A Thin Conducting Liquid Film on a Spinning Disk in the Presence of a Magnetic Field: Dynamics and Stability

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
B. Uma ◽  
R. Usha
Keyword(s):  
Magnetic Field ◽  
Evolution Equation ◽  
Liquid Film ◽  
Hartmann Number ◽  
Film Surface ◽  
Large Wave ◽  
Spinning Disk ◽  
Wave Numbers ◽  
Small Wave ◽  
The Magnetic Field

A theoretical analysis of the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and has been solved numerically. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid film on the spinning disk have been obtained for different values of Hartmann number M, evaporative mass flux parameter E, and Reynolds number Re. The results show that the relative volume of the fluid retained on the spinning disk is enhanced by the presence of the magnetic field. The stability characteristics of the evolution equation have been examined using linear theory. For both zero and nonzero values of the nondimensional parameter describing the magnetic field, the results show that (a) the infinitesimal disturbances decay for small wave numbers and are transiently stable for larger wave numbers when there is either no mass transfer or there is evaporation from the film surface, and although the magnitude of the disturbance amplitude is larger when the magnetic field is present, it decays to zero earlier than for the case when the magnetic field is absent, and (b) when absorption is present at the film surface, the film exhibits three different domains of stability: disturbances of small wave numbers decay, disturbances of intermediate wave numbers grow transiently, and those of large wave numbers grow exponentially. The range of stable wave numbers increases with increase in Hartmann number.

scholarly journals On the fine-scale structure of vector fields convected by a turbulent fluid

1963 ◽  
Vol 16 (4) ◽  
pp. 545-572 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Vector Fields ◽  
Scale Structure ◽  
Homogeneous Turbulence ◽  
Small Scale ◽  
Ohmic Dissipation ◽  
Large Wave ◽  
Turbulent Fluid ◽  
Wave Numbers ◽  
The Magnetic Field

This paper is a contribution to the study of statistically homogeneous, dynamically passive vector fields convected by a turbulent fluid and subject to a molecular diffusivity λ that is small compared with the kinematic viscosityv. Two types are considered: the first, denoted byF, has the property that the total flux across a material surface moving with the fluid is conserved if λ = 0 (e.g. magnetic field); and the second, denoted byG, is the gradient of a conserved scalar quantity θ (e.g. temperature gradient). Attention is focused on small-scale variations with length-scale less than$(v^3|\epsilon)^{\frac {1}{4}}$. A theory of Batchelor's in terms of Eulerian correlations for the distribution of θ for the case when λ [Lt ]vis extended and applied to the vector fields, thereby giving equations for the covariance tensors ofFandGappropriate for separations less than$(v^3|\epsilon)^{\frac {1}{4}}$. According to these equations, the effect of convection on small-scale components of the fields is to amplify and also to distort by reducing the scale; the ratio of these two effects is measured by a parameter σ. It is shown that if$\sigma \textless {\frac{5}{2}$, the small-scale structure is stable against perturbations however small λ/vmay be, the amplification being eventually balanced by the dissipation which is increased by the reduction of scale. In the case of the quantityG, σ = 1. The value of σ for the case ofFis not known, but reasons are given for believing that it is less than one, and it is concluded that the behaviour of$\overline{\bf F^2}$and$\overline{\bf G^2}$in a field of homogeneous turbulence is qualitatively the same. In particular,$\overline{\bf F^2}$does not grow indefinitely with time as predicted by previous arguments. The correlation functions for small separations and the corresponding spectrum functions for a statistically steady state are obtained. The relation between this analysis and that for random vector fields in a uniform straining motion of infinite extent is considered in detail, for Pearson has shown that, if the strain is an irrotational distortion, then$\overline{\bf F^2} \rightarrow \infty$with time. It is shown that this divergence is due to the amplification of components with very small wave-numbers or, equivalently, of very large scale, and it is therefore not considered relevant to a study of homogeneous turbulence.The particular case of the magnetic field in a good conductor is considered. If the Lorentz forces are unimportant, it is estimated that the magnetic energy of a weak seed field will be in general amplified by the turbulence by a factor lying somewhere between the Reynolds and magnetic Reynolds numbers of the turbulence before ohmic dissipation as increased by the reduction of scale limits the growth, and it is suggested further that the magnetic field will eventually decay to zero in the absence of external electromotive forces.In an appendix, the theory is applied tentatively to the turbulent vorticity (which satisfies the same equation asFif λ =v) and an expression for the energy spectrum function for very large wave-numbers is deduced. This is compared with an expression given by Townsend, and is found to have a similar qualitative behaviour but gives values about one-half as large.

Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Subramanian Muthukumar ◽  
Selvaraj Sureshkumar ◽  
Arthanari Malleswaran ◽  
Murugan Muthtamilselvan ◽  
Eswari Prem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Bottom Wall ◽  
Uniform Heating ◽  
The Magnetic Field

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

SUPERCONDUCTING FILM WITH AN ARRAY OF MAGNETIC NANOSTRIPES

2013 ◽  
Vol 27 (15) ◽  
pp. 1362020 ◽  
Author(s):  
K. KIM ◽  
K. K. D. RATHNAYAKA ◽  
I. F. LYUKSYUTOV ◽  
D. G. NAUGLE
Keyword(s):  
Magnetic Field ◽  
Transport Properties ◽  
Critical Current ◽  
Film Surface ◽  
Critical Currents ◽  
Superconducting Film ◽  
Insulating Layer ◽  
Field Effects ◽  
Matching Field ◽  
The Magnetic Field

We present studies of the transport properties of a Sn superconducting film with an array of parallel nickel magnetic nanostripes (800 nm period) deposited on top of a germanium insulating layer covering the Sn film surface. The critical current parallel to the stripes is larger than the critical current perpendicular to the stripes. Both critical currents demonstrate strong hysteresis and matching field effects. We have observed strong hysteresis in the resistance dependence on the magnetic field.

Multiple-relaxation-time lattice Boltzmann study of the magnetic field effects on natural convection of non-Newtonian fluids

2017 ◽  
Vol 28 (11) ◽  
pp. 1750138 ◽  
Author(s):  
Xuguang Yang ◽  
Lei Wang
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Hartmann Number ◽  
Magnetic Field Effects ◽  
Multiple Relaxation Time ◽  
Number Formula ◽  
Power Law Index ◽  
The Magnetic Field

In this paper, the magnetic field effects on natural convection of power-law non-Newtonian fluids in rectangular enclosures are numerically studied by the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). To maintain the locality of the LBM, a local computing scheme for shear rate is used. Thus, all simulations can be easily performed on the Graphics Processing Unit (GPU) using NVIDIA’s CUDA, and high computational efficiency can be achieved. The numerical simulations presented here span a wide range of thermal Rayleigh number ([Formula: see text]), Hartmann number ([Formula: see text]), power-law index ([Formula: see text]) and aspect ratio ([Formula: see text]) to identify the different flow patterns and temperature distributions. The results show that the heat transfer rate is increased with the increase of thermal Rayleigh number, while it is decreased with the increase of Hartmann number, and the average Nusselt number is found to decrease with an increase in the power-law index. Moreover, the effects of aspect ratio have also investigated in detail.

Magnetic field effects on natural convection and entropy generation of non-Newtonian fluids using multiple-relaxation-time lattice Boltzmann method

2020 ◽  
pp. 2150015
Author(s):  
Aimon Rahman ◽  
Preetom Nag ◽  
Md. Mamun Molla ◽  
Sheikh Hassan
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Entropy Generation ◽  
Lattice Boltzmann ◽  
Hartmann Number ◽  
Magnetic Field Effect ◽  
Multiple Relaxation Time ◽  
Number Formula ◽  
Boltzmann Method ◽  
The Magnetic Field

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, [Formula: see text], Rayleigh number, [Formula: see text], PL indices, [Formula: see text]–1.4, Prandtl number, [Formula: see text], to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio [Formula: see text]. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, [Formula: see text] and decreasing the PL index, [Formula: see text]. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, [Formula: see text], fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing [Formula: see text] and [Formula: see text], respectively. In the presence of the magnetic field, [Formula: see text], the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.

Experimental study on liquid metal free surface flow under magnetic and electric field for nuclear fusion

2022 ◽  
Author(s):  
Xu Meng ◽  
Z H Wang ◽  
Dengke Zhang
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Liquid Metal ◽  
Electric Field ◽  
Liquid Film ◽  
Metal Flow ◽  
First Wall ◽  
Flowing Liquid ◽  
Liquid Metal Flow ◽  
The Magnetic Field

Abstract In the future application of nuclear fusion, the liquid metal flows are considered to be an attractive option of the first wall of the Tokamak which can effectively remove impurities and improve the confinement of plasma. Moreover, the flowing liquid metal can solve the problem of the corrosion of the solid first wall due to high thermal load and particle discharge. In the magnetic confinement fusion reactor, the liquid metal flow experiences strong magnetic and electric, fields from plasma. In the present paper, an experiment has been conducted to explore the influence of electric and magnetic fields on liquid metal flow. The direction of electric current is perpendicular to that of the magnetic field direction, and thus the Lorentz force is upward or downward. A laser profilometer (LP) based on the laser triangulation technique is used to measure the thickness of the liquid film of Galinstan. The phenomenon of the liquid column from the free surface is observed by the high-speed camera under various flow rates, intensities of magnetic field and electric field. Under a constant external magnetic field, the liquid column appears at the position of the incident current once the external current exceeds a critical value, which is inversely proportional to the magnetic field. The thickness of the flowing liquid film increases with the intensities of magnetic field, electric field, and Reynolds number. The thickness of the liquid film at the incident current position reaches a maximum value when the force is upward. The distribution of liquid metal in the channel presents a parabolic shape with high central and low marginal. Additionally, the splashing, i.e., the detachment of liquid metal is not observed in the present experiment, which suggests a higher critical current for splashing to occur.

