Laminar Magnetohydrodynamic Flow Research Articles

Energy stability analysis of MHD flow in a rectangular duct

AbstractWe study the energy stability of pressure‐driven laminar magnetohydrodynamic flow in a rectangular duct in the presence of a transverse homogeneous magnetic field. The walls of the duct are electrically insulating. The quasistatic approximation of the induction equation is used. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The linear eigenvalue problem for the energy Reynolds number depends on the streamwise wavenumber, the Hartmann number, and the aspect ratio. We focus on duct geometries with small aspect ratios in order to compare with stability results from one‐dimensional channel flow. The lift‐up mechanism dominates in the limit of zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann number in the duct. For finite streamwise wavenumbers and decreasing aspect ratio, the duct results converge to Orr's original energy stability result for spanwise uniform perturbations to the plane Poiseuille base flow.

Energy stability of magnetohydrodynamic flow in channels and ducts

We study the energy stability of pressure-driven laminar magnetohydrodynamic flow in a rectangular duct with a transverse homogeneous magnetic field and electrically insulating walls. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The problem is discretized by a double expansion in Chebyshev polynomials in the cross-stream coordinates. The linear eigenvalue problem for the critical Reynolds number depends on the streamwise wavenumber, Hartmann number and the aspect ratio. We consider the limits of small and large aspect ratios in order to compare with stability models based on one-dimensional base flows. For large aspect ratios, we find good numerical agreement with results based on the quasi-two-dimensional approximation. The lift-up mechanism dominates in the limit of a zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann numbers in the duct. As the aspect ratio is reduced away from unity, the duct results converge to Orr's original energy stability result for spanwise uniform perturbations imposed on the plane Poiseuille base flow. We also examine different possible symmetries of eigenmodes as well as the purely hydrodynamic case in the duct geometry.

An MHD boundary layer flow of Casson fluid due to a moving wedge analyzed by the Bernoulli wavelet method

AbstractThe current study adopts a Bernoulli wavelet technique to explore the magnetohydrodynamic (MHD) boundary layer flow of a Casson fluid through a wedge. A nanofluid across a wedge has been investigated for its stable laminar MHD flow, heat, and mass transport characteristics. By choosing worthwhile non‐dimensional parameters, the governing boundary layer equation is reformed into a dimensionless Falkner–Skan equation. The consequent nonlinear equation is addressed via the Bernoulli wavelet method. For a range of different values of the physical parameters, the nature of the boundary layer flow is visually observed. Fluid velocity rises with rise in the values of Casson parameter, wedge parameter, and magnetic parameter. Local wall skin friction increases with increase in wedge parameter and magnetic parameter values. To ensure the accuracy of the findings, local wall skin friction is estimated and tested with other techniques that are already reported in the existing research.

DRBEM solution of singularly perturbed coupled MHD flow equations

In this study, the numerical solution of singularly perturbed magnetohydrodynamic (MHD) flow in a square duct with no-slip, and insulated or perfectly conducting walls is investigated by using the Dual Reciprocity Boundary Element Method (DRBEM). The steady, laminar and fully-developed MHD flow of an incompressible, viscous, and electrically conducting fluid in a long channel of square cross-section (duct) is driven by a pressure gradient. The governing MHD flow equations are convection–diffusion type and coupled in terms of the velocity V(x,y) and induced magnetic field B(x,y). When the intensity of horizontally applied external magnetic field is high, the Hartmann number (Ha) which is the coefficient of convection terms becomes large, that is, the coupled MHD flow equations become convection dominated. In other words, the coefficient of the diffusion terms is very small giving singularly perturbed MHD duct flow which exhibits thin boundary layers. The numerical scheme uses Shishkin mesh which depends on the number of points on one side and Ha. Numerical results obtained by DRBEM reveal that the well-known characteristics of the MHD flow problem are found as Ha increases and it is possible to obtain V(x,y) and B(x,y) for large values of Hartmann number up to Ha=1000.

