Thermocapillary Convection Instability in Shallow Annular Pools by Linear Stability Analysis

摘要

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 Mac 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.