Thermocapillary Convection Instability in Shallow Annular Pools by Linear Stability Analysis

The thermocapillary convection instability in shallow annular pools with Prandtl numbers ( Pr ) from 0.011 to 57.9, differentially heated at the outer wall and cooled at the inner wall, is investigated numerically. The critical Marangoni numbers ( Ma c ), critical azimuthal wave numbers ( m c ) and critical phase velocities ( ω c ) for the incipience of oscillatory flow are determined by linear stability analysis. The results indicate that the Ma c increases steeply with increase of Pr number when Pr ≤15.9, while it increases slightly with increase of Pr between Pr =23.9 and 57.9. The m c and ω c decrease with increase of Pr number.