Thermocapillary flow arises under zero-gravity in a plane layer of liq
uid metal bounded by two plane fixed interfaces with a passive gas and
held by two differentially heated walls. On the interfaces the surfac
e tension depends quadratically, with a maximum, on the temperature (n
on-linear Marangoni flow). The fluid considered has a low Prandtl numb
er (Pr = 0.01) and is electrically conducting with a magnetic Prandtl
number negligible. The unsteady two-dimensional Navier-Stokes equation
s in the velocity-vorticity formulation are-salved by a Galerkin Finit
e Element semi-implicit method. For high conditional Reynolds numbers
Re the flow becomes oscillatory; by increasing further the Re the flow
reaches a new steady state. To drag the oscillations a uniform and st
eady magnetic field is applied normal to the plane of the bridge. Crit
ical Reynolds numbers are calculated for an aspect ratio A = 4 for var
ious values of the magnetic held. (C) 1998 Elsevier Science Ltd. All r
ights reserved.