scholarly journals Analytical Solution for MHD Flow of a Magnetic Fluid within a Thick Porous Annulus

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shihhao Yeh ◽  
Tsai-Jung Chen ◽  
Jik Chang Leong
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Angular Velocity ◽  
Analytical Solution ◽  
Magnetic Fluid ◽  
Mhd Flow ◽  
Induced Magnetic Field ◽  
State Problem ◽  
Closed Form Solutions ◽  
Steady State Problem

The steady-state problem of a magnetic fluid filling a porous annulus between two cylindrical walls under the influence of a nonuniform radially outward magnetic field has been investigated. The cylindrical walls are either electrically perfectly insulated or electrically perfectly conducting. The permeability of the porous annulus increases with its radial location. The governing partial differential equations were derived carefully and closed form solutions for the profiles of the velocity component and the induced magnetic component were obtained. The effect of the strength of the externally applied magnetic field, the permeability of the porous annulus, and the conductivity of the cylindrical walls were examined through the angular velocity components, as well as the induced magnetic field.

Laser Surface Hardening Considering Coupled Thermoelasticity

2009 ◽  
Vol 25 (3) ◽  
pp. 241-249 ◽  
Author(s):  
Me. Sistaninia ◽  
Ma. Sistaninia ◽  
H. Moeanodini
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Analytical Solution ◽  
Surface Hardening ◽  
Laser Surface ◽  
Lagrangian Formulation ◽  
State Problem ◽  
Laser Surface Hardening ◽  
Eulerian Formulation ◽  
Steady State Problem

AbstractThermoelastic temperature, displacement and stress in heat transfer during laser surface hardening are solved in both Lagrangian formulation and Eulerian formulation. In the Eulerian formulation, the heat flux is fixed in space and the work-piece is moved through a control volume. In the case of uniform velocity and uniform heat flux distribution, the Eulerian formulation leads to a steady-state problem, while the Lagrangian formulation remains transient. In the Eulerian formulation, the reduction to a steady-state problem increases the computational efficiency. Also, in this study, an analytical solution is developed for an uncoupled transient heat conduction equation in which a plane slab is heated by a laser beam. The thermal results of the numerical models are compared with the results of the analytical model. A comparison of the results shows that numerical solutions in the case of uncoupled problem are in good agreement with the analytical solution.

Mixed steady-state problem of torsion of a sphere with an elastic core

1976 ◽  
Vol 12 (12) ◽  
pp. 1247-1251
Author(s):  
V. A. Babeshko ◽  
V. E. Veksler
Keyword(s):  
Steady State ◽  
State Problem ◽  
Elastic Core ◽  
Steady State Problem

Scattering of a Rayleigh Wave by an Elastic Quarter Space

1985 ◽  
Vol 52 (3) ◽  
pp. 664-668 ◽  
Author(s):  
A. K. Gautesen
Keyword(s):  
Steady State ◽  
Surface Wave ◽  
Fourier Transforms ◽  
Two Dimensional ◽  
Rayleigh Surface Wave ◽  
State Problem ◽  
Free Surfaces ◽  
Linear Elastic ◽  
Quarter Space ◽  
Steady State Problem

We study the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic quarter space. We derive decoupled equations for the Fourier transforms of the normal and tangential displacements on the free surfaces. For incidence of a Rayleigh surface wave, we plot the amplitudes and phases of the surface waves reflected and transmitted by the corner. These curves were obtained numerically.

scholarly journals Rotating and propagating LIB stabilized by self-induced magnetic field

1984 ◽  
Vol 2 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Hiroyuki Murakami ◽  
Takayuki Aoki ◽  
Shigeo Kawata ◽  
Keishiro Niu
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Field Intensity ◽  
Magnetic Field Intensity ◽  
Ion Beam ◽  
Axial Direction ◽  
Induced Magnetic Field ◽  
Tearing Instability ◽  
The Mean ◽  
Steady State Solutions

Rotating motion of a propagating LIB is analyzed in order to suppress the mixed mode of the Kelvin-Helmholtz instability, the tearing instability and the sausage instability by the action of a self-induced magnetic field in the axial direction. The beams are assumed to be charge-neutralized but not current-neutralized. The steady-state solutions of a propagating LIB with rotation are first obtained numerically. Through the dispersion relation with respect to the ikonal type of perturbations, which are added to the steady-state solutions, the growth rates of instabilities appearing in an LIB are obtained. It is concluded that if the mean rotating velocity of an LIB is comparable to the propagation velocity, in other words, if the induced magnetic field intensity in the axial direction is comparable to the magnetic field intensity in the azimuthal direction, the instability disappears in the propagating ion beam.

Numerical Solution of the Planar Hydrostatic Foil Bearing

1979 ◽  
Vol 101 (1) ◽  
pp. 86-91 ◽  
Author(s):  
A. Eshel
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Computer Program ◽  
Numerical Solution ◽  
Asymptotic Approach ◽  
State Problem ◽  
Shooting Technique ◽  
Foil Bearing ◽  
Approach To Steady State ◽  
Steady State Problem

The steady state problem of the planar hydrostatic foil bearing is analyzed and solved numerically. Two techniques of solution are used. One method is simulation in time with asymptotic approach to steady state. This is achieved by a preprocessor which automatically sets up the numerical computer program. The second method is an iterative shooting technique. The results agree well with one another. Curves of pressure and typical film thickness versus flow are presented.

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