Showing papers on "Hartmann number published in 1978"

A theoretical study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann number

Abstract: Flows of incompressible, electrically conducting liquids along ducts with electrically insulating or weakly conducting walls situated in a strong magnetic field are analysed. Except over a short length along the duct where the magnetic field strength and/or the duct cross-sectional area vary, the duct is assumed to be straight and the field to be uniform and aligned at right angles to the duct. Magnitudes of the field strength B0 and the mean velocity V are taken to be such that the Hartmann number M [Gt ] 1, the interaction parameter N (= M2/Re) [Gt ] 1 (Re being the Reynolds number of the flow) and the magnetic Reynolds number Rm [Lt ] 1.For an O(1) change in the product VB0 along the duct across the non-uniform region, it is shown that:(i) In the non-uniform region the streamlines and current flow lines follow surfaces containing the field lines satisfying , the integration being carried out along the field line within the duct; these surfaces are equipotentials and isobarics. This leads to(ii) a tube of stagnant, but not current-free fluid at the centre of the duct parallel to the field lines around which the flow divides to bypass it. To accommodate this flow,(iii) the usual uniform field/straight duct flow is disturbed over very large distances upstream and downstream of this region, the maximum length O(duct radius × M½) occurring in a non-conducting duct;(iv) a large pressure drop is introduced into the pressure distribution regardless of the direction of the flow, the effect being most severe in a non-conducting duct, where the drop is O(duct radius × (uniform field/straight duct pressure gradient) × M½);(v) in the part of the duct with the lower value of VB0 a region of reverse flow occurs near the centre of the duct and the stagnant fluid.

Stability of finite-amplitude and overstable convection of a conducting fluid through fixed porous bed

Abstract: The stability of infinitestimal steady and oscillatory motions and finite amplitude steady motions of a conducting fluid through porous media with free boundaries which is heated from below and cooled from above is investigated in the presence of a uniform magnetic field. Infinitesimal steady motions are investigated using Liapunov method and its is shown that the principle of exchange of stability is valid only when Pm/Pr≤1 with a restricted value of the Hartmann number. It is shown that overstable motions are due to the zonal current induced by the magnetic field. Finite amplitude steady motions are investigated using Veronis [1] analysis and it is shown that for a restricted range of Hartmann numbers and porous parameter Pl, steady finite-amplitude motions can exist for values of the Rayleigh number smaller than that value corresponding to oscillatory motions. Since the Busse number is greater than the wave number the horizontal scale of the steady finite-amplitude motions is larger than that of the overstable motions.

Boundary-value problem for a counterrotating electrical discharge in an axial magnetic field

Abstract: An electrical discharge between two ring electrodes embedded in the mantle of a cylindrical chamber is considered, in which the plasma in the anode and cathode regions rotates in opposite directions under the influence of an external axial magnetic field. The associated boundary-value problem for the coupled partial differential equations describing the azimuthal velocity and radial current-density fields is solved in closed form. The velocity, current density, induced magnetic induction, and electric fields are presented for typical Hartmann numbers, magnetic Reynolds numbers, and geometry parameters. The discharge is shown to produce anodic and cathodic plasma sections rotating at speeds of the order 1,000,000 cm/sec for conventional magnetic field intensities. Possible application of the magnetoactive discharge as a plasma centrifuge for isotope separation is discussed.

Hydromagnetic convective heat transfer in vertical pipes

Abstract: In the present analysis, we consider the effect of radial magnetic field on the steady flow produced by the combined free and forced convection in an annulus between two coaxial vertical cylinders. A numerical solution of the problem is obtained by using Runge-Kutta-Merson method. For Rayleigh number Ra 0, there occurs back flow controlled by the effect of the magnetic field. Further, the influence of Rayleigh number and Hartmann number on the temperature is also discussed.

On the commencement of the Hartmann flow between non-conducting walls

Abstract: Ogawa andSone [1] have solved the problem of the unsteady Hartmann flow known from magnetohydrodynamics through the method of Fourier expansion, supposing that the walls bounding the fluid are perfect conductors. In the present paper this problem is solved for the case of non-conducting walls by Fourier’s method assuming the hydrodynamical Reynolds number to be equal to the magnetic one. It is determined by numerical calculation how the relaxation time of the process depends on the Hartmann number.