Effects of geometric parameters and axial magnetic field on buoyant-thermocapillary convection during detached solidification

In order to understand the effect of geometric parameters and axial magnetic field on buoyant-thermocapillary convection during detached solidification, a series of three-dimensional numerical simulations were conducted by the finite-difference method. The results indicate that the stable flow is observed when the Marangoni number (Ma) is small; however, when the value of Ma increases and exceeds a threshold value, the stable steady flow transits to be unstable flow. As the height of the melt increases, the flow is enhanced at first and then gets weakened. As the width of gap decreases gradually, the strength of flow is enhanced. The approach of using axial magnetic field is an effective way to suppress the buoyant-thermocapillary convection. As the magnetic field strength increases, the inhibition is enhanced. The critical Marangoni number increases slightly with a greater melt height, a narrower width of gap, and a more strength of magnetic field.