Magnetohydrodynamic flow regimes in an annular channel

One method and two results have contributed to the complete understanding of magnetohydrodynamic laminar flow in an annular channel with a transverse magnetic field in this paper. In terms of the method, a computationally cheap semi-analytic algorithm is developed based on the spectral method and perturbation expansion. By virtue of the fast computation, dense cases with almost continuous varying Hartmann number M, Reynolds number Re, and cross section ratio η are calculated to explore the flow patterns that are missed in previous research. In terms of the results of the inertialess regime, we establish the average velocity map and electric-flow coupling delimitation in η-M space. Seven phenomenological flow patterns and their analytical approaches are identified. In terms of the results of the inertial regime, we examine the law of decreasing order-of-magnitude of inertial perturbation on primary flow with increasing Hartmann number. The proposed semi-analytic solution coincides with the Re2/M4 suppression theory of J. A. Baylis and J. C. R. Hunt [“MHD flow in an annular channel; theory and experiment,” J. Fluid Mech. 43, 423–428 (1971)] in the case of M < 40. When M > 40, the pair of trapezoid vortices of secondary flow begins to crack, and there is, therefore, a faster drop in inertial perturbation as Re2/M5, which is a new suppression theory. When M > 80, the anomalous reverse vortices are fully developed near Shercliff layers resulting in the weaker suppression mode of Re2/M2.5, which confirms the theoretical prediction of P. Tabeling and J. P. Chabrerie [“Magnetohydrodynamic secondary flows at high Hartmann numbers,” J. Fluid Mech. 103(1), 225–239 (1981)].

MHD slip flow and heat transfer of UCM fluid with the effect of suction/injection due to stretching sheet: OHAM solution

AbstractIn this study, the optimal homotopy analysis (OHAM) technique has been examined to solve the laminar magnetohydrodynamic flow (MHD flow) on the upper‐convected Maxwell fluid on an isothermal porous stretch surface. A study on the effects of parameters like the relaxation time, suction/injection velocity, as well as the magnetic number on velocity over a sheet was conducted and these results are compared to the corresponding previously available results. It was observed that the thickness of the boundary layer is lowered by enhancing , , and values. Opposing this, it was observed that large values increase the magnituIIde. It is found that OHAM is an efficient method capable of giving a greater degree of accuracy in numerical values of flow parameters even after fewer approximations.

An extensive numerical benchmark of the various magnetohydrodynamic flows

There is a continuous need for an updated series of numerical benchmarks dealing with various aspects of the magnetohydrodynamics (MHD) phenomena (i.e. interactions of the flow of an electrically conducting fluid and an externally imposed magnetic field). The focus of the present study is numerical magnetohydrodynamics (MHD) where we have performed an extensive series of simulations for generic configurations, including: (i) a laminar conjugate MHD flow in a duct with varied electrical conductivity of the walls, (ii) a back-step flow, (iii) a multiphase cavity flow, (iv) a rising bubble in liquid metal and (v) a turbulent conjugate MHD flow in a duct with varied electrical conductivity of surrounding walls. All considered benchmark situations are for the one-way coupled MHD approach, where the induced magnetic field is negligible. The governing equations describing the one-way coupled MHD phenomena are numerically implemented in the open-source code OpenFOAM. The novel elements of the numerical algorithm include fully-conservative forms of the discretized Lorentz force in the momentum equation and divergence-free current density, the conjugate MHD (coupling of the wall/fluid domains), the multi-phase MHD, and, finally, the MHD turbulence. The multi-phase phenomena are simulated with the Volume of Fluid (VOF) approach, whereas the MHD turbulence is simulated with the dynamic Large-Eddy Simulation (LES) method. For all considered benchmark cases, a very good agreement is obtained with available analytical solutions and other numerical results in the literature. The presented extensive numerical benchmarks are expected to be potentially useful for developers of the numerical codes used to simulate various types of the complex MHD phenomena.

Heat and mass transfer in MHD boundary layer flow of a second‐grade fluid past an infinite vertical permeable surface

AbstractHeat and mass transfer of non‐Newtonian fluids is increasingly being studied by researchers due to its applications in many branches of science and engineering, such as metallurgical processes, polymer extrusion, glass blowing, crystal growing, and so forth. The present work is mainly concerned with the unsteady laminar magnetohydrodynamic flow of a heat‐generating or absorbing second‐grade fluid past an infinite vertical porous plate. The nondimensional governing equations are solved for the best analytical solution. Results for various flow characteristics are presented through graphs and tables delineating the effect of various parameters characterizing the flow. For engineering interest, the shear stresses, Nusselt number, and Sherwood number are computed and exchanged of views with reference to the important parameters. Our analysis explored that the influences of a chemical reaction and fluid oscillations reduced the concentration distribution in the entire liquid region. The rotation effect decreases the shear stress, whereas it is augmented through an increase in the permeability of porous medium and second‐grade fluid parameters' impact.

Numerical simulation of magnetohydrodynamic laminar flow in an electrically conducting circular pipe with V-shaped strips

Numerical simulation of magnetohydrodynamic laminar flow in an electrically conducting circular pipe with V-shaped strips

Long-Term Electrodeposition under a Uniform Parallel Magnetic Field. 2. Flow-Mode Transition from Laminar MHD Flow to Convection Cells with Two-Dimensional (2D) Nucleation.

