An Analysis of the Flow of a Newtonian Fluid between Two Moving Parallel Plates

A Zeb,A M Siddiqui,M Ahmed

doi:10.1155/2013/535061

Abstract

We consider flow of an incompressible Newtonian fluid produced by two parallel plates, moving towards and away from each other with constant velocity. Inverse solutions of the equations of motion are obtained by assuming certain forms of the stream function. Analytical expressions for the stream function, fluid velocity components, and fluid pressure are derived.

Highlights

Owing to the nonlinear nature of the Navier-Stokes equations, their exact solutions are far and few in number
Importance of the exact solutions lies in the fact that they serve as standards for validating the corresponding solutions obtained by numerical methods and other approximate techniques
Finding exact solution using the inverse method consists of making an assumption on the general form of the stream function ψ, involving certain unknown functions, without considering the shape of boundaries of the solution domain occupied by the fluid

Summary

Introduction

Owing to the nonlinear nature of the Navier-Stokes equations, their exact solutions are far and few in number. Finding exact solution using the inverse method consists of making an assumption on the general form of the stream function ψ, involving certain unknown functions, without considering the shape of boundaries of the solution domain occupied by the fluid. We substitute this assumed form of ψ in the compatibility equation for the stream function to find the unknown functions involved in ψ. Once the fluid velocity components are available, the second step is to compute the fluid pressure field using the component form of the Navier-Stokes equations This kind of methods with applications in various fields of continuum mechanics are given in an article by Nemenyi [1]. The results obtained are compared with the known viscous solutions by setting the relative velocity α of the disks equal to zero

Basic Equations

Problem Formulation

Solutions of the Problem