Showing papers on "Hartmann number published in 1988"
TL;DR: In this paper, a steady isolated vortex is produced in a horizontal layer of mercury (of thickness a ), subjected to a uniform vertical magnetic field, and the vortex is forced by an electric current going from an electrode in the lower plane to the circular outer frame.
Abstract: A steady isolated vortex is produced in a horizontal layer of mercury (of thickness a ), subjected to a uniform vertical magnetic field. The vortex is forced by an electric current going from an electrode in the lower plane to the circular outer frame. The flow is investigated by streak photographs of small particles following the free upper surface, and by electric potential measurements. The agreement with the asymptotic theory for high values of the Hartmann number M is excellent for moderate electric currents. In particular all the current stays in the thin Hartmann layer of thickness a/M , except in the vortex core of horizontal extension a / M ½ . For higher currents, the size of the core becomes larger and depends only on the local interaction parameters. When the current is switched off, we measure the decay due to the Hartmann friction. A similar study is carried out for a vortex created by an initial electric pulse, and for a pair of vortices of opposite sign. For all these examples, the dynamics can be described by the two-dimensional Navier-Stokes equations with Hartmann friction, except in the vortex cores. Finally a vortex is produced near a lateral wall and a detachment of the boundary layer parallel to the magnetic field occurs, by which a second vortex of opposite sign is generated.
68 citations
TL;DR: In this article, a theoretical study on the onset of the Marangoni convection in the horizontal layer of an electrically conducting liquid, to which a vertical temperature gradient and a magnetic field are applied, is made.
38 citations
TL;DR: In this paper, an exact solution for hydromagnetic convection at a continous moving surface with uniform suction is obtained, which represents a new class of boundary-layer problems, with solutions substantially different from those for boundary layer flow at a surface of finite length.
Abstract: Exact solution for hydromagnetic convection at a continous moving surface with uniform suction is obtained. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow at a surface of finite length. Moreover, this is an exact solution of the complete Navier-Stokes equations (including, buoyancy force-term). The solutions for the velocity and skin friction are evaluated numerically for several sets of values of the parameters;G, the Grashof number,P, the Prandtl number, andM, the Hartmann number. It is observed that there is a reverse flow in the boundary-layer due to heating of the fluid (close to the moving surface). That is, whenTw>T∞, the fluid in the boundary-layer will be heated up and thus the free convection currents will set in. Also, it is observed that, there is an increase in the skin friction (absolute) with increasingG, P andM.
18 citations
01 Jul 1988
TL;DR: In this article, the interaction parameter and Hartmann number are assumed to be large and the magnetic Reynolds number is small, respectively, whereas viscous and inertial effects are confined in very thin boundary layers adjacent to the walls.
Abstract: Magnetohydrodynamic flows of liquid metals in rectangular ducts with thin conducting walls in the presence of strong nonuniform transverse magnetic fields are examined. The interaction parameter and Hartmann number are assumed to be large, whereas the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined in very thin boundary layers adjacent to the walls. A significant fraction of the fluid flow is concentrated in the boundary layers adjacent to the side walls, which are parallel to the magnetic field. The analysis and numerical methods for obtaining three-dimensional solutions for flow parameters outside these layers are described without solving explicitly for the layers themselves. Numerical solutions are presented for cases that are relevant to the flows of liquid metals in fusion reactor blankets. Experimental results obtained from the Argonne Liquid-Metal Experiment (ALEX) at Argonne National Laboratory are used to validate the numerical code. In general, the agreement is excellent.
17 citations
TL;DR: In this paper, the authors studied the flow of conductive fluids in highly conductive curved pipes and found that the secondary flow field comprises a symmetric pair of counter-rotating vortices.
Abstract: The flow of conductive fluids in highly conductive curved pipes is studied analytically in this paper. The flow is assumed to be steady state, laminar, and fully developed. Coupled continuity, Navier–Stokes, and appropriate Maxwell equations are solved in toroidal coordinates. The dimensionless parameters of the problem are Dean number K and Hartmann number Ha. For low Hartmann numbers [Ha2∼θ(1)], the solution is expanded in a power series of K and Ha2. For intermediate Hartmann numbers [Ha2∼θ(1000)], the solution is expressed as a power series of K. The axial velocity contours are shown to be shifted towards the outer wall. For low Ha, these contours are nearly circular. The effect of a strong transverse magnetic field is to enhance the compression of fluid towards the outer wall. The secondary flow field comprises a symmetric pair of counter‐rotating vortices. A strong magnetic field is found to confine the secondary flow streamlines to a thin layer near the tube wall. The secondary flow rate in the near‐wall boundary layer is increased by the magnetic field. This increase in flow rate raises the possibility of efficient convective cooling of curved first wall tubes in magnetic confinement fusion reactors (MFCR).
