Thermocapillary convection in a 2D floating-zone with time-periodic temperature at the hot wall under reduced gravity

Abstract

Numerical solutions are made of thermocapillary convection of an incompressible fluid in a two-dimensional square floating-zone having a cold wall with constant temperature and an opposite hot wall with time-periodic sinusoidal temperature. Surfaces running between ends of the two walls having the temperature difference are assumed to be flat and adiabatic. The fluid in the floating-zone has normal thermocapillarity, and the Prandtl number is fixed to a unity. This study is aimed at investigating the effects of amplitude and frequency of temperature oscillations at the hot wall with varying the Marangoni number. Maximal fluctuations of the Nusselt number defined as the inner heat transfer at vertical mid-plane occur at the resonant frequency which is approximately the same with the main frequency in an oscillatory transient part of the Nusselt number for the steady state. The resonant frequency is depending on the Marangoni number but irrespective of the amplitude of the artificial temperature oscillations. The resonance phenomenon is caused by the phase difference of the surface flow and the return flow.