Inverse problem for the solidification of binary alloy in the casting mould solved by using the bee optimization algorithm

Abstract

of solidification in the temperature interval is based on the heat conduction equation with the included source element in which the latent heat of fusion and the volume contribution of solid phase are taken into account. Having the assumed form of function describing this contribution we can transform the equation into the heat conduction equation with the so called substitute thermal capacity. In this way, the considered differential equation defines the heat conduction in the entire homogeneous domain (in solid phase, in twophase zone (mushy zone) and in liquid phase) [1][2][3][4].Process of the alloy solidification is also affected by the process of segregation of the alloy components, for example, the change of concentration corresponds with the change of liquidus and solidus temperatures. Models, the most often used for describing the concentration, are these ones in which the immediate equalization of chemical composition of the alloy in the liquid phase and solid phase is assumed (the lever arm rule) [5][6][7][8] as well as the Scheil model [6,7,9,10].In this paper we consider a model in which the distribution of temperature is described by means of the heat conduction equation [2][3][4] with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependence on the concentration of the alloy component. Whereas for describing the concentration we apply the model based on the lever arm rule. And the discussed problem lies in determination of the heat transfer coefficient appearing in the third kind boundary condition defined on the boundary of solidifying alloy. Additionally, the reconstruction of temperature in the region of solidifying alloy should be also obtained. The sought elements will be calculated on the basis of temperature measurements read in selected point of the mould.Since the considered problem consists in reconstruction of some missing part of input information on the basis Abstract In this paper the procedure for solving the inverse problem for the binary alloy solidification in the casting mould is presented. Proposed approach is based on the mathematical model suitable for describing the investigated solidification process, the lever arm model describing the macrosegregation process, the finite element method for solving the direct problem and the artificial bee colony algorithm for minimizing the functional expressing the error of approximate solution. Goal of the discussed inverse problem is the reconstruction of heat transfer coefficient and distribution of temperature in investigated region on the basis of known measurements of temperature.

Inversion of Thermal Conductivity in Two-Dimensional Unsteady-State Heat Transfer System Based on Finite Difference Method and Artificial Bee Colony

“…The artificial bee colony algorithm (ABCA) is a kind of non-gradient-based optimization algorithm, which is more simple and flexible compared to other colony-based algorithms [33][34][35] and is mostly applied to the treatment of constrained optimization and integer programming, such as in issues of transportation, reaction-diffusion, and generalized assignment [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. E. Hetmaniok et al [38,39] solved the inversion of the heat transfer coefficient and studied the inverse problem of binary alloy solidification in a casting mold using ABCA. Few uses of ABCA for inverse thermal conductivity have been reported.…”

Boundary Shape Inversion of Two-Dimensional Steady-State Heat Transfer System Based on Finite Volume Method and Decentralized Fuzzy Adaptive PID Control

“…There are inverse heat conduction problems (IHCPs) that are well known to be ill posed. The IHCP has been successfully applied in many industrial and engineering fields [1][2][3][4][5][6][7][8][9][10][11].…”