Entropy Generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

In the present study, the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered. The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations. Runge-Kutta-Fehlberg method is used to solve the governing problem. The effects of magnetic field parameter M, local slip parameter λ, generalized Biot number γ, Sisko fluid material parameter A, Eckert number Ec, Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity, temperature, local entropy generation number N_G and Bejan number Be are inspected. Moreover, the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited. The current results are helpful in checking the entropy generation for Sisko-fluid. It is found that, an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity. For shear thinning fluids (n < 1), the temperature dominates and the velocity rises. Local entropy generation number is more for larger generalized Biot number, magnetic field parameter and Brinkman number. The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases. The local Nusselt number decreases as magnetic field parameter, local slip parameter and Eckert number are increase, while it increases as material parameter, generalized Biot number and Prandtl number are increase.     

Hall Coefficient of Equilibrium Supercurrents Flowing inside Superconductors

We study augmented quasiclassical equations of superconductivity with the Lorentz force, which is missing from the standard Ginzburg–Landau and Eilenberger equations. It is shown that the magnetic Lorentz force on equilibrium supercurrents induces a finite charge distribution and the resulting electric field to balance the Lorentz force. An analytic expression is obtained for the corresponding Hall coefficient of clean type-II superconductors with simultaneously incorporating the Fermi-surface and gap anisotropies. It has the same sign and magnitude at zero temperature as the normal state for an arbitrary pairing, having no temperature dependence specifically for s-wave pairing. The gap anisotropy may bring about a considerable temperature dependence in the Hall coefficient and can lead to its sign change as a function of temperature, as exemplified for a model d-wave pairing with a two-dimensional Fermi surface. The sign change may be observed in some high-T _c superconductors.     

Distribution of heat flux transported by a magnetically driven arc

An alternating magnetic field is applied to a transferred arc to create a plasma arc for heating a large metal surface. The arc root oscillates on the metal surface at the frequency of alternating electromagnetic force (I × B force). The magnitude of the applied magnetic field controls the amplitude of the oscillatory motion. By changing the waveform of the applied field, the distribution of the heat flux density is adjustable. An overly strong magnetic field renders the oscillatory arc motion unstable. Experimental observations reveal that the heat flux is affected considerably by the neutral gas flow surrounding the arc.     

Jc enhancement and flux pinning of Se substituted YBCO compound

Y_2/3 Se_1/3Ba₂Cu₃O_x compound was fabricated by using solid state fabrication technique. Optimum heat treatments conditions for Y_0.77Se_0.33Ba₂Cu₃O_x were investigated. It was determined that the XRD results of these samples were similar to Y-123 phase with some impurities. Magnetization dependence of applied magnetic fields was measured in the range of 0–9 T at 10–50 K. The symmetric and asymmetric M–H loops were obtained for the samples. Magnetization loops obtained from measurements were successfully described by the extended Valkov–Khrustalev model. The temperature and applied magnetic field dependencies of magnetization of sample were estimated and critical current density of samples was calculated by Bean model and pinning force of samples was calculated by using Lorentz force. It is found from critical current density values that Se additions were acted as a pinning center which increased critical current density.     

Charge Expulsion, Spin Meissner Effect, and Charge Inhomogeneity in Superconductors

Superconductivity occurs in systems that have a lot of negative charge: the highly negatively charged (CuO₂)⁼ planes in the cuprates, negatively charged (FeAs)⁻ planes in the iron arsenides, and negatively charged B ⁻ planes in magnesium diboride. And, in the nearly filled (with negative electrons) bands of almost all superconductors, as evidenced by their positive Hall coefficient in the normal state. No explanation for this charge asymmetry is provided by the conventional theory of superconductivity, within which the sign of electric charge plays no role. Instead, the sign of the charge carriers plays a key role in the theory of hole superconductivity, according to which metals become superconducting because they are driven to expel negative charge (electrons) from their interior. This is why NIS tunneling spectra are asymmetric, with larger current for negatively biased samples. The theory also offers a compelling explanation of the Meissner effect: as electrons are expelled towards the surface in the presence of a magnetic field, the Lorentz force imparts them with azimuthal velocity, thus generating the surface Meissner current that screens the interior magnetic field. In type II superconductors, the Lorentz force acting on expelled electrons that do not reach the surface gives rise to the azimuthal velocity of the vortex currents. In the absence of applied magnetic field, expelled electrons still acquire azimuthal velocity, due to the spin–orbit interaction, in opposite direction for spin-up and spin-down electrons: the “Spin Meissner effect.” This results in a macroscopic spin current flowing near the surface of superconductors in the absence of applied fields, of magnitude equal to the critical charge current (in appropriate units). Charge expulsion also gives rise to an interior outward-pointing electric field and to excess negative charge near the surface. In strongly type II superconductors this physics should give rise to charge inhomogeneity and spin currents throughout the interior of the superconductor, to large sensitivity to (non-magnetic) disorder and to a strong tendency to phase separation.     

Mechanical Behaviours in Bi2223/Ag/Ag Alloy Composite Tape with Different Volume Fractions

Bi₂Cr₂Ca₂Cu₃O _x (Bi2223) composite tapes consisting of Bi2223 filaments, metal Ag and Ag alloy are usually exposed to a high magnetic field. The mechanical behaviour of composites is determined by the distribution and content of Bi2223 filaments in a magnetic field. Several Bi2223 composite tapes have different volume fractions of Bi2223 filaments, and the volume fraction is of fundamental importance in the determination of mechanical behaviour. In this paper, we present mechanical response to understand the effect of volume fraction of Bi2223 filaments. The critical current density is determined with consideration of the self field effect firstly. Then, the results of effective elastic moduli and mechanical stresses are presented based on the micromechanics approach. The mechanical response depends not only on the material properties but also on the Lorentz force. It is concluded from the computational results that the reduction of volume fraction of filaments can increase the mechanical stability, while the critical current density is decreased. Thus, it is necessary to consider both the mechanical limitation and requirement of the critical current of tape.     

Microwave characterization of laser ablated Y1Ba2Cu3O7−x thin films

In the present study we report the measurements of microwave surface resistance (R_s) of YBCO thin films on LaAlO₃ substrate as a function of temperature, thickness and magnetic field by microstrip resonator technique. The T_c(R = 0) of the films is 90 K and J_c > 10⁶ A/cm² at 77 K. The microwave surface resistance has been measured for films of various thicknesses. The value of R_s has been found to be initially decreased with increasing film thickness due to increase in number of defects. A minimum microwave surface resistance has been obtained for film thickness of about 300 nm. The increase of R_s with film thickness above 300 nm is possibly due to degradation of the film microstructure as observed with Atomic Force Microscopy. Temperature dependence of surface resistance has been studied for best quality films. The field induced variations of surface resistance are also investigated by applying dc magnetic field perpendicular to stripline structure and surface of the film. A general linear and square field dependence of R_s at low and high value of fields has been observed with critical field value of 0.4 T which confirms the microwave dissipation induced by flux flow in these resonators at 10 GHz frequency. The hysteresis of R_s in dc field observed for field value above critical field shows the higher value of surface resistance in decreasing field than in increasing field which is in agreement with one state critical model and is a characteristic of homogeneous superconductors.     

In situ analysis of three-dimensional electrolyte convection evolving during the electrodeposition of copper in magnetic gradient fields

A novel three-dimensional particle tracking velocimetry technique was used to examine the flow during electrodeposition of Cu. For the first time electrode-normal, circumferential, and radial velocities were spatially resolved during deposition in superimposed low and high magnetic gradient fields. In this way the complex interaction of magnetic field gradient force and Lorentz force induced convective effects could be measured and analyzed. Magnetic field gradient force induced electrolyte flow was detected only in high gradient magnetic fields, and it was found to be directed toward regions of gradient maxima. Since this electrode-normal flow causes enhanced transport of Cu(2+) ions from the bulk electrolyte to those regions of the working electrode where maxima of magnetic gradients are present, a structured deposit is formed during diffusion-limited electrodeposition. Lorentz force driven convection was observed during deposition in the low and the high magnetic gradient experiments. The overall fluid motion and the convection near the working electrode were determined experimentally and discussed with regard to the acting magnetic forces and numerical simulations.     