10 citations
TL;DR: In this paper, laminar liquid-metal flows, currents, and power losses in a rectangular channel in a uniform, skewed high external magnetic field were studied for high Hartmann numbers, high interaction numbers, low magnetic Reynolds numbers, and different aspect ratios.
Abstract: Fully developed, laminar liquid‐metal flows, currents, and power losses in a rectangular channel in a uniform, skewed high external magnetic field were studied for high Hartmann numbers, high interaction numbers, low magnetic Reynolds numbers, and different aspect ratios. The channel has insulating side walls that are skewed to the external magnetic field. Both the perfectly conducting moving top wall with an external potential and the stationary perfectly conducting bottom wall at zero potential act as electrodes and are also skewed to the external magnetic field. A solution is obtained for high Hartmann numbers by dividing the flow into three core regions, connected by two free‐shear regions, and Hartmann layers along all the channel walls. Mathematical solutions are presented in each region in terms of singular perturbation expansions in negative powers of the Hartmann number. The free‐shear layers are treated rigorously and in detail with fundamental magnetohydrodynamic theory. Numerical calculations ...
9 citations
TL;DR: In this paper, a mathematical solution was obtained for high Hartmann numbers by dividing the flow into three core regions, two free shear layers, and six Hartmann layers along the channel walls.
Abstract: In a previous paper the authors initiated studies of fully developed laminar liquid‐metal flows, currents, and power losses in a rectangular channel with a moving perfectly conducting wall and with a skewed homogeneous external magnetic field for high Hartmann numbers, high interaction parameters, low magnetic Reynolds numbers, and different aspect ratios. The channel had insulating side walls that were skewed to the external magnetic field, while the perfectly conducting moving top wall with an external potential and the stationary perfectly conducting bottom wall at zero potential acted as electrodes. These electrodes were also skewed to the external magnetic field. A mathematical solution was obtained for high Hartmann numbers by dividing the flow into three core regions, two free shear layers, and six Hartmann layers along the channel walls. The free shear layers were treated rigorously and in detail with fundamental magnetohydrodynamic theory. The previous work, however, left the solution for the vel...
7 citations
01 Jul 1988
TL;DR: In this article, the magnetic field effects on convective flow oscillations of a conducting fluid are calculated from different Grashof and Hartmann numbers (AIPs) using the AIP model.
Abstract: The magnetic field effects on the convective flow oscillations of a conducting fluid are calculated from different Grashof and Hartmann numbers (AIP)
3 citations
01 Jul 1988
TL;DR: In this paper, the authors treated the liquid-metal flow in an elbow between two straight, rectangular ducts and derived the solutions for the velocity at each cross section of the elbow and for the pressure drop due to three-dimensional effects.
Abstract: This paper treats the liquid-metal flow in an elbow between two straight, rectangular ducts. There is a uniform magnetic field in the plane of the elbow. The duct has thin, electrically conducting walls. The Hartmann number and the interaction parameter are assumed to be large, while the magnetic Reynolds number is assumed to be small. Solutions for the velocity at each cross section of the elbow and for the pressure drop due to three-dimensional effects are presented. 10 refs., 5 figs.
3 citations
01 Jul 1988
TL;DR: In this paper, the authors treated the liquid-metal flow in an elbow between two straight, rectangular ducts and derived the solutions for the velocity at each cross section of the elbow and for the pressure drop due to three-dimensional effects.
Abstract: This paper treats the liquid-metal flow in an elbow between two straight, rectangular ducts. There is a uniform magnetic field in the plane of the elbow. The duct has thin, electrically conducting walls. The Hartmann number and the interaction parameter are assumed to be large, while the magnetic Reynolds number is assumed to be small. Solutions for the velocity at each cross section of the elbow and for the pressure drop due to three-dimensional effects are presented. 10 refs., 5 figs.
3 citations
TL;DR: In this paper, an analytical solution has been developed for the velocity field and the induced magnetic field by reducing the problem to the solution of a Fredholm's integral equation of the second kind, which has been solved numerically.
Abstract: We investigate the magnetohydrodynamic flow (MHD) on the upper, half of a non-conducting plane for the case when the flow is driven by the current produced by an electrode placed in the middle of the plane. The applied magnetic field is perpendicular to the plane, the flow is laminar, uniform, steady and incompressible. An analytical solution has been developed for the velocity field and the induced magnetic field by reducing the problem to the solution of a Fredholm's integral equation of the second kind, which has been solved numerically. Infinite integrals occurring in the kernel of the integral equation and in the velocity and magnetic field were approximated for large Hartmann numbers by using Bessel functions. As the Hartmann number M increases, boundary layers are formed near the non-conducting boundaries and a parabolic boundary layer is developed in the interface region. Some graphs are given to show examples of this behaviour.
