A series of numerical computations is used to study both the amount of power required to form a molten zone and the fluid flow inside the melt. The Navier-Stokes equations and energy equation are solved by a finite difference method, employing a boundary-fitted curvilinear coordinate system. The influences considered include: the magnitude of the input power, the width of the heated region, the fluid properties in the melt, and the heat-transfer condition of the ambient on the solid-melt interface. The present results show that the height of the molten zone increases significantly as the strength of the thermocapillary convection increases. For small Prandtl number fluids, when the input power increases, thermocapillary-flow instability in the melt may appear before the capillary instability (originating from the gas-melt interface) sets in. For higher Prandtl number fluids, the appearance of the capillary instability is more likely than thermocapillary-flow instability. The appearance of thermocapillary-flow instability may be also influenced by the ratio of the surface tension to the viscous force in the melt, the width of the heated region, and the heat loss to the ambient.
