NON-PHYSICAL ENTHALPY METHOD FOR PHASE CHANGE MODELLING IN THE SOLIDIFICATION PROCESS

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Abstract

This research is concerned with the development of a mathematical approach for energy and mass transport in solidification modelling involving a control volume (CV) technique and finite element method (FEM) and incorporating non-physical variables in its solution. The former technique is used to determine an equivalent capacitance to describe energy transport whilst the latter technique provides temperatures over the material domain.The numerical solution of the transport equations is achieved by the introduction of two concepts, i.e. weighted transport equations and non-physical variables. The main aim is to establish equivalent transport equations that allow exact temporal integration and describe the behaviour of non-physical variables to replace the original governing transport equations.The variables defined are non-physical in the sense that they are dependent on the velocity of the moving CV. This dependence is a consequence of constructing transport equations that do not include flux integrals. The form of the transport equations facilitate the construction of a FEM formulation that is applicable to heat and mass transport problems and caters for singularities arising from phase-change, which can prove difficult to model. However, applying the non-physical enthalpy method (NEM) any singularity involved in the solidification process is precisely identified and annihilated

Keyword(s)

Non-physical, Transport equations, heat transfer, finite elements; solidification

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