A Generalized Squeezing Flow of a Power-Law Fluid Between Two Plane Annuli

1986 ◽  
Vol 108 (1) ◽  
pp. 80-85 ◽  
Author(s):  
A. F. Elkouh ◽  
N. J. Nigro ◽  
A. Glowacz
Keyword(s):  
Pressure Distribution ◽  
Newtonian Fluid ◽  
Power Law ◽  
Load Capacity ◽  
Numerical Results ◽  
Squeezing Flow ◽  
Power Law Model ◽  
Power Law Fluid ◽  
Newtonian Behavior

A generalization of the problem of laminar squeezing flow of a non-Newtonian fluid between plane annular surfaces is presented. The generalization considers the effect of difference in the pressures at the inner and outer boundaries. The fluid is assumed to be incompressible, and the non-Newtonian behavior of the fluid is described by a power-law model. Expressions for the pressure distribution and load capacity are presented along with tables that are used for obtaining numerical results.

Flow of a Power-Law Fluid in a Rayleigh Step

1991 ◽  
Vol 113 (3) ◽  
pp. 428-433 ◽  
Author(s):  
A. F. Elkouh ◽  
Der-Fa Yang
Keyword(s):  
Exact Solution ◽  
Pressure Gradient ◽  
Power Law ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Power Law Model ◽  
Algebraic Equations ◽  
Power Law Fluid ◽  
Dimensionless Pressure ◽  
Newtonian Behavior

An exact solution of the lubrication equations of motion for flow in a Rayleigh step of infinite width is presented. The fluid is assumed to be incompressible, and the non-Newtonian behavior of the fluid is described by a power-law model. The dimensionless pressure gradient and load capacity are obtained by the solution of a system of six algebraic equations. Optimum dimensions and load capacity for Rayleigh step bearing are presented.

scholarly journals Particularities of the Pseudo-Plastic Lubrication, with Application to the Sinovial Liquid

2015 ◽  
Author(s):  
I. Radulescu ◽  
A.V. Radulescu ◽  
J. Javorova
Keyword(s):  
Friction Coefficient ◽  
Synovial Fluid ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Power Law ◽  
Hip Joint ◽  
Load Capacity ◽  
Squeeze Film ◽  
Power Law Model ◽  
Spherical Surfaces

The present paper proposes a new model for lubrication of the hip joint with hyaluronan solutions, considering the squeeze film process of non-Newtonian fluid between rigid spherical surfaces. The heological model that approximately describes the behaviour of the synovial fluid is the power law model. For the considered case, the pressure distribution, the load capacity, the film thickness and the friction coefficient have been determinated. The conclusions of the paper offer an explication to the development of the osteoarthritis and to the problems of the arthritic patients.

Non-Newtonian Squeeze Film Between Two Plane Annuli

1982 ◽  
Vol 104 (2) ◽  
pp. 275-278 ◽  
Author(s):  
A. F. Elkouh ◽  
N. J. Nigro ◽  
Y. S. Liou
Keyword(s):  
Thin Film ◽  
Power Law ◽  
Load Capacity ◽  
Parallel Plane ◽  
Squeeze Film ◽  
Squeezing Flow ◽  
Fluid Inertia ◽  
Power Law Fluid ◽  
Analytic Expressions ◽  
Time Relation

An analysis is presented for the laminar squeezing flow of an incompressible power-law fluid between parallel plane annuli. The results obtained are based on the thin-film approximation, and negligible fluid-inertia. Analytic expressions for the load capacity of the squeeze film and its thickness-time relation are presented.

A Comparison of Differential and Integral Descriptions of the Annular Flow of a Power-Law Fluid

1969 ◽  
Vol 9 (03) ◽  
pp. 311-315
Author(s):  
G.C. Wallick ◽  
J.G. Savins
Keyword(s):  
Shear Rate ◽  
Newtonian Fluid ◽  
Power Law ◽  
Flow Problem ◽  
Axial Flow ◽  
Past Experience ◽  
Radial Coordinate ◽  
Power Law Model ◽  
Power Law Fluid ◽  
Model Parameter

