This work is concerned with the problem of the transient behaviours of the
axisymmetric thermocapillary laminar flow occurring inside a half zone subj
ected to a variable thermal boundary condition during a heating process. Th
e molten liquid with its deformable free surface is considered incompressib
le with constant Physical properties except for its density in buoyancy for
ces where Boussinesq's approximation has been applied The system of governi
ng equations has been successfully solved by using the modified-SIMPLE meth
od, while the instantaneous position of the free surface was determined by
employing a special procedure. Numerical simulations have been carried out
for both NaNO3 and Silicon float zones operating under 1-g and mu-g conditi
ons. The transient behaviours as well as the influence of the Marangoni num
ber and the aspect ratio have been investigated.