Showing papers on "Hartmann number published in 1994"

Hiemenz flow in hydromagnetics

Abstract: The laminar flow of an incompressible, viscous, electrically conducting fluid impinging normal to a plane in the presence of a transverse magnetic field is investigated. Using finite-differences and quasilinearization, an exact numerical solution is presented which takes into account the asymptotic boundary condition. It is demonstrated that iff denotes the dimensionless stream function, the value off″(0) increases monotonically withM, the Hartmann number, where a prime denotes the derivative normal to the plane.

Boundary element method solution of MHD flow in a rectangular duct

Abstract: SUMMARY The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with an external magnetic field applied transverse to the flow has been investigated. The walls parallel to the applied magnetic field are conducting while the other two walls which are perpendicular to the field are insulators. The boundary element method (BEM) with constant elements has been used to cast the problem into the form of an integral equation over the boundary and to obtain a system of algebraic equations for the boundary unknown values only. The solution of this integral equation presents no problem as encountered in the solution of the singular integral equations for interior methods. Computations have been carried out for several values of the Hartmann number (1 < M < 10). It is found that as M increases, boundary layers are formed close to the insulated boundaries for both the velocity and the induced magnetic field and in the central part their behaviours are uniform. Selected graphs are given showing the behaviours of the velocity and the induced magnetic field.

Thermocapillary convection in a cylinder with a strong non-uniform axisymmetric magnetic field

Abstract: This paper treats a surface-tension-driven liquid-metal flow in a cylinder with a steady externally applied non-uniform axisymmetric magnetic field. The top boundary consists of an annular free surface around a solid disk, modelling the Czochralski growth of silicon crystals. A radial temperature gradient produces a decrease of the surface tension from the disk edge to the vertical cylinder wall. The magnetic flux density is sufficiently large that inertial effects and convective heat transfer are negligible. First we present large-Hartmann-number asymptotic solutions for magnetic fields with either a non-zero or a zero axial component at the free surface. The asymptotic solutions indicate that a purely radial magnetic field at the free surface represents a singular limit of more general magnetic fields. Secondly we present numerical solutions for arbitrary values of the Hartmann number, and we treat the evolution of the thermocapillary convection as the axial magnetic field at the free surface is changed continuously from the full field strength to zero.

Change in velocity in silicon melt of the Czochralski (CZ) process in a vertical magnetic field

Abstract: The influence of a magnetic field on the velociry of molten silicon has been characterized both theoretically and experimentally. The velocity decrease observed by X-ray radiography in the magnetic field is in good agreement with the results obtained by numerical modelling. It is found that the rate of decrease in velocity in a vertical magnetic field is well presented using the magnetic number rather than the Hartmann number. Accordingly, the analytical expression using the square of the magnetic number, M, well describes the velociry changes as v/v0=(1+M2/4)1/2-M/2, for experimental as well as numerically calculated data.

Is the Hartmann number relevant to tokamak physics

Abstract: Montgomery and Shan (1992, 1993) have argued that in calculating resistive MHD instability thresholds, both resistivity and viscosity play an equally important role and may significantly modify conventional views of resistive MHD. The author discusses these arguments and puts them in perspective in the context of tokamak physics. The crucial point is the following: while it is indeed true that for a given q-profile, the marginal stability thresholds of linear visco-resistive MHD equations depend, in principle, upon both resistivity and viscosity jointly through the Hartmann number, physical considerations of tokamak experiments suggest that this is an insignificant modification of well known results in tearing-mode theory as far as its applications to tokamaks are concerned. Furthermore, the uniform q (equivalent resistivity) model used by Montgomery and Shan to motivate many of their arguments and to some extent their computational techniques is non-generic in a sense to be explained and is therefore not a helpful starting point for discussions of MHD stability in tokamaks. Apart from this general observation, the actual results obtained by Montgomery and co-workers regarding linear instability are all contained in the 'standard' approach used in the fusion community: specific examples are provided using the linear version of the CUTIE code developed at Culham to solve the relevant MHD equations. The CUTIE results show explicitly that JET-like tokamaks operate in a different parameter regime and involve qualitatively and quantitatively different physics to those studied by Montgomery and Shan.

Entrance Flows of Electrically Conducting Fluids between Two Parallel Plates : Transient and Steady Flows

Abstract: In the present paper, using a new finite-element method for incompressible electrically conducting fluid, transient and steady entrance flows are simulated The GSMAC method is employed as the main algorithm of calculation to satisfy the conservation laws of both mass and magnetic flux Entrance flows between two parallel plates under a uniform magnetic field are calculated to verify this method Meanwhile, the entrance length can approximately be expressed as an explicit function of the Hartmann number, using the Oseen approximation and the momentum integral method Numerical and theoretical results obtained here agree well with other numerical results or exact solutions

Hartmann numbers and MHD activity

Abstract: A recent inquiry into the relevance of the Hartmann number to tokamak dynamics, due to Thyagaraja (1994), is commented upon. The possible roles of shear viscous stresses and ion parallel viscous stresses are discussed further. Somewhat different conclusions are offered.