Thermovibrational convection in an enclosure with magnetic field damping

The problem of natural convection with magnetic field effect on laminar flow in a two-dimensional square enclosure subject to a vertical mechanical vibration has been studied numerically by using the time marching method. The study is carried out according to a Rayleigh number of 10(4) and a vibration Grashof number at 10(6) with different values of the Hartmann number and frequency of vibration. The magnetic field application at a certain value of vibration frequency has a damping effect of vibration oscillation on thermo-vibrational convection. The nonuniform oscillation behavior of the Nusselt number at a high value of vibration frequency was abatable by a magnetic field application and a uniform oscillation generation. The amplitude of the Nusselt number oscillation decreases with an increase in a magnetic field strength. This result means that the Nusselt number value decreases while the magnetic field strength increases. The average Nusselt number at a low value of vibration frequency increases when a moderate magnetic field is applied, but decreases under a stronger magnetic field.