An artificial immune system algorithm applied to the solution of an inverse problem in unsteady inward solidification

Abstract The numerical simulation and optimization in solidification involving geometries beyond one dimension normally requires expensive computational approaches in memory and data processing, generating consequently high cost associated with runtime execution. When boundary conditions are unknown, such as how heat is extracted from the casting surface, which is a typical inverse heat transfer problem (IHTP), the search for such conditions by trial-and-error makes the whole process less feasible. In this sense, this work introduces the application of an artificial immune system (AIS) algorithm as a possible meta-heuristic alternative, with a view to returning acceptable objective values to converge on a set of acceptable solutions. In the present work, the search process of the heat transfer coefficient ( h g ) at the casting surface during two-dimensional inward solidification of Al-1.5 wt.%Fe alloy castings of Cartesian and Cylindrical geometries in chilled molds is optimized. Two water-cooled solidification apparatuses were designed to in situ melt the alloy by a set of electrical resistances, in which heat is extracted only through the chilled faces of the molds. The thermal history during solidification was obtained via thermocouples placed at different positions in the castings. A Finite Difference heat transfer model integrated to an optimized version of the artificial immune network algorithm, which uses the experimental thermal profiles as inputs, has been applied to solve the IHTP through the search for acceptable values of heat transfer coefficient. It is shown that fast convergence of the developed algorithm can be achieved for a relatively small number of iterations. The mean relative errors associated with differences between simulated and experimental temperatures are shown to be 1% and 0.07% for Cartesian and Cylindrical geometries, respectively and expressions relating h g to time have been determined for both geometries.