The numerical analysis of surface tension driven convection in a liquid droplet with a solid heat sources set in the center

摘要

A method is developed to analyze the three-dimensional transient Marangoni convection in a liquid droplet that is heated from a concentric warm rigid sphere set in the center and cooled uniformly from its surroundings. As the field is unstable and is very sensitive to the temperature gradients along the surface, it is required for the numerical scheme to be highly accurate and be free from the effects of the polar singularties. For the purpose, a spherical harmonic spectoral method was developed to analyze the flow and temperature fields in the droplet on the spherical coordinates. In this study, effects of size of the solid heat source and the initial distribution of temperature are investigated. It is found that the convection develops faster and the number of the cells of convection decreases as a solid heat source is smaller.