Search Results (91)

An analytical study is conducted on unsteady, one-directional magnetohydrodynamic (MHD) flows of electrically conducting, incompressible, and viscous fluids, where the viscosity varies with pressure following a power-law relationship. The flow takes place within a planar channel and is driven by the lower plate, which moves along its own plane with an arbitrary, time-dependent speed. The effects of gravitational acceleration are also considered. General exact formulas are derived for both the dimensionless velocity of the fluid and the resulting non-zero shear stress. Moreover, these are the only general solutions for the MHD motions of the fluids considered, and they can produce precise solutions for any motion of this type for respective fluids. The proposed analytical method leads to simple forms of analytical solutions and can be useful in the study of other cases of fluids with viscosity depending on pressure. As an example, solutions related to the modified Stokes’ second problem are presented and confirmed through graphical validation. These solutions also help highlight the impact of the magnetic field on fluid dynamics and determine the time needed for the system to achieve a steady state. Graphical representations indicate that a steady state is reached more quickly and the fluid moves more slowly when a magnetic field is applied. Full article

The Taylor–Couette flow of electrically conducting incompressible Oldroyd-B fluids induced by time-dependent couples in an annulus is analytically investigated when magnetic and porous effects are taken into account. Closed-form expressions are established for the dimensionless shear stress, fluid velocity and Darcy’s resistance by means of the integral transforms. Similar solutions for the MHD Taylor–Couette flow of the same fluids through a porous medium induced by a time-dependent couple in an infinite circular cylinder are obtained as limiting cases of previous results. In both cases, the obtained results can generate exact solutions for any motion of this kind of the respective fluids. Consequently, the two MHD motions of the respective fluids through a porous medium are completely solved. For illustration, two case studies are considered and the fluid behavior is graphically investigated. The convergence of the starting solutions to their permanent components is proved and the required time to touch the permanent state is determined. Full article

The isothermal motion of incompressible second-grade fluids induced by an infinite circular cylinder that rotates around its symmetry axis is analytically and numerically investigated when the magnetic and porous effects are taken into consideration. General closed-form expressions are established for the dimensionless velocity field and the corresponding motion problem is completely solved. For illustration, some special cases are considered, and the results’ correctness is graphically proved. Based on a simple but important observation, the obtained results have been used to provide a general expression for the shear stress corresponding to MHD motions of the same fluids through a porous medium induced by a longitudinal shear stress on the boundary. Finally, graphical representations are used to bring to light the influence of the magnetic field and porous medium on the fluid behavior. It was found that the fluid flows slower and the steady state is reached earlier in the presence of a magnetic field or porous medium. Full article

The ‘dynamo problem’ requires that the origin of the primarily dipole geomagnetic field be found. The source of the geomagnetic field lies within the outer core of the Earth, which contains a turbulent magnetofluid whose motion is described by the equations of magnetohydrodynamics (MHD). A mathematical model can be based on the approximate but essential features of the problem, i.e., a rotating spherical shell containing an incompressible turbulent magnetofluid that is either ideal or real but maintained in an equilibrium state. Galerkin methods use orthogonal function expansions to represent dynamical fields, with each orthogonal function individually satisfying imposed boundary conditions. These Galerkin methods transform the problem from a few partial differential equations in physical space into a huge number of coupled, non-linear ordinary differential equations in the phase space of expansion coefficients, creating a dynamical system. In the ideal case, using Dirichlet boundary conditions, equilibrium statistical mechanics has provided a solution to the problem. As has been presented elsewhere, the solution also has relevance to the non-ideal case. Here, we examine and compare Galerkin methods imposing Neumann or mixed boundary conditions, in addition to Dirichlet conditions. Any of these Galerkin methods produce a dynamical system representing MHD turbulence and the application of equilibrium statistical mechanics in the ideal case gives solutions of the dynamo problem that differ only slightly in their individual sets of wavenumbers. One set of boundary conditions, Neumann on the outer and Dirichlet on the inner surface, might seem appropriate for modeling the outer core as it allows for a non-zero radial component of the internal, turbulent magnetic field to emerge and form the geomagnetic field. However, this does not provide the necessary transition of a turbulent MHD energy spectrum to match that of the surface geomagnetic field. Instead, we conclude that the model with Dirichlet conditions on both the outer and the inner surfaces is the most appropriate because it provides for a correct transition of the magnetic field, through an electrically conducting mantle, from the Earth’s outer core to its surface, solving the dynamo problem. In addition, we consider how a Galerkin model velocity field can satisfy no-slip conditions on solid boundaries and conclude that some slight, kinetically driven compressibility must exist, and we show how this can be accomplished. Full article

