Effect of Heat Dissipation on Thermocapillary Convection of Low Prandtl Number Fluid in the Annular Pool Heated from Inner Cylinder

Abstract

This paper presents a series of numerical simulations on the effect of heat dissipation on the thermocapillary convection of a low Prandtl number (Pr = 0.011) fluid in an annular pool heated from its inner cylinder. The radius ratio and the aspect ratio of the annular pool set as η = 0.5 and e = 0.1, respectively. The results show that with the increase of Biot number, the isotherms of the two-dimensional basic flow are seriously compressed near the hot inner cylinder and the thermocapillary flow pattern will be impaired. With the increase of Marangoni number, the thermocapillary convection first evolves from the basic flow to a three-dimensional stationary flow with longitudinal stationary stripes on the free surface, and then to a three-dimensional oscillatory flow featured with the combination of stationary stripes and azimuthal waves, which is caused by the mutual effect of the radial convection, azimuthal local flow and heat dissipation. After the flow destabilization, the amplitude of temperature fluctuation increases and the wave number decreases with the increase of Marangoni number when the free surface is adiabatic. Furthermore, the temperature fluctuation pattern is changed due to the surface heat dissipation. In addition, with the increase of Biot number, the wave number almost keeps constant when Marangoni number is small, but it increases significantly at a large Marangoni number.