Growth of diffusion layers at liquid Al–solid Cu interface under uniform and gradient high magnetic field conditions

The effect of high magnetic fields on interfacial reactive diffusion in liquid/solid (Al/Cu) couples was experimentally investigated at a temperature of 973 K. Regardless of any magnetic field, compound layers consisting of the δ, ξ₂, η₂ and θ phases were produced at the interface. The magnetic flux density, B, exerted a non-monotonic influence on the growth of the diffusion layers. Moreover, the mean thickness of the diffusion layers (parallel to B) was found to be always greater than that of the diffusion layers (perpendicular to B) under the applied magnetic fields. These phenomena should be attributed to the effects of two types of the Lorentz force under a uniform high magnetic field on diffusion behavior. In addition, the growth of intermetallic phases could be retarded by a magnetic field gradient due to the magnetic force in the axial direction.     

Evanescent magnetic field effects on entropy generation at the onset of natural convection

This paper numerically investigates the effect of an externally evanescent magnetic field on total entropy generation in a fluid enclosed in a square cavity by using a control volume finite element method to solve the conservation equations at Prandtl number of 0·71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for, fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number varying from 10⁴ to 10⁵. The effects of the Hartman number and the magnetic field inclination angle on the evolution of total entropy generation throughout the transient regime were investigated. Results show that the application of evanescent magnetic field not only suppresses the fluctuation of the total entropy generation in the transient state, but also reduces the gap for magnetic field relaxation time less than 1/10.     

Effect of Pre-magnetization on Quasi-static Force Characteristics in a Space Superconducting Interface Structure Adopting High T c Superconductors

Flux-pinned interaction between high T _c superconductors (HTSs) and an applied magnetic field provides a new, no-contact interface approach that can be used in docking and assembling process of space module systems. Unlike operations on the Earth, the magnetization of the HTS happens in orbit which differs from the traditional field cooling (FC) magnetization, and the additional field has to be used to magnetize the HTS in advance and make it produce a self-stable force in the interacting process with the interfacing magnet. This paper presents a type of superconducting interface structure configuration consisting of bulk HTSs, actuation electromagnets and interfacing magnets, and discusses the effects of different magnetization conditions on the quasi-static force interaction between the HTS and the interfacing magnet. Primary experiments show that the HTS after pre-magnetization can show self-stable force behavior, which often happens in the traditional FC magnetization, and the self-stable force is further enhanced with the increase of the pre-magnetizing current. Multi-pulse field magnetization after the pre-magnetization is also applied to raise the trapped field strength (B _T ) of the superconductor. The results show that B _T is added with the increasing number of the pulsed field, and the corresponding self-stable force properties are also improved. Therefore, the pre-magnetization combined with the pulsed field magnetization can enhance the flux trapping in the HTS and bring more stable force for the superconducting interface structure.     

Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor

It is well known that the London model (valid for a hard type II superconductor) predicts an externally applied magnetic field decays exponentially as a function of depth into the superconductor on a length scale λ. Direct measurements of the field profile using low energy μSR on high-Tc superconductors, such as YBa₂Cu₃ O _x measure deviations from a simple exponential decay. In particular, there is a short length scale δ close to the surface where the magnetic field does not decay. It has been proposed that this is due to surface roughness, which leads to a suppression of the order parameter near the surface. A model of surface roughness has been studied for the case of a sinusoidally modulated surface roughness on an isotropic superconductor showing that in some cases the profiles resulting from surface roughness may be qualitatively similar to the dead layer phenomena in that the field magnitude decay rate may be slowed near the surface relative to a flat interface but that for modest roughness, the quantitative value of the length over which the field decay is slowed is much smaller than the experiments measure. In this paper, we extend this work in two directions: firstly, by using atomic force microscopy data of YBa₂Cu₃ O _x crystals, we predict the expected field profiles within the context of the Isotropic London model of superconductivity given their actual surface geometry; and secondly, we consider how surface roughness could affect experimental values for λ and δ. The main finding is that roughness within an isotropic model does not produce the dead layers found in experiments on YBa₂Cu₃ O _x . However, we suggest that roughness in a highly anisotropic superconductor could account for the observed dead layer.     

