A theoretical investigation of the laminar squeeze flow of a couple-stress fluid between a flat circular static disk and an axisymmetric curved circular moving disk has been carried out using modified lubrication theory and microcontinuum theory. The combined effects of fluid inertia forces, curvature of the disk and non-Newtonian couple stresses on the squeeze film behavior are investigated analytically. Each of these effects and their combinations show a significant enhancement in the squeeze film behavior, and these are studied through their effects on the squeeze film pressure and the load carrying capacity of the fluid film as a function of time. Two different forms of the gapwidth between the disks have been considered, and the results have been shown to be in good agreement with the existing literature.

Theoretical Investigation of Couple Stress Squeeze Films in a Curved Circular Geometry

An investigation has presented to analyze the heat transfer in a boundary layer flow of an incompress- ible couple stress fluid over a nonlinear stretching sheet. The heat transfer problem have been analyzed for the two heating processes, 1) PST (prescribed surface temperature case) and 2) PHF (prescribed heat flux case). The govern- ing partial differential equations for flow and heat transfer are transformed to ordinary differential equations. The nu- merical solutions have been obtained by using fourth order Runge-Kutta method coupled with shooting method. The effects of dimensionless surface temperature, couple stress parameter , Prandtl number Pr , Eckert number Ec, non- linear stretching sheet parameter n and 1; 2 have been observed by graphical illsurations. Chen (8) described the effects of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. Alinejad (9) investigate the flow and heat transfer characteristics of viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation, Khan et al. (10) presented an analysis of the axisymmet- ric flow of a non-Newtonian fluid over a radially stretch- ing sheet, Mehmood et al. (11) investigates the theoretical study of steady stagnation point flow with heat transfer of a second grade nano fluid towards a stretching surface, Khan et al. (12) gives an analytical study for the effects of slip factors on unsteady stagnation point flow and heat transfer towards a stretching sheet. Asghar (13) reveals all possible similarity transformations for the flow of power-law fluid over a stretching surface by a Lie group analysis. The rota- tion of the fluid particles and its effect has studied under the theory of couple stresses which describes the rotation field in specification of the velocity field. The examples of cou- ple stress fluids include blood, rheologically complex flu- ids, lubricant oil with long chain additives, polymeric sus- pensions, etc. Stokes (14) considered the effects of couple stresses in fluids. Soundalgekar (15) carried out an analysis for the dispersion of a solute in a channel flow of fluid with

Heat Transfer Analysis for Couple Stress Fluid over a Nonlinearly Stretching Sheet

Analysis of Static and Dynamic Characteristic of Hydrostatic Spherical Hinge

This study presents combined effects of couple stress fluids and rotational inertia together with considering lubricant viscosity variation with pressure in squeeze film characteristics of parallel annular plates. Squeeze film characteristics are obtained by combined solution of modified Reynolds equation and Stoke's microcontinuum for couple stress fluids with consideration of viscosity variation with pressure. Various cases of couple stress, inertial, and noninertial characteristics with isoviscous and piezoviscous contributions are investigated. The pressure distribution and load-carrying capacity for lubricant film are obtained in a closed form, using a small perturbation method. Furthermore, numerical solution of the film height versus response time is calculated employing the fourth-order Runge–Kutta method. The result shows that the combined effects of couple stresses and viscosity–pressure dependency improve the load-carrying capacity and lengthen the response time, as compared to the classical Newtonian lubricant with constant viscosity. However, increasing rotational inertia parameter decreases squeeze film characteristics.

Investigation of Combined Effects of Rotational Inertia and Viscosity–Pressure Dependency on the Squeeze Film Characteristics of Parallel Annular Plates Lubricated by Couple Stress Fluid

Since times immemorial it is known that the application of a material classified as lubricant to two relatively moving surfaces causes motion. The real mechanism of lubrication was explained by Reynolds of the role of lubricants is to support the load between two moving curved surfaces and thus minimizing wear and energy losses reducing friction between them. Thus the proper knowledge and understanding of the process of lubrication becomes a prime necessity to improve standard of design and efficiency of the mechanical system. A study of the behavior of any lubricated system can be best made by developing a mathematical model based on the above factors which depends upon a given a physical situation. The bearing characteristics such as load, flow flux, friction force etc. depends upon the pressure generated in the film and the lubrication process. An attempt has been made to obtain the governing equation for pressure in the lubricant film that are surveyed and summarized in this paper. RÉSUMÉ. Depuis des temps immémoriaux, il est connu que l'application d'un matériau classé comme lubrifiant sur deux surfaces relativement mobiles provoque un mouvement.Le mécanisme réel de lubrification a été expliqué par Reynolds que le rôle de lubrifiants est de supporter la charge entre deux surfaces courbes en mouvement, minimisant ainsi l'usure et les pertes d'énergie, réduisant ainsi les frictions entre elles.Ainsi, la connaissance et la compréhension appropriées du processus de lubrification deviennent une nécessité primordiale pour améliorer les normes de conception et l'efficacité du système mécanique.Une étude du comportement de tout système lubrifié peut être mieux réalisée en développant un modèle mathématique basé sur les facteurs ci-dessus, qui dépend d'une situation physique donnée. Les caractéristiques des roulements, telles que la charge, le flux, la force de friction, etc., dépendent de la pression générée dans le film et du processus de lubrification.Une tentative a été faite pour obtenir l'équation régissant la pression dans le film de lubrifiant qui sont enquêtés et résumées dans le présent document.

Effects of viscosity variation and thermal effects in squeeze films

The laminar squeeze flow of couple-stress fluids between a flat circular disc and an axisymmetric curved disc of arbitrary shape is taken into consideration. Based on the modified lubrication theory and the microcontinuum theory, the problem is solved analytically. The combined effects of fluid inertia forces, curvature and non-Newtonian couple stresses on the squeeze film behaviour are investigated through the variations in the Reynolds number, curvature and the couple stress parameters. Each of these effects and their combinations show a significant enhancement in the squeeze film behaviour and these are studied through their effects on the squeeze film pressure and the load carrying capacity of the fluid film as a function of time. It is understood that the operating life of the squeeze film discs are lengthened, especially for larger couple stress parameters, larger Reynolds numbers and concave nature of the curved discs.Copyright © 2009 by ASME

Vimala Manivasakan

Papers

Theoretical Investigation of Couple Stress Squeeze Films in a Curved Circular Geometry

Combined Effects of Non-Newtonian Rheology, Curvature and Fluid Inertia Forces on the Squeeze Film Behaviour