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 ε = 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.

中文翻译：

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散热对内缸加热环形池中低普朗特数流体的热毛细管对流的影响

本文介绍了一系列数值模拟，这些数值模拟 了内缸加热的环形池中低普朗特数（Pr = 0.011）的流体对热毛细管对流的影响。环形池的半径比和纵横比分别设置为η  = 0.5和ε 分别为0.1。结果表明，随着Biot数的增加，二维基本流的等温线在热内缸附近被严重压缩，热毛细管流型将受到损害。随着Marangoni数的增加，热毛细管对流首先从基本流演化为在自由表面上具有纵向固定条纹的三维固定流，然后发展为具有固定条纹和方位角组合的三维振荡流。径向对流，方位角局部流和热耗散的相互影响引起的波浪。流动失稳后，当自由表面绝热时，温度波动幅度随Marangoni数的增加而增大，波数减小。此外，温度波动模式由于表面散热而改变。另外，随着毕奥数的增加，当Marangoni数小时，波数几乎保持恒定，而当Marangoni数大时，波数显着增加。