Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Introduction
- 0 Mathematical Preliminaries
- 1 Fluid-Mechanical Modelling of the Scroll Compressor
- 2 Determining the Viscosity of a Carbon Paste Used in Smelting
- 3 The Vibrating Element Densitometer
- 4 Acoustic Emission from Damaged FRP-Hoop-Wrapped Cylinders
- 5 Modelling the Cooking of a Single Cereal Grain
- 6 Epidemic Waves in Animal Populations: A Case Study
- 7 Dynamics of Automotive Catalytic Converters
- 8 Analysis of an Endothermic Reaction in a Packed Column
- 9 Simulation of the Temperature Behaviour of Hot Glass during Cooling
- 10 Water Equilibration in Vapor-Diffusion Crystal Growth
- 11 Modelling of Quasi-Static and Dynamic Load Responses of Filled Viscoelastic Materials
- 12 A Gasdynamic–Acoustic Model of a Bird Scare Gun
- 13 Paper Tension Variations in a Printing Press
- Index
2 - Determining the Viscosity of a Carbon Paste Used in Smelting
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Contributors
- Preface
- Introduction
- 0 Mathematical Preliminaries
- 1 Fluid-Mechanical Modelling of the Scroll Compressor
- 2 Determining the Viscosity of a Carbon Paste Used in Smelting
- 3 The Vibrating Element Densitometer
- 4 Acoustic Emission from Damaged FRP-Hoop-Wrapped Cylinders
- 5 Modelling the Cooking of a Single Cereal Grain
- 6 Epidemic Waves in Animal Populations: A Case Study
- 7 Dynamics of Automotive Catalytic Converters
- 8 Analysis of an Endothermic Reaction in a Packed Column
- 9 Simulation of the Temperature Behaviour of Hot Glass during Cooling
- 10 Water Equilibration in Vapor-Diffusion Crystal Growth
- 11 Modelling of Quasi-Static and Dynamic Load Responses of Filled Viscoelastic Materials
- 12 A Gasdynamic–Acoustic Model of a Bird Scare Gun
- 13 Paper Tension Variations in a Printing Press
- Index
Summary
Preface
In the following case study, the slow viscous flow of blocks of “carbon paste” is analysed. The paste blocks are essential components of an electric smelting process by which a variety of ferro-alloys and other substances are produced. The problem is first proposed in its most general form. A nondimensionalisation using typical parameter values of the process then shows that a much simpler set of equations may be used to analyse the flow. After examining the qualitative details of the fluid motion in various key regions of the flow, an asymptotic analysis of a long thin block of paste allows us to develop a good general understanding of the main principles of slow viscous flow in paste blocks. The theory highlights the key differences between various tests that are used to determine the viscosity of carbon paste. Finally, some fairly straightforward numerical analysis is used to show that the general problem is amenable to simple methods; the numerical results also show that in many cases the “long thin” analysis used earlier can produce remarkably accurate results.
The work outlined below is part of research that was produced during and after the 1988 European Study Group with Industry, which was held at the University of Heriot-Watt, Scotland. Some extensions to the work presented here are suggested as projects for the interested student in section 2.6. Close links have continued to be maintained between industrial mathematicians and the ELKEM ASA, the Norwegian company that originally proposed the problem. A number of other problems (see [1], [4], and [3]) concerning various aspects of the electric smelting industry have also been considered in detail and have led to some interesting mathematical problems.
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- Chapter
- Information
- Mathematical ModelingCase Studies from Industry, pp. 46 - 65Publisher: Cambridge University PressPrint publication year: 2001