydrodynamics (MHD) equations. It is a fully decoupled projection method which combines the Gauge and Uzawa methods within a variational formulation. Firstly, the temporal discretization is based on backward Euler technique for the linear term and semi-implicit scheme for the nonlinear term. Secondly, the spatial approximation of fluid velocity, hydrodynamic pressure, and magnetic field apply the mixed element method. Finally, the validity, reliability, and accuracy of the proposed algorithms are supported by numerical experiments.

Unsteady MHD rear stagnation-point flow over off-centred deformable surfaces

PurposeThe purpose of this paper is to present both an analytical and a numerical analysis of the unsteady magnetohydrodynamic (MHD) rear stagnation-point flow over off-centred deformable surfaces.Design/methodology/approachThe numerical MATLAB solver bvp4c suitable for routine boundary value problem is used for the set of ordinary differential equations reduced from the governing partial differential equations.FindingsMultiple solutions are found for particular eigenvalues. The physical solution is computed by the help of a linear stability analysis. The authors have succeeded in discovering the second solutions, and it is suggested that these solutions are unstable and not physically realisable in practice. The current findings add to a growing body of literature on MHD stagnation-point flow problems. It is also found that the governing parameters have different effects on the flow characteristics.Practical implicationsEven though problems of steady MHD flows have been extensively studied for stagnation-point flows, limited findings can be found on the unsteady MHD rear stagnation-point flow over off-centred deformable surfaces.Originality/valueThe originality of this work is the application of a magnetic field on a time-dependent MHD rear stagnation-point flow over off-centred deformable surfaces.

Recent Advances in understanding Solar Wind-Mars Interaction with Global Magnetohydrodynamic (MHD) Modeling

This paper presents recent progress in understanding the Solar Wind-Mars interaction using a sophisticated global magnetohydrodynamic (MHD) model. Mars has only localized crustal magnetic fields, so the solar wind plasma flow interacts directly with the Mars atmosphere/ionosphere system. Such an interaction generates an induced current in the ionosphere, modifies the magnetic field environment around Mars, and more importantly, causes the erosion of the Mars atmosphere. The non-uniformly distributed crustal magnetic field also plays an important role in the interaction process, which is modulated by planetary rotation. Recent advances in computing power allow the inclusion of the continuous crustal field rotation in the simulation with a time-dependent MHD model. Model results have been validated with observations from previous and ongoing Mars missions. The validated time-dependent MHD model is useful in quantifying the variation of ion loss rates with planet rotation and the internal response time scale of the Martian ionosphere.