Magnetohydrodynamic Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime

1999 ◽  
Vol 66 (4) ◽  
pp. 1021-1023 ◽  
Author(s):  
R. Usha ◽  
P. Vimala
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Bubble Radius ◽  
Fluid Film ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Circular Plates ◽  
Air Bubble ◽  
Approximate Analytical Solutions

In this paper, the magnetic effects on the Newtonian squeeze film between two circular parallel plates, containing a single central air bubble of cylindrical shape are theoretically investigated. A uniform magnetic field is applied perpendicular to the circular plates, which are in sinusoidal relative motion, and fluid film inertia effects are included in the analysis. Assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained by approximating the momentum equation governing the magnetohydrodynamic squeeze film by the mean value averaged across the film thickness. Approximate analytical solutions for the air bubble radius, pressure distribution, and squeeze film force are determined by a perturbation method for small amplitude of sinusoidal motion and are compared with the numerical solution obtained by solving the nonlinear differential equation. The combined effects of air bubble, fluid film inertia, and magnetic field on the squeeze film force are analyzed.

Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime

1995 ◽  
Vol 117 (3) ◽  
pp. 513-518 ◽  
Author(s):  
H. Hashimoto
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Bubble Radius ◽  
Isothermal Condition ◽  
Fluid Film ◽  
Squeeze Film ◽  
Cylindrical Shape ◽  
Parallel Plates ◽  
Air Bubble ◽  
Film Characteristics

In this paper, the effects of an air bubble on the Newtonian squeeze film characteristics between two circular parallel plates with sinusoidal relative motion are theoretically investigated by considering the fluid film inertia effects. In the derivation of the lubrication equation, a single central air bubble of a cylindrical shape is considered. Approximating the momentum equation governing the squeeze film flow by the mean value averaged across the film thickness and assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained. The nonlinear differential equation is solved by the Runge-Kutta-Gill method, and then the squeeze film force is determined. Moreover, the analytical solutions for the air bubble radius and pressure distribution are derived based on the perturbation method for a small amplitude of sinusoidal motion, and the analytical results are compared with the numerical results. From the calculated results, the combined effects of air bubble and fluid film inertia on the squeeze film force are clarified.

Magnetohydrodynamic Squeeze Films

1964 ◽  
Vol 86 (3) ◽  
pp. 441-444 ◽  
Author(s):  
D. C. Kuzma
Keyword(s):  
Magnetic Field ◽  
Film Thickness ◽  
Applied Magnetic Field ◽  
Conducting Fluid ◽  
Squeeze Film ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Fluid Film Thickness

An analysis of hydrodynamic squeeze films is presented for the case of an electrically conducting fluid in the presence of a magnetic field. Circular plates and infinitely long rectangular plates are considered with a uniformly applied magnetic field. The relationships between fluid-film thickness and time are determined analytically and compared with the ordinary hydrostatic squeeze films. It is shown that the application of a magnetic field improves the squeeze-film action.

HOMOTOPY ANALYSIS OF TRANSIENT MAGNETO-BIO-FLUID DYNAMICS OF MICROPOLAR SQUEEZE FILM IN A POROUS MEDIUM: A MODEL FOR MAGNETO-BIO-RHEOLOGICAL LUBRICATION

2012 ◽  
Vol 12 (03) ◽  
pp. 1250051 ◽  
Author(s):  
O. ANWAR BÉG ◽  
M. M. RASHIDI ◽  
T. A. BÉG ◽  
M. ASADI
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Angular Velocity ◽  
Differential Equations ◽  
Darcy Number ◽  
Squeeze Film ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Viscosity Parameter ◽  
Homotopy Analysis

The transient squeezing flow of a magneto-micropolar biofluid in a noncompressible porous medium intercalated between two parallel plates in the presence of a uniform strength transverse magnetic field is investigated. The partial differential equations describing the two-dimensional flow regime are transformed into nondimensional, nonlinear coupled ordinary differential equations for linear and angular momentum (micro-inertia). These equations are solved using the robust Homotopy Analysis Method (HAM) and also numerical shooting quadrature. Excellent correlation is achieved. The influence of magnetic field parameter (Ha) , micropolar spin gradient viscosity parameter (Γ) and unsteadiness parameter (S) on linear and angular velocity (micro-rotation) are presented graphically, for specified values of the micropolar vortex viscosity parameter (R), Darcy number (Da i.e. permeability parameter) and medium porosity parameter (ε). Increasing magnetic field (Ha) serves to decelerate both the linear and angular velocity i.e. enhances lubrication. The excellent potential of HAM in bio-lubrication flows is highlighted.

