XGBoost-Based and Finite Element Analysis of Internal Heat Generation in 3D Magnetohydrodynamic Convection with Symmetrical Ellipsoidal Orientation

This study investigates three-dimensional magnetohydrodynamic convection in a cubic cavity with a symmetrical ellipsoidal obstacle in two different scenarios, under the combined effect of internal heat source and magnetic field strength. The significance of this research is based on understanding the interlinking of geometric orientation, buoyancy, and magnetic damping on the dynamics of the flow and thermal transfer phenomena. The approach taken is based on finite element simulations using COMSOL Multiphysics (version 6.3), coupled with a surrogate model of XGBoost to predict the Nusselt numbers for each of the configurations. The results show that the increase of the heat source parameter promotes the circulation driven by buoyancy and heat transport, while the increase of the Hartmann number suppresses fluid motion by the Lorentz force, leading to the reduction of heat transport. The orientation of the symmetrical ellipsoid has a major influence on the asymmetry of the flow and the properties of mixing. The extraordinary agreement between the numerical results and the predicted results is a validation of the accuracy of the proposed analytical framework. These insights have important implications for practical applications in energy systems, electronic cooling, and magnetically controlled heat processes.