Magnetic damping of axisymmetric, unsteady thermocapillary convection in floating zones in microgravity

This paper explores the time-dependent thermocapillary convection in an electrically-conducting liquid cylinder with a strong, uniform magnetic field applied parallel to the axis of the cylinder. The top and bottom boundaries are electrically insulating solids, while the remaining boundary is a cylindrical free surface surrounded by an inviscid, electrically-insulating atmosphere. There is a heat flux into the free surface which leads to a strong thermocapillary convection in the liquid. These conditions correspond to the growth of high-purity semiconductor crystals by the floating-zone process in space. One of our objectives was to investigate whether an axial magnetic field would change the nature of the instability, leading to the possibility of periodic, axisymmetric flows, and we found no evidence of such a change. While the 2D analysis was computationally demanding, a 3D one would be even more so, due to the thin boundary layers which occur in MHD flows. We illustrate how asymptotic simplifications to the governing equations for large values of Hartmann number are possible without loss of accuracy for certain magnetic field strengths. (Author)