APPLICATION OF IMPROVED AMPLITUDE-FREQUENCY FORMULATION TO NONLINEAR DIFFERENTIAL EQUATION OF MOTION EQUATIONS

2009 ◽  
Vol 23 (28) ◽  
pp. 3427-3436 ◽  
Author(s):  
A. G. DAVODI ◽  
D. D. GANJI ◽  
R. AZAMI ◽  
H. BABAZADEH
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Nonlinear Oscillations ◽  
Equation Of Motion ◽  
Energy Balance Method ◽  
Approximate Analytical Solutions ◽  
Relativistic Oscillator ◽  
High Degree ◽  
General Motion ◽  
New Algorithms

This paper presents an approach for solving accurate approximate analytical solutions for strong nonlinear oscillators called improved amplitude-frequency formulation. For illustrating the accuracy of the method, we also solved equations with He's energy balance method and compared results. New algorithms offer promising approaches, which are useful for nonlinear oscillations. We find that these attained solutions not only benefit from a high degree of accuracy, but are also uniformly valid in the whole solution domain which is so simple to do and effective. The studied equations are the general motion equation and the non-dimensional nonlinear differential equation of motion for the relativistic oscillator, which their solution can be useful for researchers to extend this ability into their other works.

FLOW OF A FOURTH GRADE FLUID

2002 ◽  
Vol 12 (06) ◽  
pp. 797-811 ◽  
Author(s):  
T. HAYAT ◽  
Y. WANG ◽  
K. HUTTER
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Nonlinear Equation ◽  
Fourth Grade ◽  
The Other ◽  
Parallel Plates ◽  
Suction Velocity ◽  
Material Parameters ◽  
Grade Fluid ◽  
Fourth Grade Fluid

The governing nonlinear equation for the unsteady flow of an incompressible fourth grade fluid is modelled. The fluid is also subjected to a magnetic field. In addition, we investigate steady flow between parallel plates with one plate at rest and the other moving parallel to it at constant speed with a suction velocity normal to the plates. Boundary conditions play a significant role. We construct the numerical solution to the sixth order nonlinear differential equation. It is found that the velocity increases with the increase in the material parameters of the fourth grade terms of the fluid.

On the Computation of Inertial Coefficients in Squeeze-Film Bearings

1987 ◽  
Vol 201 (2) ◽  
pp. 125-131
Author(s):  
M D Ramli ◽  
J Ellis ◽  
J B Roberts
Keyword(s):  
Differential Equation ◽  
Diameter Ratio ◽  
Fluid Film ◽  
Squeeze Film ◽  
Eccentricity Ratio ◽  
Film Pressure ◽  
Static Eccentricity ◽  
Computational Simplicity ◽  
Analytical Expressions ◽  
Good Agreement

Inertial coefficients for full squeeze-film bearings are evaluated theoretically using Smith's differential equation relating fluid-film pressure to journal acceleration (1). The variations of the non-dimensionalized inertial coefficients with static eccentricity ratio in the radial and transverse directions are compared with some corresponding values obtained from Reinhardt and Lund (2) and Szeri et al. (3). The results from these three methods show good agreement, especially for short bearings (that is bearings with low values of length–diameter ratio). However, Smith's approach has the advantage of computational simplicity and leads to fairly simple, asymptotic, analytical expressions for very short, and very long, bearings.

scholarly journals Effect of Surface Roughness on the Squeeze Film Characteristics of Circular Plates in the Presence of Conducting Couplestress Fluid and Transverse Magnetic Field

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Syeda Tasneem Fathima ◽  
N. B. Naduvinamani ◽  
J. Santhosh Kumar ◽  
B. N. Hanumagowda
Keyword(s):  
Magnetic Field ◽  
Surface Roughness ◽  
Transverse Magnetic ◽  
Squeeze Film ◽  
Circular Plates ◽  
Roughness Effects ◽  
Modified Equations ◽  
Load Carrying ◽  
Film Characteristics ◽  
Effect Of Surface

The combined effect of surface roughness and magnetic field on the performance characteristic of the circular plates lubricated with conducting couplestress fluid (CCSF) has been studied. On the basis of the Christensen Stochastic model, the generalized stochastic Reynold’s equation is derived. Modified equations for the nondimensional pressure, load load-carrying capacity, and squeeze film time are derived. The results are presented both numerically and graphically and compared with conducting smooth surface case. It is observed that the surface roughness effects are more pronounced for couplestresses as compared to nonconducting Newtonian fluid (NCNF) in the presence of magnetic field.

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