Precise Density Measurements for Electromagnetically Levitated Liquid Combined with Surface Oscillation Analysis

A new method is proposed for accurately measuring the densities of high-temperature liquids which involves analyzing the surface oscillations of levitated droplets. This method makes it easy to improve on the accuracy of density measurements obtained by using conventional electromagnetic levitation systems. In addition, the errors in density measurements made on the ground are further reduced by applying a static magnetic field to suppress surface oscillations in levitated liquid droplets. The magnetic field interacts with electrical currents in the levitated droplet, thereby generating a Lorentz force; this force suppresses flow within the liquid droplet. By combining both these methods, the scatter in density measurements for molten Si at temperatures in the range from 1,500 K to 1,900 K is reduced by an order of magnitude compared with previously reported data. Using this new method, the density of molten SiGe has been measured at temperatures from 1,350 K to 1,650 K.     

The Lorentz forces on an electrically conducting sphere in analternating magnetic field

A method to calculate the Lorentz force on an electrically conducting sphere placed in an arbitrary sinusoidally varying magnetic field is developed. The crux of this method lies in expressing the external magnetic held and the eddy current density in the sphere in terms of a “source function” of the current sources and a “skin depth dependent function”. The general formula for the Lorentz force is used to derive the special case of a sphere in an axisymmetric stack of circular current loops. Numerical results for this case are presented as a function of the stack geometry. Approximations of the skin depth functions for practical situations are presented. Finally, a procedure to determine the magnetic pressure distribution on the surface of a levitated liquid metal droplet is given     

Irreversibility Effects and Low Field Magnetovoltage Measurements in Superconducting MgB2 Near the Critical Temperature T c

We have investigated the hysteresis effects in magnetovoltage measurements (V–H curves) in a polycrystalline superconducting MgB₂ near critical temperature T _c . The measurements were carried out as functions of temperature (T) and transport current (I), and sweep rates of the external magnetic field (dH/dt) and perpendicular and parallel orientations of external magnetic field (H) with respect to I, i.e., the V _⊥–H curves for $\vec{H} \bot\vec{I}$ and V _∥–H curves for $\vec{H}\parallel \vec{I}$ . The hysteresis effects related to both forward and reverse regions of V–H curves were interpreted within two level magnetic system mainly flux trapping inside the grains. A series of expansion of V(H) in terms of H was approximated to describe macroscopically the experimental V–H curves. The analysis of zero field I–V curves obtained by standard and reverse procedures gives an evidence of nearly absence of macroscopic surface pinning. The instabilities in V–H curves were interpreted in terms of defective flow of flux lines and also local fluctuations in magnetic flux structure. Further, the anisotropic effects in MgB₂ sample were explored by measuring the angular dependence of dissipation at the fixed values of T, H and I by varying the angle (θ) between H and I, i.e., V–θ curves. The analysis of V–θ curves reveals that the measured dissipation does not exhibit any agreement with the Lorentz force driven free flux motion, V(θ)～sin²(θ). This suggests that the anisotropic effects are screened by the random distribution of the grains in different sizes.     

The Edge Effect of a Microstrip Resonator on the Field Dependence of the Surface Resistance of a High-T c Superconducting Thin Film

A new behavior of the field dependence of microwave surface resistance (R _s), which was observed on a microstrip resonator and may be caused by the edge of the center strip, is reported in this paper for epitaxial high-T _c superconducting (HTSC) thin films. The exhibited behavior is that R _s remains almost unchanged below a certain rf magnetic field H _rf, and then increases abruptly at this field, after which it increases in proportion to H _rf. To explain the behavior, the morphology of the microstrip resonator was examined by atomic force microscopy (AFM), which showed that the edge of the resonator was damaged in some regions because of the acid etching. If the damaged edge is considered as a weakened granular superconductor, the observed R _s behavior could be explained well in terms of the high-frequency critical state model. This implies that the edge condition should be considered in studying the field dependence of R _s when the planar resonator technique is used.     

