Non-Newtonian couple-stress squeeze film behaviour between oscillating anisotropic porous circular discs with sealed boundary

The thrust of this paper is to investigate theoretically the non-Newtonian couple stress squeeze film behaviour between oscillating circular discs based on V. K. Stokes micro-continuum theory. The lubricant squeezed out between parallel porous and rigid facings is supposed to be a concentrated suspension which consists of small particles dispersed in a Newtonian base fluid (solvent). The effective viscosity of the suspension is determined by using the Krieger-Dougherty viscosity model for a given volume fraction of particles in the base fluid. For low frequency and amplitude of sinusoidal squeezing where cavitation as well as turbulence are unlikely, the governing equations including the modified Reynolds equation coupled with the modified Darcy's equation are derived and solved numerically using the finite difference method and a sub-relaxed iterative procedure. The slip velocity at the porous-fluid interface is directly evaluated by means of the modified Darcy's law considering laminar and isothermal squeezing flow. For a given volume fraction, the couple stress effects on the squeeze film characteristics are analyzed through the dimensionless couple stress parameter ℓ˜ considering sealed and unsealed boundary of the porous disc. The obtained relevant results reveal that the use of couple stress suspending fluids as lubricants and the effect of sealing the boundary of the porous matrix improves substantially the squeeze film behaviour by increasing the squeeze film force. On the other hand, side leakage flow calculated in the sealed case remains constant in comparison to that of open end (unsealed) porous disc for all values of couple stress parameter and volume fraction of particle.

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Effect of couple stress parameter on steady-state and dynamic characteristics of three-lobe journal bearing operating on TiO2 nanolubricant

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650119866028 ◽

2019 ◽

Vol 234 (4) ◽

pp. 528-540

Author(s):

Ashutosh Kumar ◽

SK Kakoty

Keyword(s):

Steady State ◽

Couple Stress ◽

Volume Fraction ◽

Dynamic Performance ◽

Significant Rise ◽

Flow Coefficient ◽

Performance Parameters ◽

Stress Parameter ◽

Load Carrying ◽

Stiffness And Damping

Steady-state and dynamic performance parameters of three-lobe fluid film bearing, operating on TiO2 nanolubricant have been obtained. The effective viscosity for a given volume fraction of TiO2 nanoparticle in base fluid is obtained by using Krieger–Dougherty viscosity model. Various bearing performance parameters are obtained by solving remodeled Reynolds equation, which includes couple stress parameter. The stiffness and damping coefficients are also obtained for different values of the couple stress parameter. Results show a significant rise in the nondimensional load-carrying capacity and flow coefficient while there is a decrease in friction variable. It also reveals a significant improvement in the dynamic coefficient of bearing.

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Flow and heat transfer of couple stress nanofluid sandwiched between viscous fluids

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-12-2018-0715 ◽

2019 ◽

Vol 29 (11) ◽

pp. 4262-4276 ◽

Cited By ~ 1

Author(s):

C. Jawali Umavathi ◽

Mikhail Sheremet

Keyword(s):

Heat Transfer ◽

Couple Stress ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Viscous Fluids ◽

Temperature Fields ◽

Content Type ◽

Stress Parameter ◽

Transfer Behavior ◽

Velocity And Temperature Fields

Purpose The purpose of this study is a numerical analysis of steady-state heat transfer behavior of couple-stress nanofluid sandwiched between viscous fluids. It should be noted that this research deals with the development of a cooling system for the electronic devices. Design/methodology/approach Stokes model is used to define the couple-stress fluid and the single-phase nanofluid model is used to define the nanofluid transport processes. The fluids in all regions are assumed to be incompressible, immiscible and the transport properties in all the three layers are assumed to be constant. The governing coupled linear ordinary differential equations are made dimensionless by using appropriate fundamental quantities. The exact solutions obtained for the velocity and temperature fields are evaluated numerically for various model parameters. Findings The results are demonstrated using different types of nanoparticles such as copper, silver, silicon oxide (SiO2), titanium oxide (TiO2) and diamond. The investigations are carried out using copper–water nanofluid for different values of couple-stress parameter a with a range of 0 = a = 12, solid volume fraction ϕ with a range of 0.0 ≤ ϕ ≤ 0.05, Eckert number Ec with a range of 0.001 ≤ Ec ≤ 6 and Prandtl number Pr with a range of 0.001 ≤ Pr ≤ 6. It was found that the Nusselt number increases by increasing the couple stress parameter, Eckert number and Prandtl number and it decreases with a growth of the solid volume fraction parameter. It was also observed that using SiO2–water nanofluid, the optimal Nusselt number is obtained. Further, using copper, silver, diamond and TiO2, nanoparticles and water as a base fluid does not show any significant changes in the rate of heat transfer. The couple-stress parameter enhances the velocity and temperature fields whereas the solid volume fraction suppresses the flow field for both Newtonian and couple-stress fluid. Originality/value The originality of this work is to analyze the heat transfer behavior of couple-stress nanofluid sandwiched between viscous fluids. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer and flow structures in nanofluids and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.

