Magnetohydrodynamic pipe flow Part2. High Hartmann number

1962 ◽  
Vol 13 (4) ◽  
pp. 513-518 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Magnetic Fields ◽  
Pressure Gradient ◽  
Cross Section ◽  
Pipe Flow ◽  
Hartmann Number ◽  
Gradient Flow ◽  
Transverse Magnetic ◽  
Arbitrary Cross Section ◽  
Conducting Liquid ◽  
Experimental Pressure

The paper presents an improved, second approximation for the laminar motion of a conducting liquid at high Hartmann number in non-conducting pipes of arbitrary cross-section under uniform transverse magnetic fields. A satisfactory comparison with the author's previously experimental pressure gradient/flow results is made for the case of a circular pipe.

Some extremum principles for magnetohydrodynamic flow in conducting pipes

1972 ◽  
Vol 72 (2) ◽  
pp. 303-313 ◽  
Author(s):  
P. Smith
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Hartmann Number ◽  
Circular Cross Section ◽  
Arbitrary Cross Section ◽  
Upper And Lower Bounds ◽  
Asymptotic Estimates ◽  
Conducting Liquid ◽  
Straight Pipe ◽  
Arbitrary Thickness

AbstractExtremum principles are obtained for the laminar flow of a conducting liquid in a straight pipe of arbitrary cross-section with conducting walls of arbitrary thickness, which is subject to a uniform applied magnetic field. These extrema provide upper and lower bounds for the mass-flow rate in the pipe. These bounds are particularly useful in the construction of asymptotic estimates for the flow rate at high Hartmann number. The method is illustrated by its application to the pipe of circular cross-section and to pipes with thin conducting walls.

Pressure Distributions in Porous Ducts of Arbitrary Cross Section

1973 ◽  
Vol 95 (3) ◽  
pp. 342-348 ◽  
Author(s):  
J. C. P. Huang ◽  
H. S. Yu
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Cross Sections ◽  
Porous Plate ◽  
Porous Wall ◽  
Design Criterion ◽  
Arbitrary Cross Section ◽  
Solid Particles ◽  
Equivalent Diameter ◽  
Pressure Distributions

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.

Laminar Flow of an Incompressible Fluid in a Conduit With Arbitrary Cross Section, Arbitrary Time-Varying Pressure Gradient, and Arbitrary Initial Velocity

1972 ◽  
Vol 94 (1) ◽  
pp. 27-32 ◽  
Author(s):  
H. K. Hepworth ◽  
W. Rice
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Initial Velocity ◽  
Solution Method ◽  
Initial Conditions ◽  
Arbitrary Cross Section ◽  
Computational Time ◽  
Time Varying ◽  
Arbitrary Time ◽  
Gram Determinant

A computer-oriented solution is given for the flow described in the title of the paper. The boundary shape is represented by specification of the coordinates of N points on the boundary; the initial velocity is represented by specification of L values of the velocity in the cross section at time zero; the arbitrary time-varying pressure gradient is implemented by use of Duhamel’s Theorem. In the solution method presented, boundary and initial conditions are satisfied in the least squares sense. The Gram determinant is used to determine eigenvalues and the Gram-Schmidt orthonormalizing procedure is used to construct a set of functions appropriate for a finite series solution. Computer programs are referenced which have been used to investigate the correctness of the solution and the accuracy obtainable with reasonable digital computational time.

Magnetohydrodynamic flow in rectangular ducts

1965 ◽  
Vol 21 (4) ◽  
pp. 577-590 ◽  
Author(s):  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Boundary Layers ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Rectangular Duct ◽  
Conducting Liquid ◽  
The Core ◽  
Thin Walls ◽  
The Magnetic Field

The paper presents an analysis of laminar motion of a conducting liquid in a rectangular duct under a uniform transverse magnetic field. The effects of the duct having conducting walls are investigated. Exact solutions are obtained for two cases, (i) perfectly conducting walls perpendicular to the field and thin walls of arbitrary conductivity parallel to the field, and (ii) non-conducting walls parallel to the field and thin walls of arbitrary conductivity perpendicular to the field.The boundary layers on the walls parallel to the field are studied in case (i) and it is found that at high Hartmann number (M), large positive and negative velocities of order MVc are induced, where Vc is the velocity of the core. It is suggested that contrary to previous assumptions the magnetic field may in some cases have a destabilizing effect on flow in ducts.

