Principles and applications of mathematical and physical modelling of metallurgical processes

This article reviews the principles and methods for formulating mathematical or physical models that are useful in the design, analysis and optimization of metallurgical processes. Mathematical models based on first principles are emphasised. Examples of developing new processes based on a first-principle mathematical model or a physical model are presented. Cautions and pitfalls associated with the formulation and application of mathematical models are discussed. The reader is encouraged to carefully examine correctness of the approach and assumptions made in the formulation in order to avoid an erroneous application of a model. For complex processes requiring harsh conditions, physical models are useful. The interpretation and utilisation of the results from physical models can be difficult and sometimes even misleading. This problem is greatly assuaged by combining physical modelling with mathematical modelling. For example, the use of computational fluid dynamics greatly improves the physical modelling of systems involving complex fluid flow.