Numerical Analysis of Nano-Encapsulated Pcm Magnetohydrodynamics Double-Diffusive Convection and Entropy Generation in Vertical Enclosures with Porous Layer
Mohammed Azeez AlomariAhmed M. HassanAbdullah F. AlajmiAbdellatif M. SadeqFaris AlqurashiMujtaba A. Flayyih
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Magnetohydrodynamics (MHD) is a fluid model that describes the macroscopic equilibrium and stability properties of a plasma. Actually, there are several versions of the MHD model. The most basic version is called “ideal MHD” and assumes that the plasma can be represented by a single fluid with infinite electrical conductivity and zero ion gyro radius. Other, more sophisticated versions are often referred to as “extended MHD” or “generalized MHD” and include finite resistivity, two-fluid effects, and kinetic effects (e.g. finite ion gyro radius, trapped particles, energetic particles, etc.). The present volume is focused on the ideal MHD model.
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We prove some regularity conditions for the MHD equations withpartial viscous terms and the Leray-$\alpha$-MHD model. Since thesolutions to the Leray-$\alpha$-MHD model are smoother than that ofthe original MHD equations, we are able to obtain better regularityconditions in terms of the magnetic field $B$ only.
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MHD instabilities in toroidal herical systems based on theory and reduced MHD equations by assuming the stellarator expansion are discussed. This approach sabrifices some physics compared to the three-dimensional culculation using the full MHD equations, but the improved resolution and computational speed offer a better understanding to explore the large parameeter space. The experimental results concerning MHD instabilities could be explained by the reduced MHD equations. Investigation of nonlinear evolution for the unstable mode can be pursued straightforwardly.
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Global, three‐dimensional, ideal MHD simulations of Earth's bow shock are reported for low Alfven Mach numbers M A and quasi‐perpendicular magnetic field orientations. The simulations use a hard, infinitely conducting magnetopause obstacle, with axisymmetric three‐dimensional location given by a scaled standard model, to directly address previous gasdynamic (GD) and field‐aligned MHD (FA‐MHD) work. Tests of the simulated shocks’ density jumps X for 1.4 ≲ M A ≲ 10 and the high M A shock location, and reproduction of the GD relation between magnetosheath thickness and X for quasi‐gasdynamic MHD runs with M A ≫ M S , confirm that the MHD code is working correctly. The MHD simulations show the standoff distance a s increasing monotonically with decreasing M A . Significantly larger a s are found at low M A than predicted by GD and phenomenological MHD models and FA‐MHD simulations, as required qualitatively by observations. The GD and FA‐MHD predictions err qualitatively, predicting either constant or decreasing a s with decreasing M A . This qualitative difference between quasi‐perpendicular MHD and FA‐MHD simulations is direct evidence for a s depending on the magnetic field orientation θ. The enhancement factor over the phenomenological MHD predictions at M A ∼ 2.4 agrees quantitatively with one observational estimate. A linear relationship is found between the magnetosheath thickness and X , modified both quantitatively and intrinsically by MHD effects from the GD result. The MHD and GD results agree in the high M A limit. An MHD theory is developed for a s , restricted to sufficiently perpendicular θ and high sonic Mach numbers M S . It explains the simulation results with excellent accuracy. Observational and further simulation testing of this MHD theory, and of its predicted M A , θ, and M S effects, is desirable.
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Fundamentals of mathematical magnetohydrodynamics (MHD) start with definitions of major variables and parameters in MHD fluids (also known as MHD media) and specifically plasmas encountered in nature
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Three models have been introduced to investigate the MHD equilibrium and stability properties of a general multidimensional magnetic fusion configuration: ideal MHD, kinetic MHD, and double adiabatic MHD. Ideal MHD is by far the most widely used model although there is concern since the collision dominated assumption used in the derivation is not satisfied in fusion-grade plasmas. The collisionless kinetic MHD model provides the most reliable description of the physics but is difficult to solve in realistic geometries because of the complex kinetic behavior parallel to the magnetic field. Double adiabatic MHD is a collisionless fluid model that is much easier to solve than kinetic MHD but the closure assumptions cannot be justified by any rigorous mathematical or physical arguments.
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We show the stepped-pressure equilibria that are obtained from a generalization of Taylor relaxation known as multi-region, relaxed magnetohydrodynamics (MRXMHD) are also generalizations of ideal magnetohydrodynamics (ideal MHD). We show this by proving that as the number of plasma regions becomes infinite, MRXMHD reduces to ideal MHD. Numerical convergence studies illustrating this limit are presented.
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This paper is a summary of the first Euromech Colloquium to be held on Magnetohydrodynamics (MHD). It was organized in conjunction with the Centre National de la Recherche Scientifique and held at Grenoble from 16–19 March 1976 with 60 participants from 10 countries present. Papers were presented on laminar and turbulent MHD duct flows; heat transfer and two-phase flows in MHD; the effects of magnetic fields on instabilities and turbulence; the motion of and forces on solid objects in MHD flows; flow-measurement methods, and applications of MHD in the metallurgical industries, in sodium technology and in liquid-metal power generation. Our main conclusion is that there are many industrial applications of the existing body of research findings in MHD, but that quite new research problems have arisen as a result of the new applications, and that these need investigation. MHD lives!
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