PERISTALTIC FLOW OF A COMPRESSIBLE NON-NEWTONIAN MAXWELLIAN FLUID THROUGH POROUS MEDIUM IN A TUBE

2010 ◽  
Vol 03 (02) ◽  
pp. 255-275 ◽  
Author(s):  
ISLAM M. ELDESOKY ◽  
A. A. MOUSA
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Order Approximation ◽  
Cylindrical Tube ◽  
Peristaltic Transport ◽  
Navier Stokes ◽  
Mathematical Representation ◽  
Physical Parameters ◽  
Permeability Parameter ◽  
Modified Darcy’S Law

This work is concerned with the peristaltic transport of a Newtonian and non-Newtonian Maxwellian fluid in an axisymetric cylindrical tube filled with a homogenous porous medium, in which the flow is induced by traveling transversal waves on the tube wall. Like in peristaltic pumping, the traveling transversal waves induce a net flow of the liquid inside the tube. The viscosity as well as the compressibility of the liquid is taken into account. Modified Darcy's law has been used to model the governing equation. The present theoretical model may be considered as mathematical representation to the case of gall bladder and bile duct with stones and dynamics of blood flow in living creatures. The Navier–Stokes equations for an axisymmetric cylindrical tube are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the tube is small parameter. In the second order approximation, a net flow induced by the traveling wave is calculated for various values of the compressibility of the liquid, relaxation time and the permeability parameter of porous medium. The calculations disclose that the compressibility of the liquid, the permeability parameter of porous medium and non-Newtonian effects in presence of peristaltic transport have a strong influence of the net flow rate. Finally, the graphical results are reported and discussed for various values of the physical parameters of interest.

scholarly journals Peristaltic transport in a cylindrical tube through a porous medium

2000 ◽  
Vol 24 (4) ◽  
pp. 217-230 ◽  
Author(s):  
Elsayed F. El Shehawey ◽  
Wahed El Sebaei
Keyword(s):  
Porous Medium ◽  
Physical Parameter ◽  
Axial Velocity ◽  
Amplitude Ratio ◽  
Cylindrical Tube ◽  
Fluid Phase ◽  
Momentum Equation ◽  
Numerical Results ◽  
Peristaltic Transport ◽  
Permeability Parameter

The problem of peristaltic transport in a cylindrical tube through a porous medium has been investigated. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio is small. The results show that the fluid phase mean axial velocity increases with increasing the permeability parameterk. The phenomena of reflux is discussed. Numerical results are reported for various values of the physical parameter

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

Heat and Mass Transfer Porous Medium Saturated with Compressible Fluid with Boundary Domain Integral Method

2008 ◽  
Vol 273-276 ◽  
pp. 808-813 ◽  
Author(s):  
Janja Kramer ◽  
Renata Jecl ◽  
Leo Škerget
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Compressible Fluid ◽  
Integral Method ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Domain Integral

A numerical approach to solve a problem of combined heat and mass transfer in porous medium saturated with compressible fluid is presented. Transport phenomena in porous media is described using the modified Navier-Stokes equations, where for the governing momentum equation the Brinkman extended Darcy formulation is used. Governing equations are solved with the Boundary Domain Integral Method, which is an extension of classical Boundary Element Method.

scholarly journals Analytic Comparison of MHD Squeezing Flow in Porous Medium with Slip Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Transform Method ◽  
Slip Boundary ◽  
Adomian Decomposition

The aim of this paper is to compare the efficiency of various techniques for squeezing flow of an incompressible viscous fluid in a porous medium under the influence of a uniform magnetic field squeezed between two large parallel plates having slip boundary. Fourth-order nonlinear ordinary differential equation is obtained by transforming the Navier-Stokes equations. Resulting boundary value problem is solved using Differential Transform Method (DTM), Daftardar Jafari Method (DJM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Optimal Homotopy Asymptotic Method (OHAM). The problem is also solved numerically using Mathematica solver NDSolve. The residuals of the problem are used to compare and analyze the efficiency and consistency of the abovementioned schemes.

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

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