Problem Of Magnetohydrodynamic Flow Research Articles

An Efficient and Accurate Penalty-projection Eddy Viscosity Algorithm for Stochastic Magnetohydrodynamic Flow Problems

An Efficient and Accurate Penalty-projection Eddy Viscosity Algorithm for Stochastic Magnetohydrodynamic Flow Problems

Effects of viscous dissipation, gravity modulation and Joule heating on MHD Casson fluid flow over a vertically moving plate with second-order slip velocity

The study of magnetohydrodynamic flow problems for non-Newtonian fluids is significant in many engineering problems. The current inquiry is concerned with a time-dependent, incompressible magnetohydrodynamic Casson fluid flow in a vertically moving plate. The aim of this study is to analyse the effect of viscous dissipation, gravity modulation, heat source and Joule heating with second-order slip velocity. Governing equations are converted to non-dimensional ones using appropriate similarity transformations. To solve the altered equations, the perturbation method is applied, together with MATLAB software. The important physical outcome of this research is that the gravity modulation parameter increases the temperature and velocity of fluid inside the boundary layer. The Eckert number enhances the fluid velocity, concentration boundary layer, skin friction and Nusselt number, whereas the temperature boundary layer reduces for heat sink parameter. The permeability of the porous parameter raises the fluid’s concentration. The work of Kodi et al. [2021. “Investigation of MHD Casson Fluid Flow Past a Vertical Porous Plate Under the Influence of Thermal Diffusion and Chemical Reaction.” Heat Transfer 51 (1): 377–394] has been expanded in this study by adding the novel effects of gravity modulation, Joule heating and viscous dissipation. In addition, the boundary condition includes second-order slip velocity. The obtained results are compared with Kodi et al. [2021. “Investigation of MHD Casson Fluid Flow Past a Vertical Porous Plate Under the Influence of Thermal Diffusion and Chemical Reaction.” Heat Transfer 51 (1): 377–394] and it shows an excellent agreement when added effects are neglected.

The moving finite element method with streamline-upwind Petrov–Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers

It is widely acknowledged that both the streamline-upwind Petrov–Galerkin (SUPG) method and moving mesh method can enhance the stability of finite element method in solving convection-dominated convection–diffusion problems. However, in the case of strong convection-dominated conditions, they still exhibit numerical oscillations and the solutions will not even converge. In order to address similar phenomena observed in solving magnetohydrodynamic (MHD) flow problems at high Hartmann numbers with strong convective dominance, the MHD equation was first decoupled into two convection–diffusion equations. Subsequently, a new approach called the moving mesh streamline-upwind Petrov–Galerkin method (MM-SUPG) was proposed by coupling the moving mesh technique with SUPG method. The MM-SUPG method contains two independent part: the finite element method with SUPG for solving the decoupled MHD equation and a mesh-redistribution algorithm. To verify its effectiveness for solving the MHD equation at high Hartmann number, a classical MHD fluid flow problem was numerically tested using both the MM-SUPG method and the moving finite element method (MFEM). Compared to the MFEM, the proposed method not only yields stable numerical solutions under strong convective dominance while reducing unnecessary false oscillations, but also improves calculation accuracy to some extent using the same mesh.

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.

Influence of thermophoretic deposition and viscous dissipation on magnetohydrodynamic flow with variable viscosity and thermal conductivity

AbstractIn this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow‐regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth.

Numerical investigation of damped wave type MHD flow with time-varied external magnetic field

