Finite Element Analysis of Non-Newtonian Flow

1 Introduction.- 1.1 Preamble.- 1.2 Objectives and Layout.- 2 Governing Differential Equations.- 2.1 Introduction.- 2.2 Governing Equations.- 2.3 Constitutive Equation.- 2.4 Elastic Liquids.- 2.5 Equation in Steady State Flow.- 2.6 Initial and Boundary Conditions.- 2.7 Stream Function.- 3 Finite Element Method.- 3.1 Introduction.- 3.2 Variational Principle and Rayleigh-Ritz Method.- 3.3 Galerkin Weighted Residual Method.- 3.4 Virtual Work Principle.- 3.5 Finite Element Method in Two Dimensions.- 4 Steady Non-Newtonian Flow.- 4.1 Introduction.- 4.2 Creeping Motion.- 4.3 Finite Element Formulation for Creeping Flow....57.- 5 Temporal Discretisation.- 5.1 Introduction.- 5.2 Finite Element Formulation.- 5.3 Temporal Discretisation.- 5.4 Solution of Nonlinear System of Equations.- 6 Finite Element Analysis for Transient non-Newtonian Flow.- 6.1 Introduction.- 6.2 The Taylor-Galerkin Method.- 6.3 The Pressure Correction Method.- 6.4 Transient Non-Newtonian Flow.- 6.5 Non-isothermal Flow.- 6.6 Adaptive Analysis.- 6.7 Error Estimation for Fluid Flow.- 6.8 Numerical Examples.- A Software Description for NSTEAD.- A.1 Introduction....129.- A.2 Glossary of Variable Names.- A.2.1 Main variables.- A.2.2 Main arrays.- A.2.3 Main subroutines.- A.3 Program Overview.- A.4 Input Instructions.- A.5 Element Stiffness Calculations.- A.6 Documented Examples.- A.6.1 Example 1: Flow in a plane channel.....147.- A.6.2 Example 2: Flow over a step.- B Software Description for NFLOWG.- B.1 Introduction.- B.2 Glossary of Variable Names.- B.2.1 Main logical variables for the code.- B.2.2 Main variables for the geometry and mesh data.....181.- B.2.3 Main arrays used in the Code.- B.2.4 Main subroutines.- B.3 Main Routine of NFLOWG.- B.4 Input Instructions.- B.4.1 Input instruction for file PARA.DAT.-B.4.2 Input instruction for file GEOM.DAT.- B.5 Documented Example.