Showing papers on "Hartmann number published in 1968"

Three-dimensional MHD duct flows with strong transverse magnetic fields Part 1. Obstacles in a constant area channel

Abstract: This paper is an analysis of incompressible three-dimensional flows of electrically conducting fluids under the action of transverse magnetic fields which are assumed to be sufficiently strong that the interaction parameter N (= M2/R) [Gt ] 1, where M is the Hartmann number and R is the Reynolds number. We also assume that R [Gt ] 1 and Rm (magnetic Reynolds number) [Lt ] 1, so that experimental verification of the theory may be possible.The main results are: (i) when a thick body is placed in a parallel-sided channel with non-conducting walls the flow over it is highly dependent on the conductivity of the body, in a surprising way. If the body is non-conducting, there is no flow within that cylinder which circumscribes the body and is parallel to the magnetic field; outside the cylinder the flow is plane and potential and enters or leaves the surface shear layer of this cylinder at right angles. If the body is conducting, flow over it is possible and is of a different nature outside and inside the cylinder. (ii) When a non-conducting flat plate is placed in such a channel no blocking of the flow occurs. If the plate is elongated in the flow direction, the flow over it becomes identical to that calculated by Hasimoto (1960) and, if elongated at right angles to the flow, becomes identical to that calculated by Dix (1963).Of particular interest in our analysis are the two types of layer which occur in these flows, the first being the Hartmann boundary layer, which is shown to have a controlling influence on the vorticity of the core flow in three-dimensional situations analogous to that of the Eckman layer in rotating-fluid flows. The second type, the free shear layer at the circumscribing cylinder, is of interest because of its internal structure and effect on the external flow.

Some electrically driven flows in magnetohydrodynamics. part 2. theory and experiment.

Abstract: In this part we first extend the theory of part 1 to analyse the distribution of velocity and electric current in an electrically conducting liquid between two circular electrodes of finite diameter, when a current is passed between them. The electrodes are set opposite to each other in insulating planes and a magnetic field is applied perpendicular to these planes. When the Hartmann number M [Gt ] 1 we find that the current is confined to the cylinder of fluid joining the electrodes. This effect is accounted for by the velocity which is induced in thin layers of thickness O(M−½), at the circumference of the cylinder. In our analysis we concentrate on these interesting layers and, amongst other results, we find that in the limit M → ∞ the resistance of the fluid between the electrodes becomes that of the cylinder of fluid joining the electrodes.We then describe some experiments to test the validity of this theory. In these experiments we measured, as a function of the magnetic field, (a) the potential difference between the copper electrodes, the fluid being mercury, (b) the electric potential distribution in the fluid between the disks and in the thin layers between the electrode edges, by means of an electric potential probe, and (c) the velocities induced in the layers using a Pilot tube. Our conclusions were: (i) the overall predictions of the theory were correct; (ii) the results of the two probes approximately correlated with each other, despite the theory still having some limitations and the behaviour of these probes still being somewhat uncertain.

Hydromagnetic flow in a rotating straight pipe.

Abstract: A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. It is assumed for the purpose of mathematical analysis, the angular velocity about the axis of rotation, is small. A solution is developed by successive approximations in ascending powers of the Hartmann number, the first approximation corresponds to the non-magnetic case, formulated and discussed by Barua. The stream lines in the central plane and the projection of the stream lines on the cross-section of the pipe are compared with those in the non-magnetic case. An expression for the induced electric potential difference and sensitivity has been obtained.

Magnetohydrodynamic flow along cylindrical pipes under non-uniform transverse magnetic fields

Abstract: The unidirectional flow of an incompressible, electrically conducting, viscous fluid along cylindrical pipes is considered. An external magnetic field, B0, which lies in the plane transverse to the flow is applied. It is shown that the governing equations, written in the co-ordinate system traced out by B0, are mathematically very similar to those for a uniform field.The paper deals mainly with ducts whose walls are insulators. Though exact solutions (valid for all values of the Hartmann number) are derived, the limit of high Hartmann number is taken for detailed discussion. Transition layers (or, loosely, ‘wakes’) can arise which are centred on curved field lines. In some cases, reversed flow occurs in part of the core (‘radial-type’ fields). Situations also arise where the magnitude (and sign) of the velocity remains the same as for B0 = 0, whatever the strength of the applied, transverse (azimuthal) magnetic field.

Some electrically driven flows in magnetohydrodynamics Part 2. Theory and experiment By J. C. R. HUNT

Abstract: Part 1 of this paper (Hunt & Williams 1968) was an analysis of the flows induced in an electrically conducting fluid by passing current between electrodes placed in non-conducting planes surrounding the fluid, a magnetic field being applied perpendicular to the planes. The analysis was largely concentrated on the interesting physical phenomena which occur when the Hartmann number M = Boa(cr/y)9 3 1. (B, is the applied magnetic flux density, u is a typical length, CT is the fluid’s conductivity and y is its viscosity.) The solutions to the problems

Magnetohydrodynamic flow through a rectangular duct due to a periodic pressure gradient-II

Abstract: The flow of an incompressible, viscous, electrically conducting fluid in a long channel of rectangular cross section due to a periodic pressure gradient, in the presence of a uniform transverse magnetic field is investigated. Exact solutions are obtained and asymptotic forms valid for large Hartmann numbers are discussed.

The Influence of Axial Conduction on the Thermal Entry-Region Heat Transfer in Magnetohydrodynamic Channel Flow

Abstract: The influence of axial conduction on thermal entry-region temperature distribution and heat transfer in Hartmann's flow through a magnetohydrodynamic channel is analytically investigated. Viscous d...

Hydromagnetic stabilization experiments with jet-driven vortex flow

Abstract: Experiments are described which demonstrate the stabilizing influence of an axial magnetic field on confined vortex flow of an aqueous electrolytic conductor generated by two-dimensional, tangential wall jets. For example, using a 10 cm dia. x 40 cm long vortex tube having two feed jets and a single exit orifice at the centre of one end, the tangential Reynolds modulus at trnasition to instability was increased from 500 with no magnetic field to 7600 under the influence of a 75 kG field (corresponding to a Hartmann modulus based on tube radius of 172). The experimental magnetic stabilization results for 1, 2 and 4 slit injection are correlated empirically.

A singular perturbation problem of laminar flow in a uniformly porous channel with large injection and with an applied transverse magnetic field

Abstract: The problem of the steady flow of an electrically conducting viscous fluid through porous walls of a channel in the presence of an applied transverse magnetic field is considered. A solution for the case of small M2/R (where M = Hartmann number, R = suction Reynolds number) with large blowing at the walls has been given by Terrill and Shrestha [3]. Their solution, on differentiating three times, is found to become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and Terrill and Shrestha are neglecting the shear layer. In this paper the solution given by Terrill and Shrestha is extended by obtaining an extra term of the series of expansion and the method of inner and outer expansion is used to obtain the complete solution which includes the viscous layer. The resulting series solutions are confirmed by numerical results.

Liquid Mercury Heat Transfer in Circular Tube under Transverse Magnetic Field

Abstract: This paper deals with channel flow and heat transfer experiments undertaken toexamine the influence of a transverse magnetic field on the heat transfer of an electrically conducting fluid. Measurements were made of the velocity distribution, friction factor, critical Reynolds number for transition from laminar flow, and heat transfer coefficient on liquid mercury flowing through several tubes 1m long under the effect of uniform transverse magnetic field. The experimental results were correlated with the Reynolds number(<2×105) and the Hartmann number(<55referred to inner radius of tube).The magnetic field reduces the heat transfer coefficient in the region between the Peclet number=2×10102 and 4×103. The Hartmann number as well as the Peclet number affects the Nusselt number which drops as much as 40% in the most prominent case when the Hartmann number=55.

Rotation of axisymmetric bodies in hydromagnetics (finite conductivity)

Abstract: This paper deals with the disturbance due to the steady rotation of some axisymmetric bodies in a viscous incompressible fluid of finite conductivity in which the uniform ambient flow field is collinear with the uniform magnetic field. The known results of Sowerby [1] for the couple on a rotating spheroid in a slow stream in an incompressible viscous fluid are generalized. The special case of a disk is investigated in detail. The assumed conditions of flow permit the use of Oseen's approximation. The couple is found to first order approximation in terms of R and M, where R is the Reynolds number and M the Hartmann number.