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Stefan and Kolmogoroff models of solidification. Comparison of numerical solutions

Szopa R., Pawlak E., Siedlecki J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

185-192

Problems connected with the mathematical description of pure metals solidification (macro approach) are often called the Stefan ones. The second generation models (micro/ macro approach) discussed in this paper base on a theory presented by Kolmogoroff (Mehl-Johnson-Avrami-Kolmogoroff models). Both macro and micro/macro problems can be analyzed using the numerical methods. The aim of investigations presented here was a comparison of numerical solutions obtained by use of macro and micro/macro approach. On a stage of numerical modelling the finite difference method has been applied.

The linear, exponential and generalized models of pure metals solidification process. Part 1

Mochnacki B., Szopa R., Pawlak E.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

2007

Vol. 321, z. 89

61-62

In this paper the considerations concerning the mathematical micro/macro model of pure metals solidification is presented. In particular the mutual connections between the well known linear and exponential models are discussed. The possibility of the basic models generalization is also discussed.

The linear, exponential and generalized models of pure metals solidification process. Part 2

Mochnacki B., Szopa R., Lara S.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

2007

Vol. 321, z. 89

63-64

The mathematical model of pure metals solidification being a generalization of well known linear and exponential models is discussed. The examples of numerical results obtained on the basis of model proposed are also shown.

Distribution of internal heat sources in solidifying metal according to mould parameters

Szopa R., Siedlecki J., Wojciechowska W.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

2007

Vol. 321, z. 89

65-66

The mathematical micro/macro model of pure metal solidification is considered. On the basis of direct sensitivity analysis method the mutual connections between the function controlling the course of solidification (source function) and thermophysical parameters of mould are analyzed. In the final part of paper the example of numerical computations is shown.