Hartmann flow over a permeable bed

Hartmann flow past a permeable bed is investigated in the presence of a transverse magnetic field with an interface at the surface of the permeable bed. The flow above the bed, called Zone 1, is governed by the Hartmann equation and that below the bed, called Zone 2, is governed by the modified Darcy law. Solutions for these two zones are separately obtained and are matched at the interface using suitable boundary conditions. The mass efflux, change in volume rate of flow, the induced magnetic field and current density are evaluated to determine whether a magnetic method might be potentially useful in the study of pore-size distribution.We find that, for mercury flowing over a long permeable channel of width 0.7 cm, the effect of magnetic field (of strength 0.25 Web/m², i.e. the Hartmann number M = 8.8) in the presence of a porous wall (of porosity k = 5 × 10^?6 Darcy) is to retard the mass flow and to increase the friction factor relative to the corresponding quantities for non-magnetic flow. The amount of retardation is 22 per cent more than that obtained by Wallace et al. [12] in the experiments on the flow of mercury in porous media in a transverse magnetic field. Since the magnitude of retardation is related to the pore size distribution, our model is potentially useful to study the pore size distribution than that of Wallace et al. [12]. In addition, transition to turbulence occurs at a higher Reynolds number owing to the presence of a magnetic field.     

Possible explanation for trapped field enhancement on REBaCuO bulk by modified multi-pulse technique with stepwise cooling (MMPSC)

The time evolutions of the local fields B_L(t) have been measured on the surface of the superconducting bulk disk magnetized by a two-stage pulse-field magnetizing technique, called a modified multi-pulse technique combined with stepwise cooling (MMPSC), and the magnetic flux movement and the flux trapping have been investigated. The optimum concaved (“M-shaped”) trapped field profile, which is a necessary condition at the first stage to enhance the final trapped field B_T, makes a larger magnetic gradient (dB/dx) at the bulk periphery in the ascending stage of the applied magnetic pulse at the second stage due to the large viscous force F_v. The magnetic fluxes, which stay at the bulk periphery, start to flow to the center of the bulk, after the applied pulse field reaches a maximum, at which the flux velocity v is nearly zero and then F_v decrease. As a result, a large number of the magnetic fluxes are trapped at the bulk center. The effect of the “M-shaped” profile at the first stage in MMPSC on the enhancement of B_T is discussed.     

MHD Boundary Layer Flow of a Power-Law Nanofluid Containing Gyrotactic Microorganisms Over an Exponentially Stretching Surface

This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic (MHD) and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective heating. The nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg method. The impacts of the transverse magnetic field, bioconvection parameters, Lewis number, nanofluid parameters, Prandtl number and power-law index on the velocity, temperature, nanoparticle volume fraction, density of motile microorganism profiles is explored. In addition, the impacts of these parameters on local skin-friction coefficient, local Nusselt, local Sherwood numbers and local density number of the motile microorganisms are discussed. The results reveal that the power law index is considered an important factor in this study. Due to neglecting the buoyancy force term, the bioconvection and nanofluid parameters have slight effects on the velocity profiles. The resultant Lorentz force, from increasing the magnetic field parameter, try to decrease the velocity profiles and increase the rescaled density of motile microorganisms, temperature and nanoparticle volume fraction profiles. Physically, an augmentation of power-law index drops the reduced local skin-friction and reduced Sherwood number, while it increases reduced Nusselt number and reduced local density number of motile microorganisms.     

Pinning in superconductors with anisotropic defects

By calculating the volume pinning force in superconductors with anisotropic pinning centers we have shown that the critical current densitiesj _c in NbTi by both current and magnetization measurements can be explained. The critical current density in fields parallel toj _c can also be included. We conclude therefore that in superconductors with strong pinning centers the critical state is always determined by the equilibrium condition between the Lorentz force and the volume pinning force and not by the instability of the force-free configuration. By detailed investigation of thej _c dependence on field direction, useful information can be obtained with respect to the volume and surface contributions to the pinning force.