The Effect of a Longitudinal Magnetic Field on Pipe Flow of Mercury

1961 ◽  
Vol 83 (4) ◽  
pp. 445-453 ◽  
Author(s):  
Samuel Globe
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Longitudinal Magnetic Field ◽  
Hartmann Number ◽  
Characteristic Length ◽  
Axial Magnetic Field ◽  
Turbulent Friction ◽  
The Magnetic Field

An experimental investigation has been made of the effect of an axial magnetic field on transition from laminar to turbulent flow and on the turbulent friction factor for pipe flow of mercury. Magnetic-flux densities up to 5700 gauss were obtained with a water-cooled solenoid. Pipes of glass and aluminum were used of approximately 0.1 to 0.2 in. diam. The maximum Hartmann number, with the hydraulic radius (half the actual radius) taken as the characteristic length, was about 20. Measurements were made of the pressure gradient and velocity of flow. The transition Reynolds number was determined from the curve of friction factor against Reynolds number. The results show an increasing value of minimum transition Reynolds number with Hartmann number. The magnetic field also brought about a decrease in the turbulent friction factor and corresponding shear force at the wall.

Untersuchung der Stabilität eines gravitierenden Plasmas in gekreuzten Magnetfeldern

1958 ◽  
Vol 13 (12) ◽  
pp. 1016-1020 ◽  
Author(s):  
F. Meyer
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Field Strength ◽  
Equilibrium Configuration ◽  
Horizontal Magnetic Field ◽  
Large Wave ◽  
Small Wave ◽  
The Stability

Es wird die Stabilität einer Plasmaanordnung untersucht. Dabei wird ein gravitierendes Plasma mit horizontalem innerem Magnetfeld von einem dagegen um den Winkel α verdrehten horizontalen Vakuummagnetfeld getragen. Das Beispiel ist eine Erweiterung des von Kruskal und Schwarzschild untersuchten Falles α = 0 mit parallelem innerem und äußerem Feld. Es ergibt sich die Stabilisierbarkeit aller Störungen mit kleinen Wellenlängen einschließlich der Kruskal-Schwarzschild-Instabilität durch endliche Verdrehungswinkel α. Für große Wellenlängen tauchen stets instabile Störungen auf von der Art hydromagnetischer Rayleigh-Taylor-Instabilitäten.The stability of a plasma in crossed magnetic fields is investigated for the following equilibrium configuration. A plasma with an interior horizontal magnetic field is supported against gravity by a horizontal vacuum magnetic field which is inclined at some angle α to the interior field. This example is an extension of the case α=0 investigated by Kruskal und Schwarzschild. It is found that for all disturbances with small wave lengths, including those disturbances which give the Kruskal-Schwarzschild instability, stability can be restored by using a non-zero α. Perturbations of sufficiently large wave lengths are found unstable for every α and every ratio of field strength.

scholarly journals I. On the magnetic rotation of the plane of polarisation of light in doubly refracting bodies

1890 ◽  
Vol 46 (280-285) ◽  
pp. 65-71
Keyword(s):  
Magnetic Field ◽  
Centrifugal Force ◽  
Magnetic Rotation ◽  
Spinning Disk ◽  
Axis Of Rotation ◽  
Elliptic Polarisation ◽  
Incident Plane ◽  
Polarised Light ◽  
The Magnetic Field ◽  
Lines Of Force

In repeating Villari’s experiment on the rotation of the plane of polarisation of light in a spinning disk of heavy glass, placed with its axis of rotation perpendicular to the lines of force in a magnetic field, it was observed that the incident plane polarised light became elliptically polarised. The elliptic polarisation was due to the centrifugal force which had the effect of stretching the glass along the radii of the disk and compressing it parallel to the axis of rotation. The strained glass in the magnetic field has, therefore, the double property of elliptically polarising plane polarised light, and at the same time rotating the plane of polarisation.

The invariant theory of isotropic turbulence in magneto-hydrodynamics

1951 ◽  
Vol 204 (1079) ◽  
pp. 435-449 ◽  
Keyword(s):  
Magnetic Field ◽  
Invariant Theory ◽  
Isotropic Turbulence ◽  
Equations Of Motion ◽  
Stationary Condition ◽  
Electrical Conductor ◽  
Large Wave ◽  
Triple Correlation ◽  
Constant Rate ◽  
The Magnetic Field

In this paper the invariant theory of isotropic turbulence in magneto-hydrodynamics is developed on the basis of the equations of motion recently derived by Batchelor to describe the hydrodynamics of an incompressible fluid which is also a good electrical conductor. The theory allows for the interaction between the electromagnetic field and the turbulent motion when there is no externally imposed electric or magnetic field. Various double and triple correlation tensors involving the components of the velocity and the magnetic field intensity are defined, and three equations governing the scalars defining these tensors are derived; these latter equations admit integrals of Loitsiansky’s type. The equations governing the dissipation of energy by viscosity and conductivity are also derived; they exhibit the manner in which energy is exchanged between the velocity and the magnetic fields. Finally, the equations appropriate for the case, when an external agency supplies kinetic energy to the system at a constant rate and a stationary condition prevails, are obtained; they suggest that the energy in the magnetic field is contained, principally, in the eddies with large wave numbers.

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