The article shows the usage of swarming algorithms for reconstructing the heat transfer coefficient regarding the continuity boundary condition. Numerical calculations were performed using the authors’ own application software with classical forms of swarm algorithms implemented. A functional determining error of the approximate solution was used during the numerical calculations. It was minimized using the artificial bee colony algorithm (ABC) and ant colony optimization algorithm (ACO). The considered in paper geometry comprised a square (the cast) in a square (the casting mold) separated by a heat-conducting layer with the coefficient $$\kappa $$κ . Due to the symmetry of that geometry, for calculations, only a quarter of the cast-mold system was considered. A Robin’s boundary condition was assumed outside the casting mold. Both regions’ inside boundaries were insulated, but between the regions, a continuity boundary condition with nonideal contact was assumed. The coefficient of the thermally conductive layer was restored using the swarm algorithms in the interval $$900{-}1500 \; [\mathrm{W/m}^{2}\textrm{K} $$900 - 1500 [ W / m 2 K ] and compared with a reference value. Calculations were carried out using two finite element meshes, one with 111 nodes and the other with 576 nodes. Simulations were conducted using 15, 17, and 20 individuals in a population with 2 and 6 iterations, respectively. In addition, each scenario also considered disturbances at 0 $$\%$$% , 1 $$\%$$% , 2 $$\%$$% , and 5 $$\%$$% of the reference values. The tables and figures present the reconstructed value of the $$\kappa $$κ coefficient for ABC and ACO algorithms, respectively. The results show high satisfaction and close agreement with the predicted values of the $$\kappa $$κ coefficient. The numerical experiment results indicate significant potential for using artificial intelligence algorithms in the context of optimization production processes, analyze data, and make data-driven decisions.

The article presents the use of swarming algorithms in selecting the heat transfer coefficient, taking into account the boundary condition of the IV types. Numerical calculations were made using the proprietary TalyFEM program and classic form of swarming algorithms. A function was also used for the calculations, which, during the calculation, determined the error of the approximate solution and was minimalised using a pair of individually employed algorithms, namely artificial bee colony (ABC) and ant colony optimisation (ACO). The tests were carried out to select the heat transfer coefficient from one range. Describing the geometry for a mesh of 408 fine elements with 214 nodes, the research carried out presents two squares (one on top of the other) separated by a heat transfer layer with a κ coefficient. A type III boundary condition was established on the right and left of both edges. The upper and lower edges were isolated, and a type IV boundary condition with imperfect contact was established between the squares. Calculations were made for ABC and ACO, respectively, for populations equal to 20, 40 and 60 individuals and 2, 6 and 12 iterations. In addition, in each case, 0%, 1%, 2% and 5% noise of the reference values were also considered. The obtained results are satisfactory and very close to the reference values of the κ parameter. The obtained results demonstrate the possibility of using artificial intelligence (AI) algorithms to reconstruct the IV type boundary condition value during heat conduction modelling.

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Cz?stochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

The research shows how to use swarming algorithms to rebuild the heat transfer coefficient, especially in regard to the continuous border condition. The authors utilized their application software to do numerical computations, employing classical variants of swarm algorithms. The numerical...