Reconstruction of the Boundary Condition in the Binary Alloy Solidification Problem with the Macrosegregation and the Material Shrinkage Phenomena Taken into Account

Abstract

In this paper we solve the inverse problem of the binary alloy solidification including two phenomena: macrosegregation and creation of the air gap between the cast and the mold in result of the metal shrinkage during the solidification. Aim of inverse problem is to reconstruct the heat transfer coefficient on the external boundary of the mold separating the cast from the environment, by using the measurements of temperature taken from the sensor located in the middle of the mold. The solidification process is described by using the model of solidification in the temperature interval, the shrinkage of metal is modeled basing on the mass balance equation and the macrosegregation process is approximated with the aid of two models: the Scheil model and the lever arm model - the results received from those two approaches are then compared. For retrieving the sought coefficient, we minimize the proper functional by using the Artificial Bee Colony algorithm.

Additional information

Funding

Publication supported within the framework of grants in the area of scientific research and developmental works founded by Rector of the Silesian University of Technology, 09/010/RGJ17/0019 and 09/010/RGJ17/0020.

Notes on contributors

Adam Zielonka

Adam Zielonka is an adjunct employed in the Institute of Mathematics at the Silesian University of Technology, Gliwice, Poland. He received his master degree in Mathematics and PhD in Technical Science, in the area of Mechanical Engineering. He is currently working on numerical methods, particularly, in solving the heat conduction problems by applying the swarm intelligence algorithms and by using the wavelets theory.

Edyta Hetmaniok

Edyta Hetmaniok is an adjunct employed in the Institute of Mathematics at the Silesian University of Technology, Gliwice, Poland. She received her master degree in Mathematics, PhD in Physics and MSc in Mechanics. She is currently working on theoretical and applied mathematics, particularly, in applications of artificial intelligence algorithms in solving the heat conduction problems.

Damian Słota

Damian Słota is a professor employed in the Institute of Mathematics at the Silesian University of Technology, Gliwice, Poland. He graduated with master diploma in the discipline of Applied Mathematics, he received his PhD in Technical Science, in the area of Mechanical Engineering, and MSc in Mechanics. He is currently working on applied mathematics, particularly, in numerical methods used for solving the direct and inverse heat conduction problems, he is also dealing with the elements of number theory and some related problems.