Y. Kamotani et S. Ostrach, THEORETICAL-ANALYSIS OF THERMOCAPILLARY FLOW IN CYLINDRICAL COLUMNS OF HIGH PRANDTL NUMBER FLUIDS, Journal of heat transfer, 120(3), 1998, pp. 758-764
Steady and oscillatory thermocapillary flows of high Prandtl number fl
uids in the half-zone configuration are analyzed theoretically Scaling
analysis is performed to determine the velocity and length scales of
the basic steady flow. The predicted scaling laws agree well with the
numerically computed results. The physical mechanism of oscillations i
s then discussed. It is shown that the deformation of free surface pla
ys an important role for the onset of oscillations in that it alters t
he main thermocapillary driving force of the flow by changing the temp
erature field near the hot-corner region. This phenomenon triggers osc
illation cycles in which the surface flow undergoes active and slow pe
riods. Based on that concept a surface deformation parameter is derive
d by scaling analysis. The deformation parameter correlates available
data for the onset of oscillations well.