Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes

2016 ◽  
Vol 37 (1) ◽  
pp. 297-305
Author(s):  
Eduard Marušić-Paloka ◽  
Igor Pažanin
Keyword(s):  
Fluid Flow ◽  
Asymptotic Analysis ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity

scholarly journals Asymptotic Analysis of the Curved-Pipe Flow with a Pressure-Dependent Viscosity Satisfying Barus Law

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Igor Pažanin
Keyword(s):  
Asymptotic Analysis ◽  
Pressure Dependence ◽  
Circular Cross Section ◽  
Main Idea ◽  
Curvilinear Coordinates ◽  
Inverse Transformation ◽  
Curved Pipe ◽  
Pressure Dependent Viscosity ◽  
Central Curve ◽  
Dependent Viscosity

Curved-pipe flows have been the subject of many theoretical investigations due to their importance in various applications. The goal of this paper is to study the flow of incompressible fluid with a pressure-dependent viscosity through a curved pipe with an arbitrary central curve and constant circular cross section. The viscosity-pressure dependence is described by the well-known Barus law extensively used by the engineers. We introduce the small parameterε(representing the ratio of the pipe’s thickness and its length) into the problem and perform asymptotic analysis with respect toε. The main idea is to rewrite the governing problem using the appropriate transformation and then to compute the asymptotic solution using curvilinear coordinates and two-scale asymptotic expansion. Applying the inverse transformation, we derive the asymptotic approximation of the flow clearly showing the influence of pipe’s distortion and viscosity-pressure dependence on the effective flow.

scholarly journals Asymptotic Modeling of the Thin Film Flow with a Pressure-Dependent Viscosity

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Eduard Marušić-Paloka ◽  
Igor Pažanin
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Asymptotic Analysis ◽  
Film Flow ◽  
Thin Film Flow ◽  
Asymptotic Modeling ◽  
Governing System ◽  
Expansion Technique ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity

We study the lubrication process with incompressible fluid taking into account the dependence of the viscosity on the pressure. Assuming that the viscosity-pressure relation is given by the well-known Barus law, we derive an effective model using asymptotic analysis with respect to the film thickness. The key idea is to conveniently transform the governing system and then apply two-scale expansion technique.

Stochastic Reynolds equation for the combined effects of piezo-viscous dependency and squeeze-film lubrication of micropolar fluids on rough porous circular stepped plates

2021 ◽  
pp. 135065012110224
Author(s):  
Hanumagowda Bannihalli Naganagowda ◽  
Sreekala Cherkkarathandayan Karappan
Keyword(s):  
Carrying Capacity ◽  
Stochastic Approach ◽  
Squeeze Film ◽  
Closed Form Expression ◽  
Load Carrying Capacity ◽  
Micropolar Fluids ◽  
Pressure Dependent Viscosity ◽  
Load Carrying ◽  
Dependent Viscosity ◽  
Film Characteristics

The aim of this paper is to presents a theoretical analysis on squeeze-film characteristics of a rough porous circular stepped plate in the vicinity of pressure-dependent viscosity and lubrication by micropolar fluids. A closed-form expression for non-dimensional pressure, load, and squeezing time is derived based on Eringen’s theory, Darcy’s equation, and Christensen’s stochastic approach. Results indicate that the effects of pressure-dependent viscosity, surface roughness, and micropolar fluids play an important role in increasing the load-carrying capacity and squeezing time, whereas the presence of porous media decreases the load-carrying capacity and squeezing time of the rough porous circular stepped plates.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

scholarly journals Effect of Pressure Dependent Viscosity on Couple Stress Squeeze Film Lubrication between Rough Parallel Plates

2015 ◽  
Vol 10 (1) ◽  
pp. 76-83 ◽  
Author(s):  
Neminath Bujappa Naduvinamani ◽  
Siddangouda Apparao ◽  
Hiremath Ayyappa Gundayya ◽  
Shivraj Nagshetty Biradar
Keyword(s):  
Couple Stress ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Effect Of Pressure ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity ◽  
Film Lubrication
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