A Mathematical Model of Macrosegregation Formation in Binary Alloy Solidification

doi:https://doi.org/10.1007/978-1-4612-1984-2_7

Book Chapter10.1007/978-1-4612-1984-2_7

A Mathematical Model of Macrosegregation Formation in Binary Alloy Solidification

Einar Haug,Torgeir Rusten,Håvard J. Thevik-1997-01-01-Birkhäuser Boston eBooks

4

TL;DRAbstract

The purpose of this chapter is to introduce a mathematical model of binary alloy solidification. A binary alloy solidifies over a temperature range, giving rise to a mushy zone in which liquid and solid coexist. The modelling of the liquid and solid zones are straightforward using well known continuum mechanical models. In order to model the mushy zone volume averaging techniques are applied. The volume averaged liquid and solid equations are combined to give a mixture formulation of the differential equations. In addition, suitable constitutive relations are introduced to give a closed model.

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The purpose of this chapter is to introduce a mathematical model of binary alloy solidification. A binary alloy solidifies over a temperature range, giving rise to a mushy zone in which liquid and solid coexist. The modelling of the liquid and solid zones are straightforward using well known continuum mechanical models. In order to model the mushy zone volume averaging techniques are applied. The volume averaged liquid and solid equations are combined to give a mixture formulation of the differential equations. In addition, suitable constitutive relations are introduced to give a closed model.

Keywords

Binary alloyBinary numberAlloyMaterials scienceThermodynamicsVolume (thermodynamics)MechanicsConstitutive equation

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