The Library
Phase field modelling of alloy solidification
Tools
Stinner, Björn (2009) Phase field modelling of alloy solidification. In: Invited Speaker : Analysis Seminar, Department of Mathematics, University of Bristol, University of Bristol, 2 Oct 2009 (Unpublished)
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://www.maths.bris.ac.uk/events/seminars/series...
Abstract
Based on the principles of irreversible thermodynamics and on the phase field approach, a general framework for modelling alloy solidification has been developed. Balance equations for the internal energy and the concentrations of the components are coupled to evolution equations of Allen-Cahn type for phase field variables describing phases and phase boundaries. In the limit of vanishing interface thickness a corresponding free boundary problem is found. In particular, the calibration with respect to possibly anisotropic surface energies is an interisting problem in this context. The reduced grand canonical potential is an appropriate thermodynamic quantity to formulate the model in terms of the chemical potentials and the temperature as variables (instead of the conserved quantities energy and mass). Certain growth properties motivated from
thermodynamics make it difficult to show existence of weak solutions to the parabolic differential equations governing the evolution but immediately yield the correct range of certain thermodynamic quantities as, for example, positivity of the temperature. We conclude with a few simulations results of dendritic and eutectic growth.
Item Type: | Conference Item (Paper) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Official Date: | 2 October 2009 | ||||
Dates: |
|
||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | Invited Speaker : Analysis Seminar, Department of Mathematics, University of Bristol | ||||
Type of Event: | Other | ||||
Location of Event: | University of Bristol | ||||
Date(s) of Event: | 2 Oct 2009 |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |