TY - JOUR
N2 - In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidification rate ¶ fS/¶ t (fS Î [0, 1], is a temporary and local volumetric fraction of solid state). The value of fS can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fS can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.
L1 - http://journals.pan.pl/Content/111185/PDF-MASTER/(55-1)107.pdf
L2 - http://journals.pan.pl/Content/111185
PY - 2007
IS - No 1
EP - 113
KW - micro/macro model of solidification
KW - inverse problems
KW - boundary element method
KW - numerical modelling
A1 - Mochnacki, B.
A1 - Majchrzak, E.
VL - vol. 55
DA - 2007
T1 - Identification of macro and micro parameters in solidification model
SP - 107
UR - http://journals.pan.pl/dlibra/publication/edition/111185
T2 - Bulletin of the Polish Academy of Sciences Technical Sciences
ER -