## Application of the immune algorithm IRM for solving the inverse problem of metal alloy solidification including the shrinkage phenomenon

**Adam Zielonka, Edyta Hetmaniok, Damian Słota**

Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland.

**DOI:**

https://doi.org/10.7494/cmms.2018.1.0608

**Abstract:**

In the paper the mathematical model of the inverse one-dimensional problem of binary alloy solidification, with the material shrinkage phenomenon taken into account, is defined. The process is described by using the model of solidification in the temperature interval, whereas the shrinkage of material is modeled basing on the mass balance equation. The inverse problem consists in reconstruction of the heat transfer coefficient on the boundary of the casting mould separating the cast from the environment. Lack of this data is compensated by the measurements of temperature in the control point located inside the mould. The method of solving the investigated problem is based on two procedures: the implicit scheme of finite difference method supplemented by the procedure of correcting the field of temperature in the vicinity of liquidus and solidus curves and the immune optimization algorithm IRM.

**Cite as:**

Zielonka, A., Hetmaniok, E., Słota, D. (2018). Application of the immune algorithm IRM for solving the inverse problem of metal alloy solidification including the shrinkage phenomenon.

Computer Methods in Materials Science, 18(1), 1 – 10. https://doi.org/10.7494/cmms.2018.1.0608

**Article (PDF):**

**Keywords:**

Solidification, Binary Alloy, Material shrinkage, Immune algorithm

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