Dimensionless numbers for tundish modelling and the Guthrie number (Gu)

Abstract

Modelling the transport phenomena in tundishes has been a vast area of research for the last three decades. Many papers have been published and are available in the literature on this subject. The basics of modelling involve a similarity criterion between the model and the full scale prototype and are well documented in major textbooks. However, the similarity criteria are different for different cases. For example, for fluid flow in a tundish, the Re and Fr similarity is considered, whereas for heat transfer, the Pr and Pe number similarity should be considered. Numerous other examples can be cited. It is really important to know which similarity criteria should be used for a particular case. In this paper, a new dimensionless number Gu has been proposed when dealing with the modelling of inclusions separating out in a tundish. All dimensionless numbers can be represented as a ratio of two characteristic time scales, and this fact is highlighted in the present paper.