Graphical methods used in the numerical solution of Jeffery-Hamel flow at fixed flow rates

摘要

A basic problem in the area of Fluid Dynamics is the solution of the Navier-Stokes equations describing the radial flow of viscous incompressible fluid between non-parallel plane walls. Since the known solutions involve transcendental equations containing elliptic functions, there are no explicit equations or methods available for determining the shape of the velocity profile for specified boundary conditions that do not require an iterative or graphical technique. The purpose of this paper is to describe the computer generated graphical solutions which allow for an easy determination of the velocity profile for fixed flow conditions. The paper will describe the step by step process of extending the solution of the problem by working back and forth between the graphical representation of the equations and the numerical solution.