Abstract Some physical processes may be described mathematically in both differentialand integral equation form. Formulation choice for numerical solution often isbased upon personal preference rather than upon problem characteristics. Wecompare differential and integral methods for the numerical description of thesteady-state flow of a non-Newtonian, power-law fluid through an annulus. Forthis application, our data indicate that the integral formulation is superiorboth in solution accuracy and computational efficiency. Our integral solutionmethod is a generalization of an earlier analytic solution that was restrictedto integer values of the power-law model parameter N. The new method ispower-law model parameter N. The new method is more directly applicable inpractical applications and is valid for all N, integer and non-integer. Introduction In many instances differential and integral equations may be used with equalvalidity for the mathematical description of a physical precess. The choice ofmethods often is dictated more by the past experience and predilection of theanalyst than past experience and predilection of the analyst than by the natureof the problem. Yet the efficiency and efficacy of the solution process may bestrongly dependent upon the problem formulation selected. As an example of thisprocedural dichotomy we will consider the numerical description of thesteady-state isothermal axial flow of an incompressible time independentnon-Newtonian fluid through the annular spacing between two fixed concentriccylinders of radii Ri and R, R greater than Ri.* We assume that the cylindersare infinite in length (no end effects) and that the flow is produced by theapplication of a constant pressure gradient in the axial z-direction. This flowproblem has been treated by a number of investigators, and has practicalapplication, e.g., flow of drilling fluids, extrusion of molten plastics, etc. Fredrickson and Bird have shown that, subject to the above assumptions, theflow equation may be written in the form ...........(1) where J = -dp/dz= constant p represents the pressure, the radial coordinate, and = z pressure, the radial coordinate, and = z represents the shearingstress. We seek a solution of Eq. 1 subject to the adherence boundaryconditions ...........(2) where v = vz is the axial flow velocity. For this flow problem it can beshown that .............(3) where is the shear-dependent viscosity function, and that the shear rate maybe expressed in the forms ..............(4) The minus sign is used in Eq. 4 to insure that and always have the samesign, greater than 0. In principle, the flow problem outlined here may besolved for any non-Newtonian fluid for which the shear-dependent viscosityfunction can be established as a known analytic function of the rate of shearfrom an investigation of any of the viscometric flows. However, it isconvenient for our purpose to use the particular viscometric function .............(5) which is referred to as the power-law model. The parameters n and Kcharacterize the relationship between shear rate and shear stress for a powerlaw liquid. The parameter n is a measure of the departure from Newtonianbehavior. If n less than 1, the flow behavior is of the "shearthinning" type; if n greater than 1, it is of the "shearthickening" category.

A Non-Newtonian Fluid Flow Model for the Slip Condition on Blood Flow through a Stenosed Artery using Power-law Fluid

2018 ◽  
Vol 9 (7) ◽  
pp. 871-879
Author(s):  
Rajesh Shrivastava ◽  
R. S. Chandel ◽  
Ajay Kumar ◽  
Keerty Shrivastava and Sanjeet Kumar
Keyword(s):  
Blood Flow ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Power Law ◽  
Flow Model ◽  
Slip Condition ◽  
Power Law Fluid ◽  
Stenosed Artery ◽  
Flow Through

Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640010 ◽  
Author(s):  
A. G. Fareo ◽  
D. P. Mason
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Numerical Solutions ◽  
Invariant Solution ◽  
Two Dimensional ◽  
Initial Length ◽  
Power Law Fluid ◽  
Group Invariant ◽  
Permeable Rock ◽  
Fluid Leak

Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.

Reduced Order Model for a Power-Law Fluid

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
M. Ocana ◽  
D. Alonso ◽  
A. Velazquez
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Reduced Order Model ◽  
Processing Unit ◽  
Order Model ◽  
Power Law Fluid ◽  
Reduced Order ◽  
Polymeric Fluid ◽  
Central Processing ◽  
Highly Nonlinear

This article describes the development of a reduced order model (ROM) based on residual minimization for a generic power-law fluid. The objective of the work is to generate a methodology that allows for the fast and accurate computation of polymeric flow fields in a multiparameter space. It is shown that the ROM allows for the computation of the flow field in a few seconds, as compared with the use of computational fluid dynamics (CFD) methods in which the central processing unit (CPU) time is on the order of hours. The model fluid used in the study is a polymeric fluid characterized by both its power-law consistency index m and its power-law index n. Regarding the ROM development, the main difference between this case and the case of a Newtonian fluid is the order of the nonlinear terms in the viscous stress tensor: In the case of the polymeric fluid these terms are highly nonlinear while they are linear when a Newtonian fluid is considered. After the method is validated and its robustness studied with regard to several parameters, an application case is presented that could be representative of some industrial situations.

scholarly journals Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1959
Author(s):  
Adrian S. Halifi ◽  
Sharidan Shafie ◽  
Norsarahaida S. Amin
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Power Law ◽  
Vortex Formation ◽  
Shear Thickening ◽  
Power Law Model ◽  
Governing Equations ◽  
Power Law Fluid ◽  
Transfer Parameters ◽  
Power Law Index

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

The Modeling of Form Drag in a Porous Medium Saturated by a Power-Law Fluid

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Porous Medium ◽  
Newtonian Fluid ◽  
Power Law ◽  
Power Law Fluid ◽  
Form Drag ◽  
Current Usage

The alternative ways of modeling form drag in a porous medium saturated by a power-law fluid in current usage are discussed. It is argued that the best alternative is to use the same expression as that used in the case of a Newtonian fluid, but with a modified Forchheimer coefficient.

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