In recent years, the MHD flow problems has received a significant attention as the behaviour of the flow changes when the Lorentz force (electromagnetic force) acts on the fluid. The aim of this study is to observe numerically the behavior of damped wave-type magnetohydrodynamic (MHD) flow in a sufficiently long rectangular channel having time-varied oblique magnetic field. The mathematical model of the considered problem is coupled convection–diffusion heat-type for the velocity of the fluid and convection–diffusion wave-like for the induced magnetic field. To obtain the numerical simulation, we have used the finite difference method for the discretization of the temporal variable and we also have considered the Galerkin finite element method for the discretization of the spatial variable. In the numerical investigation procedure, the time-varied oblique magnetic field has been considered several functions of the time as polynomial, exponential, and trigonometric e.t.c. We have also considered the several values of the Hartmann number and several directions of the induced magnetic field. In literature, there are many studies about numerical solution of steady and unsteady magnetohydrodynamic flow problems using finite element method, boundary element method and finite difference method e.t.c. For all that, it is the first time in the literature, the damped wave type MHD flow has been considered numerically in this study. The numerical results show Hartmann layer occurs for the high Hartmann numbers in accordance with the nature of the MHD flow. We have obtained numerical results in good agreement with the numerical results available in the literature. The acquired numerical results have been presented by the contour plots. • The damped wave-type magnetohydrodynamic flow with time-varied external magnetic field has been considered. • The time-varied external magnetic field applied with different direction. • Friction factor of the magnetohydrodynamic flow ha calculated for the different time steps. • Finite difference/Finite element hybrid numerical procedure has been applied to obtain the numerical solution.

Stabilized solution of the 3-D MHD flow problem with FEM–BEM coupling approach

In this study, we obtain the numerical solution of the different problem configurations of the 3-D Magnetohydrodynamic (MHD) flow. We solve the MHD flow inside an unbounded conducting domain or around a conducting solid problems which require to consider both MHD equations and the Laplace equation on the connected domains with the coupled boundary conditions. As a numerical procedure we will propose the BEM (Boundary Element Method) and FEM (Finite Element Method) coupling approach with stabilization in order to eliminate the instabilities due to the numeric formulation. We consider the formulations of the MHD equations on the spherical or cubic domains inside an unbounded domain as a first problem and also on the annular spherical or annular cubic region around a conducting solid for the second problem with stabilized FEM. Then obtained discretized equations are combined with BEM formulation of the Laplace equations just only on the boundary. Finally, the BEM is used in order to obtain the rest of the unknown values on the Laplace domain using the boundary values obtained from the coupled formulation. Different values of the problem parameters and configurations are tested, and obtained solutions are displayed in terms of the figures as the 2-D slices of the 3-D solutions.

Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Chebyshev wavelet collocation method for magnetohydrodynamic flow equations

This study proposes Chebyshev wavelet collocation method for partial differential equation and applies to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Approximate solutions of velocity and induced magnetic field are obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. Numerical results of the MHD flow problem show that the accuracy of proposed method is quite good even in the case of a small number of grid points. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number Ha ≤ 1000.

NUMERICAL SOLUTION OF MAGNETOHYDRODYNAMIC FLOW PROBLEM USING RADIAL BASIS FUNCTION BASED FINITE DIFFERENCE METHOD

This paper focuses on the application of Radial Basis Function generated Finite Difference Method (RBF-FD) to solve Magnetohydrodynamic (MHD) flow equation in a rectangular duct in the presence of the transverse external oblique magnetic field. Multiquadric (MQ) Radial Basis Function is used to obtain the numerical solution of the MHD flow problem. Accuracy of the solution can be improved by varying the shape parameter in MQ function. The solution obtained from RBF-FD method is compared with the analytical solution and classical Finite Difference solution. Contours are presented for various Hartmann numbers with different grid sizes and directions of the applied magnetic field. The behaviour of velocity and the magnetic field of the MHD flow have been studied using the contours.

Parameter Identification in MHD Duct Flow Cauchy Problem using the DRBEM

In this study, the Hartmann number (Ha) is identified through the inverse formulation of Cauchy problem for magnetohydrodynamic (MHD) flow in a duct with insulated but no-slip or variably slipping walls. The solutions for direct and inverse problems are obtained using the dual reciprocity boundary element method (DRBEM), and Tikhonov regularization with L-curve method is used for solving ill-conditioned linear system of equations resulted from the inverse problem. The velocity and the induced magnetic field profiles are simulated from the direct solution depicting the well-known MHD characteristics. The Hartmann number is reconstructed from the inverse problem with an accuracy of 10−4 to 10−6. The DRBEM provides overdetermined information needed in the inverse MHD flow problem since it gives both the solution and its normal derivatives on the boundary points.

