Finite Element Analysis of Nonisothermal Reactive Flows

This document will outline the theoretical background and operating principles of a general finite element code which has been developed for research and teaching of materials processing operations, and present examples of its use. Some of this information is rather condensed, and the reader will probably wish to consult additional sources such as those listed in the References section for more thorough treatment of topics in transport theory and finite element methodology. The finite element code to be discussed here has been developed for plane or axisymmetric problems in viscous fluid flow, such as might occur in polymer melt processing. Many other flow types can be handled as well, but polymer processing provides a convenient means of outlining the code’s features and underlying numerical algorithms. Polymer processing problems typically involve the flow of incompressible viscous liquids at low Reynolds’ numbers (“creeping” flow), in irregular geometries. It is common in such problems to have nonisothermal conditions prevail, and for the polymer to experience chemical reaction during processing. To model such problems satisfactorily, the code has been developed to solve for velocities, temperatures, and extent of chemical reaction simultaneously. The finite element method consists of recasting the governing differential equations of engineering boundary value problems as a sequence of linear or nonlinear algebraic equations: