Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

We introduce a unique model for a fermion-antifermion pair interacting via Dirac oscillator coupling in the presence of an external uniform magnetic field. This model is based on an exact solution of the corresponding form of a fully-covariant two-body Dirac equation (one-time). The dynamic symmetry of the system allows to study in $$2+1$$ 2 + 1 dimensions and we choose the interaction of the particles with the external uniform magnetic field in the symmetric gauge. The corresponding equation leads $$4\times 4$$ 4 × 4 dimensional matrix equation for such a static composite system. For spin antisymmetric state of the fermion-antifermion pair, we perform an exact solution of the matrix equation and obtain relativistic Landau levels of a fermion-antifermion pair interacting via Dirac oscillator coupling. The results show that such a composite system behaves like a single relativistic quantum oscillator carrying total rest mass of the particles. We discuss several interesting features of this system and show that the obtained energy spectrum agrees well with the previously announced results for one-body systems. We think that the introduced model in this manuscript has a great potential for many theoretical and experimental applications.

Magnetohydrodynamic Moving Liquid Plug Within a Microchannel: Analytical Solutions

The wide applications of plug flows in microscale in science and engineering help them attract a great deal recent interest. An analytical study is undertaken here to study the impacts of a transversely applied external uniform magnetic field affecting the motion of liquid in the plug in terms of hydrodynamic mixing properties. The well-known symmetric vortex structure occurring in a long plug with moderate aspect ratio is observed to be preserved, while the recirculation phenomenon is highly affected by the action of the magnetic field. The decelerating feature of Lorentz force on the liquid motion is illuminated by reducing the strength of the recirculating vortex moving towards the upper and lower walls. The effects of magnetic field on the flow resistance of the liquid plug as well as on the plug circulation rate and on the axial flux are also clarified. The liquid plug considered here is shown to be fully consistent with the continuous liquid flow in a channel whose exact solution is further extracted.

Mixed Magnetoconvection of Nanofluids in a Long Vertical Porous Channel

This paper aimed to study the flow of a nanofluid in a long vertical porous channel when an external uniform magnetic field is impressed. The Buongiorno two-phase model of nanofluid is supposed to be slightly compressible in order to assume the Oberbeck–Boussinesq approximation. The velocity, the induced magnetic field, the temperature, and the nanoparticle volume fraction are analytically obtained. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of plots illustrating the influence of various parameters involved in the problem is presented and discussed.

Numerical simulation of the motion of a micropolar Casson fluid through a porous medium over a stretching surface

The present study examines the motion of a micropolar non-Newtonian Casson fluid through a porous medium over a stretching surface. The system is pervaded by an external uniform magnetic field. The heat transfer and heat generation are taken into consideration. The problem is modulated mathematically by a system of non-linear PDE which describe the equations of continuity, momentum, and energy. Suitable similarity solutions are utilized to transform the system of equation ordinary non-linear differential equations. In accordance with the appropriate boundary conditions, are numerically solved by means of the finite difference technique. Also, the system is solved by using multistep differential transform method. The effects of the various physical parameters, of the problem at hand, are illustrated through a set of diagrams.

Nonlinear Dynamo in Obliquely Rotating Stratified Electroconductive Fluid in an Uniformly Magnetic Field

In this paper, we investigated a new large-scale instability that arises in an obliquely rotating convective electrically conducting fluid in an external uniform magnetic field with a small-scale external force with zero helicity. This force excites small-scale velocity oscillations with a small Reynolds number. Using the method of multiscale asymptotic expansions, we obtain the nonlinear equations for vortex and magnetic disturbances in the third order of the Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The linear stage of the magneto-vortex dynamo arising as a result of instabilities of -effect type is investigated. The mechanism of amplification of large-scale vortex disturbances due to the development of the hydrodynamic - effect taking into account the temperature stratification of the medium is studied. It was shown that a «weak» external magnetic field contributes to the generation of large-scale vortex and magnetic perturbations, while a «strong» external magnetic field suppresses the generation of magnetic-vortex perturbations. Numerical methods have been used to find stationary solutions of the equations of a nonlinear magneto-vortex dynamo in the form of localized chaotic structures in two cases when there is no external uniform magnetic field and when it is present.

The motion of a non-Newtonian nanofluid over a semi-infinite moving vertical plate through porous medium with heat and mass transfer

The motion of a non-Newtonian nanofluid over a semi-infinite moving vertical plate through porous medium stressed by an external uniform magnetic field with heat and mass transfer is investigated. The fluid under consideration obeys Eyring-Powell model. The effects of the physical parameters of the problem such as, permeability, chemical reaction as well as the fluid material parameters such as Hartmann number, Eckert number, and Reynolds number are discussed. The effects of external cooling (Gr > 0) of the plate by the free convection are considered. Graphical results are presented to highlight effects of various emerging parameters on velocity, temperature and concentration profiles.

Stability of Poiseuille-type flows for an MHD model of an incompressible polymeric fluid

We study a new rheological model describing flows of melts and solutions of incompressible viscoelastic polymeric media in an external uniform magnetic field in the presence of a temperature drop and a conduction current. We derive an asymptotic representation of the spectrum of the linear problem resulting from the linearization of the initial boundary value problem in an infinite plane channel about a Poiseuille-type flow. For this Poiseuille-type flow, we also determine the parameter domain of linear Lyapunov stability.

Dense quark–gluon plasma in strong magnetic fields

A non-perturbative (np) method of Field correlators (FCM) was applied to study QCD at temperatures above the deconfinement transition ($$1<T/T_c<3,~T_c\sim 0.16~\mathrm{GeV}$$1<T/Tc<3,Tc∼0.16GeV) and nonzero baryon densities (baryon chemical potential $$\mu _B<0.5~\mathrm{GeV}$$μB<0.5GeV) in an external uniform magnetic field ($$eB<0.5~\mathrm{GeV}^2$$eB<0.5GeV2). Within FCM, the np high-temperature dynamics is embodied in the Polyakov loop and in the Debye mass due to the Color-Magnetic confinement. Analytic expressions for quark pressure and magnetic susceptibility were obtained. The expressions were represented as series and in integral form. Magnetic susceptibility was found to increase rapidly with temperature and slowly with density. The results at the zero density limit are in agreement with lattice data.