Abstract: This paper presents a numerical analysis for the dynamic performance of a finite journal bearing lubricated with couple stress fluid taking into account the effect of the deformation of the bearing liner. The modified Reynolds equation has been solved by using finite difference technique. The dynamic characteristics in terms of stiffness coefficients, damping coefficients, critical mass and whirl ratio are evaluated for different values of eccentricity ratio and elastic coefficient for a journal bearing lubricated with a couple stress fluids and a Newtonian fluid. The results show that the dynamic characteristics of journal bearings lubricated with couple stress fluids are improved compared to journal bearings lubricated with Newtonian fluids.
Abstract: In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique
is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.
Abstract: Steady incompressible couple stress fluid flow through two dimensional symmetric channel with stenosis is investigated. The flow consisting of a core region to be a couple stress fluid and a peripheral layer of plasma (Newtonian fluid). Assuming the stenosis to be mild, the equations governing the flow of the proposed model are solved using the slip boundary condition and closed form expressions for the flow characteristics (the dimensionless resistance to flow and wall shear stress at the maximum height of stenosis) are derived. The effects of various parameters on these flow variables have been studied. It is observed that the resistance to flow as well as the wall shear stress increase with the height of stenosis, viscosity ratio and Darcy number. However, the trend is reversed as the slip and the couple stress parameter increase.
Abstract: The paper presents an analytical solution for dispersion
of a solute in the peristaltic motion of a couple stress fluid
through a porous medium with slip condition in the presence of both
homogeneous and heterogeneous chemical reactions. The average
effective dispersion coefficient has been found using Taylor-s limiting
condition and long wavelength approximation. The effects of various
relevant parameters on the average coefficient of dispersion have been
studied. The average effective dispersion coefficient tends to increase
with permeability parameter but tends to decrease with homogeneous
chemical reaction rate parameter, couple stress parameter, slip parameter
and heterogeneous reaction rate parameter.
Abstract: A mathematical model for the hydrodynamic
lubrication of parabolic slider bearings with couple stress lubricants
is presented. A numerical solution for the mathematical model using
finite element scheme is obtained using three nodes isoparametric
quadratic elements. Stiffness integrals obtained from the weak form
of the governing equations were solved using Gauss Quadrature to
obtain a finite number of stiffness matrices. The global system of
equations was obtained for the bearing and solved using Gauss Seidel
iterative scheme. The converged pressure solution was used to obtain
the load capacity of the bearing. Parametric studies were carried out
and it was shown that the effect of couple stresses and profile
parameter are to increase the load carrying capacity of the parabolic
slider bearing. Numerical experiments reveal that the magnitude of
the profile parameter at which maximum load is obtained increases
with decrease in couple stress parameter. The results are presented in
graphical form.
Abstract: An analytical solution for dispersion of a solute in the
peristaltic motion of a couple stress fluid in the presence of magnetic
field with both homogeneous and heterogeneous chemical reactions is
presented. The average effective dispersion coefficient has been found
using Taylor-s limiting condition and long wavelength approximation.
The effects of various relevant parameters on the average effective
coefficient of dispersion have been studied. The average effective
dispersion coefficient tends to decrease with magnetic field parameter,
homogeneous chemical reaction rate parameter and amplitude ratio
but tends to increase with heterogeneous chemical reaction rate
parameter.
Abstract: The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.
Abstract: Avalanche velocity (from start to track zone) has been estimated in the present model for an avalanche which is triggered artificially by an explosive devise. The initial development of the model has been from the concept of micro-continuum theories [1], underwater explosions [2] and from fracture mechanics [3] with appropriate changes to the present model. The model has been computed for different slab depth R, slope angle θ, snow density ¤ü, viscosity μ, eddy viscosity η*and couple stress parameter η. The applicability of the present model in the avalanche forecasting has been highlighted.