MHD Flows Research Articles

MHD flows through ferromagnetic rectangular ducts in liquid metal blankets

MHD flows through ferromagnetic rectangular ducts in liquid metal blankets

A checkerboard-free symmetry-preserving conservative method for magnetohydrodynamic flows

Simulating MHD flows at high Hartmann numbers and low magnetic Reynolds numbers is of high interest for the design of a nuclear fusion breeding blanket, for which high accuracy and conservation of physical properties are of great importance. In this work, a solver is developed that offers these properties through the symmetry-preserving method, while at the same time warranting unconditional stability. Since this method uses predictor values for the pressure and electric potential fields, it can be prone to checkerboarding. Therefore it is extended to include a dynamical checkerboarding solution, which balances this problem with numerical dissipation. This is done through run-time measurements of the intensity of checkerboarding, which is then used as a negative feedback onto the predictor values. The symmetry-preserving discretisation and the dynamical solution to checkerboarding were successfully tested using an magnetohydrodynamic Taylor-Green vortex. The newly introduced method shows results free from numerical dissipation in smooth cases, whereas it avoids checkerboarding in more challenging cases. Finally, the method shows to be unconditionally stable, even on highly distorted meshes.

Experimental investigation of MHD flows in a WCLL TBM mock-up

Experiments have been performed in the MEKKA laboratory of the Karlsruhe Institute of Technology to characterize the influence of a magnetic field on liquid metal flows in a scaled mock-up of the water-cooled lead-lithium test blanket module of ITER. The test section consists of eight breeder units that are fed and drained by long electrically coupled manifolds oriented along the poloidal direction. Pressure differences between several points of the mock-up have been recorded for various liquid metal flow rates and strengths of the imposed magnetic field. The main contributions to the total pressure drop in the test section have been identified as a function of characteristic flow parameters. For sufficiently strong magnetic fields, the experimental data shows that the non-dimensional pressure loss is practically independent of the flow rate, i.e. inertia forces become negligible. The experiments also confirm previous conclusions of magnetohydrodynamic experiments performed in a scaled-down mock-up of a helium-cooled lead-lithium blanket, namely that the largest pressure drop in the blanket module originates from the flow in the distributing and collecting manifolds. Moreover, the experimental study demonstrates that the current manifold design does not allow the flow to be uniformly distributed among all the breeder units.

Unsteady Mixed Convection Flows in a Rectangular Duct and Dynamical Behaviors of Flow Channel Insert

Buoyancy-assisted upward MHD flows and dynamical behaviors of flow channel insert (FCI) in the dual-coolant lead-lithium (DCLL) blanket are studied numerically. Based on our internally developed and validated solver, the dynamical behaviors of magneto-thermo-fluid-structure coupled multiphysical field are investigated. A large amplitude, low frequency, and quasiperiodic unsteady reverse flow at high Re (31000), high Gr (3.5×1011), and moderate magnetic field (0.7~1.7T) is found in the DCLL blanket. This intricate phenomenon has been discovered for the first time, representing a combination of separate experimental results from Melnikov et al. (2016) and Khanal and Lei (2012). In our study of this large amplitude, low frequency, and quasiperiodic unsteady reverse flows, the importance of the cold helium gas to the instability of fluid flow in the bulk region and the thermal conductivity of the FCI to convection structure and instability are first found and recognized. Additionally, we take into account the effects of the temperature field and flow field on structural deformation and mechanical behavior of FCI, and we have discovered several intriguing phenomena, such as (1) the stability of fluid flow in the bulk region depends on the strength of the heat source, the magnitude of the magnetic field, and thermal conductivity of FCI; (2) the instability and periodicity of the fluid flow are primarily related to the unsteady reverse flow, which rises up and falls down periodically in the bulk region; (3) the physical mechanism of unsteady flow influenced by reverse flow, pressure drop, and Lorentz force has been concluded. It has been discovered that the breakdown of a reverse flow vortex causes a rapid reduction in pressure drop. (4) To avoid this phenomenon in engineering, a phase map of unsteady and steady flows in the DCLL blanket has been created. (5) The quasiperiodic characteristics of solid (flow channel insert) affected by flow are found and analyzed.

