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

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.

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

2021 ◽  
Vol 16 ◽  
pp. 204-212
Author(s):  
M. S. Abu Zaytoon ◽  
Yiyun (Lisa) Xiao ◽  
M. H. Hamdan
Keyword(s):  
Drag Coefficient ◽  
Flow Velocity ◽  
Control Parameter ◽  
Flow Model ◽  
Flow Characteristics ◽  
Permeability Model ◽  
Proportionality Constant ◽  
Variable Permeability ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity

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.

scholarly journals Non - Darcian and Non - Uniform Salinity Gradients on Triple Diffusive Convection in Composite Layers

2019 ◽  
Vol 8 (6S) ◽  
pp. 835-849
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Lower Boundary ◽  
Velocity Shear ◽  
Physical Parameters ◽  
Perturbation Approach ◽  
Salinity Gradients ◽  
Composite Layers ◽  
Diffusive Convection

The effect of uniform and non-uniform salinity gradients on the onset of triple diffusive convection in a system of composite layers enclosing an incompressible, three component, electrically conducting fluid which lies above a saturated porous layer of the identical fluid is studied analytically. The upper boundary of the fluid layer and the lower boundary of the porous layer are static and both the boundaries are insulating to heat and mass. At the interface, the velocity, shear stress, normal stress, heat, heat flux, mass and mass flux are presumed to be continuous, intended for Darcy-Brinkman model. An Eigenvalue problem is attained and the same is solved by the regular perturbation approach. The critical Rayleigh number which is the guiding principle for the invariability of the system is accomplished for every salinity profile individually. The effects of various physical parameters on the onset of Triple diffusive convection are considered for all the profiles graphically.

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.

scholarly journals Stokes drift through corals

2021 ◽  
Author(s):  
Joseph J. Webber ◽  
Herbert E. Huppert
Keyword(s):  
Coral Reef ◽  
Coral Reefs ◽  
Porous Layer ◽  
Large Scale ◽  
Fluid Layer ◽  
Ocean Waves ◽  
Stokes Drift ◽  
Inviscid Fluid ◽  
Porous Bed ◽  
Vertical Drift

AbstractMotivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

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