Effects of Pr and pool curvature on thermocapillary flow instabilities in annular pool

•Detailed linear stability analysis of thermocapillary flow in annular pools.•First report on the effects of pool curvature on the stability of thermocapillary flow.•First report on the effect of the Prandtl number over a wide range from 0 to 100.•Instabilities in low Prandtl number fluids are hydrodynamic in nature.•Hydrothermal waves are dominant only for Prandtl number larger than 0.02.