Following the analysis of the self-organization of two-dimensional (2D) nuclei in Part 1, the flow-mode transition from laminar magnetohydrodynamics (MHD) flow to convection cells accompanied by 2D nucleation under a uniform parallel magnetic field was theoretically examined using the statistical mechanics of nonequilibrium fluctuation. As a result, it was clarified that secondary nodules of 2D nuclei develop with multiple nucleations during the transition, forming a one-upon-another structure. Then, the evolution of the convection cells as well as the secondary nodules requires unstable growth of the asymmetrical fluctuations by the specific adsorption of an ion. As predicted by the theory, the electrolytic current in copper deposition with specific adsorption of hydrogen ions under a parallel magnetic field developed with time, resulting in a nonlinear steplike curve in a 1200 s deposition time.

Analysis of boundary layer MHD Darcy-Forchheimer radiative nanofluid flow with soret and dufour effects by means of marangoni convection

In the current article, the analysis of magnetohydrodynamic laminar flow past a vertical permeable surface is presented. The flow is considered in the existence of Dufour as well as Soret effects. There is a diffusion-thermo process when heat transmission is encouraged by the concentration gradient and thermo diffusion process when the transfer of mass is encouraged by the thermal gradient. The set of partial differential equations (PDEs) for a modeled problem is changed into a set of ordinary differential equations by applying selected non-dimensional similarity transformations. The semi-analytical method HAM is used to determine a solution for the modeled problem. The features of flow characteristics such as velocity, temperature, and concentration profiles in response to the variations of the emerging parameters are simulated and examined in detail. This research article aims to analyze the impacts of surface tension thermo-solutal quotient, Soret parameter, Dufour parameter, Schmidt number, and Prandtl number on the fluid momentum, transfer of heat, and mass. It is noticed in this article that, the gradient of temperature and concentration at the surface is escalated with enhancement in thermo-solutal surface tension. It is further noted that augmentation in the Prandtl number augmented the transfer in heat.

Evaluation of a nonlinear variational multiscale method for fluid transport problems

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMSn approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMSn approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Simulation results show that VMSn leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

Numerical simulation of 3D magnetohydrodynamic liquid metal flow in a spatially varying solenoidal magnetic field

Abstract Motivated by experiments currently under investigation in the MEKKA laboratory at KIT, numerical simulations have been performed for a liquid metal pipe flow entering a strong magnetic field. Magnetohydrodynamic (MHD) flows in non-uniform magnetic fields are relevant in blanket engineering, in regions where the liquid breeder PbLi enters or exits the magnetic field confining the fusion plasma. Simulations provide insight into 3D phenomena near the non-uniform region of the magnetic field in particular velocity distribution and electric current pattern that cannot be directly observed in the experiments. Moreover, simulations describe the transition from a highly turbulent hydrodynamic entrance flow to a fully established laminar MHD flow. The present work addresses in particular a conservative formulation of the magnetic field, generation and decay of inlet turbulence by means of direct numerical simulation, as well as fluid–wall interaction by electric currents that are exchanged between the liquid metal and the thick electrically conducting pipe wall.

Hall and ion slip effects on MHD laminar flow of an elastico‐viscous (Walter's‐B) fluid

AbstractWe investigated the magnetohydrodynamic (MHD) laminar flow of an elastico‐viscous electrically conducting (Walter's‐B) fluid through a circular cylinder or pipe, loosely packed with a porous material subjected to Hall and ion‐slip effects. The innovation of the study is to consider the entire flow domain without boundary layer approximation in the governing equations. Fully developed solutions of the velocity and pressure drop are obtained making use of perturbation approximation and computationally discussed with reference to flow governing parameters. It is quite exciting that the elastic parameter almost reduces the speed of the liquid in the center of the channel and then continuously expands into the cylinder. For engineering interest, we found the analytical solution and then computationally discussed for skin friction. The occurrence of a magnetic field and a porous matrix gives a fairly uneven flow between the pipes. Elasticity and suction are resistant to experience greater skin friction and are therefore useful for controlling flow separation. A porch has been made to include studies of non‐Newtonian fluids with Hall and ion‐slip effects due to the vast number of possible engineering applications, like power generators, MHD accelerators, refrigeration coils, electric transformers, and heating elements.

