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# Volume 1. Numerical Simulation of Non-Newtonian Flow

## 1st Edition

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Numerical Simulation of Non-Newtonian Flow focuses on the numerical simulation of non-Newtonian flow using finite difference and finite element techniques. Topics range from the basic equations governing non-Newtonian fluid mechanics to flow classification and finite element calculation of flow (generalized Newtonian flow and viscoelastic flow). An overview of finite difference and finite element methods is also presented.
Comprised of 11 chapters, this volume begins with an introduction to non-Newtonian mechanics, paying particular attention to the rheometrical properties of non-Newtonian fluids as well as non-Newtonian flow in complex geometries. The role of non-Newtonian fluid mechanics is also considered. The discussion then turns to the basic equations governing non-Newtonian fluid mechanics, including Navier Stokes equations and rheological equations of state. The next chapter describes a flow classification in which the various flow problems are grouped under five main headings: flows dominated by shear viscosity, slow flows (slightly elastic liquids), small deformation flows, nearly-viscometric flows, and long-range memory effects in complex flows. The remainder of the book is devoted to numerical analysis of non-Newtonian fluids using finite difference and finite element techniques.
This monograph will be of interest to students and practitioners of physics and mathematics.

Preface

Section 1 : Non-Newtonian Fluid Mechanics

1. General Introduction

1.1 Introduction

1.2 Rheometrical Properties of Non-Newtonian Fluids

1.3 Non-Newtonian Flow in Complex Geometries

1.4 The Role of Non-Newtonian Fluid Mechanics

2. Basic Equations

2.1 Introduction

2.2 Field Equations

2.3 Navier Stokes Equations

2.4 Rheological Equations of State. Formulation Principles

2.5 The Simple Fluid

2.6 Approximate Constitutive Equations

2.7 A Pragmatic Approach to Constitutive Equations

2.8 Constraints on Rheological Equations of State

2.9 Boundary Conditions

Appendix I

3. Flow Classification

3.1 Introduction

3.2 Flows Dominated by Shear Viscosity

3.3 Slow Flow (Slightly Elastic Liquids)

3.4 Small-Deformation Flows

3.5 Nearly-Viscometric Flows

3.6 Highly Elastic Liquids Flowing in Complex Geometries

3.7 General Comments Concerning Flows Involving Abrupt Changes in Geometry

3.8 Some Remarks on Non-Dimensional Parameters

3.9 Basic Equations for the Flow of a Maxwell Fluid

4. An Overview of Numerical Simulation

4.1 Introduction

4.2 Step 1 : Formulating the Governing Equations and Boundary Conditions

4.3 Step 2 : Time Discretization

4.4 Step 3 : Space Discretization

4.5 Step 4 : Linearization

4.6 Step 5 : Solution of the Linearization Equation

4.7 Step 6 : Termination of the Nonlinear Iteration Loop

Section 2 : Finite Difference Techniqu

- Language:
- English

- Copyright:
- © 1984

- Published:
- 1st February 1984

- Imprint:
- Elsevier Science

- Print ISBN:
- 9780444422910

- Electronic ISBN:
- 9780444598554

University of Wales, Aberystwyth, UK

@qu:Overall, the book is highly recommended and will be a necessity for anyone working in this field.
@source: Applied Mechanics Reviews
@qu:This is a good book, and in parts a very good book, largely because it is easy to read and understand and because it is a most felicitous blend of textbook and research monograph... If Elsevier can maintain the same standard for later volumes in the Rheology Series, of which this is the first, then they will do a singular service to modern scientific literature, in helping to make available to a wide readership some of the almost impenetrable specialist literature that has been produced in the last thirty years.
@source: Journal of Fluid Mechanics