Thermocapillary convection in shallow liquid layers for moderate Prandtl number liquids using different cylinder configurations

Abstract

In this paper, the influence of thermocapillary convection in a shallow annular pool using different cylinder configurations is numerically investigated. An axisymmetric, two-dimensional, cylindrical geometry with two concentric cylinders kept at two different temperatures constitutes the model. The main cylinder has a radius of 40 mm and the secondary cylinder has a radius of 20 mm. The effects of Prandtl numbers (Pr = 6.7, 16.1, and 25.2) and layer depths (d = 3.0 mm and 11.0 mm) on the streamlines, isotherms, velocity, and temperature profiles at various locations of the flow are investigated. Depending on the position of the secondary cylinder, three different configurations: 1) an internal cylinder 2) an external cylinder, and a 3) central cylinder is analysed. The flow is characterized by a rapid inward flow along the hot outer wall towards the colder inner wall. In deeper pool at lower Prandtl numbers, flow patterns are characterized by a single rolling cell structure. Conversely, secondary cell formations appear in shallow pool regardless of the Prandtl number. Based on the comparative analysis of various cylinder configurations, it is clear that the external cylinder generates greater velocities and temperatures along its surface. The maximum disparity in surface velocity between an external cylinder and other configurations is 7%, 12%, and 13% for Prandtl numbers of 6.7, 16.1, and 25.2 respectively. Therefore, positioning the cylinder externally promotes swifter convection and more effective mixing of the fluid.