Computational investigation of magnetohydrodynamic convective flow in a trapezoidal cavity with multiple obstacles via finite element analysis

The present research deals with magnetohydrodynamic (MHD) natural convection within a trapezoidal cavity under the influence of inner solid obstacles of different shapes. The cavity includes two horizontal plates and two heated circular cylinders and is subjected to a uniform horizontal magnetic field. The walls of the domain can either be heated or cooled isothermally. The finite element method is used to solve the Oberbeck-Boussinesq equations that govern the fluid flow and heat transfer process. Three different thermal conditions are considered for the horizontal plates: isothermal heating, isothermal cooling, and adiabatic. The investigation explores the impact of varying Rayleigh numbers (Ra = 104-106), Hartmann numbers (Ha = 0-100), and thermal boundary conditions for inner horizontal plates on the flow patterns and heat transfer efficiency. The results indicate that as the Rayleigh number rises and the magnetic field strength diminishes, a noticeable improvement in heat transfer is observed, particularly in cases where the horizontal plates are subjected to cooling. Conversely, the heated inner horizontal plates exhibit less effective energy transport across the considered three configurations. It should be noted that the heat transfer rate for Ra = 106 can be increased more than 5 % when cooled ones will replace the heated inner plates. Whilst a transition between the adiabatic inner plates to cooled ones allows improving the average Nusselt number at the bottom heated wall at about 3 %. Moreover, the convective flow intensity can be described using the kinetic energy, where a growth of the magnetic field strength from 0 till 100 for Ra = 105 decreases the total kinetic energy at 76 times for heated plates, at 100 times for cooled plates and at 92 times for adiabatic plates.