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Derivation of non-Newtonian squeeze-film Reynolds equation between convex surfaces and application to two different cylinders

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1243/13506501jet295 ◽

2007 ◽

Vol 221 (7) ◽

pp. 813-821 ◽

Cited By ~ 2

Author(s):

J-R Lin

Keyword(s):

Couple Stress ◽

Reynolds Equation ◽

Continuum Theory ◽

Type Equation ◽

Squeeze Film ◽

Convex Surfaces ◽

Couple Stresses ◽

Load Carrying ◽

Film Characteristics ◽

Couple Stress Fluids

The derivation of non-Newtonian squeeze-film Reynolds-type equation between two convex surfaces and its application are of interest in the present study. Based upon the Stokes micro-continuum theory, the non-Newtonian squeeze-film Reynolds-type equation between two convex surfaces is derived to take into account the effects of couple stresses resulting from the lubricant blended with various additives. This non-Newtonian squeeze-film Reynolds-type equation is applicable to squeeze-film bearings lubricated with couple stress fluids when the general upper film shape and the lower film shape are specified. To guide the use of the equation, the squeeze-film mechanism between two different cylinders of infinite width with non-Newtonian couple stress fluids is illustrated. Comparing with the Newtonian-lubricant case, the presence of non-Newtonian couple stresses provides an increase in the load-carrying capacity, and therefore lengthens the approaching time. In addition, the effects of couple stresses on the squeeze film characteristics are more pronounced at lower squeeze-film height with larger couple stress parameters and larger radius ratios of cylinders. As the value of radius ratio approaches infinity, the present results agree closely with those of the previous studies by Hamrock [6] and by Lin et al. [19], respectively; it provides a support to the present study.

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Performance Characteristics of a Long Porous Partial Journal Bearing using Couple Stress Fluid

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.d7888.118419 ◽

2019 ◽

Vol 8 (4) ◽

pp. 4235-4240

Keyword(s):

Flow Rate ◽

Couple Stress ◽

Journal Bearing ◽

Fluid Model ◽

Performance Characteristics ◽

Fluid Film ◽

Couple Stress Fluid ◽

Squeeze Film ◽

Stress Parameter ◽

Matlab Programming

After effects of studies led on a long porous partial journal bearing for couple stress fluid are thus displayed. Performance characteristics presently determined incorporate the time-height relationship, Fluid film force, Flow rate, frictional force alongside the coefficient of friction. Plan/Technique/Approach -The paper shows a solution for the squeeze film lubrication of a thick, porous, with couple stress fluid model. It is determined that the changed Reynolds condition inferred the fluid film pressures. The modified state of Reynolds equation is analytically solved and closed form expressions are shown for the time-height, the flow rate and friction force with frictional coefficient numerically with the given starting condition using MATLAB programming, the first non-linear equation in the time-height relationship is resolved. The effects on the squeeze film characteristics of couple stresses and permeability are discussed. Findings – It can be seen that the couple stress parameter enhances the bearing characteristics. The bearing performance can be improved with the increase of couple stress parameter ( l  ), eccentricity ratio (ϵ), permeability parameter (ψ). Additional study may be performed using the couple stress fluid model, including the magnetic effect with heat and mass transfer. This model can be used to compare further with other models such as micropolar fluid, rabinowitsch fluid and for comparative study, which models are the most suitable for improving bearing system performance.

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Homotopy Analysis of Circular Plates Squeeze Film Bearings Lubricated with Couple Stress Fluids: Piezo-Viscous Model

Science & Technology Journal ◽

10.22232/stj.2020.08.02.14 ◽

2020 ◽

Vol 8 (2) ◽

pp. 95-102

Author(s):

J.P. Tripathi ◽

◽

U.P. Singh ◽

B.K. Singh ◽

◽

...

Keyword(s):

Couple Stress ◽

Load Capacity ◽

Closed Form Solution ◽

Continuum Theory ◽

Form Solution ◽

Squeeze Film ◽

Bearing Plate ◽

Homotopy Analysis ◽

Pressure Parameter ◽

Couple Stress Fluids

The piezo-viscous effect is crucial in fluid flows under high-pressure applications such as fluid film lubrication, microfluidics, and geophysics. We have investigated the combined influences of piezo-viscous dependence and non-Newtonian couple stresses on the performance of circular plate squeeze film bearings using Stokes Micro-Continuum theory of couple stress fluids together with the exponential variation of viscosity with pressure. A closed-form solution for film pressure has been obtained using the homotopy analysis method. The numerical results for pressure and load capacity with different values of the viscosity-pressure parameter have been calculated and compared with iso-viscous couple stress and Newtonian lubricants. An enhanced pressure and load capacity are observed in the analysis. The response time for the bearing (plate approach time) has also been calculated and a significant increase is observed.

