Finite Element Solution of Thermal Gee-Lyon Flows in a Circular Tube

Abstract

The goal of this project is to calculate the temperature distribu- tion of certain pressure-driven non-Newtonian ows inside a circular tube. The rheology under consideration is the type in which the shear stress is an implicit function of the shear rate de ned as the inverse function of an odd function. The uid velocity in the tube is approximated by the steady state velocity pro le along the tube length and the viscosity is assumed to be independent of the temperature. The velocity pro le is computed by using Mathematica's build-in ODE solver semi-analytically. The corresponding steady state temperature pro le at tube length is then calculated taking into account of heat source generated by shear rate from the uid ow by solving an ODE. The temperature distribution from the entrance to the fully developed region is then approximated numerically by using the axisymmet- ric linear triangular nite elements. Material and geometric constants and data for extrusion of chemical Lucite through the tube in literature are used for the numerical example. Comparison of the numerical result with the industrial experimental result is made at a point along the central axis of the tube.