Substitute thermal capacity of binary alloys : review of hypotheses

In the paper the problems connected with the mathematical modeling of alloys solidification (macro scale) are presented. The similar lecture was delivered by the authors during the IV Conference on Mathematical Modelling in Physics and Technique, Kleszczów, 28-30 June 2012. In particular the one domain method (fixed domain approach) in which the parameter called 'a substitute thermal capacity' appears will be discussed. The one domain method bases on the Fourier equation describing the thermal processes in the whole conventionally homogeneous casting domain. The substitute thermal capacity (STC) can be defined in the different ways. The first group of definitions results from the differentiation of the function determining the local volumetric solid state fraction in the neighborhood of the point considered, while the second one is based on the direct assumption of the STC form, at the same time this function should fulfill the condition resulting from the change of alloy physical enthalpy during the phase change. The details of these approaches will be presented in the Sections 2 and 3.