Multi-objective optimization of natural convection in a cylindrical annulus mold under magnetic field using particle swarm algorithm

In the continuous casting process, natural convection occurs in mold containing a liquid metal. Natural convection in the melt causes the impurities to move and this phenomenon can lead to poor product. Therefore, by reducing natural convection, the quality of the product is improved. In this paper, 3D numerical simulation and multi-objective optimization of natural convection in a cylindrical annulus mold filled with molten potassium under a magnetic field is carried out. The inner and outer cylinders are maintained at uniform temperatures and other walls are thermally insulated. Two objective functions including the natural convection heat transfer rate (average Nusselt number) and magnetic field strength have been considered simultaneously. The multi-objective particle swarm optimization algorithm (MOPSO) has been employed. Four decision variables are the Hartmann number, inclination angle, and magnetic field angles. For the optimization process, the calculations of three-dimensional Navier–Stokes, energy, and electrical potential equations are combined with MOPSO. Using the numerically evaluated objective functions, the optimum frontier is estimated by a second order polynomial based on objective functions.