Magnetohydrodynamic (MHD) generators are direct energy conversion devices that transform the motion of an electrically conducting fluid into electricity through interaction with a magnetic field. Developed as an alternative to conventional turbine-generator systems, MHD generators evolved through the 20th century from large units, which are intended to transform thermal energy into electricity using plasma as a working fluid, to smaller units that can harness heat from a variety of sources. In the last few decades, an effort has been made to develop energy conversion systems that incorporate MHD generators to harvest renewable sources such as solar and ocean energy, strengthening the sustainability of this technology. This review briefly synthesizes the main steps in the evolution of MHD technology for electricity generation, starting by outlining its physical principles and the proposals to convert thermal energy into electricity, either using a high-temperature plasma as a working fluid or a liquid metal in a one- or two-phase flow at lower temperatures. The use of wave energy in the form of acoustic waves, which were obtained from the conversion of thermal energy through thermoacoustic devices coupled to liquid metal and plasma MHD generators, as well as alternatives for the transformation of environmental energy resources employing MHD transducers, is also assessed. Finally, proposals for the conversion of ocean energy, mainly in the form of waves and tides, into electric energy, through MHD generators using either seawater or liquid metal as working fluids, are presented along with some of the challenges of MHD conversion technology. Full article

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated. Full article

The motion of viscous incompressible magnetohydrodynamics (MHD) is considered in a domain that is bounded by a free surface. The motion interacts through the free surface with an electromagnetic field located in a domain exterior to the free surface and bounded by a given fixed surface. Some electromagnetic fields are prescribed on this fixed boundary. On the free surface, jumps in the magnetic and electric fields are assumed. The global existence of solutions to this problem assuming appropriate smallness conditions on the initial and boundary data is proved. Full article

Attributed to the lack of an Earth-like global intrinsic dipole magnetic field on Mars, the induced electromagnetic field environment plays a crucial role in the evolution of its atmosphere. The dominant motional electric field (${\mathit{E}}_{\mathit{M}}$) induced by the bulk motion of the magnetic field within the Martian magnetosheath serves to accelerate ions toward escape velocity, thereby forming a plume escape channel. However, the distribution morphology of ${\mathit{E}}_{\mathit{M}}$ itself has received limited attention in previous research. In this study, by taking advantage of the multi-fluid Hall-MHD model cooperating with the Martian crustal field model, we focus on elucidating the physical mechanisms underlying the asymmetrical distribution of ${\mathit{E}}_{\mathit{M}}$ and examining the influence of the crustal field on this asymmetry. The results obtained from the simulation conducted in the absence of the crustal field indicate that the ${\mathit{E}}_{\mathit{M}}$ is more intense within the ${-Z}_{MSE}$ magnetosheath, where ${\mathit{E}}_{\mathit{M}}$ is directed toward Mars, primarily due to its corresponding higher velocity and a stronger magnetic field at lower solar zenith angles. The Martian crustal field has the ability to enhance the local ${\mathit{E}}_{\mathit{M}}$ around the inner boundary of the magnetosheath by amplifying both the magnetic field and its associated velocity. Accordingly, these findings provide valuable insights into the asymmetric nature of ${\mathit{E}}_{\mathit{M}}$ within the Martian magnetosheath under typical quiet-time solar wind conditions. Full article

The heat and mass transfer phenomenon in the presence of a moving magnetic field has a wide range of applications, spanning from industrial processes to environmental engineering and energy conversion technologies. Understanding these interactions enables the optimization of various processes and the development of innovative technologies. This manuscript is about a non-integer-order heat-mass transfer model for Maxwell fluid over an inclined plate in a porous medium. The MHD flow of non-Newtonian fluid over the plate due to the natural convection of the symmetric temperature field and general motion of the inclined plate is investigated. A magnetic field is applied with a certain angle to the plate, and it can either be fixed in place or move along with the plate as it moves. Our model equations are linear in time, and Laplace transforms form a powerful tool for analyzing and solving linear DEs and systems, while the Stehfest algorithm enables the recovery of original time domain functions from their Laplace transform. Moreover, it offers a powerful framework for handling fractional differential equations and capturing the intricate dynamics of non-Newtonian fluids under the influence of magnetic fields over inclined plates in porous media. So, the Laplace transform method and Stehfest’s numerical inversion algorithm are employed as the analytical approaches in our study for the solution to the model. Several cases for the general motion of the plate and generalized boundary conditions are discussed. A thorough parametric analysis is performed using graphical analysis, and useful conclusions are recorded that help to optimize various processes and the developments of innovative technologies. Full article

This study explores the synergistic impact of zero flux and convective boundary conditions on the magnetohydrodynamic (MHD) boundary-layer slip flow of nanofluid over a moving surface, utilizing Buongiorno’s model. In a landscape of expanding nanofluid applications, understanding boundary condition interactions is crucial. Employing a systematic approach, we varied key parameters, including surface velocity, thermophoresis, Brownian motion, Eckert number, Prandtl number, and Lewis number, systematically investigating their effects on flow and heat transfer. Numerical simulations focused on critical metrics such as skin friction coefficients; Nusselt and Sherwood numbers; and temperature, concentration, and velocity profiles. Noteworthy findings include the amplifying effect of a magnetic field and viscous dissipation on temperature profiles and the dual impact of heightened velocity slip on temperature and velocity profiles, which result in a thicker concentration boundary layer. Beyond academia, we envision our research having practical applications in optimizing high-temperature processes, bio-sensors, paints, pharmaceuticals, coatings, cosmetics, and space technology. Full article

