Flow of a Fluid with Pressure-Dependent Viscosity through Variable Permeability Porous Layer

In this work, we consider flow of a fluid with pressure-dependent viscosity down an inclined porous plane with variable permeability that is incorporated in the pressure-dependent drag coefficient. We provide a solution to a recently developed flow model, and study the effects of flow and domain parameters (viscosity control parameter, permeability proportionality constant, and angle of inclination) on the flow characteristics. Suitability of a variable permeability model that considers permeability proportional to the flow velocity is investigated. Results show that large values of the permeability proportionality constant have little or no effects on flow characteristics.

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Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefﬁcient

Journal of Applied Fluid Mechanics ◽

10.29252/jafm.09.06.25756 ◽

2016 ◽

Vol 9 (6) ◽

pp. 3101-3107

Author(s):

Igor Pažanin ◽

Marcone Pereira ◽

Francisco Javier Suarez-Grau ◽

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...

Keyword(s):

Drag Coefficient ◽

Asymptotic Approach ◽

Pressure Dependent Viscosity ◽

Brinkman’S Equation ◽

Dependent Viscosity

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Flow Characteristics of a Bluff Body Cut From a Circular Cylinder

Journal of Fluids Engineering ◽

10.1115/1.2819155 ◽

1997 ◽

Vol 119 (2) ◽

pp. 453-454 ◽

Cited By ~ 15

Author(s):

S. Aiba ◽

H. Watanabe

Keyword(s):

Circular Cylinder ◽

Drag Coefficient ◽

Flow Velocity ◽

Bluff Body ◽

Pressure Coefficient ◽

Angular Position ◽

Flow Characteristics ◽

Uniform Flow ◽

Base Pressure ◽

Singular Flow

This is a report on an investigation of the flow characteristics of a bluff body cut from a circular cylinder. The volume removed from the cylinder is equal to d/2(1 − cos θs), where d and θs are the diameter and the angular position (in the case of a circular cylinder, θs, = 0 deg), respectively. θs, ranged from 0 deg to 72.5 deg and Re (based on d and the upstream uniform flow velocity U∞) from 2.0 × 104 to 3.5 × 104. It is found that a singular flow around the cylinder occurs at around θs = 53 deg when Re > 2.5 × 104, and the base pressure coefficient (−Cpb,) and the drag coefficient CD take small values compared with those for otherθs.

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Effects of the Porous Microstructure on the Drag Coefficient in Flow of a Fluid with Pressure-Dependent Viscosity

International Journal of Mechanics ◽

10.46300/9104.2021.15.15 ◽

2021 ◽

Vol 15 ◽

pp. 136-144

Author(s):

M.S. Abu Zaytoon ◽

S. Jayyousi Dajani ◽

M.H. Hamdan

Keyword(s):

Porous Structure ◽

Drag Coefficient ◽

Volume Averaging ◽

Intrinsic Volume ◽

Friction Factors ◽

Pressure Dependent Viscosity ◽

Variable Function ◽

Porous Microstructure ◽

Dependent Viscosity

Equations governing the flow of a fluid with pressure-dependent viscosity through an isotropic porous structure are derived using the method of intrinsic volume averaging. Viscosity of the fluid is assumed to be a variable function of pressure, and the effects of the porous microstructure are modelled and included in the pressure-dependent drag coefficient. Five friction factors relating to five different microstructures are used in this work

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Fluid Mechanics at the Interface between a Variable Viscosity Fluid Layer and a Variable Permeability Porous Medium

WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER ◽

10.37394/232012.2021.16.19 ◽

2021 ◽

Vol 16 ◽

pp. 159-169

Author(s):

M.S. Abu Zaytoon ◽

M.H. Hamdan

Keyword(s):

Porous Layer ◽

Variable Viscosity ◽

Fluid Layer ◽

Work Conditions ◽

Velocity Shear ◽

Variable Permeability ◽

Pressure Dependent Viscosity ◽

Model Equations ◽

Dependent Viscosity ◽

Viscosity Fluid

Coupled parallel flow of fluid with pressure-dependent viscosity through an inclined channel underlain by a porous layer of variable permeability and variable thickness is initiated in this work. Conditions at the interface between the channel and the porous layer reflect continuity assumptions of velocity, shear stress, pressure and viscosity. Viscosity is assumed to vary in terms of a continuous pressure function that is valid throughout the channel and the porous layer. Model equations are cast in a form where the pressure as an independent variable and solutions are obtained to illustrate the effects of flow and media parameters on the dynamics behaviour of pressure-dependent viscosity fluid. A permeability and a viscosity adjustable control parameters are introduced to avoid unrealistic values of permeability and viscosity. This work could serve as a model for flow over a mushy zone.

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Some Remarks on the Navier-Stokes Equations with a Pressure-Dependent Viscosity.

10.21236/ada163726 ◽

1985 ◽

Author(s):

Michael Renardy

Keyword(s):

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Pressure Dependent Viscosity ◽

Dependent Viscosity

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

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

10.1177/13506501211022452 ◽

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.

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

Mathematics ◽

10.3390/math9040334 ◽

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.

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