Hall effect on the asymptotic stability of the planar compressible MHD flows

Hall effect on the asymptotic stability of the planar compressible MHD flows

Influence of temperature dependent heat source/sink on transient MHD free convective flow in an infinite rigid impermeable vertical cylinder with chemical reaction

It is increasingly apparent that the inclusion of mass transfer aspects, together with certain thermal conditions, in the momentum and energy equations governing MHD flows leads to a numbers of real life applications. Keeping this in view, we have attempted an exact analysis of heat and mass transfer aspects in transient hydromagnetic free convective flow of an incompressible viscous fluid through a vertical pipe under an externally applied magnetic field, assuming presence of chemical reaction and heat source/sink. The governing PDEs, which simplify to a set of 3 linear ODEs in the physical set up considered here, have been solved using Laplace transform technique, with solutions for key physical variables presented in the term of Bessel and modified Bessel functions. The influence of governing non-dimensional parameters, namely, Hartmann number, Schmidt number, source/sink parameter, Prandtl number and chemical reaction parameter, has been illustrated on the developing velocity and some concentration profiles. Some important quantities of engineering interest-surface skin friction and volumetric flow rates-have been computed too and analysed. Some notable finding worth mentioning are: (a) heat source presence causes higher fluid velocity as compared to the heat sink; (b) all important surface shear stress can be suitably controlled, among others, by chemical reaction parameter and Schmidt number. The key challenge of this study has been to obtain exact closed-form solutions of the field equations, including cumbersome Laplace inverses. This study finds innovative applications in the emerging fields such as magnetic materials processing, chemical processes, solar energy systems, etc.

Transient MHD Flows Through an Exponentially Accelerated Isothermal Vertical Plate with Viscous Dissipation and Heat Source Embedded in a Porous Medium

In this article, an unsteady free convection flow of an incompressible viscous fluid past an exponentially accelerated isothermal vertical plate in the presence of the viscous dissipation and heat source is observed. The problem is governed by coupled nonlinear partial differential equations. Dimensionless equations of the problem have been solved numerically by the Galerkin finite element method. The effect of magnetic parameter M, Grashof number Gr, Eckert number Ec, time and an acceleration parameter ‘a’ on velocity, temperature fields are investigated through graphs. Skin friction coefficient is derived, discussed numerically.

A Radiative Chemical Process for the Methylene Blue Degradation by Natural Convective Nanofluid Flow over an Upright Cone.

An upstraight cone with nonisothermal surface velocity, temperature, and concentration was investigated using a numerical solution approach to simulate MHD, MB dye, and various nanofluid flows. Numerical evaluation of the flow field equation was carried out using an excellent finite difference method after it has been converted into a dimensionless form. Different heat transfer occurrences were observed depending on temperature, velocity, and concentration when using several types of nanofluids (TiO, Ag, Cu, and Al2O3Z3). The amount of MB dye that was degraded by the synthesized nanofluids under the influence of sunlight irradiation was 81.40 percent as a catalyst (carbon nanodots). The parametric analysis of various features of flow fields has been shown using graphs. It was observed that heat is generated from the cone during the sun light irradiation reaction, heat is transferred to MB dye containing nanofluids, and heat interacts with nanofluids and is involved in the chemical reaction with the assistance of electrons. As MB dye degrades in the absence of catalysts (carbon nanodots), it is only 52 percent effective. MB dye is degraded at 81.40 percent, then becomes stable, and takes 120 minutes to degrade in nanofluids containing MB dye with catalysts (carbon nanodots).

