In this study, thermocapillary convection in a two-dimensional rectangular cavity with an upper, deformable free surface has been studied numerically. A wide range of values of the Marangoni number, Ma, is considered for the low Prandtl number fluid (Pr = 0.01) with the aspect ratio (A = height/length) fixed to be 0.5. The present computational results show that the thermocapillary flow may undergo an oscillatory motion when the Marangoni number is larger than a certain critical value, with a frequency of oscillation. If the Marangoni number is less than this critical value, the steady thermocapillary convection is obtained. The critical Marangoni number for the appearance of the oscillatory flow increases as the capillary number decreases and the Biot number increases.