Initial value problem for the free-boundary magnetohydrodynamics with zero magnetic boundary condition

We show local existence and uniqueness of plasma(fluid)-vaccum free boundary problem of magnetohydrodynamic flow in three-dimensional space with infinite depth setting when magnetic field is zero on the free boundary. We use Sobolev-Slobodetskii space which was used in usual free boundary problem in [3,5,6,7,8,9]. We also show that this solution can be extended as long as we want for sufficiently small initial data. Using the result of this paper we will get a unique solution of (kinematic inviscid) - (magnetic non diffusive) free boundary magnetohydrodynamics problem via (kinematic viscosity) - (magnetic diffusivity) limit in [10].

Suction/Injection Effects on MHD Flow of a Non-Newtonian Power-Law Fluid Past a Continuously Moving Porous Flat Plate with Heat Flux and Viscous Dissipation

In the present work, we studied the problem of magneto-hydro dynamic flow and heat transfer to the non-Newtonian power-law fluid flow past a continuously moving porous permeability flat plate in the presence of radiation and suction/injection with heat flux by taking into consideration the viscous dissipation. The local similarity solution is used to transform the system of partial differential equations, describing the problem into a system of highly coupled nonlinear ordinary differential equations. The non linear ordinary differential equations are first linearized by using the Quasi-linearization technique and then solved numerically by an implicit finite difference scheme. The solution is found to be dependent on various governing parameter including magnetic field parameter M, power-law index n, suction/injection parameter $$f_{w}$$ , Prandtl number Pr, permeability Kp, Eckert number Ec and radiation parameter R. A systematical study is carried out to illustrate the effects of these major parameters on the velocity profiles, temperature profile, skin friction coefficient and the rate of heat transfer and the local Nusselt number.

Algebraic approximation of sub-grid scales for the variational multiscale modeling of transport problems

Variational Multiscale (VMS) Finite Element Methods (FEMs) are robust for the development of general formulations for the solution of multiphysics and multiscale transport problems. To obtain a tractable and computationally efficient model, VMS methods often rely on a residual-based algebraic approximation of the sub-grid scales (small or unresolved features of the solution field not captured by the discretization) using a so-called intrinsic time scales matrix, which depends on the problem’s overall differential operator and represents the main model parameter. A novel technique for approximating the intrinsic time scales matrix for generic transport problems in a relatively inexpensive manner (e.g., does not rely on eigenvalue computations) is presented. The method is denoted Transport-Equivalent Scaling (TES) and is based on the monolithic casting of the transport problem as a system of transient–advective–diffusive–reactive (TADR) equations and a subsequent scaling of the coefficient matrices such to preserve each type of transport flux. An algebraic VMS formulation incorporating the TES method is complemented with a discontinuity-capturing (DC) approach and implemented within a FEM solver for the solution of TADR problems. The solution of the global discrete system is accomplished using a generalized-alpha time-stepper together with a globalized inexact Newton–Krylov nonlinear solver. The effectiveness of the TES formulation is verified with the simulation of benchmark incompressible, compressible, and magnetohydrodynamic flow problems. The results demonstrate that the TES method seamlessly handles incompressible–compressible flows in a unified manner (e.g., without assessing the compressibility of the flow). The convergence process using the TES approach and a more standard approximation for the intrinsic time scales, as well as the effect of the DC approach, are also investigated. Analysis of the intrinsic time scales for a one-dimensional incompressible flow model reveals the similitudes and differences between the TES formulation and other conventional methods.

