Effect of Free Surface Heat Transfer on Oscillatory Thermocapillary Flow in Differentially Heated Cylindrical Annulus

Abstract

Oscillatory thermocapillary flow of high Pr silicon oil in a differentially heated cylindrical annulus is numerically investigated under micro gravity conditions. Heat loss and heat gain effects on thermocapillary flow with fixed flat free surface are computed. Beyond a certain imposed temperature difference (ΔTcr) between the hot and cold walls, the steady thermocapillary flow is observed to transition to an unsteady oscillatory state. Considerable variation in the critical temperature difference (ΔTcr), or critical Marangoni number (Macr) is observed in both heat loss and heat gain situations. The heat loss / gain conditions are imposed by variation of ambient temperature (TA), while keeping heat transfer coefficient (h) constant. Typically, critical temperature difference (ΔTcr) increases with decreasing heat loss and when ambient temperature (TA) is greater than the cold wall temperature (TH), heat gain starts at the liquid free surface in the low temperature region adjacent to the cold wall. It is observed that critical temperature difference increases with increasing heat gain. It is also reported that critical temperature difference with free surface heat loss at room temperature is not much different from the insulated free surface case. Generally, effect of significant heat gain at the free surface is stabilizing in nature. Velocity & temperature fields are also analyzed to get an insight into the mechanism of critical temperature difference (ΔTcr), or critical Marangoni number (Macr) variation under heat loss and heat gain conditions. The computed oscillatory flow exhibits similarity with micro-gravity experiments data available in literature for similar configuration.