| Abstract: | A finite element method is proposed for solving two dimensional flow problems in complex geometrical configurations commonly encountered in polymer processing. The method is applicable to flow in relatively narrow gaps of variable thickness and any desired shape. It was developed for analyzing flow in injection molding dies and certain extrusion dies. The fluid can be any non-Newtonian fluid which is incompressible, inelastic, and time independent. The flow field is divided into an Eulerian mesh of cells. Around each node, located at the center of the cell, a local flow analysis is made. The analysis around all nodes results in a set of linear algebraic equations with the pressures at the nodes as unknowns. The simultaneous solution of these equations results in the required pressure distribution, from which the flow rate distribution is obtained. Solution for the isothermal Newtonian flow problem is obtained by a one-time solution of the equations, whereas solution of a non-Newtonian problem requires iterative solution of the equations. |
