This paper concerns a numerical study of the flow characteristics of thermocapillary convection in a system composed of two immiscible liquid layers subject to a temperature gradient along their interface. We consider the two-layer system : B2O3 (encapsulant) and GaAs (melt), for its experimental relevance in crystal growth by the directional solidification method; Two cases have been studied : a system with only one liquid interface (melt/encapsulant) and a system where the outer surface of encapsulant is open to air (and so, subject to a second thermocapillary force). Both the liquid-liquid interface and the outer surface are assumed to be undeformable and flat, which is a valid assumption according to earlier theoretical and experimental results. A 2-D numerical simulation of convection is carried out in a rectangular cavity by solving the system of Navier-Stokes equations using a finite difference method with a staggered grid for the pressure. Having in perspective a Spacelab experimentation we disregarded gravity (g = 0). We show that a strong damping of the melt flow can be obtained by using an encapsulant liquid layer having appropriate viscosity, heat conductivity and/or thickness.