The solutions of Navier–Stokes equations in squeezing flow between parallel plates

2014 ◽  
Vol 48 ◽  
pp. 40-48 ◽  
Author(s):  
A.G. Petrov ◽  
I.S. Kharlamova
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Navier Stokes Equations

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

scholarly journals A COMPARISON OF THE ADOMIAN AND HOMOTOPY PERTURBATION METHODS IN SOLVING THE PROBLEM OF SQUEEZING FLOW BETWEEN TWO CIRCULAR PLATES

2010 ◽  
Vol 15 (4) ◽  
pp. 491-504 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Tahira Haroon ◽  
Saira Bhatti ◽  
Ali R. Ansari
Keyword(s):  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Computational Effort ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Circular Plates ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The objective of this paper is to compare two methods employed for solving nonlinear problems, namely the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). To this effect we solve the Navier‐Stokes equations for the unsteady flow between two circular plates approaching each other symmetrically. The comparison between HPM and ADM is bench‐marked against a numerical solution. The results show that the ADM is more reliable and efficient than HPM from a computational viewpoint. The ADM requires slightly more computational effort than the HPM, but it yields more accurate results than the HPM.

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 CENTRIFUGAL DESTABILIZATION AND RESTABILIZATION OF PLANE SHEAR FLOWS

1996 ◽  
Vol 06 (02) ◽  
pp. 409-413
Author(s):  
A. J. CONLEY
Keyword(s):  
Viscous Fluid ◽  
Linear Stability ◽  
Stokes Equations ◽  
Path Following ◽  
Incompressible Viscous Fluid ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Plane Shear ◽  
Navier Stokes Equations ◽  
Spectral Techniques

The flow of an incompressible viscous fluid between parallel plates becomes unstable when the plates are tumbled. As the tumbling rate increases, the flow restabilizes. This phenomenon is elucidated by path-following techniques. The solution of the Navier-Stokes equations is approximated by spectral techniques. The linear stability of these solutions is studied.

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.

scholarly journals Instability of Rayleigh-Bernard Convection Affected by Upper Wall Temperature Variation

2020 ◽  
Author(s):  
Sadoon Ayed ◽  
Keyword(s):  
Energy Equation ◽  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Chebyshev Collocation Method ◽  
Step Method ◽  
Navier Stokes Equations ◽  
Numeric Simulation ◽  
Pseudo Spectral

This paper represents the analysis of Rayleigh-Bernard convection between two parallel plates. Lower wall is being cooled while upper is heated according to periodic spatial distribution. This process has been modeled using Navier-Stokes equations, equation of continuity and energy equation. Solution of the differential equations has been obtained using pseudo spectral numeric method. For discretization in homogeneous direction, Fourier-Galerkin model has been used, while for discretization in inhomogeneous direction Chebyshev collocation method is applied. Time discretization has been performed using Adams-Bashworth two step method of second order. The results of numeric simulation have been presented by figures where vorticity fields, stream-function and velocity are shown for six different time steps.

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