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Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

Science and Engineering of Composite Materials ◽

10.1515/secm-2019-0033 ◽

2019 ◽

Vol 26 (1) ◽

pp. 491-501 ◽

Cited By ~ 1

Author(s):

Mehran Karimi Zeverdejani ◽

Yaghoub Tadi Beni

Keyword(s):

Natural Frequency ◽

Couple Stress ◽

Volume Fraction ◽

Couple Stress Theory ◽

Shear Deformation Theory ◽

Continuum Theory ◽

Dynamics Simulation ◽

Physical Parameters ◽

Stress Theory ◽

Size Dependent

AbstractThis paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.

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Effects of couple stresses and convective inertia forces in parallel circular squeeze‐film plates

Industrial Lubrication and Tribology ◽

10.1108/00368790410558220 ◽

2004 ◽

Vol 56 (6) ◽

pp. 318-323 ◽

Cited By ~ 6

Author(s):

Jaw‐Ren Lin ◽

Rong‐Fang Lu ◽

Won‐Hsion Liao ◽

Chia‐Chuan Kuo

Keyword(s):

Couple Stress ◽

Numerical Solutions ◽

Continuum Theory ◽

Momentum Equation ◽

Mean Value ◽

Squeeze Film ◽

Combined Effects ◽

Fluid Inertia ◽

Couple Stresses ◽

Inertia Forces

A theoretical study of the combined effects of non‐Newtonian couple stresses and fluid inertia forces on the squeeze‐film behaviors for parallel circular plates is presented in this paper. Based upon the micro‐continuum theory, the Stokes constitutive equations are used to account for the couple stress effects resulting from the lubricant blended with various additives. The convective inertia forces included in the momentum equation are approximated by the mean value averaged across the fluid film thickness. Numerical solutions for the squeezing film characteristics are presented for various values of couple stress parameter and Reynolds number. Comparing with the classical Newtonian non‐inertia flow, the combined effects of couple stresses and convective inertia forces result in a larger load‐carrying capacity and therefore, increase the response time of the squeezing film plates.

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Coupled effects of surface interaction and damping on electromechanical stability of functionally graded nanotubes reinforced torsional micromirror actuator

The Journal of Strain Analysis for Engineering Design ◽

10.1177/03093247211036826 ◽

2021 ◽

pp. 030932472110368

Author(s):

Weidong Yang ◽

Menglong Liu ◽

Linwei Ying ◽

Xi Wang

Keyword(s):

Casimir Force ◽

Volume Fraction ◽

Nonlocal Parameter ◽

Saddle Points ◽

Functionally Graded ◽

Heteroclinic Orbits ◽

Phase Portraits ◽

Squeeze Film ◽

Squeeze Film Damping ◽

Tilting Angle

This paper demonstrated the coupled surface effects of thermal Casimir force and squeeze film damping (SFD) on size-dependent electromechanical stability and bifurcation of torsion micromirror actuator. The governing equations of micromirror system are derived, and the pull-in voltage and critical tilting angle are obtained. Also, the twisting deformation of torsion nanobeam can be tuned by functionally graded carbon nanotubes reinforced composites (FG-CNTRC). A finite element analysis (FEA) model is established on the COMSOL Multiphysics platform, and the simulation of the effect of thermal Casimir force on pull-in instability is utilized to verify the present analytical model. The results indicate that the numerical results well agree with the theoretical results in this work and experimental data in the literature. Further, the influences of volume fraction and geometrical distribution of CNTs, thermal Casimir force, nonlocal parameter, and squeeze film damping on electrically actuated instability and free-standing behavior are detailedly discussed. Besides, the evolution of equilibrium states of micromirror system is investigated, and bifurcation diagrams and phase portraits including the periodic, homoclinic, and heteroclinic orbits are described as well. The results demonstrated that the amplitude of the tilting angle for FGX-CNTRC type micromirror attenuates slower than for FGO-CNTRC type, and the increment of CNTs volume ratio slows down the attenuation due to the stiffening effect. When considering squeeze film damping, the stable center point evolves into one focus point with homoclinic orbits, and the dynamic system maintains two unstable saddle points with the heteroclinic orbits due to the effect of thermal Casimir force.

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