TL;DR: In this paper, the stability of a horizontal layer of Boussinesq fluid, heated from below and cooled from above, rotating uniformly about the vertical in the presence of a uniform vertical magnetic field is studied for the case where the thermal diffusivity K is much larger than the magnetic diffusivities η( = 1/μσe' where μ is the magnetic permeability and σe is the electrical conductivity).
Abstract: The stability of a horizontal layer of Boussinesq fluid, heated from below and cooled from above, rotating uniformly about the vertical in the presence of a uniform vertical magnetic field is studied for the case where the thermal diffusivity K is much larger than the magnetic diffusivity η(= 1/μσe' where μ is the magnetic permeability and σe is the electrical conductivity). The stability problem depends on the five dimensionless numbers Ra, T, M, q, qb . The Rayleigh number, Ra, is a measure of the buoyancy force, the Taylor number, T, is a measure of the Coriolis force, the Hartmann number, M, is a measure of the Lorentz force and q=k/η, while qb =Kμσb' where σb is the electrical conductivity of the boundary. The critical Rayleigh number Rac (which is a measure of the buoyancy force required for instability) in the magnetostrophic regime is found to depend significantly on σb. It is shown that the global minimum Rayleigh number, Ram' has the dependence T½/q only if either (i) σb≧O(K/μη2) or (ii...
01 Feb 1988
TL;DR: In this paper, the interaction parameter and Hartmann number are assumed to be large and the magnetic Reynolds number is small, whereas the viscous and inertial effects are confined in very thin boundary layers adjacent to the walls.
Abstract: Magnetohydrodynamic flows of liquid metals in thin conducting ducts of various geometries in the presence of strong nonuniform transverse magnetic fields are examined. The interaction parameter and Hartmann number are assumed to be large, whereas the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined in very thin boundary layers adjacent to the walls. At walls parallel to the magnetic field lines, as at the side walls of a rectangular duct, the boundary layers (side layers) carry a significant fraction of the volumetric flow rate in the form of high velocity jets. The presence of these jets strongly enhances heat transfer performance. In addition, heat transfer can be further improved by guiding the flow toward a heated wall by proper variation of wall thicknesses, duct cross sectional dimensions and/or shape. Flows in nonconducting circular ducts are also examined. Experimental results obtained from the ALEX experiments at the Argonne National Laboratory are used to validate the numerical predictions. 6 refs., 7 figs.
TL;DR: In this paper, a finite-difference solution of MHD flow past an impulsively started vertical infinite plate in an electrically conducting fluid has been presented on taking into account the viscous dissipative heat.
Abstract: Finite-difference solution of MHD flow past an impulsively started vertical infinite plate in an electrically conducting fluid has been presented on taking into account the viscous dissipative heat. Results for velocity and temperature are shown graphically whereas the numerical values of the skin-friction and the rate of heat transfer are entered in the table. The results are discussed in terms of the parameters M (the Hartmann number), G (the Grashof number, G>0, cooling of the plate by free convection, G<0, heating of the plate by free convection currents), E (the Eckert number) and P (the Prandtl number).
01 Oct 1988
TL;DR: In this paper, the shear flow of an electrically conducing liquid exposed to a direct electric current is considered as a function of Hartmann number (AIP) in terms of the AIP.
Abstract: The shear flow of an electrically conducing liquid exposed to a direct electric current is considered as a function of Hartmann number (AIP)
TL;DR: In this paper, a prototype annular electromagnetic flow coupler was tested with high temperature sodium and it worked successfully, verifying the operational principle, and the pump head-flow characteristics of the coupler were clarified from an analysis of its equivalent electric circuit.
Abstract: A prototype annular electromagnetic flow coupler was tested with high temperature sodium and it worked successfully, verifying the operational principle. The pump head-flow characteristics of the coupler were first clarified from an analysis of its equivalent electric circuit. The pump head and the generator pressure drop decrease linearly with the pump flow rate under the conditions of constant generator flow rate and external magnetic flux density. The gradients of the linear changes are given by ratios of equivalent resistances in the electrical analog, and are independent of the generator flow rate, if the magnetic flux density is kept constant. Sodium tests of the prototype confirmed the above results when the Hartmann number of the test conditions is larger than 170. Both ratios of the differential pressures and the volumetric flow rate between pump and generator ducts exceed 50% while the wall loss of around 40% appears at peak efficiency due to the lack of electrical insulation and the relatively ...