scholarly journals Signal Propagation in Soil Medium: A Two Dimensional Finite Element Procedure

2021 ◽  
Author(s):  
Frank Kataka Banaseka ◽  
Kofi Sarpong Adu-Manu ◽  
Godfred Yaw Koi-Akrofi ◽  
Selasie Aformaley Brown
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Scattered Field ◽  
Radar Cross Section ◽  
Transverse Magnetic ◽  
Arbitrary Cross Section ◽  
Observation Angle ◽  
Two Dimensional ◽  
Total Field ◽  
Dimensional Finite Element

A two-Dimensional Finite Element Method of electromagnetic (EM) wave propagation through the soil is presented in this chapter. The chapter employs a boundary value problem (BVP) to solve the Helmholtz time-harmonic electromagnetic model. An infinitely large dielectric object of an arbitrary cross-section is considered for scattering from a dielectric medium and illuminated by an incident wave. Since the domain extends to infinity, an artificial boundary, a perfectly matched layer (PML) is used to truncate the computational domain. The incident field, the scattered field, and the total field in terms of the z-component are expressed for the transverse magnetic (TM) and transverse electric (TE) modes. The radar cross-section (RCS), as a function of several other parameters, such as operating frequency, polarization, illumination angle, observation angle, geometry, and material properties of the medium, is computed to describe how a scatterer reflects an electromagnetic wave in a given direction. Simulation results obtained from MATLAB for the scattered field, the total field, and the radar cross-section are presented for three soil types – sand, loam, and clay.

scholarly journals MHD Flow of a Dusty Viscous Conducting Liquid Between Two Parallel Plates

2009 ◽  
Vol 1 (2) ◽  
pp. 220-225 ◽  
Author(s):  
P. Sreeharireddy ◽  
A. S. Nagarajan ◽  
M. Sivaiah
Keyword(s):  
Magnetic Field ◽  
Pressure Gradient ◽  
Incompressible Fluid ◽  
Transverse Magnetic Field ◽  
Magnetic Parameter ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Dust Particles ◽  
Parallel Plates ◽  
Conducting Liquid

In this paper, the flow of a viscous conducting liquid with uniform distribution of dust particles in a channel is considered under the influence of a uniform transverse magnetic field with pressure gradient varying linearly with time. The velocities of fluid and dust are found to decrease with the increase of the magnetic parameter. Further that the velocity of the fluid particles is observed to be more than that of dust particles.Keywords: Viscous conducting liquid; Uniform transverse magnetic field; Fluidization; Incompressible fluid; Stoke’s resistance coefficient. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i2.2280

Oscillating Flow in Ducts of Arbitrary Cross Section

1969 ◽  
Vol 73 (706) ◽  
pp. 894-896
Author(s):  
A. M. Abu-Sitta ◽  
D. G. Drake
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Arbitrary Cross Section ◽  
Oscillating Flow ◽  
Elliptic Case ◽  
Uniform Cross Section

The rectilinear flow of an incompressible viscous fluid along a duct of uniform cross section due to an oscillating pressure gradient has been considered by a number of investigators. The duct of circular cross .section has been treated by Richardson and Tyler and Sexl, the elliptic case by Khamrui, and the rectangular case by Drake and Fan and Chao. Recently Jeng has discussed the importance of this type of flow and has given a procedure for calculating a numerical solution for a duct of arbitrary cross-section. An interesting feature of these flows is that, at large frequencies when the flow is of boundary-layer type, the velocity at any instant has its maximum near the walls, the velocity overshooting its almost uniform distribution at the centre of the duct.

Size effect variation of the electrical conductivity of metals

1950 ◽  
Vol 203 (1073) ◽  
pp. 223-240 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Cross Section ◽  
Theoretical Work ◽  
Transverse Magnetic ◽  
Experimental Results ◽  
Metallic Films ◽  
Thin Wires ◽  
General Statistical

This paper records experiments and theoretical work concerned with the variation of conductivity with size in metals. Experimental results for the conductivity in thin wires of pure sodium of varying diameter in the absence of a magnetic field and also in the presence of longitudinal and transverse magnetic fields are given. Using the general statistical theory of metals the variation of resistance with size in the case of conductivity wires of square cross-section is calculated for comparison with the first set of experiments. A theoretical investigation follows of the alteration in conductivity produced in metallic films by the application of transverse magnetic fields, and this is compared with the corresponding experimental results obtained on the sodium cylinders.

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