Application of ANSYS FLUENT MHD code for liquid metal magnetohydrodynamic studies

Several benchmark problems recommended by the fusion community have been analysed using the ANSYS FLUENT magnetohydrodynamic (MHD) code and the results have been compared with available literature data. The selected problems are: (i) 2D fully developed laminar steady MHD flow inside the electrically insulating square duct, (ii) 3D laminar steady developing MHD flow in a non-uniform magnetic field and (iii) natural convection transient MHD flow. Fairly good agreement has been found between the simulation and reported results. The FLUENT has been found to be capable of predicting 3D MHD effects, which arise in the presence of the transverse fringing magnetic field. The natural convection phenomena under the uniform constant magnetic field have also been successfully captured by the code.

Magneto-Hydrodynamic Flow of a Viscous Fluid in a Channel with a Porous Bounding Wall of Different Permeabilities

In this paper, the effects of permeability parameter on the magneto-hydrodynamic laminar flow of a viscous incompressible fluid in a channel with a porous bounding wall have been investigated. A transverse magnetic field has been applied in the channel flow of viscous fluid and the stream function is used to reduce the governing partial differential equations into non-linear ordinary differential equation which is solved by applying Perturbation method. Numerical simulation is used to analyze the problem and the graphs have been plotted using MATLAB. It has been observed that an increase of magnetic parameter increases the velocity of the viscous fluid while the velocity decreases with the increase of permeability parameter. The flow of viscous fluid has also been investigated with the variation of Reynolds number and the slip coefficient.

Heat and mass transfer analysis of MHD couple stress fluid flow through expanding or contracting porous pipe with cross diffusion effects

This article investigates the effects of an incompressible laminar magnetohydrodynamic flow of couple stress fluid through an expanding or contracting porous pipe with cross diffusion has been considered. It is assumed that the pipe wall expands or contracts uniformly at time dependent rate. The system of governing partial differential equations and with associate boundary conditions are transformed into non-linear coupled system of equations by using suitable similarity transformations and obtained a solution by homotopy analysis method based Mathematica package BVPh2.0. The behaviour of various non-dimensional important parameters on velocity profiles, temperature and concentration distributions and also the rate of heat and mass transfers are studied and exhibited in the form of graphs. We noticed that the temperature of the fluid is enhanced by cross diffusion effects, whereas the concentration of the fluid decreased. In addition, the concentration of the fluid is decreased as Hartmann and inverse Darcy’s parameters increase.

Further validation of liquid metal MHD code for unstructured grid based on OpenFOAM

In fusion liquid metal blankets, complex geometries involving contractions, expansions, bends, manifolds are very common. The characteristics of liquid metal flow in these geometries are significant. In order to extend the magnetohydrodynamic (MHD) solver developed on OpenFOAM platform to be applied in the complex geometry, the MHD solver based on unstructured meshes has been implemented. The adoption of non-orthogonal correction techniques in the solver makes it possible to process the non-orthogonal meshes in complex geometries. The present paper focused on the validation of the code under critical conditions. An analytical solution benchmark case and two experimental benchmark cases were conducted to validate the code. Benchmark case I is MHD flow in a circular pipe with arbitrary electric conductivity of the walls in a uniform magnetic field. Benchmark cases II and III are experimental cases of 3D laminar steady MHD flow under fringing magnetic field. In all these cases, the numerical results match well with the benchmark cases.

Laminar Flow of an Electrically Conducting Incompressible Fluid Between Walls in the Presence of a Transverse Magnetic Field

Magnetohydrodynamic laminar flow of an electrically conducting, viscous, incompressible fluid between two wavy walls, whose equations are taken in the form of Fourier Series, has been investigated under the assumptions that epsional, the coefficient of roughness and R, the Reyond's number of the flow, are small. The stream function has been determined to the first order in epsional. For numerical investigation, the walls are considered to have the sinusoidal deformation. The velocity profiles for the longitudinal and the transverse velocities are drawn at various cross sections for M=0,1,2,epsional=0.5, R=0.1 and P/sub c,x/ R/sup 2/=0.1.

Numerical Study on Steady Magnetohydrodynamics (MHD) Flow and Heat Transfer in a Heated Rectangular Electrically Insulated Duct under the Action of Strong Oblique Transverse Magnetic Field

laminar magnetohydrodynamics flow and heat transfer of an electrically conducting fluid in a rectangular duct in the presence of oblique transverse magnetic field is considered. The walls of the duct are electrically insulated and kept at constant temperature( ). The fluid is kept in motion by a constant pressure gradient and the viscous and Joule dissipations are considered in the energy equation. The dimensionless coupled partial differential equations are solved numerically employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature are visualized in terms of graphics for different values of oblique angle( ), Hartmaan number , Prandtl number and the aspect ratio , the ratio of the length to the breadth. Keywordsflow, electrically insulated walls, rectangular duct, heat