A mathematical model for the dissolution of particles in multi - componentalloysFred

Dissolution of stoichiometric multi-component particles is an important process ocurring during the heat treatment of as-cast aluminium alloys prior to hot extrusion. A mathematical model is proposed to describe such a process. In this model equations are given to determine the position of the particle interface in time, using a number of diiusion equations which are coupled by nonlinear boundary conditions at the interface. This problem is known as a vector valued Stefan problem. Moreover the well-posedness of the moving boundary problem is investigated using the maximum principle for the parabolic partial diierential equation. Furthermore, for an unbounded domain and planar coordinates an analytical asymptotic approximation based on self-similarity is derived. Moreover, this self-similar solution and the asymptotic approximation are extended to the vector valued Stefan problem. The approaches are compared to each other and the asymptotic approximation is used to gain rapid insight into the innuence of all components on the dissolution. Subsequently a numerical treatment of the vector valued Stefan problem is described, analysed and compared to the analytical methods. Finally, an example is shown. Note: The paper will appear in 1998.