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.

This paper investigates axial unsteady flows of nanofluid filling a vertical rectangular channel with a mobile wall with time-dependent velocity. The nanofluid is Boussinesquian and the flow is induced by time-dependent pressure gradient, the buoyancy and Lorentz forces. The magnetic field is applied uniformly and oriented normal to the fluid velocity. The channel walls are maintained at different, constant temperatures. The induced magnetic field included in the analysis as well. For the nanofluid, Buongiorno’s model is employed. The differential equations with partial derivatives that determine the fields of velocity, temperature, volume fraction of nanoparticles and the induced magnetic field are transformed into dimensionless form together with the initial and boundary conditions. A numerical scheme based on the Crank-Nicolson approximation formulas is formulated; the proposed scheme determines the values of the unknown functions at the discretization points by solving some three-diagonal systems of linear algebraic equations. The associate electric field is also determined. The solutions of concrete problems characterized by particular forms of the functions that give the velocity of the wall movement and the pressure gradient are studied and interpreted with the help of numerical values and graphic illustrations.