Thermocapillary convection of moderate Prandtl number fluid in a shallow annular pool heated from inner cylinder with surface heat dissipation

Abstract

This paper presents a series of three-dimensional numerical simulations on thermocapillary convection of moderate Prandtl number (Pr = 6.7) fluid in a shallow annular pool heated from the inner cylinder with surface heat dissipation. The aspect ratio and radius ratio of the annular pool are respectively fixed at ε = 0.05 and η = 0.5. Biot number varies from 0 to 40 and Marangoni number varies from 0.1 × 105 to 6.0 × 105. Results show that there is a large temperature drop near the heated cylinder and the flow becomes more intense than those when the outer cylinder is heated at adiabatic free surface. With the increase of Marangoni number, the flow will transit from the axisymmetric steady flow to the three-dimensional oscillatory flow. The critical Marangoni number decreases first, and then increases with the increase of Biot number. After the flow destabilization, thermocapillary convection with adiabatic free surface exhibits the multicellular wave pattern when the inner cylinder is heated, which is different from that when the outer cylinder is heated. The temperature fluctuation pattern depends on the coupling effect of thermocapillary convection and heat exchange on the free surface. The wave number increases first, and then decreases with the increase of Marangoni number at a fixed Biot number. Furthermore, as Marangoni number increases, the temperature fluctuation on the free surface will radially extend from the inner cylinder to the outer cylinder gradually, and the amplitude of temperature fluctuation increases obviously.