Alumina hydrate produced by the Bayer-Hall-Heroult process is calcined at ~1100°C in either a rotary kiln, or a stationary vertical flash or fluid bed calciner. The latter calcination process is more thermally efficient than the rotary kiln, but the difficult nature of the process environment (pressurised, high temperature combustion in an abrasive dust laden atmosphere) makes any investigation of the furnace operation very difficult. This paper describes how physical and mathematical models have been developed to enable operators and designers to understand the process dynamics. A number of modelling techniques are used to fully simulate the system, including physical modelling of the aerodynamics and mixing, zero and one dimensional heat transfer models, and CFD models of the two-phase material flows. These models have been validated against unique plant measurements using special probe techniques. The resulting models have been used to improve existing designs, and to develop a new generation of larger, more efficient flash calcination units.