Feature
Magneto-
hydrodynamic squeeze
film characteristics for
finite rectangular
plates
Jaw-Ren Lin
The author
Jaw-Ren Lin is an Associate Professor in the Department
of Mechanical Engineering, Nanya Institute of Technology,
Chung-Li, Taiwan, Republic of China.
Keywords
Magnetic fields, Surface films, Lubricants
Abstract
The squeeze-film characteristics between two parallel
rectangular plates with an electrically conducting fluid in
the presence of a transverse magnetic field are analyzed.
The squeeze-film Reynolds equation applicable to the
curved surfaces is derived using the continuity equation
and the magneto-hydrodynamic (MHD) motion equations.
A closed-form solution is obtained for the squeeze-film
pressure of parallel rectangular plates, and applied to
predict the squeeze-film behavior. According to the results,
the presence of magnetic fields signifies an enhancement
in the squeeze-film pressure. On the whole, the magnetic-
field effect characterized by the Hartmann number
provides an increase in value of the load-carrying capacity
and the response time as compared to the classical
non-conducting lubricant case, especially for larger values
of the aspect ratio or smaller values of film height.
Electronic access
The research register for this journal is available at
http://www.emeraldinsight.com/researchregister
The current issue and full text archive of this journal is
available at
http://www.emeraldinsight.com/0036-8792.htm
Nomenclature
a ¼ length of the plate
b ¼ width of the plate
B
0
¼ applied magnetic field
h ¼ film thickness
h
0
¼ film thickness at t ¼ 0
h* ¼ dimensionless film thickness, h/h
0
M ¼ Hartmann number,
M ¼ B
0
h
0
ð
s
=
m
Þ
1=2
p ¼ squeeze film pressure
p* ¼ dimensionless film pressure,
2ph
3
0
=
m
a
2
ðdh=dtÞ
x, y, z¼ Cartesian coordinates
x*, y*¼ dimensionless coordinates, x/a, y/a
t ¼ time
t* ¼ dimensionless time, Wh
2
0
t=
m
a
3
b
u,v,w ¼ velocity components
V ¼ squeezing velocity, dh/dt
W ¼ load-carrying capacity
W* ¼ dimensionless load-carrying
capacity, 2Wh
3
0
=
m
a
3
bðdh=dtÞ
b
¼ aspect ratio, b/a
m
¼ lubricant viscosity
s
¼ electrical conductivity
1. Introduction
Studies of squeeze-film characteristics play an
important role in many areas of engineering
application. Traditionally, analyses of
squeeze-film behavior for different
mechanisms were based upon the use of a
non-conducting viscous lubricant. In order to
prevent the unexpected variation of lubricant
viscosity with temperature under severe
operating conditions, the increasing use of
electrically conducting fluids as lubricants is
becoming of interest. In the presence of a
magnetic field, a number of authors have
applied the electrically conducting lubricant
to study various magneto-hydrodynamic
(MHD) lubrication problems. Typical articles
are observed in the MHD externally
pressurized bearings (Maki and Kuzma,
1966), the MHD slider bearings (Agrawal,
1970; Anwar and Rodkiewicz, 1972; Gupta
and Bhat, 1979), the MHD journal bearings
(Kamiyama, 1969; Kuzma, 1963; Malik and
Singh, 1980), the MHD squeezing film plates
(Shukla, 1965), the MHD squeeze-film
circular disks (Hamza, 1988), and the MHD
squeeze-film annular disks (Lin, 2001).
Although, the MHD squeeze-film motion
between one-dimensional parallel plates has
Industrial Lubrication and Tribology
Volume 55 · Number 2 · 2003 · pp. 84–89
q MCB UP Limited · ISSN 0036-8792
DOI 10.1108/00368790310470912
84