Effect of the electric conductivity and Seebeck coefficient of the rods on the oscillatory Marangoni convection in the presence of a uniform axial magnetic field

Abstract

Effect of electric conductivity of the supporting rods on Marangoni convection of low-Prandtl-number fluid under the influence of axial magnetic field has been numerically studied. An end of the supporting rod is heated and an opposing end of the rod is cooled both isothermally while the surface of cylindrical liquid bridge is supposed to be adiabatic. An axial magnetic field is applied to this configuration to investigate the influence of such magnetic effect on the liquid metal Marangoni convection. In addition, the Seebeck coefficients in both the liquid and the rod region are taken into consideration. In the numerical analyses, the Joule heating and the induced magnetic field are neglected. The governing equations of mass conservation, momentum, energy, Ohm's law and conservation of electric charge for a cylindrical coordinate system have been numerically solved with a finite difference method using the SMAC algorithm. The numerical results reveal that the conductivity of the rods affects the azimuthal disturbance and tends to prevent transition effectively under the magnetic field. This trend is found especially for the transition to the 1T+R-type oscillation mode. In addition to the conductivity of rods, when the Seebeck effect is taken into account, azimuthal flow is induced and 2T+R type rotating oscillatory mode, which cannot be observed in the Marangoni flow without magnetic effect, takes place.