The contributions of magnetohydrodynamic (MHD) vortexes to chiral electrodeposition in a vertical magnetic field were theoretically examined based on the three-generation model of the 2D nucleus, 3D nucleus, and screw dislocation; for the vortexes to rotate in the second and third-generation, the kinematic viscosity must be at least 10⁻¹⁸ and 10⁻³⁰ times lower than the ordinary value in the first generation, i.e., almost equal to zero. This implies that the ionic vacancy created on the electrode surface works as an atomic-scale lubricant. At the same time, the vortexes played three roles: promotion and suppression of nucleation, and transport of the chirality from the upper generation to the lower generation through precessional motion. Then, the rule of the chirality transfer was established, and finally, the relationship between the chiral activity and magnetic field was clarified in the presence and absence of chloride ions. Full article

In this work, we investigate isothermal MHD motions of a large class of rate type fluids through a porous medium between two infinite horizontal parallel plates when a differential expression of the non-trivial shear stress is prescribed on the boundary. Exact expressions are provided for the dimensionless steady state velocities, shear stresses and Darcy’s resistances. Obtained solutions can be used to find the necessary time to touch the steady state or to bring to light certain characteristics of the fluid motion. Graphical representations showed the fluid moves slower in presence of a magnetic field or porous medium. In addition, contrary to our expectations, the volume flux across a plane orthogonal to the velocity vector per unit width of this plane is zero. Finally, based on a simple remark regarding the governing equations of velocity and shear stress for MHD motions of incompressible generalized Burgers’ fluids between infinite parallel plates, provided were the first exact solutions for MHD motions of these fluids when the two plates apply oscillatory or constant shear stresses to the fluid. This important remark offers the possibility to solve any isothermal MHD motion of these fluids between infinite parallel plates or over an infinite plate when the non-trivial shear stress is prescribed on the boundary. As an application, steady state solutions for MHD motions of same fluids have been developed when a differential expression of the fluid velocity is prescribed on the boundary. Full article

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’. Full article

Some MHD unidirectional motions of the electrically conducting incompressible Maxwell fluids between infinite horizontal parallel plates incorporated in a porous medium are analytically and graphically investigated when differential expressions of the non-trivial shear stress are prescribed on the boundary. Such boundary conditions are usually necessary in order to formulate well-posed boundary value problems for motions of rate-type fluids. General closed-form expressions are established for the dimensionless fluid velocity, the corresponding shear stress, and Darcy’s resistance. For completion, as well as for comparison, all results are extended to a fractional model of Maxwell fluids in which the time fractional Caputo derivative is used. It is proven for the first time that a large class of unsteady motions of the fractional incompressible Maxwell fluids becomes steady in time. For illustration, three particular motions are considered, and the correctness of the results is graphically proven. They correspond to constant or oscillatory values of the differential expression of shear stress on the boundary. In the first case, the required time to reach the steady state is graphically determined. This time declines for increasing values of the fractional parameter. Consequently, the steady state is reached earlier for motions of the ordinary fluids in comparison with the fractional ones. Finally, the fluid velocity, shear stress, and Darcy’s resistance are graphically represented and discussed for the fractional model. Full article

The numerical study of relativistic magnetohydrodynamics (MHD) plays a crucial role in high-energy astrophysics but unfortunately is computationally demanding, given the complex physics involved (high Lorentz factor flows, extreme magnetization, and curved spacetimes near compact objects) and the large variety of spatial scales needed to resolve turbulent motions. A great benefit comes from the porting of existing codes running on standard processors to GPU-based platforms. However, this usually requires a drastic rewriting of the original code, the use of specific languages like CUDA, and a complex analysis of data management and optimization of parallel processes. Here, we describe the porting of the ECHO code for special and general relativistic MHD to accelerated devices, simply based on native Fortran language built-in constructs, especially do concurrent loops, few OpenACC directives, and straightforward data management provided by the Unified Memory option of NVIDIA compilers. Thanks to these very minor modifications to the original code, the new version of ECHO runs at least 16 times faster on GPU platforms as compared to CPU-based ones. The chosen benchmark is the 3D propagation of a relativistic MHD Alfvén wave, for which strong and weak scaling tests performed on the LEONARDO pre-exascale supercomputer at CINECA are provided (using up to 256 nodes corresponding to 1024 GPUs, and over 14 billion cells). Finally, an example of high-resolution relativistic MHD Alfvénic turbulence simulation is shown, demonstrating the potential for astrophysical plasmas of the new GPU-based version of ECHO. Full article