MHD flows are governed by the Navier-Stokes equations coupled with the Maxwell equations. Broadly, MHD flows in astrophysics occur at large magnetic Reynolds numbers while those in terrestrial applications, such as liquid metals, occur at small magnetic Reynolds numbers, the case considered herein. The physical processes of fluid flows and electricity and magnetism are quite different and numer...

We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein’s equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic M...

The preceding chapter discussed the microscopic, kinetic and two-fluid decsriptions of a plasma. But we would actually like a simpler model — one that would include most of the macroscopic properties of a plasma in a “one-fluid” model. The simplest such model is magnetohydrodynamics (MHD), which is a combination of a one-fluid (hydrodynamic-type plus Lorentz force effects) model for the plasma ...

The limitations of Hall MHD as a model for turbulence in weakly collisional plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic theory over a wide range of parameter space. The validity of Hall MHD in the cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD when the ion temperature is finite. It is argued that turbulence in the dissipation range ...

The present study investigates magnetohydrodynamic flow and heat transfer of a Maxwell fluid using a spectral relaxation method. The method is based on simple iteration schemes formed by reduction of the order of the momentum equation followed by a rearrangement of the resulting governing nonlinear equation systems which are then solved using spectral methods. The effect of the flow parameters ...

Space plasma is a collisionless, multi-scale, and highly nonlinear medium. There are numerous types of selfconsistent computer simulations that treat space plasma according to various approximations. The global-scale dynamics are commonly described by magneto-hydrodynamic (MHD), Hall-MHD and multi-fluid models, while electron-scale processes are described by the kinetic model, i.e., the Maxwell...

This paper presents an exact solution for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions in terms of Fox H-function are obtained by using the Laplace transform. When 0 = N the solutions corresp...

We describe local shearing box simulations of turbulence driven by the magnetorotational instability (MRI) in a collisionless plasma. Collisionless effects may be important in radiatively inefficient accretion flows, such as near the black hole in the Galactic Center. The MHD version of ZEUS is modified to evolve an anisotropic pressure tensor. A fluid closure approximation is used to calculate...

The magnetohydrodynamic(MHD) flow and heat transfer of viscoelastic fluid over an accelerating plate with slip boundary are investigated. Different from most classical works, a modified time-space dependent fractional Maxwell fluid model is proposed in depicting the constitutive relationship of the fluid. Numerical solutions are obtained by explicit finite difference approximation and exact sol...

The effects of both wall slip conditions and heat transfer on the magnetohydrodynamics (MHD) peristaltic flow of a Maxwell fluid in a porous planar channel with elastic wall properties have been studied. Mathematical formulation is based upon the modified Darcy’s law. The analytical solution has been derived for the stream function and temperature under the assumptions of small wave number.The ...