A TAYLOR-GALERKIN FINITE-ELEMENT METHOD FOR NON-NEWTONIAN FLOWS

Some recent results are reviewed that indicate the appropriate nature of Taylor-Galerkin based algorithms for solving model convection-diffusion problems accurately in time and for simulating more complex non-Newtonian flows, such as those arising in the polymer industry. Initially attention is given therefore to linear and non-linear convection-diffusion model problems in two space dimensions, and then to transient problems involving heating effects. Newtonian and generalized Newtonian models are considered for both power-law and Carreau models for various parameters. Effects of shear-rate changes and temperature variations through transient build up periods are discussed in relation to their influence on the viscosity and viscous heating for thermal Peclet numbers of 1 and 100.