Entropy analysis along thermophoretic particle deposition on nanofluid flow through different geometries with thermal radiation

The current study analyses the entropy of nanofluid flow over three different geometries with thermophoretic particle deposition and thermal radiation. It is essential while considering heat exchangers, transpiration, fiber coating, and other similar processes, to have a solid understanding of the transfer of both heat and mass that occurs during MHD flows across three dissimilar shapes. A mathematical model will be utilized to explore magnetohydrodynamic flows including energy transfer with heat and mass variations. In this model, some of the innovative concepts include thermophoresis, Brownian motion, the Cattaneo–Christov dual flux with the application of an external magnetic field, and the entropy generation effect are considered. By the appropriate similarity transformations, fundamental PDE’s converted into ODE’s. To solve these ODE's, the Runge–Kutta fourth order is used along with the shooting technique. The results are displayed in graphs and tables. It is observed that the velocity gets decreases with the increase of the porous parameter and magnetic field and gets stronger with the increase of the Grashof number. The temperature increases with an increase in the magnetic field, radiation parameter, Brownian motion parameter, and thermophoresis parameter. Concentration increases with the increase in a magnetic field and Brownian motion parameter but reduces with the increase of other parameters. Entropy generation gets enhanced with an increase in the magnetic field, temperature difference, concentration difference and diffusion parameters. When a flow is directed through geometries the heat and mass transfer rates are both affected by a parameter known as the thermal relaxation parameter. The influence of skin friction, Nusselt number and Sherwood number were analyzed and results were discussed.

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

Stability and Convergence of Stabilized Finite Volume Iterative Methods for Steady Incompressible MHD Flows with Different Viscosities

Stability and Convergence of Stabilized Finite Volume Iterative Methods for Steady Incompressible MHD Flows with Different Viscosities

Effects of Activation Energy on Reactive MHD Flows with Joule Heating

Effects of Activation Energy on Reactive MHD Flows with Joule Heating

Effect of MHD mixed convection on a heat-generating element cooling inside a ventilated square cavity filled with Fe3O4–water ferrofluid

This work groups a set of numerical results on the investigation of the external magnetic field effect on mixed convection in a ventilated square cavity with a heat source located in the middle of its bottom wall and filled with a ferrofluid. The behavior of the magnetic field was treated according to three different scenarios illustrated by magnetic Reynolds number value (Rm = 0.1, 0.001, and 0.00001). The dimensionless governing equations were solved numerically by the finite volume method and the SIMPLE algorithm was chosen for the treatment of coupling between the momentum and continuity equations using the QUICK scheme of Leonard. The numerical results for a large range of Hartmann numbers and volume fractions and for horizontal and vertical magnetic field directions are discussed in terms of streamlines, isotherms, Nusselt numbers, and maximal temperature of fluid and heat source. The results highlighted different scenarios showing the heat exchange rate enhancement and heat source cooling as a function of the magnetic field strength and direction and as a function of the internal fluid constitution and behavior. The diversity of these results as a function of the magnetic Reynolds number also underlines the limitation of theory based on low-Rm model in the treatment of MHD flows.

One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws

A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyzes the one-dimensional magnetohydrodynamics flows with cylindrical symmetry in the mass Lagrangian coordinates. The medium is assumed inviscid and thermally non-conducting. It is modeled by a polytropic gas. Symmetries and conservation laws are found. The cases of finite and infinite electric conductivity need to be analyzed separately. For finite electric conductivity σ(ρ,p) we perform Lie group classification, which identifies σ(ρ,p) cases with additional symmetries. The conservation laws are found by direct computation. For cases with infinite electric conductivity variational formulations of the equations are considered. Lie group classifications are obtained with the entropy treated as an arbitrary element. A variational formulation allows to use the Noether theorem for computation of conservation laws. The conservation laws obtained for the variational equations are also presented in the original (physical) variables.

Homogenization of MHD flows in porous media

The paper is concerned with the homogenization of a nonlinear differential system describing the flow of an electrically conducting, incompressible and viscous Newtonian fluid through a periodic porous medium, in the presence of a magnetic field. We introduce a variational formulation of the differential system equipped with boundary conditions. We show the existence of a solution of the variational problem, and derive uniform estimates of the solutions depending on the characteristic parameters of the flow. Using the two-scale convergence method, we rigorously derive a two-scale equation for the two-scale current density, and a two-pressure Stokes system. We derive, in the case of constant magnetic permeability, an explicit relation expressing the macroscopic velocity as a function of the macroscopic Lorentz force, the pressure gradient, the external body force, and the macroscopic current density, via two permeability filtration tensors. When the magnetic field is absent, this relation reduces to the Darcy law.

On Hydromagnetic Boundary Layer of Casson Fluid Over Porous Inclined Magnetized Surface With Radiation and Convective Boundary Conditions

The boundary layer of a non-Newtonian Casson fluid flow over inclined porous magnetized surfaces with radiation and convective boundary conditions have been considered. The effects of the magnetic field, thermal radiation, convection with temperature fields at the boundaries of the surface are considered. The governing models have been transformed to ordinary differential equations imploying the similarity approach. The effects of surface magnetization along with bulk parameters on the flow are presented in tables. The thickness of the thermal boundary layer has been enhanced due to the induced magnetic field leading to considerable improvement in the rate of heat transfer. The induced magnetized surface showed a similar influence on the skin friction, Nusselt number, and the Sherwood number. The study, therefore, recommends the incorporation of magnetized surfaces in MHD flows for efficient flows control.

Global existence and large time behavior of strong solutions to the Cauchy problem of the 3D heat conducting incompressible MHD flows

In this paper, we consider an initial value problem of inhomogeneous heat conducting magnetohydrodynamic equations in R3. Through some time-weighted a priori estimates, we prove the global existence of strong solution provided that (‖ρ0u0‖L22+‖b0‖L22)(‖∇u0‖L22+‖∇b0‖L22) is suitably small, which extends the corresponding Zhong's results [16,17] to the whole space R3. Furthermore, we also derive the algebraic decay estimates of the solution.

Exact Solutions of non-Newtonian Fluid of Rotating MHD Flows Through Porous Media with Hall Effect by Complex Variable Technique

In this paper steady, two dimensional, incompressible, electrically conducting, MHD fluid through porous media in a rotating reference frame with Hall effect under the presence of magnetic field is considered. The magnetic field is applied along the z-axis. Using complex variable technique the governing equations are recast in solvable form. Exact solutions are obtained for straight parallel flows.

Modeling and Analysis of MHD Oscillatory Flows of Generalized Burgers’ Fluid in a Porous Medium Using Fourier Transform

In this article, exact solutions of unsteady oscillatory generalized Burgers’ fluid are proposed for three different cases using Fourier transform approach. The fluid is electrically conducting under the influence of uniform transverse magnetic field and passing through the porous medium. MHD flows are induced by imposed periodic pressure gradients with smaller oscillations. Closed form solutions are obtained using Fourier sine transform, and several existing results are recovered as limiting cases. Furthermore, effects of different fluid parameters on the velocity profile are studied graphically. Analysis reveals that magnetic field and porosity parameter increases the velocity profile in case of Oldroyd‐B and generalized Burgers’ fluid. It is also observed that magnetic field has more prominent effect on Burgers’ fluid as compared to Oldroyd‐B fluid, while porosity parameter showed noticeable effect on Oldroyd‐B fluid as compared to Burgers’ fluid.

Regularity criteria for 3D MHD flows in terms of spectral components

<abstract><p>We extend the spectral regularity criteria of the Prodi-Serrin kind for the Navier-Stokes equations in a torus to the MHD equations. More precisely, the following is established: for any $ N > 0 $, let $ {{\boldsymbol x}}_{N} $ and $ {{\boldsymbol y}}_{N} $ be the sum of all spectral components of the velocity and magnetic field whose wave numbers possess absolute value greater that $ N $; then, it is possible to show that for any $ N $ the finiteness of the Prodi-Serrin norm of $ {{\boldsymbol x}}_{N} $ implies the regularity of the weak solution $ ({{\boldsymbol u}}, {{\boldsymbol h}}) $; thus, no restriction on the magnetic field is needed.</p></abstract>