Transient thermocapillary convection under a surface of a linear temperature distribution

Abstract

Transient thermocapillary convection under a surface of a linear temperature distribution in a top open cavity at a zero-gravity condition is investigated using scaling analysis and numerical simulation. Induced by the linear temperature distribution on a surface, a surface flow (SF) occurs. Then the pressure gradient near the sidewall drives a vertical flow (VF). The evolution in dynamics and heat transfer of the SF and the VF is argued, which is determined by Marangoni number (Ma), Prandtl number (Pr), and aspect ratio (A). Scaling analysis shows that there are four typical evolutions of the VF and two typical evolutions of the thermal boundary layer. Furthermore, velocity, boundary layer thickness, and Nusselt number of transient thermocapillary convection are scaled under different regimes in different evolutions, and a number of new scaling laws are proposed. Additionally, the flow structures under different regimes are characterized, and selected scaling laws obtained in scaling analysis are validated by numerical simulation results.