Generalised vortex motion of compressible fluid with and without magnetic field and suction

The laminar boundary layer over a stationary infinite disk induced by a rotating compressible fluid is considered. The free stream velocity has been taken as tangential and varies as a power of radius, i.e. v∞ ˜ r−n. The effect of the axial magnetic field and suction is also included in the analysis. An implicit finite difference scheme is employed to the governing similarity equations for numerical computations. Solutions are studied for various values of disk to fluid temperature ratio and for values of n between 1 and −1. In the absence of the magnetic field and suction, velocity profiles exhibit oscillations. It has been observed that for a hot disk in the presence of a magnetic field the boundary layer solutions decay algebraically instead of decaying exponentially. In the absence of the magnetic field and suction, the solution of the similarity equations exists only for a certain range of n.

Fiber Bragg grating magnetic field sensor

In this paper we demonstrate experimentally a magnetic field sensor using a fiber Bragg grating. The shift in the Bragg condition as a result of strain applied on the fiber mounted on a nickel base by the magnetic field gives an indirect measure of the field. The proposed method overcomes the need for long fiber lengths required in methods such as Faraday effect sensors.

Reduction in magnetic field induced broadening of the resistive transition in laser‐deposited YBa2Cu3O7−x thin films on MgO

The magnetic field induced broadening of the normal to superconducting resistive transition of YBa2Cu3O7−x thin films laser deposited on (100) MgO substrates for field oriented parallel to the c axis is found to be significantly reduced in comparison with that found previously in single crystals and in films deposited on SrTiO3. This reduction in broadening is associated with a high density of defects which, while causing a slight decrease in Tc and an increase in the zero‐field transition width, seems to provide strong vortex pinning centers that reduce flux creep

Study of magnetic field effect on the specific heat and entropy in DyBa2Cu3O7-x

The change in the specific heat by the application of magnetic field up to 161 for high temperature superconductor system for DyBa2Cu3O7-x by Revaz et al. [23] is examined through the phenomenological Ginzburg-Landau(G-L) theory of anisotropic Type-II superconductors. The observed specific heat anomaly near T-c with magnetic field is explained qualitatively through the expression <Delta C > = (B-a/T-c) t/(1 - t)(alpha Theta(gamma)lambda(2)(m)(0)), which is the anisotropic formulation of the G-L theory in the London limit developed by Kogan and coworkers; relating to the change in specific heat Delta C for the variation of applied magnetic field for different orientations with c-axis. The analysis of this equation explains satisfactorily the specific heat anomaly near T-c and determines the anisotropic ratio gamma as 5.608, which is close to the experimental value 5.3 +/- 0.5given in the paper of Revaz et al. for this system. (C) 2010 Elsevier B.V. All rights reserved.

Flow And Heat-Transfer Over An Upstream Moving Wall With A Magnetic-Field And A Parallel Free Stream

The flow and heat transfer over an upstream moving non-isothermal wall with a parallel free stream have been considered. The magnetic field has been applied in the free stream parallel to the wall and the effect of induced magnetic field has been included in the analysis. The boundary layer equations governing the steady incompressible electrically conducting fluid flow have been solved numerically using a shooting method. This problem is interesting because a solution exists only when the ratio of the wall velocity does not exceed a certain critical value and this critical value depends on the magnetic field and magnetic Prandtl number. Also dual solutions exist for a certain range of wall velocity.

Comment on “Southward magnetic field in the neutral sheet produced by wavy motions Propagating in the dawn‐dusk direction”

In a recent paper Nakagawa and Nishida [1989] have suggested that wavy motions of the neutral sheet can be generated by the Kelvin‐Helmholtz instability if the dawn‐dusk flow of only several tens of km/s is present. However, their mathematical analysis is based on the choice of particular magnetic field directions in the three regions consisting of north, south lobes and the neutral sheet. In an earlier paper Uberoi [1986] discussed the Kelvin‐Helmholtz instability of a similar structured plasma layer without any assumptions either on velocity field directions or on the magnetic field directions, thus pointing out the angle effect due to variation in magnetic field directions on the instability criterion. The relevance of these results to the problem of wavy motions of the neutral sheet are pointed out. In particular it is found that when the y‐component of the magnetic field in each lobe is taken into consideration the Kelvin‐Helmholtz instability can be exicted only when the dawn‐dusk flow is of several hundreds of km/s a order of ten higher than that arrived in the analysis by Nakagawa and Nishida [1989].

Hypersonic stagnation‐point boundary layers with massive blowing in the presence of a magnetic field

The effect of massive blowing rates on the steady laminar hypersonic boundary‐layer flow of an electrically conducting fluid in the stagnation region of an axisymmetric body with an applied magnetic field has been studied. The governing equations have been solved numerically by combining the implicit finite‐difference scheme with the quasi‐linearization technique. It is observed that the effect of massive blowing rates is to remove the viscous layer away from the boundary, whereas the effect of the magnetic field is just the opposite. It is also found that the velocity overshoot increases with blowing rates and also with magnetic field. The effect of the variation of the density‐viscosity product across the boundary layer is strong only when the blowing rate is small, but for the massive blowing rate the effect is negligible.

Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow in the low-conductivity limit. Our treatment is non-perturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Re-m), but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Re-m. Our principal results are as follows: (i) the magnetic fluctuations are determined to the lowest order in Rem by explicit calculation of the resistive Green's function for the linear shear flow; (ii) the mean electromotive force is then calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the 'C' and 'D' terms, respectively, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the space-time integrals; (iii) the contribution of the D term is such that its contribution to the time evolution of the cross-shear components of the mean field does not depend on any other components except itself. Therefore, to the lowest order in Re-m, but to all orders in the shear strength, the D term cannot give rise to a shear-current-assisted dynamo effect; (iv) casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) the integral kernels are expressed in terms of the velocity-spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) the C term couples different components of the mean magnetic field, so they can, in principle, give rise to a shear-current-type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non-helical velocity dynamics at low fluid Reynolds number does not result in a shear-current-assisted dynamo effect.

Ground State of N Harmonically Bound Anyons in a Magnetic Field

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

Unsteady free convection flow under the influence of a magnetic field

The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, and x-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer and x-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer and x-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction and x-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024(3) collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr-M over a large range, namely 0.01 <= Pr-M <= 10. We obtain data for a wide variety of statistical measures, such as probability distribution functions (PDFs) of the moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterize intermittency, isosurfaces of quantities, such as the moduli of the vorticity and current density, and joint PDFs, such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from a larger intermittency in the magnetic field than in the velocity field, at large Pr-M, to a smaller intermittency in the magnetic field than in the velocity field, at low Pr-M. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr-M, multiscaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

Single-molecule thermodynamics: the heat distribution function of a charged particle in a static magnetic field

Interest in the applicability of fluctuation theorems to the thermodynamics of single molecules in external potentials has recently led to calculations of the work and total entropy distributions of Brownian oscillators in static and time-dependent electromagnetic fields. These calculations, which are based on solutions to a Smoluchowski equation, are not easily extended to a consideration of the other thermodynamic quantity of interest in such systems-the heat exchanges of the particle alone-because of the nonlinear dependence of the heat on a particle's stochastic trajectory. In this paper, we show that a path integral approach provides an exact expression for the distribution of the heat fluctuations of a charged Brownian oscillator in a static magnetic field. This approach is an extension of a similar path integral approach applied earlier by our group to the calculation of the heat distribution function of a trapped Brownian particle, which was found, in the limit of long times, to be consistent with experimental data on the thermal interactions of single micron-sized colloids in a viscous solvent.