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

In this article, we establish an exponential high-order compact (EHOC) difference scheme on non-uniform grids for the solution of the coupled equations representing the steady incompressible, viscous magnetohydrodynamic (MHD) flow through a straight channel of rectangular section. A main advantage of the non-uniform grids-based EHOC scheme is that it could use coarser mesh to capture the details within the computational domain for the MHD flow problems with high Hartmann numbers. Numerical experiments are carried out to validate the performance of the currently proposed scheme. Computation results of the MHD flow in the 2D square-channel problems are presented for Hartmann numbers ranging from 10 to 106. The numerical solutions obtained with the newly developed EHOC scheme are also compared with analytic solutions and numerical results by other available methods in the literature. All of these numerical results demonstrate that the currently proposed scheme is accurate, efficient and robust for the wide range of Hartmann numbers 10 to 106.

Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid

Abstract The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible and electrically conducting dusty fluid over an unsteady stretching sheet is analyzed numerically. The fluid viscosity and thermal conductivity are assumed to vary as an exponential function of temperature. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations using similarity transformations. The obtained similarity equations are solved numerically using RKF-45 method. Numerical computation has been carried out for horizontal velocity profiles, temperature, Nusselt number and skin friction coefficient for various values of the flow parameters that are presented for both VWT and VHF respectively. A comparison with previously published work is performed and the results are found to be in good agreement.

Viscous and Joules Dissipation on MHD Flow past a Stretching Porous Surface Embedded in a Porous Medium

This paper investigates the influence of both viscous and joules dissipation on the problem of magneto-hydrodynamic flow past a stretching porous surface embedded in a porous medium for rotating case. Using similarity approach the system of partial differential equations is transformed into ordinary differential equations which strongly depend on the magnetic parameter, stretching parameter, rotation parameter, permeability parameter and Prandtl number. The coupled differential equations are numerically simulated using the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration schemes. The velocity and temperature profiles are discussed and presented graphically. The comparisons for dimensionless skin friction coefficient and local Nusselt number are also taken into account and discussed and presented graphically.

Numerical simulations of a fully developed liquid-metal magnetohydrodynamic flow in a circular duct

In this paper, a kind of new meshless method, two-level radial point interpolation method, has been developed to analyze the fully developed liquid-metal Magnetohydrodynamic (MHD) flow under the externally applied magnetic field in a circular duct with thin conducting walls. This method applied the radial point interpolation method (RPIM) to solve the two levels Galerkin weak form formulations. As the shape functions from RPIM possess Kronecker delta function properties, the essential boundary conditions of MHD flow problems are easily to be enforced. Numerical simulations of MHD flow in the circular duct with partial conducting walls are carried out, showing that the method is very stable in the computation.

MHD Flow of the Micropolar Fluid between Eccentrically Rotating Disks.

This analytical investigation examines the magnetohydrodynamic flow problem of an incompressible micropolar fluid between the two eccentrically placed disks. Employing suitable transformations, the flow governing partial differential equations is reduced to ordinary differential equations. An exact solution representing the different flow characteristic of micropolar fluid has been derived by solving the ordinary differential equations. Analysis of the flow characteristics of the micropolar fluid has been done graphically by varying the Reynolds number and the Hartmann number. This analysis has been carried out for the weak and strong interactions.

Wavelet optimized finite difference mesh for MHD flow in a circular duct

There is a large class of important problems in scientific and engineering applications where the solution shows very little variation in the core region but very rapid changes close to the boundary of the domain of interest. Magnetohydrodynamic flow problems belong to this category. Treatment of such problems numerically, therefore, requires a non-uniform mesh, which is very fine near the boundary. The determination of the size of the grid in different parts of the domain is, therefore, a challenging problem. Some recent studies suggest that wavelet methods can be effectively applied to create an optimized mesh. The method has mostly been used for one dimensional problems. The present paper investigates the problem for fully developed MHD duct flow problems which are basically two dimensional. The boundary layer character is more pronounced in one direction as compared to the other. The governing equations comprise a coupled system of two partial differential equations with Dirichlet boundary conditions. Wavelet based adaptive mesh is first created and then the system is discretized over this mesh. Computations have been carried out at different precision levels for various Hartmann numbers for a pipe of circular section. Contours are also drawn to depict the core and the boundary layer region.