An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.

https://downloads.hindawi.com/journals/mpe/2009/603916.pdf

Approximate Analysis of MHD Squeeze Flow between Two Parallel Disks with Suction or Injection by Homotopy Perturbation Method

The present paper analyses the unsteady 2‐dimensional flow of a viscous MHD fluid between two parallel infinite plates. The two infinite plates are considered to be approaching each other symmetrically, causing the squeezing flow. A similarity transformation is used to reduce the partial differential equations modeling the flow, to a single fourth‐order non‐linear differential equation containing the Reynolds number and the magnetic field strength as parameters. The velocity functions are obtained for a range of values of both parameters by using the homotopy perturbation method. The total resistance to the upper plate is presented.

Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method

The problem of an electromagnetic wave packet, incident on a relativistically moving plane ionization or recombination front in a stationary gas, is considered. The frequency of the reflected wave packet is found to obey the usual double Doppler shift relation. However, the reflection coefficients and the physics can differ significantly from the case of reflection from moving material objects. In the unmagnetized case, the ratio of the energy in the reflected wave packet to that in the incident wave packet is found to be er*/ei*=ωi*/ωr* for an oncoming overdense ionization front, for which ωi*<ωr* (where ωi* and ωr* are the incident and reflected wave frequencies in the laboratory frame). For an oncoming ionization front in the presence of an applied magnetic field normal to the front, er*/ei* can considerably exceed ωi*/ωr*. For a retreating recombination front (ωi*≳ωr*), in the overdense unmagnetized case, er*/ei*=ωr*/ωi*. These results have important implications for the production of sub‐millimeter w...

Interaction of electromagnetic waves with a moving ionization front

: Magnetohydrodynamic squeeze films are investigated theoretically and experimentally. The theory of magnetohydrodynamic lubrication as applied to squeeze films is extended to include fluid-inertia effects and buoyant forces. Excellent agreement is obtained between theory and experiment. (Author)

The magnetohydrodynamic squeeze film

On the basis of Christensen's stochastic model of rough surfaces, this study theoretically analyzes the effect of surface roughness on the dynamic stiffness and damping characteristics of compensated hydrostatic circular step thrust bearings. Both the stochastic Reynolds equation with rotational inertia effect and the recess flow continuity equation with recess volume fluid compressibility effect are derived to take into account the presence of roughness on the bearing surfaces. Using a small perturbation method, the dynamic coefficients of bearings are evaluated. According to the results, the mean stiffness and damping behaviours are significantly affected by the roughness pattern and the height of roughness. The effect of circumferential roughness provides an increase in the mean bearing stiffness and damping characteristics as compared to the smooth-bearing case. However, these trends are reversed for the bearing having radial roughness structure. An illustration of a design example is also included for industrial practice.

Surface roughness effect on the dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings

The motion of an electrically conducting, incompressible, viscous fluid in the presence of a magnetic field is analyzed for flow between two parallel disks, one of which rotates at a constant angular velocity. The specific application to liquid metal lubrication in thrust bearings is considered. The two field configurations discussed are: an axial magnetic field with a radial current and a radial magnetic field with an axial current. It is shown that the load capacity of the bearing is dependent on the MHD interactions in the fluid and that the frictional torque on the rotor can be made zero for both field configurations by supplying electrical energy through the electrodes to the fluid.

Magnetohydrodynamic lubrication flow between parallel rotating disks

Magnetohydrodynamic pressurization of liquid metal bearings

The Magnetohydrodynamic Finite Step Slider Bearing

The magnetohydrodynamic inclined slider bearing with a transverse magnetic field

Eine Untersuchung wurde durchgefuhrt uber die adiabatische Stromung der Luft zwischen zwei parallelen Platten, bei einem Druckunterschied quer uber die sich bewegende Platte. Die Losung lasst eine thermale Keilwirkung der hydrodynamischen Schmierung erwarten und gibt eine quantitative Analyse des allgemeineren Problems, wo ein Druckunterschied quer uber die Gleitplatte vorhanden ist. Die Ergebnisse deuten an, dass der Beitrag des hydrodynamischen Druckes oft ausserst klein sein kann (fur massige Geschwindigkeiten) im Vergleich zum hydrodynamischen Druck in den dem Druck ausgesetzten Lagern. Im Falle von stillstehenden Platten ist die adiabatische Losung gleich der isothermen Losung; weswegen keine Temperaturerhohung stattfindet.

W. F. Hughes

Papers

Magnetohydrodynamic lubrication flow between parallel rotating disks

Magnetohydrodynamic pressurization of liquid metal bearings

The Magnetohydrodynamic Finite Step Slider Bearing

The magnetohydrodynamic inclined slider bearing with a transverse magnetic field

On the Adiabatic Couette Flow of a Compressible Fluid